Amy paid ?$69.77 for a pair of running shoes during a 25 ?%-off sale. What was the regular? price?

Answer:

Option a is correct

given data in the table represents an exponential function

The possible formula for the function is, [tex]y = f(x) = 12.5 (1.10)^x[/tex]

An exponential function is in the form of [tex]f(x) = ab^x[/tex] where a is the initial value and b ≠ 0 ,  b> 1.

Consider any two points from the table as shown;

(0, 12.5) and (1, 13.75)

Substitute these in [1] we have;

For (0, 12.5)

where x = 0 and f(x) = 12.5 in [1]

[tex]12.5 = ab^0[/tex]

12.5 = a

For (1, 13.75)

[tex]13.75 = ab^1[/tex]

13.75 = ab

Substitute the value of a =12.5 we have;

13.75 = 12.5b

divide both sides by 12.5 we get;

[tex]b = \frac{13.75}{12.5} = 1.10[/tex]

since, y =f(x)

therefore, we have the following exponential function as:

[tex]y= 12.5 (1.10)^x[/tex]

Answer:

Yes that is the correct answer, good job

Answer:

Translation 2 units to the left and 5 units down.

Step-by-step explanation:

Consider the parent function [tex]y=g(x)[/tex] and its graph.

1. The translation 2 units to the left forms from the graph of the parent function the graph of the function [tex]y=g(x+2).[/tex]

2. Then the translation 5 units down forms from the graph of the function [tex]y=g(x+2)[/tex] the graph of the function [tex]h(x)=g(x+2)-5.[/tex]

Answer:

the answer is d for plato users

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

The measure of Angles XWZ is 120 degrees.

To find the measure of XWZ, we need to consider the relationships between different angles in the diagram.

First, we know that angle XYZ is 50 degrees.

Since XY and YZ are tangent to circle O, angle XYZ is equal to angle OXZ. Therefore, angle OXZ is also 50 degrees.

Next, we know that the circumference of circle O is 120 degrees.

A full revolution around a circle is 360 degrees, so the ratio of the circumference of circle O to a full revolution is 120/360 = 1/3.

Since angle OXZ is one-third of a full revolution, it will be equal to one-third of 360 degrees, which is 120 degrees. So, the measure of angle XWZ is 120 degrees.

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The probable question may be:

In the diagram below XY and YZ are tangent to circle O . What is the measure of XWZ? As Angle XYZ is 50 degree and circumference of circle O is 120 degree.

A. 150 degree

B. 180 degree

C. 240 degree

D. 210 degree

Answer:

1/7 is the probability hope this helps

Answer:

A) 1/15

Step-by-step explanation:

The probability of picking a white marble is 3/10. Then 2 of the remaining 9 marbles are white, so the probability of picking one is 2/9.

The joint probability is (3/10)·(2/9) = 6/90 = 1/15

Answer:

I am 42 years old

Step-by-step explanation:

Given : In 2 years i will be twice as old as i was 20 years ago.

To Find : Current age

Solution :

Let the current age be x years.

After two years i will be (x+2) years

20 years ago i was (x-20)years

Since we are given that in 2 years i will be twice as old as i was 20 years ago.

⇒[tex]x+2 = 2 (x-20)[/tex]

⇒[tex]x+2 = 2x-40[/tex]

⇒[tex]40+2 = 2x-x[/tex]

⇒[tex]42 = x[/tex]

Thus my current age 'x' = 42 years.

Hence i am 42 years old

Answer:

All positive integers less than or equal to 5

(Imagine Math)

The domain of f(x) is all the positive integer values up to 5

A function is defined as a relation between a set of inputs having one output each.

The domain of a function is the set of all possible inputs for the function.

According to the problem,

So, the values of x will be all the positive integer values up to 5 , as the maximum number of splits is 5.

∴ we can write , x∈ {1 , 5}

This is the domain of f(x)

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Answer:

The expression for the amount Mr. Parker will pay for the van be

x = 50 + 0.35m

Step-by-step explanation:

Let us assume that the  amount Mr. Parker will pay for the van be x.

As given

Mr. Parker wants to rent a cargo van for a day.

It will cost the daily fee of $50 plus $0.35 per mile driven.

Let m = the number of miles .

Than the expression for the amount Mr. Parker will pay for the van.

x = 50 + 0.35m

Therefore the expression for the amount Mr. Parker will pay for the van be

x = 50 + 0.35m

Answer:

50+0.35m or 50+ .35m

your welcome, angel!

Answer:

25%

Step-by-step explanation:

percent discount = [tex]\frac{discount}{original}[/tex] × 100%

discount = $200 - $150 = $50

percent discount = [tex]\frac{50}{200}[/tex] × 100% = 25%

Final answer:

To find the percent of discount, calculate the difference between the original and sale prices ($50), divide this by the original price, and multiply by 100 to get a 25% discount.

Explanation:

To calculate the percent of discount given on the water skis, you need to determine the difference between the original price and the sale price, and then find what percentage that difference is of the original price.

First, subtract the sale price from the original price to find the amount of discount:

Discount Amount = Original Price - Sale Price

Discount Amount = $200 - $150 = $50

Next, divide the discount amount by the original price and multiply by 100 to get the discount percentage:

Discount Percentage = (Discount Amount / Original Price) × 100

Discount Percentage = ($50 / $200) × 100 = 25%

Therefore, the percent of discount on the water skis is 25%.

Answer:

11x^2 - 11x - 6

Step-by-step explanation:

I'm guessing you mean:

(10x^2 - x + 1 ) + (x^2 - 10x - 7)

First you combined like terms:

Such as :

10x^2 + x^2

-x - 10x

1 - 7

There's your answer.

11x^2 - 11x - 6

Answer:

Step-by-step explanation:

The given equation,

[tex]y=-\dfrac{1}{14}x^2+6x+3[/tex]

where,

x is the horizontal distance in feet and

y is the height of the ball in feet.

How high is the ball when it leaves the child's hand.

At the beginning when the ball leaves the hand of the child, the horizontal distance was 0, so putting x=0 we can get the height of the ball.

[tex]y_0=-\dfrac{1}{14}(0)^2+6(0)+3=3\ ft[/tex]

What is the maximum height of the ball.

As the quadratic function has negative leading coefficient, so it will open downwards and at the vertex we will get the maximum value of the function.

The coordinates of vertex are,

[tex]\left(-\dfrac{b}{2a},f\left(-\dfrac{b}{2a}\right)\right)[/tex]

Putting the values,

[tex]=\left(-\dfrac{6}{2\times -\frac{1}{14}},f\left(-\dfrac{6}{2\times -\frac{1}{14}}\right)\right)[/tex]

[tex]=\left(42,f\left(42\right)\right)[/tex]

Now,

[tex]y_{max}=f(42)=-\dfrac{1}{14}(42)^2+6(42)+3= 129\ ft[/tex]

How far from the child does the ball strike the ground.

At the end i.e when the ball touches the ground, the height of the ball is 0. So putting the value of y=0, in the equation,

[tex]\Rightarrow 0=-\dfrac{1}{14}x^2+6x+3[/tex]

[tex]\Rightarrow -\dfrac{1}{14}x^2+6x+3=0[/tex]

[tex]\Rightarrow -x^2+6x(14)+3(14)=0[/tex]

[tex]\Rightarrow -x^2+84x+42=0[/tex]

Solving the quadratic equation, we get

[tex]\Rightarrow x=-0.497,84.5[/tex]

As distance can not be negative, so only considering positive value,

[tex]x=84.5\ ft[/tex]

The ball is 3 feet high when it leaves the child's hand. The maximum height of the ball is 251 feet. The ball strikes the ground approximately 0.4 feet away from the child.

To find how high the ball is when it leaves the child's hand, we need to calculate the height when x = 0. Plugging in x = 0 into the equation, we get y = -1/14(0)^2 + 6(0) + 3 = 3 feet. Therefore, the ball is 3 feet high when it leaves the child's hand.

To find the maximum height of the ball, we need to determine the vertex of the quadratic equation. The formula for the x-coordinate of the vertex of a quadratic equation in the form y = ax^2 + bx + c is given by x = -b/2a. In this case, the x-coordinate is x = -6/(-1/14) = 84 feet. Plugging x = 84 into the equation, we find y = -1/14(84)^2 + 6(84) + 3 = 251 feet. Therefore, the maximum height of the ball is 251 feet.

To find how far from the child the ball strikes the ground, we need to find the x-intercepts of the equation, which represent the points where y = 0. Setting y to 0 and solving for x, we get: -1/14x^2 + 6x + 3 = 0. Using the quadratic formula, we find two values for x: x = 14(6 ± √187) / (-2), which simplifies to approximately x = -0.4 and x = 85.4. The ball strikes the ground approximately 0.4 feet away from the child.

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Answer:

40 square feet.    

Step-by-step explanation:

We have been given that a square foot wall of space needs 1/8 quart of paint. Terrence has 7 quarts of paint, but uses 2 quarts to paint a pipe.

The amount of paint that left will be 5 quarts (7-2=5).

To find the area of wall that can be painted with the rest of paint, we will divide amount of left paint by the amount used to paint one square foot of wall.

[tex]\text{The number of square feet that can be painted with rest of paint}=5\div \frac{1}{8}[/tex]

Dividing a number by a fraction is same as multiplying the number by the reciprocal of fraction.

[tex]\text{The number of square feet that can be painted with rest of paint}=5\times \frac{8}{1}[/tex]

[tex]\text{The number of square feet that can be painted with rest of paint}=5\times 8=40[/tex]

Therefore, 40 square feet of wall can be painted with the rest of the paint.

Terrence can paint 40 square feet of wall with the rest of the paint.

To find out how many square feet of wall Terrence can paint with the rest of the paint, we need to subtract the amount of paint he used to paint the pipe from the total amount of paint he has. Terrence has 7 quarts of paint and used 2 quarts to paint the pipe, so he has 7 - 2 = 5 quarts of paint left. Since 1/8 quart of paint is needed for 1 square foot of wall, we can find out how many square feet of wall Terrence can paint by dividing the amount of paint he has left by the amount of paint needed for 1 square foot:

Number of square feet of wall Terrence can paint = (5 quarts) / (1/8 quart per square foot) = (5 quarts) × (8/1) square feet per quart = 40 square feet.

[tex]\text{The explicit rule of geometric sequence}\\\\a_n=a_1 r^{n-1}\\------------------------------\\\text{We have the recursive form}\ a_1=3,\ a_n=\dfrac{1}{2}\cdot a_{n-1}.\\\\\text{Therefore}\ r=\dfrac{1}{2}.\ \text{Substitute:}\\\\\boxed{a_n=3\left(\dfrac{1}{2}\right)^{n-1}}[/tex]

The formula of a sum of an arithmetic sequence:

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n[/tex]

We have n = 75 and [tex]a_n=67-2n[/tex].

Calculate the first and seventy-fifth term:

[tex]a_1=67-2(1)=67-2=65\\\\a_{75}=67-2(75)=67-150=-83[/tex]

Substitute:

[tex]S_{75}=\dfrac{65+(-83)}{2}\cdot75=\dfrac{-18}{2}\cdot75=-9\cdot75=-675[/tex]

The value of [tex]\rm S_{75}[/tex] is -675 and this can be determined by using the formula of the sum of n terms in the arithmetic sequence and the given data.

Given :

[tex]\rm a_n= 67-2n[/tex]   --- (1)

The following steps can be used in order to determine the value of [tex]\rm S_{75}[/tex]:

Step 1 - Substitute the value of (n = 1) in the expression (1).

[tex]\rm a_1= 67-2(1)= 65[/tex]

Step 2 - Substitute the value of (n = 75) in the expression (1).

[tex]\rm a_{75}= 67-2(75)= -83[/tex]

Step 3 - Now, the formula of sum in an arithmetic sequence is given below:

[tex]\rm S_n=\dfrac{a_1+a_n}{2}\times n[/tex]

where n is the total number of terms, [tex]\rm a_1[/tex] is the first term, and [tex]\rm a_n[/tex] is the last term.

Step 4 - Substitute the values of the known terms in the above expression.

[tex]\rm S_{75}=\dfrac{65-83}{2}\times 75[/tex]

Step 5 - Simply the above expression.

[tex]\rm S_{75} = -675[/tex]

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Answer:

d) 2

Step-by-step explanation:

let's take the points (3, 1) and (7, 9)

Slope formula (m) = (y2 - y1)/(x2 - x1)

Here x1 = 3, y1 = 1 , x2 = 7 and y2 = 9

Now plug in these values in the formula, we get

slope (m) = (9 -1) / (7 -3)

= 8/4

Slope = 2

Answer: d) 2

Thank you.

Answer:

$30

Step-by-step explanation:

Lets use x as the price for the haircut.

If the perm is 2 * the amount of the haircut, this can be shown by 2x (2 times the value of x which is the haircut price).

We know the price for lunch so we simply need to subtract this value from 50:

50 - 5 = 45

So 45 is the total price for the perm and haircut.

Now we can add 2x (price of perm) and x (price of haircut):

2x + x = 3x

So 3x = 45

Divide both sides by three to get x:

x = 15

So if the perm is 2x the cost of the haircut, and the haircut costs 1x which is 15, then we can multiply thise value by 2:

15 * 2 = 30

So the perm cost $30!

When the order of something happens it is a permutation.

There are a total of 52 cards and you want to pick 2 different cards.

The equation for this is:

52! / (52 - 2!)

Simplified becomes 52! / 50!

Answer = 2,652 ways.

To find the number of ways to pick two different cards from a deck where order matters, we calculate the permutations, resulting in 52 times 51, which equals 2652 ways.

The question asks for the number of ways to pick two different cards from a standard deck of 52 cards considering that the order of selection matters. To calculate this, we use permutations. For the first card, there are 52 options; for the second card, since one card has already been picked, there are 51 options left. The number of permutations for two cards from a deck of 52 is therefore calculated as 52 × 51. This results in 2652 different permutations or ways to select two different cards where order is significant.

Answer: 25 cups of apple juice and 10 cups of splarking water.

Step-by-step explanation:

1. You have the following information given in the problem:

- She mixes 5 cups of apple juice with 2 cups of sparklin.

- She wants to make 35 cups of sparkling apple juice.

2. Then:

[tex]5cups+2cups=7cups[/tex] (Each lot of sparkling apple juice has 7 cups).

3. As she needs 35 cups, she needs to make 5 lots of sparkling apple juice, because:

[tex]\frac{35}{7}=5lots[/tex]

4. Therefore, you must multiply 5 lots by 5 cups of apple juice and 5 lots by 2 cups of sparkling apple juice. Then, she should use:

[tex]A.juice=5*5cups=25cups\\S.water=5*2cups=10cups[/tex]

5. The answer is:

25 cups of apple juice and 10 cups of splarking water.

To make 35 cups of sparkling apple juice, Elena will need to mix 25 cups of apple juice with 10 cups of sparkling water. This is because the initial quantity ratio is 5:2 for apple juice to sparkling water. Thus, to make a larger quantity, these original quantities are multiplied by a common factor.

The goal here is to get the quantities of apple juice and sparkling water that Elena should use to prepare 35 cups of sparkling apple juice. In the original mix, Elena combines 5 cups of apple juice with 2 cups of sparkling water to make 7 cups of the juice. This mix is thus in a ratio of 5:2 in favor of apple juice to water.

Given that the total quantity she now wants to prepare is 35 cups, which is 5 times the original quantity (because 35/7 = 5), you would multiply the quantities of each of the components (apple juice and sparkling water) by 5. This implies:

Therefore, Elena will need 25 cups of apple juice and 10 cups of sparkling water to make 35 cups of sparkling apple juice.

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Answer:

C. mass = force / accellaration

Step-by-step explanation:

184.56:7≈26.37 pounds

Answer:

Letter A:

There is a 42.857143% chance of picking a black marble out of the bag. This is because there are 7 marbles total and 42.857143% of them(3/7) are black, so that is the probability.

Letter B:

There is a 14.285714% chance of picking this. The chance of picking a black black marble first is 3/7, which you multiply by the chance of picking a marble out on your second try without putting the first black marble back in ,which is 1/3. That gives you 1/7, or the percent above.

Letter C:

The probability of picking a black marble, replacing it, then picking another black marble is 18.367347%, or 9/49. You take the probability of picking out a black marble first, 3/7,  and multiply it by the chance of picking another black marble after replacing the first one, which is also 3/7.

Letter D:

The probability is different for B and C because in B the chance for the second one is less because for the second pick there are less marbles and a third of them are black. In C the chance of picking a black marble in the second is the same as in the first because you are putting the original back in.

Answer:

A, C, & D

Step-by-step explanation:

A square root has the form [tex]\sqrt[2]{x}  = x^{1/2}[/tex] and can be represented in exponential form. Let's convert all the expressions to [tex]\sqrt{x}[/tex] this form. 4 square root 5 is [tex]4\sqrt{25} =\sqrt{16*5}=\sqrt{80}[/tex]

A. [tex]2\sqrt{20} =\sqrt{4*20}=\sqrt{80}[/tex]

B. [tex]6^{1/2}-5^{1/2} =\sqrt{6}-\sqrt{5}[/tex]

C. [tex]3*5^{1/2}+5^{1/2} =3\sqrt{5}+\sqrt{5}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}[/tex]

D. [tex]4*5^{1/2}=4\sqrt{5}=\sqrt{16*5}=\sqrt{80}[/tex]

E.[tex]2\sqrt{10} =\sqrt{4*10}=\sqrt{40}[/tex]

F.  [tex]3*5^{1/2}=3\sqrt{5}=\sqrt{9*5}=\sqrt{45}[/tex]

Answer: Choice C) Harold

Darren is correct because he subtracted c from both sides

Julie is correct because she multiplied both sides by H, and then divided both sides by L

Brenda is correct because she multiplied both sides by r

Harold is not correct. We can see this with a counter example. If A = 7 and h = 1, then the first equation Harold wrote leads to b = 14. Now plug those same values into the second equation and we get h = 2b/A turning into 1 = 2*14/7 and that simplifies to 1 = 4, which is a false statement. This contradiction is one example why the two equations Harold wrote aren't equivalent.

Answer:

C.

Step-by-step explanation:

Juile, Brenda, and Darren are all incorrect.

Answer:

16 KMH is the correct answer

Step-by-step explanation:

w - width

2w - length

60 - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 60    divide both sides by 6

w = 10 → 2w = 2 · 10 = 20

The area: A = width × length

A = (10)(20) = 200