You and your friends each buy a race t-shirt. If 3 t-shirts cost ?75.33, how much does 1 t-shirt cost?

To horizontally stretch the linear parent function f(x) = x by a factor of 2, we replace 'x' in the original function with 'x/2'. Therefore, g(x) = x becomes g(x) = x/2 or g(x) = 1/2x.

When we talk about stretching the "linear parent function" f(x) = x horizontally by a factor of 2, we are essentially changing the 'x' values of the function, and the equation of the function changes accordingly. When a function is stretched horizontally by a factor of 'b', the new function becomes f(x/b). So, in this case, as the stretch factor is 2, the new function will be f(x/2).

This means that wherever you see 'x' in the original function, you replace it with 'x/2'. So, f(x) = x becomes g(x) = x/2. Therefore, the correct answer to your question is g(x) = 1/2x.

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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:

Step-by-step explanation:

B. Vertically stretch by a factor of 3, and

D. Shift down 1 unit.

To determine which transformations were applied to the linear parent function f(x) = x to obtain the given function g(x) = 3x - 1, we need to examine the changes made to the function. Let's analyze each choice:
A. Horizontally stretch by a factor of 3.
A horizontal stretch would mean that the x-values are being multiplied by a constant factor. However, in g(x) = 3x - 1, it's the output values (y-values) that have been multiplied by 3 when compared to f(x) = x. Thus choice A is not correct.
B. Vertically stretch by a factor of 3.
In g(x) = 3x - 1, each output value has been multiplied by 3 relative to the parent function f(x) = x. In other words, y has been replaced by 3y, which causes a vertical stretch or scaling by a factor of 3. So choice B is correct.
C. Shift left 1 unit.
A horizontal shift of the graph would involve an addition or subtraction inside the function's argument (x). For instance, f(x - 1) would indicate a shift to the right by 1 unit, and f(x + 1) would be a shift to the left by 1 unit. Since there is no such term in g(x) = 3x - 1, no horizontal shift has occurred. Choice C is not correct.
D. Shift down 1 unit.
A downward shift is indicated by a subtraction outside the function. In g(x) = 3x - 1, there is indeed a "-1" applied to the entire function, which results in every point on the graph being shifted down 1 unit. Therefore, choice D is correct.
In summary, the transformations applied to f(x) = x to get g(x) = 3x - 1 are:
B. Vertically stretch by a factor of 3.
D. Shift down 1 unit.

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:

C. An ellipse

Step-by-step explanation:

If you cut a cone on the side with an angle that will produce an ellipse-shaped plane.

if you were to cut the cone perpendicularly to its height (as if the double cone on the picture was straight up), you would get a circle as the plane, because it would be a transversal cut of a circular cone.

If you cut it with an angle, you're stretching the circle... so you'll have an ellipse.

It is NOT a parabola NOR a hyperbola, since both would require the cross-section to go through the base... which it does not in this problem.  Please refer to the image below.

Answer:

An ellipse

Step-by-step explanation:

A p e x

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:

Step-by-step explanation:

Basically, just replace the x and y coordinates for the equation. For example... A. (0,-8).... -8=-4(0)-8= y=-4x-8.  A would be an answer choice.... Hope that helps !!!

Answer : If it is perpendicular to the axis, then a circle. If it is at an angle to the axis, then an ellipse. If it is parallel to the axis, then two parallel lines. Those are the only 3 cases that I can think of.

Hope this helps.

Answer:

Your answer is B. (3, 5/2)

Step-by-step explanation:

The formula to find the midpoint of a segment is

(x1 + x2) / 2 to find the x value

and (y1 + y2) / 2 to find the y value of the midpoint.

To find the midpoint of the segment in the photo, you would do...

-1 + 3 divided by 2, giving you 3 for your x

and then 2+3 divided by 2, giving you 5/2 for your y.

Hope this helps!

Answer:

B

Step-by-step explanation:

the midpoint is based on the average of the two pair of point X1 and X2 as Y1 and Y1 divided by 2, each one. So, if we settle X1 and Y1 as (-1,2) and X2 and Y1 as (7,3)

(X1 + X2)/2 = (-1+7)/2 = 6/2= 3

(Y1 + Y2)/2 = (2+3)/2 = 5/2

so, we get the Answer B (3 , 5/2)

Answer:

A bill's chances are the same as Sandra's

Step-by-step explanation:

Bill's chances are the same as Sandra's chances.

To be lucky means to be favored by some unforeseen event. Thus, the fact that a person is lucky or not has no relation to the luck that another person may or may not have. That is, there is no link between the chances of one person and those of another, when they are in the same situation.

Therefore, neither Bill nor Sandra have a different chance of rolling doubles on the next roll of the dice.

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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.

Point A is at (12,12)

Point B is at (48,24)

Use the distance formula √((x2-x1)^2 + (y2-y1)^2)

Length = √((48-12)^2 + (24-12)^2)

Length = √(36^2 + 12^2)

Length = √(1296 + 144)

Length = √1440

The answer is E.

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:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]\frac{1}{2}x-2>0[/tex]

Solve for x

[tex]\frac{1}{2}x>2[/tex]

[tex]x>4[/tex]

The solution is the interval ------> (4,∞)

All real numbers greater than 4

In a number line, the solution is the shaded area at right of x=4 (open circle, the number 4 is not included in the solution)

see the attached figure

Answer

On 4 there is a circle and the line goes to the right

Step-by-step explanation:

f(x)= 10x

It seems like c and d are the same.

Answer

b. No

Step-by-step explanation:

We can easily solve this question by using a graphing calculator or any plotting tool, to check if it is a sinusoid.

The function is

f(x) =  3*sin(2*x) - 5*cos(x)

Which can be seen in the picture below

We can notice that f(x) is a not sinusoid. It has periodic amplitudes, and the function has a period T = 2π

The maximum and minimum values are

Max = 6.937

Min = -6.937

Answer:

B

Step-by-step explanation:

No

Answer:

[tex]\sqrt{-12} = i\sqrt{12} = i\sqrt{4\cdot 3} = 2i\sqrt{3}[/tex]

Step-by-step explanation:

Answer: B) 684m

Step-by-step explanation:

From 9 to 27 is a 3 times increase, from 27 to 108 is a 4 times increase. So following the pattern, we can determine that it will increase 5 times, and fall another 540m in second 4. Then, we simply add all the numbers together to get the answer!

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:

228

Step-by-step explanation:

I would have saved $228 after 12 weeks if in the first week I deposit $8 in the account, and each week I deposit $2 more than deposited the week before

An equation is an expression that shows the relationship between two or more variables and numbers.

The savings account can be represented by an arithmetic sequence in which the first term (a) = 8, and common difference (d) = 2. Hence, money saved after 12 weeks is:

[tex]S_{n}=\frac{n}{2}(2a+(n-1)d) \\\\S_{12}=\frac{12}{2}(2(8)+(12-1)2) = 228[/tex]

I would have saved $228 after 12 weeks if in the first week I deposit $8 in the account, and each week I deposit $2 more than deposited the week before

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Answer:

Correct Option is d [tex](x+3)^2 = 11[/tex]

Step-by-step explanation:

For completing the square our equation should be in the form of [tex]a^2 +2ab + b^2 = (a+b)^2[/tex]

In the given equation we have:

[tex]x^2 +6x -2\\x^2 + 2(x) (?) +(?)^2 = 2\\for\,\, making\,\, 6x\,\, 2*x*3=6x \\so, \,\,we\,\, can\,\, add\,\, and\,\, subtract\,\, (3)^2 \,\,on\,\, both\,\, sides\\x^2 + 2(x) (3) +(3)^2 -(3)^2= 2\\(x+3)^2 -9 =2\\(x+3)^2 =2+9\\(x+3)^2 = 11[/tex]

Correct Option is d [tex](x+3)^2 = 11[/tex]

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.

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:

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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For this case we must solve the following questions:

Question 1:

We should simplify the following expression:

[tex]\frac {\frac {m ^ 2 * n ^ 3} {p ^ 3}} {\frac {mp} {n ^ 2}} =[/tex]

Applying double C we have:

[tex]\frac {m ^ 2 * n ^ 3 * n ^ 2} {mp * p ^ 3} =[/tex]

By definition of multiplication of powers of the same base we have to place the same base and add the exponents:[tex]\frac {m ^ 2 * n ^ 5} {m * p ^ 4} =[/tex]

Canceling common terms:

[tex]\frac {mn ^ 5} {p ^ 4}[/tex]

Answer:

Option A

Question 2:

We should simplify the following expression:

[tex]\frac {3xyz ^ 2} {6y ^ 4} * \frac {2y} {xz ^ 4}[/tex]

So, we have:

[tex]\frac {3xyz ^ 2 * 2y} {6y ^ 4 * xz ^ 4} =\\\frac {6xy ^ 2z ^ 2} {6y ^ 4xz ^ 4} =[/tex]

Simplifying common terms:

[tex]\frac {1} {y ^ 2z ^ 2}[/tex]

Answer:

Option D

Question 3:

We factor the following expressions to rewrite the experience:

[tex]r ^ 2 + 7r + 10[/tex]: We look for two numbers that multiplied give 10 and added 7:

[tex](r + 5) (r + 2)[/tex]

[tex]r ^ 2-5r-50:[/tex] We look for two numbers that multiplied give -50 and added -5:

[tex](r-10) (r + 5)[/tex]

[tex]3r-30 = 3 (r-10)[/tex]

Rewriting the given expression we have:

[tex]\frac {(r + 5) (r + 2) * 3 (r-10)} {3 (r-10) (r + 5)} =[/tex]

We simplify common terms in the numerator and denominator we have:

[tex](r + 2)[/tex]

Answer:

Option D

Answer:

17. The correct answer option is A.

18. The correct answer option is D.

19. The correct answer option is D.

Step-by-step explanation:

17. [tex]\frac{m^2n^3}{p^3} \times \frac{mp}{n^2}[/tex]

Changing division to multiplication by taking reciprocal of the latter fraction to get:

[tex]\frac{m^2n^3}{p^3} \times \frac{n^2}{mp}[/tex]

[tex]\frac{mn^5}{p^4}[/tex]

The correct answer option is A. [tex]\frac{mn^5}{p^4}[/tex].

18. [tex]\frac{3xyz^2}{6y^4} \times \frac{2y}{xz^4}[/tex]

[tex]\frac{1}{y^2z^2}[/tex]

The correct answer option is D. [tex]\frac{1}{y^2z^2}[/tex].

19. [tex]\frac{r^2+7r+10}{3} \times \frac{3r-30}{r^2-5r-50}[/tex]

Factorizing the terms to get:

[tex]\frac{(r+2)(r+5)}{3} \times \frac{3(r-10)}{(r+5)(r-10)}[/tex]

Cancelling the like terms to get:

[tex]r+2[/tex]

The correct answer option is D. [tex]r+2[/tex].

2*3=6 girls

Hope this helps :)

Answer:

Option A. [tex]\frac{29}{4}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x^{2} +7[/tex]

[tex]g(x)=\frac{x+2}{x}[/tex]

we know that

[tex](fog)=(\frac{x+2}{x})^{2} +7[/tex]

Evaluate the expression for x=-4

[tex](fog)(-4)=(\frac{-4+2}{-4})^{2} +7[/tex]

[tex]=(\frac{1}{2})^{2} +7[/tex]

[tex]=(\frac{1}{4})+7[/tex]

[tex]=\frac{29}{4}[/tex]

Answer:

(15−2x)(22−2x)x

Answer:

Volume of box = (15−2x)(22−2x)x

C is correct.

Step-by-step explanation:

A company is creating a box without a top from a piece of cardboard, but cutting out square corners with side length x.

The dimension of the cardboard must be 15 x 22 because all options has same value.

We have rectangle cardboard with 15 x 22. We cut square from each corner of the board with dimension x.

New length of box = 22 - 2x

New Width of box = 15 - 2x

Height of the box = x

Volume of box is equal to volume of cuboid.

Volume of box = LBH

                        = (15-2x)(22-2x)(x)

Hence, The correct volume of the box is (15-2x)(22-2x)(x)

Step-by-step explanation:

Hi there! The answer is,6 ounces of sports drink for each player. Pay attention to the following steps:

1 quart= 32 ounces

3 quarts= 32×3 =96 ounces

96÷16= 6 ounces

Final answer:

To find the probability that at least one of the investor's companies had outstanding prospects out of 400 newly formed companies, we can use the complement rule. The rounded probability is 0.0067747.

Explanation:

To find the probability that at least one of the investor's companies had outstanding prospects, we can use the complement rule. The complement of at least one company having outstanding prospects is that none of the companies have outstanding prospects. Since there are 400 companies in total and only 11 have outstanding prospects, the probability that a single company does not have outstanding prospects is 389/400. Therefore, the probability that both companies do not have outstanding prospects is (389/400)^2. The probability that at least one company has outstanding prospects is 1 - (389/400)^2.

Rounding this to seven decimal places, the probability that at least one of the investor's companies had outstanding prospects is 0.0067747.