A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.

Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.

The solution of the quadratic equation for y is given as follows:

y = 0.17 and y = 1.69.

The quadratic equation for this problem is defined as follows:

7y² - 13y + 2 = 0.

The coefficients are given as follows:

a = 7, b = -13 and c = 2.

Hence the discriminant is of:

D = (-13)² - 4 x 7 x 2

D = 113.

The first root is of:

y = (13 + sqrt(113))/14

y = 1.69.

The second root is of:

y = (13 - sqrt(113))/14

y = 0.17.

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Answer:

A

Step-by-step explanation:

For any given point on a parabola,

(x,y)

If we know the axis of symmetry x=a.

We can find the other point

If the given point x value is less than the axis of symmetry

(x+2a,y)

if the given point y value is greater than axis of symmetry

(x-2a,y)

Here, since 0<3, we use the first formula to find the new point

(0+2(3),-5)=(6,-5)

So the point is A.

The total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

The surface area of a rectangular prism is given by the sum of the areas of its six faces. To find the surface area of a rectangular prism that is 3 yards long, 2 yards wide, and 12 yards high, we need to find the area of each of its four rectangular faces and then add these areas together.

First, we find the area of the two faces that are 2 yards wide and 12 yards high. Each of these faces has an area of 2 * 12 = 24 square yards.

Next, we find the area of the two faces that are 3 yards long and 12 yards high. Each of these faces has an area of 3 * 12 = 36 square yards.

Finally, we find the area of the two faces that are 3 yards long and 2 yards wide. Each of these faces has an area of 3 * 2 = 6 square yards.

So, the total surface area of the rectangular prism is 24 * 2 + 36 * 2 + 6 * 2 = 72 + 72 + 12 = 156 square yards.

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Answer:

131,072 Zombies:

the equation: 32 x 4^6 = 131,072

the equation in scientific notation form: 3.2 x 4^7 = 131,072

Step-by-step explanation:

The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).

We can use an exponent to represent this in an equation:

32 x 4^6 = 131,072

Or, if we put it in scientific notation,

3.2 X 4^7 = 131,072.

The equation which represents the number of zombies is;

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given that

The amount of zombies = 32.

And It quadruples per hour,

Therefore,

Multiply the amount by 4 six times (as it occurs once for every hour).

The the exponent form to represent this equation:

32 x 4^6 = 131,072

Hence, in scientific notation the equation is,

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

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Answer: The probability that no man will be selected is the number of ways that only women can be selected divided by the total number of combinations of candidates for the 2 data analyst positions. There are 2 ways to choose 2 women from the 2 available women, and there are C(4,2) = 6 ways to choose 2 candidates from the 3 men and 2 women, so the probability that no man will be selected is 2/6 = 1/3.

The probability that both men will get selected is the number of ways to choose 2 men from the 3 available men divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,2) = 3 ways to choose 2 men from the 3 available men, and there are C(5,2) = 10 ways to choose 2 candidates from the 3 men and 2 women, so the probability that both men will get selected is 3/10 = 3/5.

If Jyothi gets one more resume of a woman, there will be a total of 3 men and 3 women. The probability that only one man gets selected is the number of ways to choose 1 man and 1 woman from the 3 men and 3 women divided by the total number of combinations of candidates for the 2 data analyst positions. There are C(3,1) * C(3,1) = 9 ways to choose 1 man and 1 woman, and there are C(6,2) = 15 ways to choose 2 candidates from the 3 men and 3 women, so the probability that only one man gets selected is 9/15 = 3/5.

Step-by-step explanation:

Answer:

3 and 7/8 gallons remaining

Step-by-step explanation:

You did not give the container options, but hopefully this will help

Answer:

26 oz

Step-by-step explanation:

4 lb x 16 oz/lb = 64 oz

64 oz - (2 lb)(16 oz/lb) - 6 oz = 26 oz are left

The required number of markers does Gerald has 56 markers.

Let's represent the number of markers that Gerald has with the variable "m", and the number of pens he has with the variable "p". We can set up two equations based on the information given:

m + p = 78 (equation 1)

(m + 11) + (p + 11) = 78 (equation 2)

In equation 2, we add 11 to both the number of markers and the number of pens, since Gerald has 11 more of each. We can simplify equation 2 by combining like terms:

m + p + 22 = 78

m + p = 56 (equation 3)

Now we have two equations with two variables. We can use either substitution or elimination to solve for one of the variables. Let's use substitution and solve for "m" in terms of "p" using equation 1:

m + p = 78

m = 78 - p

Now we can substitute this expression for "m" into equation 3:

m + p = 56

(78 - p) + p = 56

Simplifying the equation, we get:

78 - p + p = 56

78 = 56 + p

p = 22

Therefore, Gerald has 22 pens. To find the number of markers he has, we can substitute this value of "p" into equation 1:

m + 22 = 78

m = 56

So, Gerald has 56 markers.

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Answer:

5

Step-by-step explanation:

5.4772

To round to the nearest whole number, look at the number to the right of it (4)     if     5 or greater round the 5 up to '6'    o/w   leave it as '5'

Option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

What is meant by a broker?

An impartial party whose services are often used in several businesses is a broker. The main duty of a broker is to connect buyers and sellers; as a result, the broker acts as a neutral intermediary between a buyer and a seller.

The services which will be provided by a full-service broker but not by a discount broker are

Option I. Research of potential investment opportunities

Option III. Recommendation of investments

For any form of investment, research and recommendations are key and important components. Before you make any investments, you should conduct adequate research.

Hence, option A i.e. the first and the third service will be provided by a full-service broker but not by a discount broker.

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The measure of the angle x in the figure is 55 degrees

From the question, we have the following parameters that can be used in our computation:

The polygon and the external angles

The sum of the exterior angles of a polygon is 360°.

Using the above as a guide, we have the following:

5 * x + x + 30 = 360

Evaluate the like terms

So, we have

6x = 330

Divide by 6

x = 55

Hence, the value of x is 55

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Answer:

I think a is the right answer

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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For removing all the perfect squares of √(39y^9), we need to factor out any perfect squares from the expression under the square root.

To get rid of all the perfect squares in (39y9), factor out any perfect squares in the expression under the square root.

First, by factoring 39 and y9, we can simplify the expression under the square root:

[tex]√(39y^9) = √(313y^8y) = √(313*(y^4)^2*y)[/tex]

Because (y4)2 is a perfect square, we can take it out from under the square root:

[tex]√(39y^9) = √(313(y^4)^2y) = (y^4)√(313*y)[/tex]

By removing all of the perfect squares from (39y9), we get:

[tex](y^4)√(313y)[/tex]

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Pair of ratios can form a true proportion I would usually give 45 points but i have 35 soo ye 25/20, 16/21.

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You slept for 9 hours in those three days, calculated by multiplying 12.5% of the total hours (72) by 72, which equals 9.

To calculate the number of hours slept in three days, we first need to determine how many hours there are in three days.

As given, 1 day has 24 hours. So, three days will have 3 x 24 = 72 hours.

Now, we are told that you slept for 12.5% of those 72 hours. To calculate this, we multiply the percentage by the total number of hours:

12.5% x 72 hours = (12.5/100) x 72 = 0.125 x 72 = 9 hours

Therefore, you slept for 9 hours in those three days.

Percentage is a way to express a proportion or ratio as a fraction of 100. The sign "%" is widely used to represent it. For example, if you had 20 apples and you ate 5 of them, you would have consumed 25% of the apples (5 out of 20).

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Answer:

12

Step-by-step explanation:

If 113 divided by a number leaves a remainder of 5, then we need to find the prime factorization of 108.

If 135 divided by a number leaves a remainder of 3, then we need to find the prime factorization of 132.

If 160 divided by a number leaves a remainder of 4, then we need to find the prime factorization of 156.

108 = 2² × 3³

132 = 2² × 3 × 11

156 = 2² × 3 × 13

The GCF of 108, 132, and 156 is common factors with lower exponent.

GCF = 2² × 3 = 12

Answer: 12

The value of k in the exponential function is -3.

Taking the natural logarithm of both sides of the equation, we have:

ln [ (1 + 65/x)^(3x) ] = ln(e^k)

Using the properties of logarithms, we can simplify the left side of the equation:

3x ln(1 + 65/x) = k

Taking the limit as x approaches infinity, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

Using L'Hopital's rule, we can evaluate the limit:

lim (x → ∞) [ln(1 + 65/x) / (1/x)]

= lim (x → ∞) [-65 / (x(1+65/x))]

= -65/65

= -1

Therefore, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

= -3

Thus, the exponential equation simplifies to:

-3 = k

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We have the expression:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{3x} = e^k} \\[/tex]

As [tex]\displaystyle{x\to \infty} \\[/tex], the term [tex]\displaystyle{\dfrac{65}{x}} \\[/tex] approaches 0. Therefore, we can rewrite the expression as:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{x \cdot \dfrac{3x}{65}} = e^k} \\[/tex]

Simplifying the exponent, we get:

[tex]\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}} = e^k} \\[/tex]

Now, as [tex]\displaystyle{x\to \infty} \\[/tex], the expression [tex]\displaystyle{\left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}}} \\[/tex] approaches [tex]\displaystyle{e^{-3}} \\[/tex].

Therefore, we have:

[tex]\displaystyle{e^k = e^{-3}} \\[/tex]

Comparing the exponents, we can conclude that:

[tex]\displaystyle{k = -3} \\[/tex]

Hence, the correct value of k is indeed -3.

The cost per pound of a house blend of coffee is $ 5 per pound.

What is the cost price?

The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.

Here, we have

Weight of Central American coffee = 10 lb

Cost of Central American coffee = $7 per pound

Total value of Central American coffee = weight × cost = 10 ×7 = $ 70

Weight of South American coffee = 40 lb

Cost of South American coffee =  $ 4.50 per pound

Total value of Central American coffee = weight × cost = 40 ×4.50 = $ 180

Total weight of house blend coffee = Weight of Central American coffee + weight of South American coffee

= 10 +40 = 50 lb

The total value of house blend coffee = value of Central American coffee + value of South American coffee

= $ 70 + $ 180 = $ 250

Cost per pound of house blend coffee = ( total value of house blend coffee) / (total weight of house blend coffee)

= 250 / 50 = $ 5 per pound

Hence, the cost per pound of a house blend of coffee is $ 5 per pound.

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Using combinatorics, there are 1926 ways to distribute 9 different computer games among Wendy, Jim, and Hannah so that each person receives an odd number of games.

If each person receives an odd number of games, then the number of games must be 1, 3, 5, or 7. There are four odd numbers to choose from.

We can use combinatorics to find the odd number in each turn.

Let's consider each odd number in turn.

If each person gets 1 game, then we are looking for the number of ways to choose 3 games out of 9 to distribute. This is simply the number of combinations of 3 things taken from a set of 9 things, which is 9C3, or (9!)/(3!6!) = 84.

If each person gets 3 games, then we are looking for the number of ways to choose 3 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 6 games to distribute to the other two people. The number of ways to choose 3 games out of 9 is again 84, but we must multiply this by the number of ways to choose 3 games out of the remaining 6. This is 6C3, or (6!)/(3!3!) = 20. Therefore, the total number of ways to distribute 9 games with each person getting 3 games is 84*20 = 1680.

If each person gets 5 games, then we are looking for the number of ways to choose 5 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 4 games to distribute to the other two people. The number of ways to choose 5 games out of 9 is 126, and the number of ways to choose 4 games out of the remaining 4 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 5 games is 126*1 = 126.

If each person gets 7 games, then we are looking for the number of ways to choose 7 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 2 games to distribute to the other two people. The number of ways to choose 7 games out of 9 is 36, and the number of ways to choose 2 games out of the remaining 2 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 7 games is 36*1 = 36.

Adding up the number of ways to distribute the games in each case, we get 84 + 1680 + 126 + 36 = 1926.

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The proper way to construct a stem-and-leaf plot to display the data set {62,67,68,73, 73, 79,91,94,95,97} is to include a stem labeled ‘8’ and enter no leaf on the stem. So, the correct choice is option (b).

A stem and leaf graph is like a special table where each data value is separated into a "stem" (the first number) and a "leaf" (usually the last number). Leaves are sorted in ascending order from left to right. We have a data set with values {62,67,68,73, 73, 79,91,94,95,97}. Now, to construct the stem- leaf plot for our data.

Stem | Leaf

6 | 2 7

7 | 3 3 9

9 | 1 4 5 7

For stem and leaf diagram if some values are not present for some stem, then no leaf should be added to that stem. If we skip that stem than it would distort the shape of distribution of the data.

stem | leaf

6 | 2 7

7 | 3 3 9

8 |

9 | 1 4 5 7

Hence, include a stem labeled 8 and enter no leaves on the stem.

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Complete question:

The proper way to construct a stem-and-leaf display for the data set {62, 67, 68, 73, 73, 79, 91, 94, 95, 97} is to

a)exclude a stem labeled ‘8

b)include a stem labeled ‘8’ and enter no leaves on the stem.

c) include a stem labeled ‘(8)’ and enter no leaves on the stem.

d) include a stem labeled ‘8’ and enter one leaf value of ‘0’ on the stem.

The value of x the width of the solar panel is 18.5.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have Pythagoras theorem:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We are given that;

Length of base of panel= 40feet

Other length = 12feet

Now,

Applying the pythagoras theorum;

|AC|^2 = |AB|^2 + |BC|^2  

|AC|^2= 12^2 + 14^2

|AC|^2= 144+196

AC= 18.5

Therefore, by Pythagoras theorem x will be equal to 18.5.

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Answer:

it's d. answer d. 57/76 is the probability of landing on black. that is roughly 3 times as much as the probability of landing in white 19/76. 19 X 3 = 60 which is roughly around the ballpark of 57.

Dilation in coordinate geometry refers to the process of increasing or stretching the size of the originally drawn geometrical figure to a new figure by multiplying the co-ordinates of the original figure with a scale factor and obtain new co-ordinates to plot and form on the graph.

In the given figure, we observe that the original co-ordinates of the logo drew by Tyrone are:

A (-2,0) ; B (-2,3) ; C(2,2) ; D(2,-1)

From the graph, we see that the co-ordinates are multiplied by a scale factor of 5/2 and hence turn to new co-ordinates:

A'(-5,0) ; B'(-5, 15/2); C'(5,5) ; D'(5, -5/2)

Thus, we see that the rule followed to form the dilation of the logo on the coordinate plane was (5/2x, 5/2y).

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Answer:

Step-by-step explanation:

multiply all numbers together

2 x 6 x 3 = 36

The correct dosage to be administered is 5 ml.

To calculate the correct dosage to be administered, we can use the following formula:

Dose = (Desired dose / Stock strength) x Stock volume

In this case, the desired dose is 15 mg and the stock strength is 10 mg/0.5 ml. Therefore:

Dose = (15 mg / 10 mg/0.5 ml) x Stock volume

Simplifying this expression, we get:

Dose = 3 x Stock volume

To find the stock volume needed, we can rearrange this formula as follows:

Stock volume = Dose / 3

Substituting the values we have, we get:

Stock volume = 15 mg / 3 = 5 ml

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The solution to the equation is (a) x = ln(7/5) - 2

From the question, we have the following parameters that can be used in our computation:

4 + 5e^(x + 2) = 11

Evaluate the like terms in the equation

So, we have the following representation

5e^(x + 2) = 7

Divide through the equation by 5

This gives

e^(x + 2) = 7/5

Take the natural logarithm of both sides

x + 2 = ln(7/5)

So, we have

x = ln(7/5) - 2

Hence, the solution is x = ln(7/5) - 2

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It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered.

Given the triangle with sides ZY = 48, ZX = 50, and XY = 14, we can use trigonometry to find the value of tan(x).

First, we can use the Pythagorean theorem to find the value of YX, the length of the side opposite angle x:

[tex]YX = \sqrt{(ZY^2 + ZX^2 - 2 * ZY * ZX * cos(x))[/tex]

We know that ZY = 48 and ZX = 50, so we can substitute these values into the equation:

[tex]YX = \sqrt{(48^2 + 50^2 - 2 * 48 * 50 * cos(x))[/tex]

[tex]YX = \sqrt{(2304 + 2500 - 2400 * cos(x))[/tex]

Next, we can use the definition of tangent to find the value of tan(x):

[tex]tan(x) = YX/ZX = \sqrt{(2304 + 2500 - 2400 * cos(x)) / 50[/tex]

It is important to note that this calculation provides the value of tan(x) in terms of the cosine of the angle x, which is dependent on the specific triangle that is being considered. The exact value of tan(x) will depend on the specific angle x in the triangle.

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Answer:

x = 3

Step-by-step explanation:

2.5/x = 10/12

Multiply both sides by x

2.5 = 10/12x

Divide both sides by 10/12

3 = x

In a case whereby there are 7213 applicants for the astronaut program only one half of the applicants which is about 3607 applicants will be accepted into the program​.

The concept that will be used here is multiplication. One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

The symbols for multiplication are cross (), asterisk (*), and dot (). You seem to utilize the cross a lot when you write in your notebooks. In both algebra and computer languages, the asterisk and dot are symbols (higher mathematics).

Total applicants =7213 applicants

Then one half of the applicants  = 1/2 of 7213

=7213/2

= 3607 applicants

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complete question:

There are 7213 applicants for the astronaut program only one half of the applicants which is about ______will be accepted into the program​