The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of $113.00, and Jessica's Furniture Store marks up all furniture by 45%.

Answer:

πr^2 h

π(11)^2 (15)

= 1815π or = 5701

\( {\qquad\qquad\huge\underline{{\sf Answer}}} \)

Let's solve ~

Equation of directrix is : y = 1, so we can say that it's a parabola of form : -

\(\qquad \sf  \dashrightarrow \: (x - h) {}^{2} = 4a(y - k)\)

and since the focus is above the directrix, it's a parabola with upward opening.

\(\qquad \sf  \dashrightarrow \: (x - ( - 4)) {}^{2} = 4(2)(y - 5)\)

\(\qquad \sf  \dashrightarrow \: (x + 4) {}^{2} = 8(y - 5)\)

\(\qquad \sf  \dashrightarrow \: {x}^{2} + 8x + 16 = 8y - 40\)

\(\qquad \sf  \dashrightarrow \: 8y = {x}^{2} + 8x + 56\)

\(\qquad \sf  \dashrightarrow \: y = \cfrac{1}{8} {x}^{2} + x + 7\)

Directrix

Focus

Focus lies in Q3 and above y=1

Then

Perpendicular distance

Find a for the equation

Now the equation is

\(\\ \rm\dashrightarrow 4a(y-k)=(x-h)^2\)

\(\\ \rm\dashrightarrow 4(2)(y-5)=(x+4)^2\)

\(\\ \rm\dashrightarrow 8(y-5)=x^2+8x+16\)

\(\\ \rm\dashrightarrow 8y-40=x^2+8x+16\)

\(\\ \rm\dashrightarrow 8y=x^2+8x+16+40\)

\(\\ \rm\dashrightarrow 8y=x^2+8x+56\)

\(\\ \rm\dashrightarrow y=\dfrac{x^2}{8}+x+7\)

ANSWER

x = 21.6

EXPLANATION

We have that:

c = 23.2

To be able to solve this, we must first find angle

The sum of angles in a triangle is 180 degrees.

This means that:

=> 52 + 70 + 122+ =>

Sine Law says that the ratio of angle and side opposite the angle for any triangle equal.

This means that:

So, we can say that:

That is the value of x.

Answer:

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

Step-by-step explanation:

3j + 2a = $11

5j + 6a = $23

Multiply equation 1 by 3

9j + 6a = $33

Subtract

9j + 6a = $33

-(5j + 6a = $23)

=(4j + 0a = $10)

4j = $10

j = $2.50

Plug j into any equation.

3(2.5) + 2a = $11

7.5 + 2a = $11

2a = 3.5

a = $1.75

Jelly beans are $2.50 per pound

Almonds are $1.75 per pound

The equation that represent the number of penguins is (6 ×  4) + (3 × 6) + (3 × 6) = p.

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 ×  4) + (3 × 6) + (3 × 6) = p

where

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Answer:

the answer is 32z

Step-by-step explanation:

Answer:

I think it's true. hope this helps!!

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

A. To represent the number of grams present after n hours, we can use the equation:

N(n) = 15 × (1 - 0.2)^n

Where:

N(n) is the number of grams present after n hours,

15 is the initial amount of the substance in grams,

0.2 represents the decay rate of 20% per hour, and

^n represents the exponentiation operation.

B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:

N(24) = 15 × (1 - 0.2)^24

Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.

C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:

1 = 15 × (1 - 0.2)^n

To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:

log(0.8)(1/15) = n

Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.

Therefore, the answers are:

B. After 24 hours, approximately 2.49 grams will be left.

C. After approximately 18.13 hours, there will be approximately one gram left.

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Answer:

Step-by-step explanation:

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

Using the formula for finding slope m = (y2-y1) / (x2-x1). Plugging in the data points into the equation, we get a slope of 55. Therefore, the equation is y=55x+0 or y=55x

Step-by-step explanation:

Answer:

x * (2x + 9) = 455

Step-by-step explanation:

To express the width in terms of x, given information

x = width

The given information says the length is 9 more than 2 times the width. Length can be expressed in terms of x like this.

2x + 9 = length

The area of a rectangle is length x width, and the given area is 455.

x * (2x + 9) = 455 or 2x^2 + 9x = 455

The equation in terms of x of the area of the rectangle should be \(2x^2 + 9x = 455\)

Given that

The area of the rectangle is

= \(length \times breadth\)

\((2x + 9( (x) =455 \\\\ 2x^2 + 9x = 455\)

Therefore we can conclude that The equation in terms of x of the area of the rectangle should be \(2x^2 + 9x = 455\)

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Answer:

x>-11

Step-by-step explanation:

2x+8>-14

2x>-14-8

2x>-22

x>-22/2

x>-11

x>-11

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

Answer: To find the distance of a chord from the center of a circle, we need to use the following formula:

Distance from center = sqrt(r^2 - (c/2)^2)

Where r is the radius of the circle and c is the length of the chord.

In this case, the radius of the circle is 3.7cm and the length of the chord is 7cm.

So, substituting these values in the formula, we get:

Distance from center = sqrt(3.7^2 - (7/2)^2)

= sqrt(13.69 - 12.25)

= sqrt(1.44)

= 1.2 cm

Therefore, the distance of the chord from the center of the circle is 1.2 cm.

Step-by-step explanation:

Step-by-step explanation:

\( \frac{1}{4} (6 + x) = 6\)

Use ¼ to open the bracket

\( \frac{1}{4} \times 6 = \frac{3}{2} \\ \\ \frac{1}{4} \times x = \frac{1}{4} x\)

\( \frac{3}{2} + \frac{1}{4} x = 6\)

Collect like terms

\( \frac{1}{4} x = 6 - \frac{3}{2} \)

Simplify

\( \frac{1}{4} x = \frac{9}{2} \)

Cross Multiply

\(1x \times 2 = 4 \times 9 \\ 2x = 36\)

Divide both sides of the equation by 2

\( \frac{2x}{2} = \frac{36}{2} \)

Simplify

\(x = 18\)

We can find the value of x by solving the equation.

\(\frac{1}{4}(6+x)=6\)   This is the given equation. Solve for x and we get the answer.

First, we distribute 1/4 in 6+x.

\(\frac{1}{4}(6)+\frac{1}{4}(x)=6\\\frac{3}{2}+\frac{x}{4}=6\)

Because we have the denominators here, we have to get rid of them by multiplying whole equation by the highest denominator value.

The highest denominator value is 4, so multiply all whole equation by 4.

\(\frac{3}{2}(4)+\frac{x}{4}(4)=6(4)\\6+x=24\)

Then we move 6 to subtract on another side for the x to be the subject.

\(x=24-6\\x=18\)

Therefore, the answer is x = 18.

Total number of free throws made for player 2 are 23 using histogram.

A histogram is a graphical depiction of continuous or discrete data. In a histogram, the frequency is represented by the area of a bar. Frequency density, which is proportional to frequency, is plotted on the y-axis, and intervals representing the range of values are plotted on the x-axis. One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution. A histogram is a graph in which the horizontal axis represents the values of the observations, and the vertical axis represents the density of those observations.

Given,

Histogram given,

Total number of free throws made for player 2 are:

8 + 9 + 6

23

Total number of free throws made for player 2 are 23 using histogram.

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$105 is higher than $100, the minimum Payment due on Josiah's credit card is $105.

The minimum payment due on Josiah's credit card 3% of his outstanding balance and compare it to the minimum payment of $100. The higher amount between the two will be the minimum payment.

1. Calculate 3% of $3,500:

3% * $3,500 = 0.03 * $3,500 = $105

2. Compare the calculated amount with the minimum payment of $100:

Minimum payment = max($105, $100)

Since $105 is higher than $100, the minimum payment due on Josiah's credit card is $105.

The credit card company sets a minimum payment to ensure that the cardholder makes regular payments towards their outstanding balance. The minimum payment is usually a percentage of the balance or a fixed amount, whichever is higher. In this case, the minimum payment is calculated as 3% of the outstanding balance or $100, whichever amount is greater.

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Solution

Firstly, we need to find the equation of the line passing through the points

W(1, 3) and X(2, 6)

and also the equation of the line passing through the points Y(4, 4), and Z(7, 3)

The line WX is given as

The line YZ is given as

The gradient of WX is 3

The gradient of YZ is -1/3

Since the product of the gradient WX and YZ

Hence WX is perpendicular to YZ

Answer:

Step-by-step explanation:

tan 7 = 4.4/x

x = 4.4/ tan 7

x= 35.8 ft

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

Hi!

The slope of the line is marked as rise over run and in slope intercept form it is mx. We can tell from the way the line is slanting that it is a positive slope. It goes up 1, over 6. So therefore, the slope is 1/6.

The y intercept of the line is -4, which we know because that is where the line and the y axis meet. The y intercept is b in slope intercept form.

The slope intercept form is y = 1/6x -4.

For standard form, we subtract 1/6x from both sides to get

-1/6x + y = -4

Hope this helps!

Step-by-step explanation:

Answer:

y=2x

Step-by-step explanation:

Let y be the number of necklaces. Let x be the hours she worked.

So the equation will be y=2x.

So if she worked 2 hours then its 2×2=4.

The graph of the system of inequalities:

3x + y > 1

y < x + 2

Is on the image at the end.

We want to find the graph for the system of inequalities below:

3x + y > 1

y < x + 2

We can write both of these as lines in the slope intercept way, we will get:

y > -3x + 1

y < x + 2

So we need to graph these two lines with dashed lines (because the points on the lines aren't solutions) and then:

Shade the region above the first line (y = -3x + 1) and the region below the second line (y = x + 2)

The graph of the system of inequalities is the one below.

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The large jar has better value for money than the smaller one.

To see which jar is the best value for the money, we need to take the quotient between the cost of each jar and the size. The smaller that value gets, the best value we have.

For the first jar we have:

q = £4.10/540 = 0.0075

For the second jar we have:

q' = £2.81/360 = 0.0078

Then we can see that the large jar has the best value for money.

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Answer:

The correct answer is: u = 10,500. When the value of the alternative hypothesis is greater than that of the null hypothesis, the power of the test will be increased, so a value of u = 10,500 would yield the greatest power to reject the null hypothesis.

Answer:

$280

Step-by-step explanation:

7•40=$280