Tell whether or not f(x) = 3 sin 2 - cos x is a sinusoid.

We have three pythagoras:

4² + y² = z²

16² + y² = x²

x² + z² = 20²

Now let's think:

4² + y² = z²

y² = z² - 4²

16² + y² = x²

16² + z² - 4² = x²

x² + z² = 20²

16² + z²- 4² + z² = 20²

2z² = 20² - 16² + 4²

2z² = (2.10)² - (2^4)² + (2²)²

2z² = 2².10² - 2^8 + 2^4

z² = 2.10² - 2^7 + 2^3

z² = 200 - 128 + 8

z² = 208 - 128

z² = 80

z = √80

80 | 2

40 | 2

20 | 2

10 | 2

5 | 5

1

80 = 5.2^4

So

√80 = 4√5

z = 4√5

Answer:

Option C: 90+90 Sq. Root of 2

Step-by-step explanation:

First we find the distance from second base to home plate.  This is the diagonal of the square, which splits it into two right triangles.

Each right triangle will have legs of 90 feet.  We use the  Pythagorean theorem to find the length of the diagonal (the hypotenuse of the right triangle):

a² + b² = c²

90² + 90² = c²

8100 + 8100 = c²

16200 = c²

Take the square root of each side:

√(16200) = √(c²)

Simplifying √16200, we find the prime factorization:

16200 = 162(100)

162 = 2(81)

81 = 9(9) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

100 = 10(10) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

√16200 = √(9²×10²×2) = 9×10√2 = 90√2

This means the distance from 1st to 2nd and then from 2nd to home would be

90 + 90√2

Answer:

4, 6, 8

Step-by-step explanation:

The possible degrees of a polynomial function can be determined by observing the highest power of the variable in the polynomial. Each curve or turn in the graph represents a change in direction of the polynomial. The highest number of curves or turns is equal to the degree of the polynomial.

The possible degrees of a polynomial function in the graph can be determined by observing the highest power of the variable in the polynomial. The degree of a polynomial is the highest exponent of the variable. For example, if the highest power of the variable is 3, then the polynomial has a degree of 3.

In the graph, we can determine the degree by looking at the x-axis and counting the number of curves or turns. Each curve or turn represents a change in direction of the graph. The highest number of curves or turns is equal to the degree of the polynomial.

For example, if the graph has one curve or turn, then the polynomial has a degree of 1, which means it is a linear function. If the graph has two curves or turns, then the polynomial has a degree of 2, which means it is a quadratic function.

Answer:

the graph of y=4 x+3 is a straight line that passes through the point (0,3) and (\frac{-3}{4},0)

Step-by-step explanation:

The graph of the exponential function y = 4ˣ + 3 is attached below.

An exponential function is in the form:

y = abˣ

Where y, x are variables, a is the initial value of y and b is the multiplication factor.

Given an exponential function of y = 4ˣ + 3

The graph of the exponential function y = 4ˣ + 3 is attached below.

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Answer:

(C) 1 : 511

Step-by-step explanation:

Possible outcome for every throw = 2 (head or tail)

Total possible outcome for 9 throws

= 2⁹

= 512

Odd of getting all head

= 1 : 511

The odds in favor of getting all heads on nine coin tosses is 1 to 512.

The odds in favor of getting all heads on nine coin tosses can be calculated as the number of favorable outcomes divided by the number of possible outcomes. In this case, we want all nine coin tosses to result in heads, which is only 1 favorable outcome. The total number of possible outcomes for nine coin tosses is 2^9 = 512.

Therefore, the odds in favor of getting all heads on nine coin tosses is 1 to 512. Comparing this to the options given, the correct answer is A. 1 to 508.

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Answer:

[tex]f(x)=\dfrac{2x-1}{x+2}\\ \\f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

[tex]f(x)=\dfrac{x-1}{2x+1}\\ \\f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

[tex]f(x)=\dfrac{x+2}{-2x+1}\\ \\f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

[tex]f(x)=\dfrac{2x+1}{2x-1}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

[tex]f(x)=\dfrac{x+2}{x-1}\\ \\f^{-1}(x)=\dfrac{x+2}{x-1}[/tex] - extra

Step-by-step explanation:

1.

[tex]f(x)=y=\dfrac{2x-1}{x+2}\\ \\y(x+2)=2x-1\\ \\yx+2y=2x-1\\ \\yx-2x=-1-2y\\ \\x(y-2)=-1-2y\\ \\x=\dfrac{-1-2y}{y-2}\\ \\y=f^{-1}(x)=\dfrac{-2x-1}{x-2}[/tex]

2.

[tex]f(x)=y=\dfrac{x-1}{2x+1}\\ \\y(2x+1)=x-1\\ \\2xy+y=x-1\\ \\2xy-x=-1-y\\ \\x(2y-1)=-1-y\\ \\x=\dfrac{-1-y}{2y-1}\\ \\y=f^{-1}(x)=\dfrac{-x-1}{2x-1}[/tex]

3.

[tex]f(x)=y=\dfrac{x+2}{-2x+1}\\ \\y(-2x+1)=x+2\\ \\-2xy+y=x+2\\ \\-2xy-x=2-y\\ \\x(-2y-1)=2-y\\ \\x=\dfrac{2-y}{-2y-1}\\ \\y=f^{-1}(x)=\dfrac{2-x}{-2x-1}=\dfrac{x-2}{2x+1}[/tex]

4.

[tex]f(x)=y=\dfrac{2x+1}{2x-1}\\ \\y(2x-1)=2x+1\\ \\2xy-y=2x+1\\ \\2xy-2x=1+y\\ \\x(2y-2)=1+y\\ \\x=\dfrac{1+y}{2y-2}\\ \\y=f^{-1}(x)=\dfrac{1+x}{2(x-1)}[/tex]

5.

[tex]f(x)=y=\dfrac{x+2}{x-1}\\ \\y(x-1)=x+2\\ \\xy-y=x+2\\ \\xy-x=2+y\\ \\x(y-1)=2+y\\ \\x=\dfrac{2+y}{y-1}\\ \\y=f^{-1}(x)=\dfrac{x+2}{x-1}[/tex]

ANSWER

[tex]g(x) = \sqrt{x + 4} [/tex]

EXPLANATION

The parent square root function is

[tex]f(x) = \sqrt{x} [/tex]

The translation

[tex]g(x ) = \sqrt{x + k} [/tex]

Will shift the graph of f(x) k units to left.

The translation

[tex]g(x) = \sqrt{x -k} [/tex]

will shift the graph of f(x) to the right by k units.

Therefore if f(x) is shifted 4 units to the left its new equation is:

[tex]g(x) = \sqrt{x + 4} [/tex]

Shifting a function left involves adding a value to the x-component. Hence, shifting the square root parent function, F(x) = √x, to the left by 4 units results in a new function F(x) = √(x+4).

When a function is shifted horizontally, it impacts the input or the x-values. A shift to the left is represented by the addition of a value to the x-component of the function. Hence, to shift the square root parent function, F(x) = √x, to the left by 4 units, you would add 4 to 'x' in the function, which results in a new function F(x) = √(x+4). "This function represents the original square root parent function shifted 4 units to the left".

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Answer:

[tex] y^2 + 8y + 16 [/tex]

Step-by-step explanation:

[tex] (6y^2 + 2y + 5) - (5y^2 - 6y - 11) = [/tex]

The first set of parentheses is unnecessary, so it can just be removed.

[tex] = 6y^2 + 2y + 5 - (5y^2 - 6y - 11) [/tex]

To remove the second set of parentheses, you must distribute the negative sign that is to its left. It changes every sign inside the parentheses.

[tex] = 6y^2 + 2y + 5 - 5y^2 + 6y + 11 [/tex]

Now you combine like terms.

[tex] = 6y^2 - 5y^2 + 2y + 6y + 5 + 11 [/tex]

[tex] = y^2 + 8y + 16 [/tex]

Answer:

C

Step-by-step explanation:

Since y will have same value, y doesn't really matter. Thus,

We can solve for y in the 2nd equation as:

-3x - y = 4

-3x - 4 = y

Now we can plug it into the first and solve for x:

-9x + 4y = 8

-9x + 4(-3x - 4) = 8

-9x - 12x - 16 = 8

-21x = 8 + 16

-21x = 24

x = 24/-21

x = -8/7

Correct answer is C.

Answer: Option C

C-8/7

Step-by-step explanation:

We have the following equations

 [tex]-9x + 4y = 8[/tex] and [tex]-3x - y = 4[/tex]

We want to find a value of x that satisfies both equations and obtains the same value of y.

To find the value of x, clear the value of y in both equations

[tex]-9x + 4y = 8\\\\-9x + 4y -8 = 0\\\\-9x -8 = -4y\\\\y = \frac{9}{4}x +2[/tex]

------------------------------

[tex]-3x - y = 4\\\\\-3x -y - 4 = 0\\\\y = -3x -4[/tex]

Now solve both equations and solve for x.

[tex]\frac{9}{4}x +2 = -3x -4\\\\\frac{21}{4}x = -4-2\\\\\frac{21}{4}x = -6\\\\21x = -24\\\\x = -\frac{24}{21}\\\\x = -\frac{8}{7}[/tex]

The answer is [tex]x = -\frac{8}{7}[/tex]

Answer:

u² – 11u + 24 = 0 where u = (x² – 1)

Step-by-step explanation:

Given the equation;

(x² – 1)² – 11(x² – 1) + 24 = 0

We can let;

u = x² - 1

Substituting the value of u in the equation we get;

(u)² - 11 (u) + 24 = 0

u²- 11u + 24 = 0

Therefore;

The quadratic equation that is equivalent to the equation is;

u² – 11u + 24 = 0 where u = (x² – 1)

Answer:

option 1

Step-by-step explanation:

Answer:

9 blocks

Step-by-step:  

One way in which to do this problem is to find the volume of the rectangular prism and then divide that by the volume of one  cubic block of side length 1/6 inch.

V = (length)(width)(height) = (1/2 cm)(1/6 cm)(1/2 cm) = 1/24 cm³.

Volume of one cubic block of side length 1/6 cm is (1/6 cm)³ = 1/216 cm³.

Dividing 1/24 cm³ by 1/216 cm³ yields 216/24 blocks, or 9 blocks.

Answer:

3.2.1

Step-by-step explanation:

Answer:

Step-by-step explanation:

The information given in the problem statement lets you write two equations relating box weights (L for the large box weight; S for the small box weight).

  2L +3S = 78 . . . . . . weight of the first collection of boxes

  6L +5S = 180 . . . . . weight of the second collection of boxes

We can subtract 3S from the first equation and multiply it by 3 and we have ...

  2L = 78 -3S . . . . . . subtract 3S [eq3]

  6L = 234 -9S . . . . . multiply by 3

Now we have an expression for 6L that can substitute into the second equation:

  (234 -9S) +5S = 180

  234 -4S = 180 . . . . . . . . simplify

  54 -4S = 0 . . . . . . . . . . . subtract 180

  13.5 -S = 0 . . . . . . . . . . . divide by 4

  13.5 = S . . . . . . . . . . . . . add S

From [eq3] above, we can now find L.

  2L = 78 -3(13.5) = 37.5

  L = 37.5/2 = 18.75

The weight of the large box is 18.75 kg; the small box is 13.5 kg.

_____

A graphing calculator can provide an alternate means o finding the solution.

Answer:

[tex]\boxed{\text{144.33 m}^{2}}[/tex]

Step-by-step explanation:

The scale factor (C) is the ratio of corresponding parts of the two pyramids.  

The ratio of the areas is the square of the scale factor.

[tex]\dfrac{A_{1}}{ A_{2}} = C^{2}\\\\\dfrac{\text{327 m}^{2}}{A_{2}} = \left (\dfrac{1}{\frac{2}{3}}\right)^{2}\\\\ \dfrac{\text{327 m}^{2}}{A_{2}}= \dfrac{9}{4}\\\\\text{1308 m}^{2}= 9A_{2}\\\\A_{2} = \text{145.33 m}^{2}\\\text{The surface area of the smaller pyramid is \boxed{\text{145.33 m}^{2}}}[/tex]

f(x)= 10x

It seems like c and d are the same.

25% of the arrows are further than approximately 24.32 cm from the target's center.

To find the distance from the center of a target that 25% of arrows are further than, we need to determine the z-score that corresponds to the 75th percentile (since 100% - 25% = 75%).

Using a z-table or technology, we find that the z-score for an area of 0.75 is approximately 0.675.

Next, we use the z-score formula: z = (X - μ) / σ, where µ is the mean (20 cm) and σ is the standard deviation (6.4 cm). Setting z to 0.675, we solve for X:

0.675 = (X - 20) / 6.4

Multiplying both sides by 6.4:

4.32 = X - 20

Adding 20 to both sides gives us:

X ≈ 24.32 cm

Thus, approximately 25% of the arrows are further than 24.32 cm from the center.

Answer:

d. ≈ 37,106 ft

Step-by-step explanation:

The angle of depression to the plane to the airport is the same as the angle of elevation from the airport to the plane. Therefore, the angle of elevation form the airport to the plane is 6°.

Notice that the height of the plane is the opposite side of the angle of elevation and the ground distance is the adjacent side of the angle of elevation. To find ground distance we need to use a trig function to relate the opposite side and the adjacent side; that trig function is tangent:

[tex]tan(\alpha )=\frac{opposite-side}{adjacent-side}[/tex]

[tex]tan(6)=\frac{3900ft}{ground-distance}[/tex]

[tex]ground-distance=\frac{3900ft}{tan(6)}[/tex]

[tex]ground-distance=37106ft[/tex]

We can conclude that the plane's ground distance to the airport is approximately 37,106 feet

Answer:

  646 child tickets are sold

Step-by-step explanation:

Let c represent the number of child tickets sold. Then (c-186) is the number of student tickets sold, and (c+234) is the number of adult tickets sold. The total number sold is ...

  (c -186) + c + (c+234) = 1986

  3c +48 = 1986 . . . simplify

  c + 16 = 662 . . . . divide by 3

  c = 646 . . . . . . . . . subtract 16

The number of child tickets sold is 646.

The number of child tickets sold is 646.

To find the number of child tickets sold at the theatre, we can define some variables and set up equations based on the information provided.

Let:

From the information given, we have the following relationships:

The total number of tickets sold is 1986:
x + y + z = 1986

There are 234 more adult tickets sold than child tickets:
z = y + 234

There are 186 more child tickets sold than student tickets:
y = x + 186

Now we can substitute the equations for z and y into the first equation:

This simplifies to:
x + 2y + 234 = 1986

Now, we substitute y using the equation y=x+186:

Replace y in the equation:
x + 2(x + 186) = 1752

This simplifies to:
x + 2x + 372 = 1752
3x + 372 = 1752

Now isolate x:
3x = 1752 − 372
3x = 1380
x = 31380​
x = 460

Now that we have the value for x, we can find y:

Finally, we calculate z to confirm:  

Now we can verify:
x + y + z = 460 + 646 + 880 = 1986

So the number of child tickets sold is y = 646.

Answer:

216 degrees

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=10\ in[/tex]

substitute

[tex]C=2\pi (10)[/tex]

[tex]C=20\pi\ in[/tex]

step 2

Find the measure of the arc if the length of the arc is 12π in

Remember that

The circumference of a circle subtends a central angle of 360 degrees

so

by proportion

[tex]\frac{360}{20\pi}=\frac{x}{12\pi}\\ \\x=360*12/20\\ \\x= 216\°[/tex]

Answer:

180,000 m

Step-by-step explanation:

There are 60 seconds in a minute, so:

2 min × 60 s/min = 120 s

Distance = rate × time

d = 1500 m/s × 120 s

d = 180,000 m

Answer:

Kameron has 5 quarters in his wallet

Step-by-step explanation:

Let

x----> the number of nickels

y----> the number of quarters

remember that

1 nickel=$0.05

1 quarter=$0.25

we know that

x=3y -----> equation A

0.05x+0.25y=2

Multiply by 100 both sides

5x+25y=200

Simplify

x+5y=40 -----> equation B

Substitute equation A in equation B

(3y)+5y=40

8y=40

y=5 quarters

x=3(5)=15 nickels

Final answer:

By setting up and solving equations based on the value of quarters and nickels and their proportions, we can determine that Kameron has 5 quarters in his wallet.

Explanation:

Finding the Number of Quarters in Kameron's Wallet

To solve Kameron's problem, we can set up two equations based on the given information. Let's define Q as the number of quarters and N as the number of nickels Kameron has. Since we know that the number of nickels is three times the number of quarters, we can express this as N = 3Q.

Next, we calculate the monetary value of the quarters and nickels. Each quarter is worth 25 cents, and each nickel is worth 5 cents. Since the total amount is two dollars, which is 200 cents, we can write the equation 25Q + 5N = 200.

Substituting N with 3Q in the second equation, we get 25Q + 5(3Q) = 200, which simplifies to 40Q = 200. Solving for Q gives us Q = 200 / 40 = 5, so Kameron has 5 quarters in his wallet.

Answer:

Option A. 2/3

Step-by-step explanation:

we know that

If angle theta is in Quadrant 1

then

The value of cos(theta) is positive and the value of tan(theta) is positive

Remember that

tan(theta)=sin(theta)/cos(theta)

In this problem we have

tan(theta)*cos(theta)=[sin(theta)/cos(theta)]*cos(theta)=sin(theta)

therefore

tan(theta)*cos(theta)=sin(theta)=2/3

Final answer:

The value of (tan theta)(cos theta) is 2/3.

Explanation:

To find the value of (tan theta)(cos theta), we can use the given value of sin theta and the fact that sin² θ + cos² θ = 1.

Since the value of sin theta is known to be 2/3, we can square this value to find sin² θ = (2/3)² = 4/9.

Using the identity sin² θ + cos² θ = 1, we can solve for cos² θ by subtracting sin² θ from 1. This gives us cos²θ = 1 - 4/9 = 5/9.

Finally, we can calculate (tan θ)(cos θ) by multiplying tan θ = sin θ/ cos θ = (2/3) / [tex]\sqrt{5/9[/tex] = (2/3) / ([tex]\sqrt{5[/tex]/3) = 2 / [tex]\sqrt{5[/tex] and cos θ = [tex]\sqrt{5/9[/tex]. Therefore, (tan θ )(cos θ ) = (2 / [tex]\sqrt{5[/tex]) * [tex]\sqrt{5/9[/tex] = 2 / 3.

Answer:

100, 120

Step-by-step explanation:

The mean of the given data is 500/4, or 125.

If a score of 0 were added to this data, the mean would be smaller, because we'd have to divide the five scores by 5.  The mean would now be 100.

The median of the given data is the average of the middle two scores, that is, of 120 and 130.  It's 125.

If we were to add the score of 0 to the four data points, obtaining

0, 100, 120, 130, 150,

the median would be the middle number:  120.

Mean is the average of the data set and mode is the middle terms or average of the middle terms of the data set.

Given information-

The given data consists the values 100,120,130,150.

Total number of values is four.

Mean is the average of the given data.

The mean of the given data can be calculated as,

[tex]m=\dfrac{100+120+130+150}{4} [/tex]

[tex]m=\dfrac{500}{4} [/tex]

[tex]m=125[/tex]

For even terms the medium is the average of the middle terms.

The medium of the given data can be calculates as,

[tex]M=\dfrac{120+130}{2} [/tex]

[tex]M=125[/tex]

Adding a score of 0.

The data consists of the values will be 0,100,120,130,150.

Total number of values is five.

The mean of the given data can be calculated as,

[tex]m=\dfrac{0+100+120+130+150}{5} [/tex]

[tex]m=\dfrac{500}{5} [/tex]

[tex]m=100[/tex]

Medium for the odd terms is equal to the middle terms.

The medium of the given data can be calculates as,

For the

[tex]M=120[/tex]

Thus adding a score of 0 the mean of the given data is reduced with number 25 and the mode reduced with number 5.

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Answer:

D

Step-by-step explanation:

√(-49)

Let's rewrite this as:

√(-1) √(49)

√49 is 7, and √-1 is i.  Therefore:

7i

Answer D.

The expression √(-49) can be rewritten using the Imaginary unit "i" as follows:

[tex]\sqrt(-49) = \sqrt(49 \times (-1)) = \sqrt49 \times \sqrt(-1) = 7i[/tex]

So, the correct answer is option D) 7i.

Here, rewrite the expression √(-49) using the imaginary unit "i," you can express it as the square root of (-1) multiplied by the square root of 49. This is because the square root of -1 is represented as "i."

[tex]\sqrt(-49) = \sqrt((-1) \times 49)[/tex]

Now, we can factor out the square root of 49, which is 7:

[tex]\sqrt(-1 \times 49) = \sqrt(-1) \times \sqrt(49) = i \times 7[/tex]

So, √(-49) can be expressed as 7i.

The correct answer is:

D) 7i

Thus, √(-49) is equal to 7i, indicating that it is a complex number with a real part of 0 and an imaginary part of 7. option D) 7i is correct choice .

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I. need. more info. to solve it sorry

A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution. In this case, the area under the standard normal curve is 0.1271, and the corresponding z-score is approximately -1.14.

A z-score is a standardized value that represents the number of standard deviations a given score is above or below the mean in a normal distribution.

It allows for comparison of scores from different data sets with different means and standard deviations. In this case, we are given the area under the standard normal curve and asked to find the corresponding z-score.

To find the z-score, we can use a z-table, which shows the area under the normal curve to the left of each z-score. In the given problem, the area under the curve is 0.1271.

By looking up the closest area in the z-table, we find that the z-score is approximately -1.14.

Final answer:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution.

Explanation:

The z-score represents the number of standard deviations a value is from the mean in a standard normal distribution. To find the z-score, we can use the z-table or a calculator. In this case, the area under the standard normal curve is given as 0.1271. Using the z-table, we can find the z-score that corresponds to this area and enter it in the box.

Answer:

Use combinations because order does not matter, 1001, 0.36

Step-by-step explanation:

Answer: Combination method is used for counting.  There are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

Step-by-step explanation:

Since we have given that

Total number of members = 14

Number of girls = 9

Number of boys = 5

We will use "Combination method " to count the compound probability.

So, the total number of possible outcomes is given by

[tex]^{14}C_4\\\\=1001[/tex]

The probability that two girls and two boys are on the committee is given by

[tex]\dfrac{^9C_2\times ^5C_2}{^{14}C_4}\\\\=\dfrac{360}{1001}\\\\=0.3596\\\\=0.36[/tex]

Hence, there are 1001 possible outcomes and there is probability of 0.36 of getting two girls and two boys are on the committee.

Answer:

g/f

Step-by-step explanation:

Cosine is adjacent over hypotenuse.  The side adjacent to H is g.  The hypotenuse is f.  Therefore:

cos H = g / f

For this case we have by definition of trigonometric relations of rectangular triangles that, the cosine of an angle is equal to the leg adjacent to the angle on the hypotenuse of the triangle.

Then, according to the given figure we have:

[tex]cos (H) = \frac {g} {f}[/tex]

Answer:

[tex]cos (H) = \frac {g} {f}[/tex]

Answer:

24 girls.

Step-by-step explanation:

If the number of boys is x then:

x + 4/7 x = 66

x = 66  / 1 4/7

x = 66 *  7/11

= 6 * 7

= 42.

So the number of  girls is 66 - 42

= 24.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

The number of girls students is 24.

In the fifth grade at Lenape Elementary School, there are 4/7 as many girls as there are boys.

There are 66 students in the fifth grade.

The quantitative relation between two amounts shows the number of times one value contains or is contained within the other:

There are 66 students in fifth grade, and there is a 4:7 girl to boy ratio.

[tex]= \dfrac{66}{11}\\\\= 6[/tex]

Then,

the number of girls is = [tex]6 \times 4=24[/tex]

The number of boys is = [tex]6 \times 7 = 42[/tex]

Hence, the number of girls students is 24.

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Answer:

$3.55/workout

Step-by-step explanation:

Total cost:  $39 + ($27.50/month)(12 months) = $369

Number of visits per year:  (2 visits/week)(52 weeks/year) = 104 visits/year

Dividing the total cost by 104 visits/year results in:

 $369

--------------- = 3.55

104 visits

Each workout cost him $3.55. Each workout cost is obtained by the total cost and the number of the visit per year.

It is the sum of the variable cost and the fixed cost. The total cost is the minimum dollar cost of producing some quantity of output.

Registration fee = $39

Monthly fee = $27.50

No of visit a week for a year= 2

Total cost is found as;

Total cost = registration fee+monthly fee ×no of month

Total cost =  $39 + ($27.50/month)(12 months)

Total cost =$369

Number of visits per year= visits/week×no of week

Number of visits per year= (2 visits/week)(52 weeks/year)

Number of visits per year = 104 visits/year

When you divide the entire cost by 104 visits per year, you get:

Each workout cost = $369/104

Each workout cost =$3.55

Hence, each workout cost him $3.55

To learn more about the total cost, refer to the link;

https://brainly.com/question/14927680

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Answer:

10 mph

Step-by-step explanation:

Let x mph be Devontre rate uphill, then x+20 mph its his rate downhill.

1. Time uphill:

[tex]\dfrac{5}{x}\ hours[/tex]

2. Time downhill:

[tex]\dfrac{5}{x+20}\ hours[/tex]

3. If it took him 20 minutes (1/3 hour) longer to ride uphill than downhill, then

[tex]\dfrac{5}{x}-\dfrac{5}{x+20}=\dfrac{1}{3}[/tex]

Solve this equation:

[tex]\dfrac{5(x+20)-5x}{x(x+20)}=\dfrac{1}{3}\\ \\\dfrac{100}{x(x+20)}=\dfrac{1}{3}\\ \\300=x(x+20)\\ \\x^2+20x-300=0\\ \\D=20^2-4\cdot (-300)=400+1200=1600\\ \\x_{1,2}=\dfrac{-20\pm \sqrt{1600}}{2}=\dfrac{-20\pm 40}{2}=-30,\ 10.[/tex]

The rate cannot be negative, thus, x=10 mph (rate uphill).