Answer:
1
Step-by-step explanation:
The probability of selecting (at least)3 jacks out of a shuffled deck of 51 cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1
Answer:
1
Step-by-step explanation:
The probability of selecting (at least)3 jacks out of a shuffled deck of 51 cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1
2/ 7 y+3 1/7 y if y= 7/9
Answer:
8/3 = 2 2/3
Step-by-step explanation:
(2/7)y + (3 1/7)y = (3 3/7)y = (24/7)y
For y=7/9, this is ...
(24/7)(7/9) = 24/9 = 8/3
The value of the expression for y=7/9 is 8/3.
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
What is the median of the following values? 51,22,17,28,98,4,24,83,9,76
Answer:
The answer to your question is 26
Step-by-step explanation:
Median is the middle number of a list order from lowest to highest.
Process
1.- Order the numbers from lowest to highest
4 9 17 22 24 28 51 76 83 98
2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.
Middle numbers = 24 and 28
Median = (24 ´+ 28) / 2
Median = 52/2
Median = 26
Answer:
Step-by-step explanation:
First the numbers are arranged in ascending order from the least to the biggest number:
4 9 17 22 24 28 51 76 83 98
The numbers on the 5th and 6th position are in the middle
5th= 24
6th = 28
Since they are two numbers, we add them and divide by 2
= (24 + 28) / 2
= 52 / 2
= 26
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
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
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
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
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.
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.
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
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
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 ;)
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:
Consider the graph of quadrilateral ABCD.
What is the most specific name for quadrilateral ABCD?
square
rectangle
parallelogram
rhombus
Know the properties of each shape:
A square has all sides of equal length plus all corners are right angles
A rectangle has all right angles, but has two pairs of parallel sides
A parallelogram is a quadrilateral that has two pairs of parallel sides
A rhombus is where all sides are equal length, but no right angles at all
So the best choice given the diagram is C: parallelogram
Hope this helped you to understand better.
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
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
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
Find x
1,) -54
2.) 48
3,) 52
4.) 54
Step-by-step explanation:
[tex]m \angle \: WXZ = m \angle \: WYZ \\ ..(angles \: formed \: in \: same \: arc) \\ \therefore \: x \degree = (2x - 54)\degree \\ \therefore \: x = 2x - 54 \\ \therefore \: x - 2x = - 54 \\ \therefore \: - x = - 54 \\ \huge \purple{ \boxed{\therefore \: x = 54}}[/tex]
Answer:
The correct answer is D or 54.
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%
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:
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
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:
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.
What is the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees?
Answer:
38.9 square inches.
Step-by-step explanation:
We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.
We will use area of sector formula to solve our given problem as:
[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where, r represents radius and theta represents central angle.
Let us find area of sector with central angle 140 degree and radius 3 inch.
[tex]\text{Area of sector}=\frac{138}{360}\times \pi (3)^2[/tex]
[tex]\text{Area of sector}=\frac{138}{360}\times 9\pi[/tex]
[tex]\text{Area of sector}=10.83849[/tex]
Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:
[tex]\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)[/tex]
[tex]\text{Area of sector}=2(\frac{114}{360}\times 25\pi)[/tex]
[tex]\text{Area of sector}=\frac{114}{360}\times 50\pi[/tex]
[tex]\text{Area of sector}=49.74188[/tex]
Let us find difference of area as shown below:
[tex]\text{Difference of areas}=49.74188-10.83849[/tex]
[tex]\text{Difference of areas}=38.90339[/tex]
[tex]\text{Difference of areas}\approx 38.9[/tex]
Therefore, the difference in area covered is approximately 38.9 square inches.
Final answer:
Calculate the areas covered by differently sized and angled windshield wipers to find the difference.
Explanation:
Single 3-inch wiper:
Area covered = (1/2) × r² × (2 × pi × (angle/360))Pair of 5-inch wipers:
Each wiper's area = (1/2) × r² × (2 × pi × (angle/360))Total area covered by the pair = 2 × (area of a single wiper)The difference in area cleaned by the pair of 5-inch wipers compared to the single 3-inch wiper is:
A-diff = A-combined - A-single ≈ 31.50 sq in - 7.07 sq in ≈ 24.43 sq in
Therefore, the pair of 5-inch wipers cleans approximately 24.43 square inches more area than the single 3-inch wiper.
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.
A solid rectangular box with height 5 m and square base with side lengths 4 m is built using a lightweight material whose density is 800 kgm3. Constructing this box requires work against gravity.the required work is___________
Final answer:
The work done against gravity in constructing the rectangular box is 3136000 J.
Explanation:
To calculate the work done against gravity in constructing the rectangular box, we need to first calculate the mass of the box. The density of the lightweight material is given as 800 kg/m³. Since the base of the box is a square with side lengths of 4 m and the height is 5 m, the volume of the box is V = (4 m)(4 m)(5 m) = 80 m³.
The mass of the box can be calculated using the formula mass = density × volume. Therefore, the mass of the box is [tex](800 kg/m^3)(80 m^3) = 64000 kg.[/tex]
The work done against gravity is given by the formula work = mass × gravity × height. Assuming the acceleration due to gravity is approximately 9.8 m/s², the work done against gravity is [tex](64000 kg)(9.8 m/s^2)(5 m) = 3136000 J.[/tex]
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.
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]
Points R, T, S, and Q are
a. collinear
b. coplanar
c. neither collinear nor coplanar
d. both collinear and coplanar
The points in the diagram are neither collinear (lying on the same line) nor coplanar (lying on the same plane) as some points are not in alignment or on the same level.
The correct answer is option C.
Collinearity and coplanarity are geometric concepts used to describe the relative positions of points in space. To clarify, collinear points lie on the same straight line, while coplanar points lie on the same flat plane.
In your specific scenario, it is evident that the points under consideration do not satisfy the criteria for either collinearity or coplanarity. Here's an expanded explanation:
Collinearity:
Collinear points are points that can be connected by a single straight line. In simpler terms, if you can draw a straight line that passes through all the points without lifting your pen, those points are collinear. However, based on the provided diagram and description, it is clear that not all the points can be connected in this way. Some points are positioned in such a manner that a single straight line cannot pass through all of them.
Coplanarity:
Coplanar points are points that lie within the same flat plane. If you can imagine a flat surface that contains all the points, those points are coplanar. In the given scenario, it is apparent that the points are not all situated within the same plane. Some points are at different heights or elevations compared to others, indicating that they do not lie within a common flat plane.
In conclusion, the points in the diagram do not meet the conditions for either collinearity or coplanarity. They cannot be connected by a single straight line, nor do they all reside on the same flat plane.
Therefore, from the given options the correct one is C.
For more such information on:collinear
https://brainly.com/question/24391959
#SPJ2
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°