The required equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.
To write the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours, we can use the given information that there are 4 rooms left to clean after 7 hours.
Let's start with the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
We have the point (x₁, y₁) = (7, 4), which represents the number of rooms left after 7 hours.
Substituting the values into the point-slope form, we get:
y - 4 = m(x - 7)
Now, we need to find the slope (m) of the line.
The slope of a line can be determined by the change in y divided by the change in x. In this case, the change in y is -4 (4 rooms left to clean) and the change in x is 7 hours.
m = Δy / Δx = -4 / 7
Now, let's substitute the value of m into the equation:
y - 4 = (-4/7)(x - 7)
To eliminate fractions, we can multiply through by 7:
7y - 28 = -4(x - 7)
7y - 28 = -4x + 28
4x + 7y = 56
So, the equation in a standard form that represents the number of rooms Martin has left to clean (y) after x hours is 4x + 7y = 56.
Learn more about equation models here:
https://brainly.com/question/31529421
#SPJ4
Final answer:
To express the relationship between the number of rooms left to clean and the hours spent cleaning in a linear equation, we use the slope of -4/7 and a y-intercept of 4, assuming 4 rooms are cleaned in 7 hours. This leads to the slope-intercept form y = -4/7x + 4. Multiplying by 7 and rearranging gives us the standard form 4x + 7y = 28.
Explanation:
To find the equation of the line that represents the number of rooms, y, Martin has left to clean after x hours, we start with the information that 4 rooms take 7 hours to clean. This means that every hour, a fraction of the total rooms are cleaned. To express this situation as a linear equation, we can use the slope-intercept form, which is y = mx + b. In this context, the slope (m) will be negative since the number of rooms left to clean decreases over time, and b is the y-intercept representing the initial number of rooms before any cleaning has started. Since there are 4 rooms to begin with and it takes 7 hours to clean all, the slope is -4/7 (the change in rooms left per hour).
The equation in slope-intercept form is y = -4/7x + 4. To convert this to standard form, we multiply the entire equation by 7 to eliminate the fraction: 7y = -4x + 28. Then we add 4x to both sides of the equation to get: 4x + 7y = 28. This is the equation in standard form, representing the number of rooms left (y) after x hours of cleaning.
Dan reads 12 books over winter break. Over summer break, Dan reads 8 times the number of books he read over winter break. How many books did Dan read over summer break? Books
Answer:
96 books
Step-by-step explanation:
Given:
Dan reads 12 books over winter break.
Dan reads 8 times the number of books he read over winter break.
Question asked:
How many books did Dan read over summer break ?
Solution:
By doing multiplication:
Dan reads number of books over winter break = 12
Dan reads number of books over summer break = 8 times of winter break
[tex]= 8\times12\\\\= 96[/tex]
Therefore, 96 books is read by Dan over summer break.
Final answer:
Dan read 96 books over summer break by multiplying the 12 books he read during winter break by 8.
Explanation:
The question asks us to calculate how many books Dan reads over summer break given that he reads 8 times the number of books he read over winter break. To find the answer, we need to multiply the number of books Dan read in winter break by 8. Dan read 12 books during winter break, so for summer break, we will calculate:
12 books × 8 = 96 books
Therefore, Dan read 96 books over summer break.
The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2√7) . What is the value of cos β ? Enter your answer, in simplest radical form, in the box.
Step-by-step explanation:
Draw the triangle formed by the ray.
The hypotenuse of the triangle is:
c² = a² + b²
c² = (-5)² + (2√7)²
c² = 25 + 28
c = √53
Therefore:
cos β = -5 / √53
Or, as a proper fraction:
cos β = -5√53 / 53
The value of cos β is -5√53 / 53
Given that,
The terminal ray of angle β , drawn in standard position, passes through the point (−5, 2√7) . The calculation is:The hypotenuse of the triangle is:
[tex]c62 = a^2 + b^2\\\\c^2 = (-5)^2 + (2\sqrt7)^2\\\\c^2 = 25 + 28\\\\c = \sqrt53[/tex]
Therefore:
cos β = -5 / √53
Or, a proper fraction:
cos β = -5√53 / 53
Find out more information about cos here:
https://brainly.com/question/2193114?referrer=searchResults
what is?
y=x+5
2y-x=13
Answer:
x=3
y=8
Step-by-step explanation:
y-x=5
2y-x=13
subtract
-y=-8
y=8
8-x=5
x=8-5=3
Answer:
3
Step-by-step explanation:
y-x=5 2y-x=13 subtract -y=-8 y=8 8*5 y=8-5=3
The junior and senior students at Mathville High School are going to present an exciting musical entitled, "Math, What is it Good For?". A large group of students came out to an information meeting. After a brief introduction to the musical, 15 senior students decided that it was not for them and they left. At that point, twice as many junior students as senior students remained. Later in the meeting, after the 15 senior students had left, of the junior students and of the remaining senior students also left. This left 8 more senior students than junior students. All of the remaining students stuck it out and went on to produce an amazing product. How many students remained to perform in the school musical, "Math, What is it Good For?"
Some parts are missing in the queston. Find attached the picture with the complete question
Answer:
[tex]\large\boxed{\large\boxed{161}}[/tex]
Explanation:
Let's put the information in a table step-by step.
(number of remaining students)
Juniors Seniors
Condition
Initially J S15 seniors left S - 15Twice juniors as seniors 2(S - 15)3/4 of the juniors left 1/4×2(S - 15)1/3 of seniors left 2/3×(S - 15)At the end, there were 8 more seniors than juniors:
2/3×(S - 15) - 1/4×2(S - 15) = 8Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.
Solve the equation:
[tex]2/3\times (S - 15) - 1/4\times 2(S - 15) = 8[/tex]
Mutilply all by 12:[tex]8(S - 15)-6(S - 15)=96[/tex]
Distribution property:[tex]8S-120-6S-90=96[/tex]
Addtion property of equalities:[tex]8S-6S=96+120+90[/tex]
Add like terms:[tex]2S=306[/tex]
Division property of equalities:[tex]S=306/2=153[/tex]
That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):
[tex]2/3\times (S-15)+1/4\times 2(S-15)[/tex]
Just substitute S with 153 fo find the number of students that remained to perfom in the musical:
[tex]2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)[/tex]
[tex]161[/tex]
Rectangle ABCD is shown with diagonal AC drawn. Point F is on AC and point E on DC such that FE is perpendicular to DC. Prove triangle ABC is similar to triangle CEF
Triangle ABC is similar to triangle CEF.
Explanation:
Diagram is inserted for the reference.
ABCD is a rectangle.
ABC is a right angled triangle because all the angles of the rectangle are 90◦ - (a)
CEF is a right angled triangle because FE is perpendicular to DC – (b)
In triangles ABC and CEF,
1. Angle ABC = Angle CEF = 90◦ (Both are right angles from a and b)
2. Angle BCA = Angle EFC (Alternate angles on parallel lines are equal on intersection)
Hence using Similarity property of AA (Angle, Angle), Triangle ABC and CEF are similar.
ΔABC and ΔCEF are similar triangles by the AA similarity theorem.
What is the AA Similarity Theorem?The angle-angle similarity theorem (AA) states that when two triangles have two pairs of corresponding congruent angles, both triangles are similar triangles.
In ΔABC and ΔCEF, we have the following:
Two pairs of corresponding congruent angles - ∠FEC ≅ ∠ABC (right angles) and ∠FCE ≅ ∠BAC
Therefore, ΔABC and ΔCEF are similar triangles by the AA similarity theorem.
Learn more about the AA similarity theorem on:
https://brainly.com/question/2166570
What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x? 1. The distributive property: 4x – 12 + 4 < 10 + 6x 2. Combine like terms: 4x – 8 < 10 + 6x 3. The addition property of inequality: 4x < 18 + 6x 4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________ x < –9 x > –9 x < x is less than or equal to negative StartFraction 1 Over 9 EndFraction. X > –x is greater than or equal to negative StartFraction 1 Over 9 EndFraction.
Answer:
X>-9
X is greater than -9
Step-by-step explanation:
4(X-3)+4<10+6X
By clearing up the bracket :
4X-12+4<10+6X
Collecting like terms:
4X-6X<10+12-4
-2X<18
Dividing both sides by -2:
-2X/-2>18/-2
Therefore, X>-9
The mission step is in combining like terms which is 4X-8<10+6X instead of 4X-6X<10+8.
The missing step in solving the given inequality 4(x – 3) + 4 < 10 + 6x is; x > -9
How to solve Inequalities?We are given the inequality as:
4(x – 3) + 4 < 10 + 6x
The steps are given as:
The distributive property: 4x – 12 + 4 < 10 + 6xCombine like terms: 4x – 8 < 10 + 6xThe addition property of inequality: 4x < 18 + 6xThe subtraction property of inequality: –2x < 18The next step in solving the inequality is to apply the division property of inequality by dividing both sides by -2.
This gives; x > -9
Thus, the missing step in the inequality is x > -9
Read more about Inequalities at; https://brainly.com/question/25275758
#SPJ5
A jar contains 11 green marbles, 6 red marbles, and 9 blue marbles. A marble is selected at random, not replaced, and then a second marble is selected. What is the probability of selecting a red marble followed by a green marble?
Write In a fraction.
The probability of selecting a red marble and then a green marble, without replacement, is 33/325.
Explanation:The probability in this case is being calculated as the outcome of two independent events - selecting a red marble first and then selecting a green marble. The total number of marbles in the jar is the sum of green, red, and blue marbles which is 11+6+9 = 26.
First, let's calculate the probability of drawing a red marble. There are 6 red marbles out of a total 26 marbles, so the probability is 6/26 (which reduces to 3/13).
Next, the jar now has 25 marbles left, and 11 of them are green. So, our probability of drawing a green marble after a red one is 11/25.
For both events to happen one after the other, we multiply the individual probabilities together. Hence, the combined probability of these two events would be (3/13) * (11/25), which equals 33/325.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
The probability of first selecting a red marble and then a green marble from a jar containing 11 green, 6 red, and 9 blue marbles is 33/325.
Explanation:The subject of this question is probability, which is a branch of mathematics. The problem involves calculating the probably of two events occurring in sequence: selecting a red marble and then a green one from a jar of colored marbles. In total there are 26 marbles: 11 green, 6 red, and 9 blue.
The probability of selecting a red marble first is 6/26 as there are 6 red marbles and 26 total marbles in the jar. Once you've chosen a red marble, it's removed from the jar. So for the second event, there are now 25 marbles in the jar, with 11 of them being green. So, the probability of selecting a green marble is 11/25.
The probability of both events (Choosing a red marble then a green one) happening one after the other is the product of the individual probabilities. So, the probability is (6/26) × (11/25) which simplifies to 33/325.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ12
Monica wants to tie a ribbon around the trunk of an oak tree that has a circular trunk about 11 inches in diameter. Not counting the ribbon needed to make a bow, how many inches of ribbon are needed just to reach around the tree?
Answer: 34.57 inches.
Step-by-step explanation:
Given : Diameter of tree's trunk = 11 inches
Then, the length of ribbon needed just to reach around the tree = Circumference of trunk.
We know that the circumference of the circle is given by :-
[tex]C=\pi d[/tex] , where d= diameter
Then, Circumference of trunk. = [tex]\pi (11)[/tex]
Put [tex]\pi=\dfrac{22}{7}[/tex] , we get
Circumference of trunk. = [tex]\dfrac{22}{7}\times(11)\approx34.57\text{ inches}[/tex]
Hence , the length of ribbon needed just to reach around the tree = 34.57 inches.
A factory produces toy dolls at the rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100
Answer:
The recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
Step-by-step explanation:
The question is incomplete so below is the complete question:
A factory produces toy dolls at a rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100. How many dolls are recycled each hour during production?
Now, to express the recycle percent as a rate per 100, And to find the number of dolls are recycled each hour during production.
Number of dolls factory produces at rate per hour = 400.
Percent of recycle = 3%.
So, to express the recycle percent as a rate per 100:
[tex]3\%\ per\ 100[/tex]
[tex]=\frac{3}{100} \ per\ hour[/tex]
[tex]=0.03\ per\ hour.[/tex]
So, to get the number of dolls are recycled each hour during production:
3% of number of dolls factory produces at rate per hour.
[tex]=\frac{3}{100} \times 400[/tex]
[tex]=0.03\times 400[/tex]
[tex]=12.[/tex]
The dolls are recycled each hour = 12.
Therefore, the recycle percent as a rate per 100 is 0.03 per hour.
And 12 dolls are recycled each hour during production.
While at summer camp, Mike asked a random camper from each of the 12 cabins how many siblings he or she had. The results below display the responses. 3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1 If there are 48 campers altogether, use Mike’s data to infer the mean of the population. What is the mean number of siblings for the population rounded to the nearest unit? 1 sibling 2 siblings 3 siblings 4 siblings
Answer:
Option 2.
Step-by-step explanation:
It is given that Mike asked a random camper from each of the 12 cabins how many siblings he or she had.
The given data set is
3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1
Sum of observations = 3+2+0+1+0+2+3+4+1+2+2+1=21
Number of observations = 12
Formula for mean:
[tex]Mean=\dfrac{\text{Sum of observations}}{\text{Number of observations}}[/tex]
[tex]Mean=\dfrac{21}{12}[/tex]
[tex]Mean=1.75[/tex]
Round the population to the nearest unit.
[tex]Mean=2[/tex]
We have to use Mike’s data to infer the mean of the population. So, the mean of sample is equal to the mean of population.
The mean number of siblings for the population is 2 siblings.
Therefore, the correct option is 2.
Answer:
the right answer is B
Step-by-step explanation:
a town wants to install 28 solar panels in an array what are the possible ways the panels could be installed
Answer:
24
Step-by-step explanation:
2300 people came to the football game yesterday and the number of people decreased to 2001 what was the percentage decrease in the number of people coming to the football game
Answer: the number of people coming to the football game decreased by 13%
Step-by-step explanation:
2300 people came to the football game yesterday and the number of people decreased to 2001. This means that the amount by which the number of people that came for the football game in both days decreased would be
2300 - 2001 = 299
Therefore, the percentage decrease in the number of people coming to the football game would be
299/2300 × 100 = 13%
A class consists of 8 students (four boys and four girls) and one teacher. In how many ways can the students sit in a circle?
Answer: 5040ways
Step-by-step explanation:
This is a circular permutation question. Arrangement of objects in a circular path is (n-1)! where n is the amount of object. Since there are 8 students sitting in a circle excluding their teacher, they can sit in (8-1)! ways i.e 7! ways
7! = 7×6×5×4×3×2×1
7! = 5040ways
This means the students can sit in a circle in 5,040 ways
Final answer:
To find out the number of ways 8 students can sit in a circle, we calculate 7! (7 factorial), as the formula for arrangements in a circle is (n-1)!, resulting in 5040 ways.
Explanation:
The question involves determining the number of ways 8 students can sit in a circle. When arranging n distinct objects in a circle, the number of arrangements is given by (n-1)! .
since one position is fixed to account for the circular arrangement's rotational symmetry. In this case, with 8 students, the calculation is as follows: 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways.
Therefore, the students can sit in a circle in 5040 different ways.
Before beginning to balance an equation, you should check each formula for correctness and NEVER change the formulas once they are correct. TRUE FALSE
Answer: False
Step-by-step explanation:
Answer:
False
Step-by-step explanation:
Fibonacci follies: suppose you are playing a round of Fibonacci nim with a friend. You start with 15 sticks. You start by removing two sticks; your friend then takes one; you take two; your friend takes one. What should your next move be? Can you make it without breaking the rules of the game? Did you make a mistake at some point? If so, where?
Answer: Yes, made a mistake by taking out 2 in second step.
Step-by-step explanation:
You have started with 15 sticks= 13+2
So you take 2 which is correct.
Now, your friend takes one 13=12+1, so that leaves 12.
Now 12=8+3+1 since this involves smallest number 1 so you should have taken 1 at this point instead you took two here. So it leaves you with 10. Now, your friend takes one from it i.e. 10=9+1 leaving 9 now. Now 9=8+1, you can still take 1 from it and still be in the game. The point is to take out the smallest number involved. in the sum equal to the number that is left behind.
In Fibonacci nim, you cannot take the same number of sticks as your opponent did on the previous turn. Your next move should be to take 2 sticks, as your opponent took 1 on their last turn. You haven't yet made any mistakes in the game.
Explanation:In the game of Fibonacci nim, the only rule is that on each turn a player can take one or two sticks, but not the same amount as their opponent took on the previous turn. Let's track your game:
You start with 15 sticks.You take 2 (13 remaining).Your friend takes 1 (12 remaining).You take 2 (10 remaining).Your friend takes 1 (9 remaining).For the next move, you can take either 1 or 2 sticks, but since your friend took 1 on their last turn, you must take 2 to abide by the rules. So, your next move should be to take 2 sticks.
Learn more about Fibonacci nim here:https://brainly.com/question/35586003
#SPJ3
Jaclyn plays singles for the varsity tennis team where she won the sudden death tie breaker point with a cross-court passing shot. The 57.5 g ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331g racket, the ball rebounded in the exact opposite direction with a speed of 29.5 m/s
Answer:
Incomplete question
Complete question: Jaclyn plays singles for South's varsity tennis team. During the match against North, Jaclyn won the sudden death tiebreaker point with a cross-court passing shot. The 57.5-gram ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331-gram racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s.
a. Determine the pre-collision momentum of the ball.
b. Determine the post-collision momentum of the ball.
c. Determine the momentum change of the ball.
Answer:
A. 1.5353kgm/s
B. 1.6963kgm/s
C. 0.161kgm/s
Step-by-step explanation:
A. The pre-collision momentum of the ball = mass of ball × velocity of ball
Mass of ball = 57.5g = 0.0575kg
Velocity of ball = 26.7m/s
Pre-collision momentum of ball = 0.0575×26.7
= 1.5353kgm/s
B. Post collision momentum of the ball = mass of ball × velocity of ball after impact
Velocity of ball after impact = 29.5m/s
Post collision momentum of ball after impact = 0.0575×29.5
= 1.6963kgm/s
C. Momentum change of ball = momentum after impact - momentum before imlact
= 1.6963kgm/s - 1.5353kgm/s
= 0.161kgm/s
Which expression is equivalent to -3x - (x-1) + 3/2(3x +3)?
A. 1/2x + 11/2
B. 1/2x + 7/2
c. 5/2x + 11/2
D. 5/2x + 7/2
Answer:
The answer to your question is letter A
Step-by-step explanation:
Expression
- 3x - (x - 1) + 3/2(3x + 3)
1.- Expand
- 3x - x + 1 + 3/2(3x) + 3/2(3)
2.- Simplify
- 3x - x + 1 + 9/2 x + 9/2
3.- Associate like terms
(-3x - x + 9/2x) + (1 + 9/2)
4.- Simplify like terms
(-4x + 9/2x) + (2 + 9)/2
(-8x + 9x)/2 + 11/2
1/2x + 11/2
Where do I share a photo of my work
This year , Lara paid 2,024 for season tickets to her favorite baseball team , which is 10% more expensive than last year . What was the price of season tickets last year?
Answer:
The price of season ticket last year was 1,840.
Step-by-step explanation:
Given:
Price of season tickets this year = 2024
Also given:
The Price of season tickets this year is 10% more than amount paid last year.
We need to find the Price of season tickets last year.
Solution:
Let the Price of season tickets last year be 'x'.
Now we know that;
The Price of season tickets this year is 10% more than amount paid last year.
so equation can be framed as;
[tex]x+ \frac{10}{100}x=2024\\\\x+\frac{x}{10}=2024\\\\x+0.1x=2024\\\\1.1x=2024[/tex]
Now dividing both side by 1.1 we get;
[tex]\frac{1.1x}{1.1}=\frac{2024}{1.1}\\\\x= 1840[/tex]
Hence The price of season ticket last year was 1,840.
What is the sum of the geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 2) (negative 3) Superscript n minus 1
Answer:
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
Read more on Brainly.com - https://brainly.com/question/14504382#readmore
Answer:
The answer is C (40)
Step-by-step explanation:
PLZ HELP THIS IS TIMED
Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10.
Answer:
A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16.
Step-by-step explanation:
Let an exponential growth function is [tex]f(x) = a(b)^{x}[/tex].
Now, [tex]f(1) = a(b)^{1}[/tex], [tex]f(2) = a(b)^{2}[/tex] , [tex]f(3) = a(b)^{3}[/tex] and [tex]f(4) = a(b)^{4}[/tex].
So, the values of the function corresponding to the x-values 1, 2, 3, and 4, are in G.P. and the common ratio of b.
Now, 'a 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16' will be the exponential function as the values are in G.P. with common ratio 2. (Answer)
Answer:
its D
Step-by-step explanation:
just did the assignment
PLz Help
1)Two angles form a linear pair. The measure of one angle is twice the measure of the other angle. Find the measure of each angle.
The smaller angle measures
The larger angle measures
2)Two angles form a linear pair. The measure of one angle is 1/3 the measure of the other angle. Find the measure of each angle.
The smaller angle measures
The larger angle measures
3)The measure of an angle is nine times the measure of its complement. Find the measure of each angle.
The smaller angle measures
The larger angle measures
4)The measure of an angle is 1/4 the measure of its complement. Find the measure of each angle.
The smaller angle measures
The larger angle measures
Answer:
Step-by-step explanation:
1) the sum of the angles on a straight line is 180°.
Let x represent the measure of the smaller angle.
The measure of one angle is twice the measure of the other angle. This means that the larger angle is 2x. Therefore,
x + 2x = 180
3x = 180
x = 180/3 = 60
The measure of the smaller angle is 60°
The measure of the larger angle is 2 × 60 = 120°
2) The measure of one angle is 1/3 the measure of the other angle. If the measure of the larger angle is x, then the measure of the smaller angle is x/3. Therefore,
x + x/3 = 180
Multiplying through by 3, it becomes
3x + x = 180 × 3 = 540
4x = 540
x = 540/4 = 135
The smaller angle measures
135/3 = 45°
The larger angle measures 135°
3) the sum of complimentary angles is 180°
The measure of an angle is nine times the measure of its complement. If the measure of the smaller angle is x, then the measure of the larger angle is 9x. Therefore,
x + 9x = 90
10x = 90
x = 90/10 = 9
The smaller angle measures 9°
The larger angle measures 9 × 9 = 81°
4) The measure of an angle is 1/4 the measure of its complement.
If the measure of the larger angle is x, then the measure of the smaller angle is x/4. Therefore,
x/4 + x = 90
Multiplying through by 4, it becomes
x + 4x = 360
5x = 360
x = 360/5 = 72
The smaller angle measures 72/4 = 18°
The larger angle measures 72°
I want to seriously think about students. So 80% of the books donated to the used book sale. They sold 48 books and oil how many books would donated to the used book sale justify your answer.
Solution is in the attachment
a. Can you draw a decision tree having 100% accuracy on this training set? If you answer is yes, draw the decision tree in the space provided below. If your answer is no, explain why? b. Which attribute among A, B and C has the highest information gain? Explain your answer.
Answer:
Day Weather Temperature Humidity Wind Play?
1 Sunny Hot High Weak No
2 Cloudy Hot High Weak Yes
3 Sunny Mild Normal Strong Yes
4 Cloudy Mild High Strong Yes
5 Rainy Mild High Strong No
6 Rainy Cool Normal Strong No
7 Rainy Mild High Weak Yes
8 Sunny Hot High Strong No
9 Cloudy Hot Normal Weak Yes
10 Rainy Mild High Strong No
Step-by-step explanation:
Mauricio, a project manager at a reputed firm, has been assigned to handle a new project that the firm has received. This project involves a lot of scheduling that has to be handled by Mauricio. Mauricio estimates that the first module of the project could be completed in as few as 15 days or could take as many as 25 days, but most likely will require 20 days. Determine the expected task duration.
Answer:
20 days
Step-by-step explanation:
Expected Task duration
= (O + 4 M + P)/6
Where O = best case scenario = 15 days
P = worst case scenario = 25 days
M = Usual scenario = 20 days
Therefore, expected task duration
= [15 + 4 (20) + 25] ÷ 6
= 120 ÷ 6
= 20 days.
Therefore expected task duration is 20 days.
A machine is designed to dispense at least 12 ounces of a beverage into a bottle. To test whether the machine is working properly, a random sample of 50 bottles was selected and the mean number of ounces for the 50 bottles was computed. A test of the hypotheses H0 : μ = 12 versus HA : μ < 12 was conducted, where μ represents the population mean number of ounces of the beverage dispensed by the machine. The p-value for the test was 0.08. Which of the following is the most appropriate conclusion to draw at the significance level of α = 0.05 ?
a. Because the p-value is greater than the significance level, there is not convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
b. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is less than 12 ounces.
c. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
d. Because the p-value is less than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
Answer:
Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 12 ounces
Sample size, n = 50
Alpha, α = 0.05
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 12\\H_A: \mu < 12[/tex]
We use one-tailed test to perform this hypothesis.
P-value = 0.08
Since the p value is greater than the significance level, we fail to reject the null hypothesis and accept it.
Thus, the machine is working properly and dispense 12 ounces of a beverage into a bottle.
Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.
Thus:
"Option C): c. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.
Given that:
Proposed mean of population = [tex]\mu_0 = 12[/tex]Real population mean (unknown parameter) = [tex]\mu[/tex]Size of sample = [tex]n = 50[/tex]Null Hypothesis = [tex]H_0 : \mu = 12 = \mu_0[/tex]Alternate Hypothesis = [tex]H_A: \mu < 12 = \mu_0[/tex]p-value found = 0.08Level of significance = [tex]\alpha = 0.05[/tex]How to form the hypotheses and test them?Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.
Null hypothesis is the favored hypothesis which we test. The test's result just tells whether the null hypothesis is acceptable or not. The alternative hypothesis is accepted when the null hypothesis is rejected, else we accept the null hypothesis.
Thus, [tex]H_0 : \mu = 12 = \mu_0[/tex] is accepted as [tex]\text{p-value} = 0.08 > 0.05 = \alpha[/tex] and we deduce that:
"Option C: Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces."
is correct option.
Learn more about null hypothesis and alternative hypothesis here:
https://brainly.com/question/10758924
Rounded to the nearest whole number, what is the distance, in units, between (−3,2) and (2,−8)?
A
6
B
7
C
11
D
15
Answer:
a
Step-by-step explanation:
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
The given coordinate points are (-3, 2) and (2, -8).
Substitute (x₁, y₁) =(-3, 2) and (x₂, y₂)= (2, -8) in the distance formula, we get
Distance = √[(2+3)²+(-8-2)²]
= √[5²+(-10)²]
= √125
= 11.18
≈ 11
The distance between two given coordinate points is 11 units. Therefore, option C is the correct answer.
To learn more about the distance formula visit:
brainly.com/question/27262878.
#SPJ3
The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.
Answer:
i) The data for elementary school are more consistent than those for
middle school.
iii) About 50% of elementary school students watch between 4 and 7
hours of television each week.
v) On average, middle school students watch less television than
elementary school students each week.
Step-by-step explanation:
The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
The true statements when comparing the data in the box plots
i) The data for elementary school are more consistent than those for
middle school.
ii) More of the data for middle school lie closer to the median than the data
for elementary school.
iii) About 50% of elementary school students watch between 4 and 7
hours of television each week.
iv) About one-half of middle school students watch less than 2 hours of
television each week.
v) On average, middle school students watch less television than
elementary school students each week.
Answer:
It's 1, 3, 5 Yw
Step-by-step explanation:
I am doing the test and that's what I got
A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as much in the lower-yielding account because it is less risky. His annual interest is $3872 dollars. How much did he invest at each rate? Your answer is: Amount invested at 6% equals $ Amount invested at 10% equals $
Answer:
Amount invested at 6% equals $35200; Amount invested at 10% equals $17600
Step-by-step explanation:
For simple interest; A = P (1 + rt), where;
A= final amount, P=principal , r = rate , t = time in years
Let the amount invested in the 6% yielding account be 'x' and the amount invested in the 10% yielding account be 'y'.
From the question, the man invests twice as much in the lower yielding, Therefore;
⇒ x = 2y
Interest = A - P = Prt
Total interest = (Interest for 6% yielding account) + (Interest for 6% yielding account)
⇒ 3872 = ( [tex]x[/tex] X 0.06 x 1) + ( [tex]y[/tex] X 0.10 x 1)
⇒ 3872 = (2[tex]y[/tex] x 0.06 x 1) + ([tex]y[/tex] x 0.10 x 1)
⇒ 3872 = 0.12[tex]y[/tex] + 0.10[tex]y[/tex]
⇒ y = $17600
⇒ x = 2y = $ 35200
Answer: Amount invested at 6% equals $35200
Amount invested at 10% equals $17600
Step-by-step explanation:
Let x represent the amount invested at 6%.
Let y represent the amount invested at 10%.
He puts twice as much in the lower-yielding account because it is less risky. This means that
x = 2y
The formula for determining simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents the rate of investment
T represents the time in years.
Considering the amount invested at 6%,
I = (x × 6 × 1)/100 = 0.06x
Considering the amount invested at 10%,
I = (y × 10 × 1)/100 = 0.1y
If his annual interest is $3872, it means that
0.06x + 0.1y = 3872 - - - - - - - - - - - -1
Substituting x = 2y into equation 1, it becomes
0.06 × 2y + 0.1y = 3872
0.12y + 0.1y = 3872
0.22y = 3872
y = 3872/0.22
y = 17600
x = 2y = 2 × 17600
x = 35200
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide. Find the dimensions of the family room
Answer:
The dimensions of the room are length is 16 feet and the width is 11 feet.
Step-by-step explanation:
Given:
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.
Now, to get the dimensions.
Let the width be [tex]x.[/tex]
So, the length = [tex]x+5.[/tex]
Area = 176 square foot.
So, we put formula of area to get the dimensions:
Area = length × width.
[tex]176=(x+5)\times x[/tex]
[tex]176=x^2+5x[/tex]
Subtracting boths sides by 176 we get:
[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]
On solving the equation:
[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]
As,
[tex]x+16[/tex] = 0
[tex]x=-16[/tex]
So, we would not take the negative result.
Thus,
[tex]x-11=0\\x=11[/tex]
So, the width = 11 feet.
Now, to get the length by substituting the value of [tex]x[/tex]:
[tex]x+5\\=11+5\\=16[/tex]
The length = 16 feet.
Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.
The width is 11 feet, and the length is 5 feet longer, making it 16 feet.
To determine the dimensions of the family room, we start by defining the width of the room as w. According to the problem, the length (l) is 5 feet longer than the width, so we can write this as:
l = w + 5
We also know the area of the room is 176 square feet. The area of a rectangle is calculated by multiplying the width and length:
Area = width × length
Therefore, we get the equation:
w × (w + 5) = 176
Expanding this equation gives us:
w² + 5w = 176
We rearrange this into a standard quadratic equation:
w² + 5w - 176 = 0
Now we solve for w using the quadratic formula, w = (-b ± √(b² - 4ac)) / 2a, where:
a = 1b = 5c = -176This gives us:
w = (-5 ± √(25 + 704)) / 2
w = (-5 ± √729) / 2
w = (-5 ± 27) / 2
Which simplifies to:
w = 11 or w = -16
Since width cannot be negative, we have:
w = 11
Then the length l is:
l = 11 + 5 = 16
Therefore, the dimensions of the family room are 11 feet by 16 feet.
You are distributing candy to 20 children and there are 3 different types of candy. You have at least 20 different types of candy. If each child gets one piece of cand, how many ways are there for you to distribute the 3 types of candy?
Answer:
each child would get 3 pieces of candy
Step-by-step explanation:
hope this helps ;)