Answer:
Constant of proportionality = 24
Equation: [tex]y=24x[/tex]
Step-by-step explanation:
Given:
'x' and 'y' are proportional to each other.
At [tex]x=3,y=72[/tex]
Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.
Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:
[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]
Therefore, the constant of proportionality is 24.
Now, a proportional relationship in 'x' and 'y' is given as:
[tex]y=kx[/tex]
Now, plug in the given value of 'k' and complete the equation. This gives,
[tex]y=24x[/tex]
Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]
functions w and z are both linear functions of x which statement comparing the functions is true? select all that apply
Function Z has a greater slope and a higher y-intercept compared to Function W, making Function Z steeper and intercepting the y-axis at a higher point. Here options A and B are correct.
The two lines in the graph represent linear functions, which means they can be expressed in the following form:
y = mx + b
where:
m is the slope of the line, which tells you how steep the line is and in which direction it is slanted.
b is the y-intercept, which is the point where the line crosses the y-axis.
x is the independent variable, and y is the dependent variable.
The steeper a line is, the greater the absolute value of its slope. A positive slope means the line slants upwards from left to right, while a negative slope means it slants downwards from left to right.
In the image, you can see the equations for the two lines are:
Function W: y = 2x - 5
Function Z: y = 3x - 2
By looking at the equations, we can see that:
The slope of function W is 2.
The slope of function Z is 3.
Since 3 is greater than 2, we can say that the slope of function Z is greater than the slope of function W. This means that function Z is steeper than function W.
The y-intercepts of the lines are also different:
The y-intercept of function W is -5.
The y-intercept of function Z is -2.
Since -2 is greater than -5, we can say that the y-intercept of function Z is greater than the y-intercept of function W.
Therefore, the following statements comparing the functions are true:
The slope of Function W is less than the slope of Function Z
The y-intercept of Function W is less than the y-intercept of Function Z. Here options A and B are correct.
Function W has a slope less than Function Z, and its y-intercept is also less than that of Function Z.(options a and d)
To compare the functions W and Z, let's analyze their slopes and y-intercepts:
Function W: [tex]\(y = 0.5x - 1\)[/tex]
Function Z: Given table of values
a. The slope of Function W is [tex]\(0.5\).[/tex]
b. The slope of Function Z can be calculated using the given points. We choose two points: [tex]\((-2, -2.5)\)[/tex] and [tex]\((4, -1)\)[/tex]. Using the slope formula:
[tex]\[m = \frac{{y_2 - y_1}}{{x_2 - x_1}}\][/tex]
[tex]\[m = \frac{{-1 - (-2.5)}}{{4 - (-2)}}\][/tex]
[tex]\[m = \frac{{1.5}}{{6}}\][/tex]
[tex]\[m = 0.25\][/tex]
c. The y-intercept of Function W is -1, while the y-intercept of Function Z is the y-value when x=0, which is -2.
d. The y-intercept of Function W is greater than the y-intercept of Function Z.
e. To find the y-value when x=-4 for Function W, substitute x=-4 into the equation of Function W:
[tex]\[y = 0.5(-4) - 1 = -3\][/tex]
For Function Z, there is no direct way to determine the y-value when x=-4 as we only have specific points provided, not a continuous equation.
f. The y-value when x=-4 for Function W is not greater than the y-value when x=-4 for Function Z.
Therefore, the correct statements are:
a. The slope of Function W is less than the slope of Function Z.
d. The y-intercept of Function W is less than the y-intercept of Function Z.
The question probable maybe:
Given in the attachment
Please Help Me With My Algebra Homework
Answer:
The maximum of the sinusoidal function is 5.
Step-by-step explanation:
The maximum of the sinusoidal function is 5.
Which of the following will always represent a function?
Group of answer choices
a list of ordered pairs
a list of numbers
an equation in the form y = mx + b
a table of pairs of numbers
Two Neighbors in a rural area want to know the distance between their homes in miles. What should the Neighbors use as a conversion factor to covert 4,224 to miles
Answer:
x = 0.8 Mi
Step-by-step explanation:
for x = 4224 ft we can use the factor (1 Mi/5280 ft)
then
x = 4224 ft (1 Mi/5280 ft) = 0.8 Mi
Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets slod. How many children’s ticket and how many adult tickets did he sell?
Answer:
615 children tickets
195 adults tickets
Step-by-step explanation:
Let the number of children’s tickets be c and the number of adult tickets be a.
Children’s ticket is $3 and adult’s is $5 for a total of $2,820. This means:
3c + 5a = 2,280
This is the first equation.
The number of children’s tickets sold is 30 more than 3 times that of the adults. This means
c = 3a + 30.
This is equation ii. We now substitute ii into I to yield:
3(3a+ 30) + 5a = 2,820
9a + 90 + 5a = 2,820
14a + 90 = 2,820
14a = 2820 - 90
14a = 2730
a = 2730/14 = 195 tickets
c = 3a + 30
c = 3(195) + 30 = 615
Final answer:
By setting up a system of equations based on the total sales and the relationship between the number of adult and children's tickets sold, we can solve to find that Galen sold 130 adult tickets and 420 children's tickets for the church's carnival which is 195.
Explanation:
The question involves finding the number of children's and adult tickets sold by Galen for a church's carnival, given the total sale amount and the price of each ticket type. To solve this, we can set up a system of equations based on the information provided:
The total amount from ticket sales is $2,820.Children's tickets are $3 each, and adult tickets are $5 each.The number of children's tickets sold was 30 more than 3 times the number of adult tickets sold.Let x be the number of adult tickets sold and y be the number of children's tickets sold. The problem statements can be translated into two equations:
3y + 5x = 2820 (total sales equation)y = 3x + 30 (relationship between tickets sold)Substituting the second equation into the first gives us:
3(3x + 30) + 5x = 2820
Solving for x, we find that Galen sold 130 adult tickets. Using the relationship between x and y, we then find that 420 children's tickets were sold.
14x= 2730
x=195.
Is −8c an even integer? Yes, because −8c = 2(−4c) + 1 and −4c is an integer. Yes, because −8c = 2(−4c) and −4c is an integer. No, because −8c = 2(−4c) and −4c is an integer. No, because −8c = 2(−4c) + 1 and −4c is an integer.
Answer:
Yes, because −8c = 2(−4c) and −4c is an integer
Step-by-step explanation:
We want to determine whether [tex]-8c[/tex] is an even integer.
Recall that even integers are of the form: [tex]2n[/tex]
Let us see if we can rewrite the given expression in the form 2n, where n is an integer.
Let us factor 2 to get:
[tex]-8c=2(-4c)[/tex]
If -4c is an integer and we let m=-4c,then
[tex]-8c=2(m)=2m[/tex], where m is an integer.
Therefore the answer is Yes, because −8c = 2(−4c) and −4c is an integer
PLEASE HELPPPP Which value is equivalent to cos10∘?
Answer:
sin 80
Step-by-step explanation:
Find the vertex of the graph of the function. f(x) = (x + 4)2 - 1
a) (0,4)
b) (-1, 0)
c) (-4,-1)
d) (-1,-4)
Answer:
The vertex of the function is at point (-4,-1).
Step-by-step explanation:
Given function:
[tex]f(x)=(x+4)^2-1[/tex]
Solution:
The vertex form of a function is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
where [tex](h,k)[/tex] is the vertex of the function. At this point the function has the maximum or minimum value.
Writing the given function in the vertex form.
[tex]f(x)=(x-(-4))^2+(-1)[/tex]
On comparing the above function with the standard form we find that:
[tex]a=1\\h=-4\\k=-1[/tex]
Thus, the vertex of the function is at point (-4,-1)
The vertex of the function f(x)= (x + 4)² - 1 is at the point (-4,-1) by comparing it with the vertex form of a quadratic function f(x) = a(x - h)² + k.
Explanation:The function given is in the vertex form of a quadratic function, which is f(x) = a(x - h)² + k. In this form, the vertex of the graph of the function is at the point (h, k). For f(x)=(x + 4)² - 1, you can see that h is -4 and k is -1. Therefore, the vertex of the graph of the function is at the point (-4,-1).
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Find the exact values for sin theta, cos θ, and tan θ. A right triangle has a vertical side of length 12, a horizontal side of length 35, and a hypotenuse of length 37. The angle formed by the sides of lengths 35 and 37 is labeled θ.
Answer:
SinƟ = 12/37
CosƟ =35/37
TanƟ = 12/35
Step-by-step explanation:
The diagram of the triangle is attached
Using SOH CAH TOA
SinƟ = Opposite/Hypotenuse
SinƟ = 12/37
CosƟ= adjacent/Hypo tenuse
CosƟ =35/37
TanƟ=Opposite/Adjacent
TanƟ = 12/35
On Monday, Lou drives his ford escort with 28-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his car to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou’s tires make per second?(A) Decrease by 14.3%
(B) Decrease by 12.5%
(C) Increase by 14.3%
(D) Increase by 12.5%
(E) Cannot be determined with the given information.
Answer:
[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]
(B) Decrease by 12.5%
Step-by-step explanation:
For this case we know that the revolution is proportional to the circumference.
And we know that the average number of revolutions of 32 inch tires for Tuesday is higher than the original value of 28 inch tires for Monday.
We know that we have x mi/hr, so we can select a value fo x in order to find the average revolutions with the following formula:
[tex] Avg = \frac{x}{mi}[/tex]
Let's say that we select a value for x for example x= 28*32 = 896, since this value is divisible by 32 and 28.
If we find the average revolutions per each case we got:
Tuesday:
[tex] Avg = \frac{896}{32}=28[/tex]
Monday:
[tex] Avg = \frac{896}{28}=32[/tex]
And then we can find the % of change like this:
[tex] \% Change= \frac{|Final-Initial|}{Initial} *100[/tex]
And if we replace we got:
[tex] \% Change = \frac{|28-32|}{32} *100 = 12.5\%[/tex]
Because we are assuming that the initial amount is the value for Monday and the final value for Tuesday.
So then the best answer for this case would be:
(B) Decrease by 12.5%
In accordance with 14 CFR Part 107, at what maximum altitude can you operate an sUAS when inspecting a tower with a top at 1,000 ft AGL at close proximity (within 100 feet)?
Answer:
The max altitude you can operate an sUAS on these given conditions is 1400ft AGL.
Step-by-step explanation:
Final answer:
The sUAS can fly at a maximum altitude of 1,100 feet AGL when inspecting a tower with a top at 1,000 feet AGL, assuming it stays within 100 feet of the tower as per 14 CFR Part 107.
Explanation:
In accordance with 14 CFR Part 107, specifically considering sUAS (small Unmanned Aircraft Systems) operations around structures, there are specific altitude regulations. When a drone operator is inspecting a tower, and the drone is within 100 feet laterally of the structure, the drone can operate above the standard 400 feet above ground level (AGL) limit. For a tower with a top at 1,000 feet AGL, the sUAS can fly at a maximum altitude of 1,100 feet AGL, assuming it stays within 100 feet of the structure. This is possible because the regulations allow the sUAS to fly 400 feet above the structure's uppermost limit when it is within a close radius of the structure.
Which expression represents the area of triangle ABC in square meters?
Triangle A B C has a base of 57 meters and a height of 14 meters.
One-half times 14 times 57
One-half times 14 times 64
One-half times 24 times 40
One-half times 24 times 57
Answer:
Answer is (A) One-half times 14 times 57
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
What is the probability of being dealt exactly three of a kind (like three kings or three 7’s, etc.) in a five card hand from a deck of 52 cards?
Answer:
P=0.00564
Step-by-step explanation:
From Exercise we have 52 cards.
We calculate the number of combinations to draw 5 cards from a deck of 52 cards. We get
{52}_C_{5}=\frac{52!}{5!(52-5)!}=2598960
We now count the number of favorable combinations:
{13}_C_{1} · {48}_C_{2}= 13 · \frac{48!}{2!(48-2)!}=14664
Therefore, the probabilitiy is
14664/2598960=0.00564
P=0.00564
The cost for a cell phone service is $75 per month plus $0.17 per minute. Which expression shows the monthly cost for the phone if x represents the number of minutes?
Answer:
we can use the variable c to represent the monthly cost
75+0.17x=c
Step-by-step explanation:
The expression shows the monthly cost for the phone if x represents the number of minutes if The cost for a cell phone service is $75 per month plus $0.17 per minute, is y = 75 + 0.17x.
What is equation?An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.
Given:
The cost for a cell phone service is $75 per month plus $0.17 per minute,
Write the equation as shown below,
Total cost = Cost for a month + per minute charge × total use in minutes,
Assume the total cost is y, and the use of minute is x then,
y = 75 + 0.17 × x
y = 75 + 0.17x
Thus, the monthly cost for the phone is 75 + 0.17x.
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Weinstein, McDermott, and Roediger (2010) con- ducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a se tion, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers. a. Identify the dependent variable for this study. b. Is the dependent variable discrete or continuous? c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable? or h ctudy reports that alcohol consumption is ta university why or why not. pidor inexperiment?
Answer:
Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies.
One part of the study asked students to prepare for a test by reading a passage.
In one condition, students generated and answered questions after reading the passage.
In a second condition, students simply read the passage a second time.
All students were then given a test on the passage material and the researchers recorded the number of correct answers.
a. Identify the dependent variable for this study:
The dependent variable for this study is effectiveness.
b. Is the dependent variable discrete or continuous?
The dependent variable is discrete.
c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
The scale of measurement is ratio scale.
Step-by-step explanation:
a) To identify the dependent variable you need to find the item, circumstance, concept, sense, time frame, or any category in an specific scientific research, that is going to be measured. In this particular case, the dependent variable measured is the effectiveness of the different study strategies used based by the number of correct answers on a test. This variable could be influenced by independent variables also.
b) The method by which we obtain the resulting values make the difference between a discrete variable and a continuous variable. If measuring is the used method, then it is a continuous variable, but if counting is the utilized method to get the correct number of correct answers, as it is stated in this case, then it is a discrete, finite and countable.
c) The measurements´ accuracy are given by the different scales or levels and they are classified as:
- Nominal
- Ordinal
- Interval
- Ratio
Interval and ratio scales data are similiar is also known as called metric, sharing units, and represent quantiy., therefore the scale of measurement used in this study is ratio scale.
Confused! Need help please!! Will mark brainliest!
Find the value of x. Show all your work for full credit.
Yo sup??
This question can be solved by applying the properties of similar triangles
the triangle with sides 5x and 20 is similar to the triangle with sides 45 and 35
The similarity property used here is called AAA ie angle angle angle property as all the three angles of the 2 triangles are equal.
therefore we can say
5x/45=20/36
x=5 units
Hope this helps
describe the long-term behavior
Answer:
a. Slant asymptote with a slope of 5
Step-by-step explanation:
Dividing out the polynomials, you get ...
[tex]\dfrac{5x^2-x+13}{x+10}=5x-51+\dfrac{523}{x+10}[/tex]
As the magnitude of x gets large, the fraction goes to zero, and the behavior matches the line ...
y = 5x -51
This is a slant asymptote with a slope of 5 and a non-zero y-intercept.
If two triangles are congruent, which of the following statements must be true? Check all that apply.
Answer:
All statements are correct for two congruent triangles
Step-by-step explanation:
If two triangles are congruent than the rules states that
Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles will have the same shape and size, but one may be a mirror image of the other.
As the fig shows two triangle
Δ PQR
Δ LMN
All three corresponding sides of triangle are congruent
all three corresponding angles are congruent
Both triangle are of same size
Both are of same shape
hence all the statements are CORRECT
Keywords:Geometry
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Nina purchased apples and strawberries. She purchased a total of 9 pounds of fruit and spent a total of $16.35. Strawberries cost $1.60 per pound and apples cost $ 1.99 per pound. How many pounds of each type of fruit did she buy?
Answer:
4 pounds of strawberries and 5 pounds of apples are bought.
Step-by-step explanation:
Given:
Total number of pounds of fruit = 9 pounds
Total money spent = $16.35
Cost of 1 pound of strawberry = $1.60
Cost of 1 pound of apple = $1.99
Let 'x' pounds of strawberries and 'y' pounds of apples are bought.
So, as per question:
The sum of the pounds is 9. So,
[tex]x+y=9\\\\y=9-x----1[/tex]
Now, total sum of the fruits is equal to the sum of 'x' pounds of strawberries and 'y' pounds of apples. So,
[tex]1.60x+1.99y=16.35----2[/tex]
Now, plug in the 'y' value from equation (1) in to equation (2). This gives,
[tex]1.60x+1.99(9-x)=16.35\\\\1.60x+17.91-1.99x=16.35\\\\Combining\ like\ terms, we get:\\\\1.60x-1.99x=16.35-17.91\\\\-0.39x=-1.56\\\\x=\frac{-1.56}{-0.39}=4\ pounds[/tex]
Now, from equation 1, we have:
[tex]y=9-4=5\ pounds[/tex]
Therefore, 4 pounds of strawberries and 5 pounds of apples are bought.
A hot air balloon is descending at a rate of 2.0 m/s when a passenger drops a camera. (a) If the camera is 40 m above the ground when it is dropped, how longdoes it take for the camera to reach the ground? 1 s (b) What is its velocity just before it lands? Let upward be thepositive direction for this problem. 2 m/s
Answer:
a.) 1.23 seconds
b.) 14 m/s
Step-by-step explanation:
a.) Before commencing the calculation, we need to specify the information.
Data:
acceleration dues to gravity, g = 9.81 m/s²
initial velocity u = 2.0 m/s
height, s = 40 m
t = ?
The formula for finding the distance is s = ut + 1/2at²
Therefore, 40 = 2t + 1/2×(9.81) ×t²
80 = 4t + 9.81 t²
Solving for t by the quadratic equation gives t = 1.23 s [Note the other negative value for t is rejected because there is no negative time]
b) The final velocity is given by the following equation:
v = u + at
where v = final velocity just before the camera lands on the ground
u = initial velocity
t = time taken
a = g = acceleration dues to gravity = 9.81 m/s²
Calculating gives
v = 2 + 9.81×1.23
= 14 m/s Ans
A car can travel 25 miles per gallon on the high way and 20 miles in the city. The car's gas tank can hold 21 gallons. If the car traveled 500 miles on a full tank of gas, how many were used for city driving?
Answer: 5 gallons of gas were used for city driving.
Step-by-step explanation:
Let x represent the number of gallons of gas that the car used on the highway.
Let y represent the number of gallons of gas that the car used in the city.
The car's gas tank can hold 21 gallons. This means that
x + y = 21
A car can travel 25 miles per gallon on the high way and 20 miles in the city. If the car traveled 500 miles on a full tank of gas, it means that
25x + 20y = 500 - - - - - - - - - -1
Substituting x = 21 - y into equation 1, it becomes
25(21 - y) + 20y = 500
525 - 25y + 20y = 500
- 25y + 20y = 500 - 525
- 5y = - 25
y = - 25/ - 5
y = 5
x = 21 - y = 21 - 5
x = 16
The number of miles used for city driving is: [tex]\[{100}\][/tex].
To determine how many miles were used for city driving, we start by defining the variables and equations based on the problem's information:
1. Let \( x \) be the number of miles driven on the highway.
2. Let \( y \) be the number of miles driven in the city.
Given the problem, we have the following information:
- The car traveled a total of 500 miles: [tex]\( x + y = 500 \)[/tex]
- The car's gas consumption rates are 25 miles per gallon on the highway and 20 miles per gallon in the city.
- The gas tank holds 21 gallons.
Next, we set up the equation for total gas consumption:
[tex]\[\frac{x}{25} + \frac{y}{20} = 21\][/tex]
We now have a system of two equations:
[tex]1. \( x + y = 500 \)\\2. \( \frac{x}{25} + \frac{y}{20} = 21 \)[/tex]
To solve this system, we start with the first equation:
[tex]\[x = 500 - y\][/tex]
Substitute [tex]\( x = 500 - y \)[/tex] into the second equation:
[tex]\[\frac{500 - y}{25} + \frac{y}{20} = 21\][/tex]
Next, we find a common denominator to simplify the left-hand side of the equation. The common denominator for 25 and 20 is 100:
[tex]\[\frac{500 - y}{25} = \frac{500 - y}{25} \cdot \frac{4}{4} = \frac{4(500 - y)}{100} = \frac{2000 - 4y}{100}\]\[\frac{y}{20} = \frac{y}{20} \cdot \frac{5}{5} = \frac{5y}{100}\]\\[/tex]
So the equation becomes:
[tex]\[\frac{2000 - 4y + 5y}{100} = 21\][/tex]
Combine the terms in the numerator:
[tex]\[\frac{2000 + y}{100} = 21\][/tex]
Multiply both sides by 100 to eliminate the fraction:
[tex]\[2000 + y = 2100\][/tex]
Subtract 2000 from both sides to solve for \( y \):
[tex]\[y = 100\][/tex]
Thus, the number of miles used for city driving is:
[tex]\[{100}\][/tex].
The longer diagonal of a rhombus is three times the length of the shorter diagonal is x, what expression gives the perimeter of the rhombus? The perimeter of the rhombus is__.
Answer:
4(√2.5)x
Step-by-step explanation:
Let each side of the dragonal be P
Bringing out a Triangle out of the rhombus we have a right angle triangle with the base of x/2 and height of 3/2x.
And the hypothenus is P.
Applying Pythagoras theorem we have
p ^2= (1.5x)^2+(0.5X)^2
p ^2= 2.25X^2 +0.25X^2
P = (√2.5) X
Since the Rhombus consist of 4 triangles . The perimeter can best be expressed as 4 x the perimeter of the triangle.
P= 4(√2.5)x.
The longer diagonal of a rhombus is three times the length of the shorter diagonal. The expression that gives the perimeter of the rhombus cannot be determined with the information provided.
Explanation:The perimeter of a rhombus can be found by adding the lengths of all four sides. In this case, the longer diagonal of the rhombus is three times the length of the shorter diagonal, which is represented by x. So, the shorter diagonal is x and the longer diagonal is 3x.
Since the longer diagonal of a rhombus creates two congruent right triangles, we can use the Pythagorean theorem to find the length of its sides. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, for one of the right triangles, the hypotenuse is 3x and the two sides are x. Using the Pythagorean theorem, we have:
x² + x² = (3x)²
2x² = 9x²
2 = 9
This equation is not true, which means that x cannot be the length of the shorter diagonal.
Therefore, since the given information is incorrect, we cannot find the expression that gives the perimeter of the rhombus.
If there are 52 cards in a deck with four suits (hearts, clubs, diamonds, and spades), how many ways can you select 5 diamonds and 3 clubs?
Answer:
[tex] 12C5 *(12C3) = 792*220 =174240 ways[/tex]
Step-by-step explanation:
For this case we know that we have 12 cards of each denomination (hearts, diamonds, clubs and spades) because 12*4= 52
First let's find the number of ways in order to select 5 diamonds. We can use the combinatory formula since the order for this case no matter. The general formula for combinatory is given by:
[tex] nCx = \frac{n!}{x! (n-x)!}[/tex]
So then 12 C5 would be equal to:
[tex] 12C5 = \frac{12!}{5! (12-5)!}=\frac{12!}{5! 7!} = \frac{12*11*10*9*8*7!}{5! 7!}= \frac{12*11*10*9*8}{5*4*3*2*1}=792[/tex]
So we have 792 was in order to select 5 diamonds from the total of 12
Now in order to select 3 clubs from the total of 12 we have the following number of ways:
[tex] 12C3 = \frac{12!}{3! 9!}=\frac{12*11*10*9!}{3! 9!} =\frac{12*11*10}{3*2*1}=220[/tex]
So then the numbers of ways in order to select 5 diamonds and 3 clubs are:
[tex] (12C5)*(12C3) = 792*220 =174240 ways[/tex]
10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and is not replaced. Another card is then randomly selected. What is the probability of selecting two numbers that are less than 6?
A. 2/9
B. 5/18
C. 1/5
D. 1/4
Answer:
Option A: [tex]$ \frac{\textbf{2}}{\textbf{9}} $[/tex]
Step-by-step explanation:
Given there are 10 cards viz: 1, 2, 3, 4, . . . , 10
We find the probability of drawing two cards less than six, without replacing the first card.
Draw 1:
There are 5 cards with value less than 6. 1, 2, 3, 4, 5
The total number of cards is 10.
The probability of the number being less than 6 = [tex]$ \frac{number \hspace{1mm} of \hspace{1mm} cards \hspace{1mm} less \hspace{1mm} than \hspace{1mm} 6}{total \hspace{1mm} number \hspace{1mm} of \hspace{1mm} cards} $[/tex]
[tex]$ = \frac{5}{10} $[/tex]
Draw 2:
We are again drawing a card without replacing the card that was drawn earlier. This makes the total number of cards 9.
Also, the number of cards less than 6 will now be: 4.
Therefore, probability of drawing a number less than 6 without replacing
[tex]$ = \frac{4}{9} $[/tex]
Since, both draw 1 and draw 2 are happening we multiply the two probabilities. We get
[tex]$ \textbf{P} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{5}}{\textbf{10}} \hspace{1mm} \times \hspace{1mm} \frac{\textbf{4}}{\textbf{9}} $[/tex]
[tex]$ \therefore P = \frac{\textbf{2}}{\textbf{9}} $[/tex]
Hence, OPTION A is the required answer.
Mahnoor randomly selects times to walk into a local restaurant and observe the type of music being played She found that the restaurant was playing country 11 times rock & roll 17 times and blues 8 times Use the observed frequencies to create a probability model for the type of music the restaurant is playing the next time Mahnoor walks in.
Answer:
Type of music Country Rock & roll Blues
Observed number 11 17 8
Probabilities P(x) 11/36 17/36 8/36
Step-by-step explanation:
The probabilities can be calculated as
P(x)= observed number of times/ Total number of times.
The probability distribution for the type of music restaurant playing is
Type of music Country Rock & roll Blues Total
Observed number 11 17 8 36
Probabilities P(x) 11/36 17/36 8/36 1
Write a formula that describes the value of an initial investment of $100 that loses its value at a rate of 80% per year compounded 6 times. per year.
Answer:
see below
Step-by-step explanation:
The formula is the same whether the change in a compounding period is positive or negative. Here, it is negative.
A = P(1 +r/n)^(nt)
for P = 100, r = -0.08, n = 6. So, you have ...
A = 100(1 -0.08/6)^(6t)
Answer: option d is the correct answer
Step-by-step explanation:
Initial amount is $100. This means that the principal is
P = 100
It was compounded 6 times in a year. So
n = 6
The rate at which the principal was compounded is 8%. So
r = 8/100 = 0.08
The number of years is t
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years.
Since the amount is reducing,
A = P(1-r/n)^nt
Therefore
A = 100 (1 - 0.08/6)^6t
30 POINTS! Solve the following equation for l. A = 2πr + πrl. Explain each step.
Answer:
l = [tex]\frac{A-2\pi r}{\pi r}[/tex]
Step-by-step explanation:
Given
A = 2πr + πrl ( isolate the term in l by subtracting 2πr from both sides )
A - 2πr = πrl ( divide both sides by πr )
[tex]\frac{A-2\pi r}{\pi r}[/tex] = l
Answer: l = A/πr - 2
Step-by-step explanation:
The given equation is
A = 2πr + πrl
The first step is to subtract 2πr from the left hand side and the right hand side of the equation. It becomes
A - 2πr = 2πr + πrl - 2πr
A - 2πr = πrl
The next step is to divide the left hand side and the right hand side of the equation by πr. It becomes
(A - 2πr)/πr = πrl/πr
l = (A - 2πr)/πr
I = A/πr - 2πr/πr
I = A/πr - 2
which quadrilateral does not always have perpendicular diagonals
A. Square
B. Rhombus
C.kite
D. Isosceles trapezoid
Answer:
D. Isosceles trapezoid
Step-by-step explanation:
Answer: The answer is D. Isosceles trapezoid
PLEASEEE HELP ME ASAP!!
Answer:
Hence,
The measure of ∠A is 60.065°
[tex]\m\angle A= 60.065[/tex]
Step-by-step explanation:
Given:
ΔABC is a Right Angle Triangle at ∠ B = 90°
BC = Opposite side to ∠A = 13 unit
AC = Hypotenuse = 15 unit
To Find:
m∠A = ?
Solution:
In Right Angle Triangle ABC ,Sine Identity,
[tex]\sin A= \dfrac{\textrm{side opposite to angle A}}{Hypotenuse}\\[/tex]
Substituting the values we get
[tex]\sin A= \dfrac{BC}{AC}=\dfrac{13}{15}=0.8666\\\angle A=\sin^{-1}(0.8666)\\m\angle A= 60.065\°[/tex]
Hence,
The measure of ∠A is 60.065°
[tex]\m\angle A= 60.065[/tex]
PLLLLLEEASSEE HELLPP
Which transformations have been performed on the graph of f(x)=\sqrt[3]{x} to obtain the graph of g(x)= -\frac{1}{2} \sqrt[3]{x-9}
Select EACH correct answer
A. reflect the graph over the x-axis
B. translate the graph down
C. translate the graph to the right
D. translate the graph up
E. stretch the graph away from the x-axis
F. translate the graph to the left
G. compress the graph closer to the x-axis
Answer:
The correct answer is compress the graph closer to the x axis
reflect the graph over the x axis
translate the graph to the right
Step-by-step explanation:
I just took the test
The correct answer is (A)(C)(G) because to transform the graph, we first reflect it over the x-axis, then translate it to the right, and finally compress it closer to the x-axis.
To determine the transformations applied to the graph of [tex]\( f(x) = \sqrt[3]{x} \)[/tex] to obtain the graph of [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], let's analyze each component of the transformation step-by-step.
Given [tex]\( f(x) = \sqrt[3]{x} \)[/tex] and [tex]\( g(x) = -\frac{1}{2} \sqrt[3]{x-9} \)[/tex], the transformations are as follows:
1. Horizontal Shift:
The term [tex]\( x-9 \)[/tex] inside the function indicates a horizontal shift.
Specifically, it shifts the graph to the right by 9 units.
2. Vertical Compression and Reflection:
The coefficient [tex]\( -\frac{1}{2} \)[/tex] outside the cube root function indicates a vertical transformation.
The negative sign reflects the graph over the x-axis.
The factor [tex]\( \frac{1}{2} \)[/tex] compresses the graph closer to the x-axis.
The complete question is:
Which transformations have been performed on the graph of [tex]f(x)=\sqrt[3]{x}[/tex] to obtain the graph of [tex]g(x)= -\frac{1}{2} \sqrt[3]{x-9}[/tex] ?
A. reflect the graph over the x-axis.
B. translate the graph down.
C. translate the graph to the right.
D. translate the graph up.
E. stretch the graph away from the x-axis.
F. translate the graph to the left.
G. compress the graph closer to the x-axis.