If the base of a round wedding cake is 20 inches in diameter, the area of the base is
square inches.

According to the solution we have come to find that, The equation of the line that is parallel to y = -7 and passes through the point (7,5) is y = 5.

what is mean by parallel lines?

Parallel lines are two or more lines that are always the same distance apart and never intersect. In other words, they have the same slope and they will never meet, no matter how far they are extended in both directions. Parallel lines always remain equidistant from each other and never touch or intersect, even if they are extended to infinity.

For example, in a Cartesian coordinate system, two lines are parallel if and only if they have the same slope. If the slope of one line is m1 and the slope of another line is m2, then the two lines are parallel if m1 = m2.

The given equation is y = -7, which is a horizontal line parallel to the x-axis. Since we need to find the equation of a line parallel to this line, the slope of the new line will also be zero.

To find the equation of the new line, we need to use the point-slope form of the equation, which is:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope of the line.

Substituting the values of the given point and slope, we get:

y - 5 = 0(x - 7)

y - 5 = 0

y = 5

So, the equation of the line that is parallel to y = -7 and passes through the point (7,5) is y = 5.

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Answer:

  reflect over the x-axis and shift down 3

Step-by-step explanation:

The leading coefficient of -1 means the graph is reflected over the x-axis. The addition of -3 to the function means each graphed point is shifted down 3 units from the original.

The graph of y = -x^2 -3 is the result of the transformation ...

  reflect over the x-axis and shift down 3

The probabilities for this problem are given as follows:

a) At least five: 0.4909 = 49.09%.

b) Less than five: 0.4091 = 40.91%.

c) Between five and ten: 0.585 = 58.5%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters of the binomial distribution are given as follows:

n = 100, p = 0.05.

Hence the mean and the standard deviation of the approximation are given as follows:

Then the probability of at least five successes, using continuity correction, is P(X > 4.5), which is one subtracted by the p-value of Z when X = 4.5, hence:

\(Z = \frac{X - \mu}{\sigma}\)

Z = (4.5 - 5)/2.18

Z =  -0.23.

Z = -0.23 has a p-value of 0.4091. (probability of less than five successes).

1 - 0.4091 = 0.4909 = 49.09%.

The probability of between five and ten successes is the p-value of Z when X = 10.5 subtracted by the p-value of Z when X = 4.5, hence:

Z = (10.5 - 5)/2.18

Z =  2.52

Z = 2.52 has a p-value of 0.9941.

Z = (4.5 - 5)/2.18

Z =  -0.23.

Z = -0.23 has a p-value of 0.4091.

Hence:

0.9941 - 0.4091 = 0.585 = 58.5%.

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer:

Step-by-step explanation:

Answer:

12!

Step-by-step explanation:

А=12*11*10*9*8*7*6*5*4*3*2*1=12!=479001600

Answer:

Future population in 19 years = 3,254,580 people (Approx.)

Step-by-step explanation:

Given:

Current population of city = 900,000

Growth rate of population = 7%

Number of year = 19

Find:

Future population in 19 years

Computation:

A = P[1+r]ⁿ

Future population = Current population[1+g]ⁿ

Future population in 19 years = 900,000[1+7%]¹⁹

Future population in 19 years = 900,000[1+0.07]¹⁹

Future population in 19 years = 900,000[1.07]¹⁹

Future population in 19 years = 900,000[3.6162]

Future population in 19 years = 3,254,580

Future population in 19 years = 3,254,580 people (Approx.)

Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer: 140$

Step-by-step explanation: 15$ times 8 meals plus 20 dollar fee eaquals 140$

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

$190

Step-by-step explanation:

50% = 0.5 = 1/2

Since 95 is only one-half the cost, multiply by 2 to find the actual cost.

95 * 2 = 190

Answer:

$190

Step-by-step explanation:

One way to do it is

$95 x 2 = 190

We can do this because 50 is half of 100

Another way we can do it is

95/x = 50/100

x50 = 95 x 100

x50/50 = 9500/50

x = 190

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

Let's start by defining some variables:

Let's call Jamal's age "J".

Let's call Alex's age "A".

From the problem statement, we know that:

J = A - 5 (Jamal is 5 years younger than Alex)

J * A = 300 (the product of their ages is 300)

We can use the first equation to substitute J in the second equation:

(A - 5) * A = 300

Expanding the left-hand side:

A^2 - 5A = 300

Moving all terms to the left-hand side:

A^2 - 5A - 300 = 0

We can solve for A using the quadratic formula:

A = (-(-5) ± sqrt((-5)^2 - 41(-300))) / (2*1)

A = (5 ± sqrt(25 + 1200)) / 2

A = (5 ± sqrt(1225)) / 2

Since A is a positive integer, we take the positive solution:

A = (5 + 35) / 2 = 20

Now we can use the first equation to find J:

J = A - 5 = 20 - 5 = 15

Therefore, Jamal is 15 years old.

3. The volume of the Pringle Chips container is approximately 2034.72 cubic inches.

4. The cake takes up approximately 7317 cubic inches of space.

5. The volume of foam in the model of the volcano is approximately 7234.08 cubic centimeters.

1. The units for Volume are always cubed.

2. Volume is the amount of space an object takes up. True.

3. To calculate the volume of the Pringle Chips container, we need to find the volume of a cylinder. The formula for the volume of a cylinder is V = πr^2h, where π is a constant (approximately 3.14), r is the radius, and h is the height. Given that the diameter is 9 inches, the radius would be half of that, which is 4.5 inches. Substituting the values into the formula, we have:

V = 3.14 * (4.5)^2 * 32

V = 3.14 * 20.25 * 32

V ≈ 2034.72 cubic inches

4. To find the volume of the 3-tier cake, we need to find the volume of each tier separately and then add them together. Since all the tiers are cylinders, we can use the formula V = πr^2h.

Tier 1:

V1 = 3.14 * (12)^2 * 10 = 4521.6 cubic inches

Tier 2:

V2 = 3.14 * (8)^2 * 10 = 2010.4 cubic inches

Tier 3:

V3 = 3.14 * (5)^2 * 10 = 785 cubic inches

Total volume:

Total V = V1 + V2 + V3

Total V = 4521.6 + 2010.4 + 785

Total V ≈ 7317 cubic inches

5. To find the volume of the Styrofoam model of the volcano, we can use the formula for the volume of a cone, V = (1/3)πr^2h. Given that the diameter is 48 centimeters, the radius would be half of that, which is 24 centimeters. Substituting the values into the formula, we have:

V = (1/3) * 3.14 * (24)^2 * 12

V = (1/3) * 3.14 * 576 * 12

V ≈ 7234.08 cubic centimeters

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Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

Answer:

Step-by-step explanation:

Use the formula for the cos of an angle:

\(cos\theta=\frac{adj}{hyp}\)  where the adjacent side is the length of 4 and the hypotenuse is the "c" we are looking for. Setting up the equation:

\(.33=\frac{4}{hyp}\)

Solve that equation for hyp to get:

\(hyp=\frac{4}{.33}\)

Dividing that gives us that hyp (aka "c") = 12.121212...

c ≈ 12.12 (approximate value of side c in the right triangle).

Recall that in a right triangle, the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.

In this case, cos B = 0.33.

We are given the length of the adjacent side, a, which is 4 units.

Use the equation cos B = a/c and rearrange it to solve for c:

cos B = a/c

Multiply both sides by c: c * cos B = a

Divide both sides by cos B: c = a / cos B

Substitute the values we have: c = 4 / 0.33.

Calculate the value of c using a calculator or by performing the division:

c ≈ 12.12.

Therefore, the length of side c in the right triangle is approximately 12.12 units.

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Hello! :)

Let's use PEMDAS.

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

(5-2) = 3 Do parenthesis.

7 × 3 = 21 Multiply with what we got after doing the parenthesis.

9 + 21 = 30 Add with what we had left.

30

Hope this helps!

ELITEDIPER

Answer:

YOOOO HERES THE ANSWER, ITS 30.

Step-by-step explanation:

9 + 7 (5 - 2)

First we to the parenthesis: (5 - 2), as we know that = 3.

Next we multiply 3 x 7.

3 x 7 = 21.

Now we add 9.

21 + 9 = 30.

so the answer is 30.  

Answer:

37t-9.8

hope it helps!!!!!!

The expression that represents the monthly change in Kevin's bank account is $2,300 - $7.50 = $2,292.50

In one year, which has 12 months, the bank deducts a total of $90 in fees. To find the monthly change in Kevin's bank account, we need to divide this total by 12:

Monthly service fee = $90 / 12 = $7.50

Kevin's paycheck is deposited twice each month, so his total monthly income from his paychecks is:

Monthly income = 2 * $1,150 = $2,300

Therefore, Kevin's monthly change in his bank account is:

Monthly change = Monthly income - Monthly service fee

Monthly change = $2,300 - $7.50 = $2,292.50

So the expression that represents the monthly change in Kevin's bank account is $2,300 - $7.50 = $2,292.50

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Answer:

a. \(\tt \frac{1}{9}\)

b. \(\frac{1}{16}\)

c. 4

Step-by-step explanation:

\(\tt a. \:3^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\) So, we have:

\(\tt 3^{-2} = \frac{1}{3^2} = \frac{1}{9}\)

\(\hrulefill\)

\(\tt b.\: -2^{-4}\)

We can use the rule that \(\boxed{\tt -a^{-n} = (-1)^n \cdot a^n}.\) So, we have:

\(\tt -2^{-4} = (-1)^4 \cdot 2^{-4} = 1 \cdot \frac{1}{2^4} = \frac{1}{16}\)

\(\hrulefill\)

\(\tt c. \:(\frac{1}{2})^{-2}\)

We can use the negative exponent rule, which states that \(\boxed{\tt a^{-n} = \frac{1}{a^n}}\). So, we have:

\(\tt (\frac{1}{2})^{-2} = \frac{1}{(\frac{1}{2})^2} = \frac{1}{\frac{1}{4}} = 4\)

Answer:

Step-by-step explanation:

(a) 3^-2 = 1/9

(b) (-2)^-4 = 1/(-2)^4 = 1/16

(c) (1/2)^-2 = 1/(1/2)^2=1 / 1/4 = 4

Answer:

\(\frac{15\pi }{4}\)

Step-by-step explanation:

Degrees to radians, multiply by pi/180

675pi/180

use a calculator to simplify

You get 15pi/4

The value of 675 degree is equivalent to \(\frac{15pi}{4}\).

What is the formula to convert degree to radian?

The relation between radian and degree is given by Angle in radian=angle in degree*\(\frac{pi}{180}\).

We will substitute 675 for angle in degree into the formula to get the value in radian.

\(\frac{675*pi}{180}\)

This will be \(\frac{15pi}{4}\).

Therefore, the correct answer is \(\frac{15pi}{4}\).

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Answer 19.35 km

Step-by-step explanation:

We are looking for the Distance that Apostle Paul walked in 4.5 Hours!

I will be using the formula Distance=rate*time 1)

We DONT know the distance so I'll leave it as variable "D".

We know his rate of walking is 4.3 km/h, and we know he walked for a total of 4.5 hours.

Set up the following equation. D=4.3*4.5 2)

Simplify the equation above: D=19.35

Answer:

D

Step-by-step explanation:

if you divide 15 and 108 it will give you get 7.7 but if you do 14 by 108 its 7.2 or 3 but still it would be D

Answer:

4 W = n of songs on her playlist

\(n \leqslant 120\)

Triangle ABC and ADE are similar triangles

Similar triangles have the same corresponding angle measures and proportional side lengths.

This means that for two triangles to be similar, the corresponding angles must be equal and the ratio of corresponding sides of similar triangles are equal.

It has been shown that angles in ABC and ADE are equal.

To show that the ratio of corresponding sides are equal

6/12 = 8/16 = 10/20

The ratios all give a value of 1/2

Therefore we can say that the triangles ABC and ADE are similar.

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The similar triangles for this problem are given as follows:

RST and VUT.

Then the measure VT is given as follows:

VT = 5.4 units.

Similar triangles are triangles that share these two features listed as follows:

Hence the similar triangles for this problem are given as follows:

RST and VUT.

The proportional relationship for the side lengths is given as follows:

6/14 = (x + 2)/(4x - 1).

Applying cross multiplication, the value of x is obtained as follows:

14(x + 2) = 6(4x - 1)

14x + 28 = 24x - 6

10x = 3.4

x = 3.4.

Then the length VT is given as follows:

VT = 3.4 + 2

VT = 5.4 units.

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