Four items are on sale at a local store. A shirt was originally $9.50 and now is $7.60. A pair of jeans were $25.00, and now they are priced $20.00. A pair of boots were $55.00, and they are on sale for $44.00. Do these regular and sale prices represent a proportional relationship

Answer:

Deduct/subtract

Step-by-step explanation:

Federal Reserve board uses different methods to increase or decrease the currency in circulation. This methods are known as Monetary policy. The Central bank, at its discretion, can print more currency to increase the flow of currency in circulation

The Federal Reserve Board, which is the governing body that manages the Federal Reserve System, oversees all domestic monetary policy. The Fed"s job is to increase and decrease paper currency in circulation. This effort is to curb inflation and hyperinflation, stabilize the economy and create room for ease of doing business with the international community

The Fed can increase the money supply by lowering the reserve requirements for banks, which allows them to lend more money.

Also, by raising the banks' reserve requirements, the Fed can decrease the size of the money supply.

The Central bank modify short-term interest rates by lowering or increasing the discount rate that banks pay on short-term loans from the Fed.

Modifying Reserve Requirements : they can moderate the amount of money banks can hold.

Answer:

A. We have extremely strong evidence to reject H0.

Step-by-step explanation:

Let P be the proportion of non-retirees in 2015 who did not think that Social Security would be able to pay a retirement benefit by the time that they retire.

According to the data null and alternative hypotheses should be:

Test statistics is -4.29 and p-value of the statistics is p<0.001

At every significance levels higher than 0.001, we can reject the null hypothesis since p<0.001.

Answer:

[tex]8y^{50}[/tex]

Step-by-step explanation:

This expression is equal :

[tex]{(64y^{100})}^{\frac{1}{2}}[/tex]

Here we can use this rule :

[tex](a^mb^n)^y=a^{my}b^{ny}[/tex]

Now, 64 we can write like : [tex]8^2[/tex]

[tex](8^2y^{100})^{\frac{1}{2}}[/tex]

Now we can use our rule :

[tex]8^{2*\frac{1}{2}}y^{100*\frac{1}{2}[/tex]

When we simplify, we have :

8y^{50}

Answer:

b

Step-by-step explanation:

Answer:

[tex](1.5,2.85)[/tex]

Step-by-step explanation:

we know that

The formula to calculate the midpoint between two points is equal to

[tex]M(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

we have the endpoints:

Q(0.3, 1.8), R(2.7, 3.9)

substitute in the formula

[tex]M(\frac{0.3+2.7}{2},\frac{1.8+3.9}{2})[/tex]

[tex]M(\frac{3}{2},\frac{5.7}{2})[/tex]

[tex]M(1.5,2.85)[/tex]

Answer:

it is option a

Step-by-step explanation:

. f(x) = (4x + 1)(4x − 1) is the correct answer overall you have the check it and just make sure you fully to your capability of those steps

The equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).

A function assigns the value of each element of one set to the other specific element of another set.

As the function is given to us that f(x)=16x²-1, therefore, the equivalent function that best shows the x-intercepts on the graph can be written as,

[tex]f(x)= 16x^2-1\\\\f(x)=16x^2-1^2\\\\f(x)=(4x-1)(4x+1)[/tex]

If we solve the roots of the given function,

(4x-1)=0

x = 1/4 = 0.25

(4x+1)=0

x = -1/4 = -0.25

Thus, the x-intercept of the function is 0.25 or -0.25.

Thus, the equivalent function that best shows the x-intercepts on the graph is f(x)=(4x-1)(4x+1).

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Answer:

D.

Step-by-step explanation:

Let the number of stamps Kaye had be k and that of Alberto be a. Then we know that are in a ratio of 5 to 3.

Hence, k : a = 5:3

or 3k = 5a

Then Kaye gave Alberto 10 of her stamp to make the ratio 7:5

k - 10/a + 10 = 7/5

Cross multiply:

5(k - 10) = 7(a + 10)

5k - 50 = 7a + 70

5k - 7a = 120

Let us now solve the last equation simultaneously with the equation 3k = 5a

5k - 7a = 120

3k - 5a = 0

Multiply equation 1 by 3 and equation 2 by 5

15k - 21a = 360

15k - 25a = 0

Subtract 1 from 2, 4a = 360

and thus a = 90

We know 3k = 5a

3k = 5 * 90

k = 450/3 = 150

Now if we subtract 90 from 150, this yields 60

Answer:

D

Step-by-step explanation:

Joe already has $40 and can save $20 each week. the total amount he can save in a given number of weeks is $20 multiplied by the that number of weeks which in this case is w so 20w. To find the total T of the amount he has after w weeks, you add the amount he already has to the amount saved. So the equation would be T=40+20w

Answer:

D) T = 40 + 20w

Step-by-step explanation:

Trust me! i had this on my test/ exam, and it was correct!!

i really hoped this helped! Have a wonderful day!

Answer:

a=2

Step-by-step explanation:

Well, first let us find product of the first 8 positive integers, which is 1*2*3*4*5*6*7*8=40320. It can also be written as 40320=[tex]2^{7}[/tex]*3²*5*7. From the formula above, it can be extracted that if a=2, n can be any number from 3 to 7 (considering that a and n are not equal and greater than 1).

In (1) a^n=64 and in (2) n=6 so it can be written as 2^6=64 so a=2 and n=6. So the value of a is 2. a=2

Answer:

1/8

Step-by-step explanation:

P(B) = 1/2

Now we are considering that the three children are all boys. This means we are considering that the first is a boy, the second is a boy and the third too is a boy. This brings us to the situation BBB

That is a boy and a boy and another boy. In probability, the word and means we multiply the three.

Hence:

P(BBB) = P(B1) * P(B2) * P(B3) = 1/2 * 1/2 * 1/2 = 1/8 or 0.125

The probability of a three-child family having all boys, given that each birth is independently a boy with a probability of one half, is 1/8 or 0.125 (12.5%).

The subject of your question is based in

probability

, a key concept in mathematics. Specifically, you're asking about the

probability of a family having three boys

, with the probability of any birth resulting in a boy being given as one half. As the question indicates that all births are independent, we're dealing with independent events in probability. The probability of independent events is calculated by multiplying the probabilities of each individual event. In this case, the probability of having a boy is one half (or 0.5), and we have three independent events (the births of the three children). Therefore, the probability of all three children being boys is (1/2) * (1/2) * (1/2), which simplifies to 1/8 or 0.125. So, assuming that all births are equally likely to result in a boy or a girl, the probability of a three-child family having all boys is 0.125, or 12.5%.

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Answer:

The Total of Charlie's will be $7.16.

Step-by-step explanation:

Given:

Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.

Price of regular ticket = $9.00.

tax = 6%.

We need to find Charlie’s total.

So we will first find the price of regular ticket with 25% off.

25% percent of regular ticket  = [tex]\frac{25}{100}\times 9 = \$2.25[/tex]

Discounted Price of regular ticket will be equal to Price of regular ticket minus Discounted amount.

Discounted Price of regular ticket = 9 - 2.25 = $6.75

Now, including tax :

Tax paid will be on discounted amount.

Hence Amount paid in tax = [tex]6\% \times 6.75= \frac{6}{100}\times 6.75 = \$0.405[/tex]

Total amount paid by charlie is equal to sum of Discounted Price of regular ticket and Amount paid in tax

Total Amount paid by charlie = [tex]6.75+0.405 =\$7.155 \approx \$7.16[/tex]

Therefore, the total of Charlie's will be $7.16.

Answer:

∆AKM is a right triangle for it is inscribed in semicircle O.

AM = diameter of semi-circle O = 2R = 2(2) = 4

%22AK%22%2F%22AM%22=cos%2833%5Eo%29

AK+=+AM%2Acos%2833%5Eo%29

AK+=+4cos%2833%5Eo%29

%22KM%22%2F%22AM%22=sin%2833%5Eo%29

KM+=+AM%2Asin%2833%5Eo%29

KM+=+4sin%2833%5Eo%29

The perimeter of a triangle is the sum of the three sides.

perimeter=AK%2BKM%2BAM

perimeter=4cos%2833%5Eo%29%2B4sin%2833%5Eo%29%2B4

Approximately 9.533238412

Step-by-step explanation:

Answer:

reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

Answer:

$32,000

Step-by-step explanation:

Yearly investment = $3,000

Number of years = 20

Investments earned an average of 8 percent a year.

Total invested amount = $3,000 × 20 = $60,000

Current value of investment = $92,000.

We need to find the total earnings on the investment.

Earnings = Current value of investment - Total invested amount

Earnings = $92,000 - $60,000

Earnings = $32,000

Therefore, the total earnings is $32,000.

To find out how much was earned on the investments over a 20-year period, we subtract the total amount invested ($60,000) from the final value of the portfolio ($92,000), yielding $32,000 as the total earnings. However, this option is not offered in the question.

This type of question is typically encountered in personal finance or mathematics related to investment portfolios. The total amount invested over twenty years is calculated by multiplying the yearly investment by the number of years, so $3,000 * 20 years = $60,000. This is the amount you've put in from your own pocket. The value of the investment portfolio now is given as $92,000, which is the sum of your investment and the earnings. So to calculate your earnings alone, you subtract the total amount you invested from the current value of your portfolio: $92,000 (total value) - $60,000 (your total investment) = $32,000. So the amount you earned on your investments over this 20-year period is not given in the question as none of the options match our calculation of $32,000.

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Answer:

6 hours

Step-by-step explanation:

Suppose Madison spent x hours on her social project,

then the number of hours spent on other project will be 1/3 of x=x/3

Total hours spend on all projects will be the addition of hours spent on social project and hour spent on other project, i.e

x + x/3 = 4x/3

It si given that this is 8 hours, therefore

4x/3=8

Multiplying both sides by 3:

4x=24

Dividing across board by 4:

x= 6 hours

Answer:

100 minutes

Step-by-step explanation:

Let the number of minutes required for the two Billings to be equal be x.

Now we write this in an equation form.

7.95 + 0.05x = 9.95 + 0.03x

0.05x - 0.03x = 9.95 - 7.95

0.02x = 2

x = 2/0.02 = 100 minutes

At the 100th minute, the amount of Billings would be equal

Answer:

Every point in the line would get reflected about the x axis and we would get a new line.

Step-by-step explanation:

When you reflect a point about the x-axis , the x-coordinate of the image remains the same but the y - coordinate changes to its negative value.

Now a line is a collection of points and we have to find out what happens when we reflect a line about the x-axis.

Reflecting a line about the line is same as keeping a mirror along the x-axis and the image we see in the mirror is the same as the image we obtain in the mirror.

So every point in the line would get reflected about the x axis and we would get a new line.

Final answer:

Reflecting a line across the x-axis inverts the y-coordinates of all points on the line, while the x-coordinates remain unchanged; the reflected line appears flipped over the x-axis, preserving distance but potentially changing orientation.

Explanation:

When a line is reflected across the x-axis, each point on the original line is flipped vertically to a new position on the opposite side of the x-axis, maintaining the same distance from the x-axis. Essentially, every point's y-coordinate is multiplied by -1, causing the line to appear as a mirror image of itself with respect to the x-axis. This transformation preserves the shape and size of the original line but changes its orientation relative to the x-axis.

Answer: 60°, 72°, 90°, 120° and 180°

Step-by-step explanation:

To calculate the angle of rotational symmetry of a shape or polygon, you make use of this formula

[tex]\frac{360}{n}  where n is the number of sides of the shape[/tex]

example for a Square with 4 sides. the angle of rotational symmetry is 360/4 =90°.

Answer:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

Step-by-step explanation:

We presume you're starting with ...

  y = ax^2 +bx +c

As you would with numbers, factor the first two terms:

  y = a(x^2 +b/a·x) +c

Add half the square of the x term inside and its opposite outside parentheses:

  y = a(x^2 +(b/a)x + (b/(2a))^2) + c - a(b/(2a))^2

  y = a(x +b/(2a))^2 +c -b^2/(4a)

You can combine the last two terms to a more familiar fraction:

  y = a(x +b/(2a))^2 + (4ac -b^2)/(4a)

To write a quadratic function in vertex form, use the values of a, b, and c. Find the coordinates of the vertex using h = -b/2a and k = f(h).

Substitute the values into the vertex form.

To write a quadratic function in vertex form, you can use the values of a, b, and c.

The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k,

where (h, k) represents the coordinates of the vertex.

To find h and k, you can use the formulas h = -b/2a and k = f(h).

Once you have the values of h and k, you can substitute them into the vertex form to obtain the quadratic function in vertex form.

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Answer:

If the question is single answer correct then the answer is [tex]\frac{1}{3}[/tex] and if it's multiple options correct than the answer is [tex]\frac{1}{7}[/tex]

Step-by-step explanation:

There is a little ambiguity in the question, that whether one answer is correct or multiple options are correct, but let;s deal with both the cases.

Probability = [tex]\frac{TotalNo.OfFavourableOutcomes}{TotalOfNoOfOutcomes}[/tex]

Probability when one option is right=[tex]\frac{1}{3}[/tex]

If this is a question , where multiple options are right then the total no. of cases for it will be = TTT, TFF, FTF, FFT, TTF, TFT, FTT  (FFF is not a valid case, because the question has to have at least one valid answer.)

Probability when more than one option can be right=[tex]\frac{1}{7}[/tex]

Answer:

64 square inches

Step-by-step explanation:

The base is square, and there are 16 cupcakes, so there are 4 cupcakes along the width and 4 cupcakes along the length.

Each cupcake is 2 inches, so the base is 8 inches by 8 inches.  Therefore, the area is 64 square inches.

Answer:

104°

Step-by-step explanation:

Thinking process:

Let the triangle be:

ΔMNO

The angle be: ∠LMN.

From the description, NOP is 104°

If, segment MN and NO are marked congruent then the corresponding angle,  ∠LMN is 104°

This property of congruency applies since the segments are equal.

Answer: it will need 40 cups of lemonade to break even

Step-by-step explanation:

Break even represents the point at which there is neither profit nor loss.

It costs serine $30 to start a lemonade stand plus $0.50 per cup of lemonade. Assuming that she made x cups of lemonade, the total cost of making x cups would be

30 + 0.5x

She sells each cup of the lemonade for $1.25 . Assuming that she sold x cups of lemonade, therefore, the total amount would be 1.25×x = 1.25x

To break even,

30 + 0.5x = 1.25x

1.25x - 0.5x = 30

0.75x = 30

x = 30/0.75

x = 40

Answer:

c

Step-by-step explanation:

Answer:

x=3, y=5

Step-by-step explanation:

(16x+2) and (45x-5) are co-interior angles and they sum up to 180 degrees.

To find x

(16x+2)+(45x-5)=180

16x+45x-5+2=180

61x-3=180

61x=180+3

61x=183

x=3

(45x-5) and (26y) are corresponding angles so their values are equal

(45x-5)=(26y), x=3

(45 (3)-5)=(26y)

135-5=26y

130=26y

5=y

Answer:

There are infinite such positive integers which can be written as a sum of cubes of two positive integers. Some of them are written below:

Hence it is not possible to write all such numbers which can be written in this format. Though some of them can be enlisted if the value of maximum integer "N" is given.

Answer:

The Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Step-by-step explanation:

Given:

Number of skaters = 30

Area for each skater = 40 sq ft

We need to find the dimension of rectangular ring the are going to build.

Now we know that they building the skating ring such that they all can use at same time.

Hence if the all use at same time then we will find the total area first.

Total area can be calculated by multiplying Number of skaters with area required for each skaters.

Framing the equation we get;

Total area = [tex]30\times 40 = 1200 \ ft^2[/tex]

Hence The total area of the rectangular ring would be 1200 sq. ft.

Now we know that Total area is equal to product of length and width.

[tex]length\times width =1200ft^2[/tex]

1200 can be written as = 20 × 60, 25 × 48, 30 × 40,60 × 20,48 × 25,40 × 30

Hence the Possible dimension of the ring could be;

20 ft × 60 ft

25 ft × 48 ft

30 ft × 40 ft

60 ft × 20 ft

48 ft × 25 ft

40 ft × 30 ft

Answer:

Step-by-step explanation:

Answer:

c = 0 or c = -4

Step-by-step explanation:

According to the Mean Value Theorem

[tex]f^{'}(c) = \frac{f(0) - f(-6)}{0 - (-6)} = \frac{0 - (-6)^3 - 6*(-6)^2 - 6*(-6)}{6} = 36 - 36 + 6 = 6[/tex]

By taking the first derivative of f

[tex]f^{'}(x) = 3x^2 + 12x + 6[/tex]

Since[tex]f^{'}(c) = 6[/tex]

We can solve for c

[tex]3c^2 + 12c + 6 = 6[/tex]

[tex]3c^2 + 12c = 0[/tex]

[tex]c(c + 4) = 0[/tex]

c = 0 or c = -4

Answer:

  AB = DC = 12

  AD = BC = 10

Step-by-step explanation:

For ABCD to be a parallelogram, opposite side pairs must be congruent. That will be the case when ...

  AB = DC

  x+4 = 12 . . . . substitute expressions for length

  x = 8 . . . . . . . subtract 4

Then the lengths of AD and BC must be ...

  BC = AD = x+2 = 8+2 = 10

___

The figure will be a parallelogram when x=8 and sides have lengths ...

  AB = DC = 12

  AD = BC = 10

_____

Comment on the problem

Of course, if x ≠ 8, or BC ≠ AD, the figure will not be a parallelogram. You are asked to show the figure IS a parallelogram, but all you can really show is that the figure CAN BE a parallelogram. In order to do anything useful with the given expressions for side lengths, you must assume the figure is a parallelogram.

Answer:

1. [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]

2. [tex]E_d=-\dfrac{2}{3}[/tex]

Step-by-step explanation:

The given demand equation is

[tex]p=\dfrac{45}{q^{1.5}}[/tex]

where p is the price (in dollars) per quarter-chicken serving and q is the number of quarter-chicken servings that can be sold per hour at this price.

Part 1 :

We need to Express q as a function of p.

The given equation can be rewritten as

[tex]q^{1.5}=\dfrac{45}{p}[/tex]

Using the properties of exponent, we get

[tex]q=(\dfrac{45}{p})^{\frac{1}{1.5}}[/tex]      [tex][\because x^n=a\Rightarrow x=a^{\frac{1}{n}}][/tex]

[tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex]

Therefore, the required equation is [tex]q=(\dfrac{45}{p})^{\frac{2}{3}}[/tex].

Part 2 :

[tex]q=(45)^{\frac{2}{3}}p^{-\frac{2}{3}}[/tex]

Differentiate q with respect to p.

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{2}{3}-1}})[/tex]

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(p^{-\frac{5}{3}})[/tex]

[tex]\dfrac{dq}{dp}=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})[/tex]

Formula for price elasticity of demand is

[tex]E_d=\dfrac{dq}{dp}\times \dfrac{p}{q}[/tex]

[tex]E_d=(45)^{\frac{2}{3}}(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{(45)^{\frac{2}{3}}p^{-\frac{2}{3}}}[/tex]

Cancel out common factors.

[tex]E_d=(-\dfrac{2}{3})(\dfrac{1}{p^{\frac{5}{3}}})\times \dfrac{p}{p^{-\frac{2}{3}}}[/tex]

Using the properties of exponents we get

[tex]E_d=-\dfrac{2}{3}(p^{-\frac{5}{3}+1-(-\frac{2}{3})})[/tex]

[tex]E_d=-\dfrac{2}{3}(p^{0})[/tex]

[tex]E_d=-\dfrac{2}{3}[/tex]

Therefore, the price elasticity of demand is -2/3.

To address the question, q as a function of p is q = (45/p)^(2/3), and the price elasticity of demand when p is $4 can be found by taking the derivative of q with respect to p and substituting the given values in the elasticity formula.

The student has asked to express q as a function of p and to find the price elasticity of demand when the price is set at $4.00 per serving for a new roast chicken product. The given equation is p = 45 / q1.5.

The derivative of q with respect to p is dq/dp = -2/3 × (45/p4/3). Substituting p=4, we get the quantity q = (45/4)2/3. Plugging these values into our elasticity formula gives us the price elasticity of demand at p=$4.00.