Alan is putting money into a savings account. He starts with $550 in the savings account, and each week he had $70. Let S represent the total amount of money in the savings account in dollars, and let W represent the number of weeks Allen has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 18 weeks.

Given the statement:

Vertical angles are always equal to each other

The answer is: True

Because they are inclosed by the same lines

The Variance of a set of data is defined as the average of the square of the deviation from the mean.

The first step is to calculate the mean of the data.

Now we take the difference from the mean, square it, and then average the result.

Hence, the variance of the data is 6.7 (rounded to the nearest tenth)

we know that

The first step to find out the inverse of the function is to exchange the variables (x for y and y for x)

therefore

The volume of the cylinder is

The diameter of the cylinder is 25 feet, then

The radius of it = 1/2 x diameter

Since the height is 4.5 ft

Substitute them in the rule above

Now we will change the cubic feet to gallons

Then multiply the volume by 7.48 to find the number of gallons

Now let us divide the number of gallons by 3000 to find how many gallons of liquid chlorin he needs to buy

Then he has to buy 6 full gallons

Answer: - 9, - 3, 3, 9, 15, 21

Explanation:

The given formula is

an = a(n - 1) + 6

a1 = - 9

where

n, n - 1 and 1 are subscripts

This is a recursive formula. Each term is defined with respect to the term before it.

From the information given,

first term = a1 = - 9

Second term = a2 = a(2 - 1) + 6 = a1 + 6 = - 9 + 6

a2 = - 3

Third term = a3 = a(3 - 1) + 6 = a2 + 6 = - 3 + 6

a3 = 3

Fourth term = a4 = a(4 - 1) + 6 = a3 + 6 = 3 + 6

a4 = 9

Fifth term = a5 = a(5 - 1) + 6 = a4 + 6 = 9 + 6

a5 = 15

Sixth term = a6 = a(6 - 1) + 6 = a5 + 6 = 15 + 6

a6 = 21

Thus, the first six terms are

- 9, - 3, 3, 9, 15, 21

The GCF of these monomials i.e, 28g^5h^2 and 12g^6h^5 is 4h^2g^5

What is monomials?

Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.

First take the coefficient ie, 28 and 12 to find the GCF

The GCF of 28 and 12 is 4

Now, find out the GCF of the variables for that you take the lowest exponent from both the variables g and h

for g variable it will be g^5 and,

for h variable it will be h^2

Therefore, the GCF of these monomials is 4h^2g^5

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Explanation

the standard form of a line is in the form Ax + By = C where A is a positive integer, and B, and C are integers

so, we need to write in this form

Step 1

subtrac 1/2x in both sides

I hope this helps you

Notice that in the statement of the exercise are the values of a, b and c. Then, to evaluate the given expression, we replace the given values of a, b, and c. So, we have:

Therefore, the result of evaluating the given expression when a = 9, b = 3, and c = 7.4 is 1.4.

hello

to solve this simple equation, we need to follow some simple steps.

step 1

multiply through by 3

we are doing this to eliminate the fraction and it'll help us solve this easily

notice how the equation haas changed suddenly? well this was done to make the question simpler and faster to solve.

step 2

collect like terms and simplify

step three

divide both sides by the coefficient of k which is 6

from the calculations above, the value of k is equal to 14/3

If x=3y is the equation then y = x/3.

Two or more expressions with an Equal sign is called as Equation.

The given expression x equal to three y.

Here x and y are two variables.

The value of x is three times of y.

The value of y is x over three. If we know the value of x we can substitute in place of x and we can calculate it.

Divide both sides by 3.

y=x/3.

Hence the value of y is x/3.

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1 lote = 5/8 cup yellow + 5/8 cup blue

29 lotes = 29(5/8) +29(5/8) cups

29 lotes = 58(5/8)= (58*5)/8=290/8=145/4

145/4 =35.25 cups of paint

Since

then:

Then:

Answer:

The lateral area of a cylinder is:

r is the radius

h is the height

For the given cylinder:

As the diameter is 4m, the radius is half of the diameter:

h=12m

Given:

Required:

to show which graph is correct for the inequality.

Explanation:

Given graph is correct for the equation.

Required answer:

The given graph is correct.

1) Gathering the data

Preston

642 miles

38 miles/gallon

15 round trips

1 gallon = $2.48

2) Considering that each round trip consists of 642 miles

So Preston in 15 roundtrips is going to make

15 x 642 miles =9,630 miles

His car gets 38 miles per gallon. So we can write a proportion for that:

38 miles ---------1 gallon

9,630 miles ----- x

Cross multiplying it:

38x = 9,630 Divide by 38

x =9630/38

x=253.42 gallons

Finally, let's set another proportion to find out the cost of it

1 gallon -------------- $2.48

253.42 -------------- y

y= 253.42 x 2.48

y=628.4816

3) Rounding off to the nearest hundredth

$628. 48 That's how much Preston will spend.

The composition will be:

(g o h)(x) = 5*√x

By evaluating in x = 0, we get:

(g o h)(0) = 0

Here we have the two functions:

g(x) = 5x

h(x) = √x

And we want to get the composition:

(g o h)(x) = g( h(x))

So we need to evaluate g(x) in h(x), we will get:

g( h(x)) = 5*h(x) = 5*√x

And now we want to evaluate this in x = 0, we will et:

(g o h)(0) = 5*√0 = 0

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A. Cleo (C) has 3 times as many bananas as Arianna (A) has. Cleo has 6 bananas. How many bananas does Arianna have? Equation:

It doesn't correspond to the given equation

_______________

B. Dylan (D) has 6 oranges. Jane (J) has 3 times as many oranges as Dylan. How many oranges does Jane have? Equation:

It correspond to the given equation

___________

C. Liam (L) has 3 cherries. Brian (B) has 6 times as many cherries as Liam. How many cherries does Brian have? Equation:

It correspond to the given equation

_______________

Tina (T) has 3 more peaches than Charlie (C). Charlie has 6 peaches. How many peaches does Tina have? Equation:

It doesn't correspond to the given equation

___________________

E. Jaclyn (J) has 6 times as many grapes as Kaitlyn (K). Kaitlyn has 3 grapes. How many grapes does Jaclyn have?​ Equation:

It correspond to the given equation

____________

Probability is computed as follows:

When rolling a pair of six-sided dice, the total number of outcomes is 36 (= 6x6)

(a) number of favorable outcomes: 3 (dice: 1 and 3, 2 and 2, 3 and 1)

Then, the probability that the sum of the numbers on your dice is exactly 4 is:

(b) number of favorable outcomes: 1 (dice: 1 and 1)

Then, the probability that the sum of the numbers on your dice is at most 2 is:

(c) number of favorable outcomes: 1 (dice: 6 and 6)

Then, the probability that the sum of the numbers on your dice is at least 12 is:

Given:

There are two equation given in the question.

Required:

We have to find the lowest common denominator of both equation.

Explanation:

are given equations

first of all we need to factorization both denominator

so here (p+2) is common in both so take (p+2) for one time only

so now the lowest common denominator is

Final answer:

The lowest common denominator for given two equations is

Answer: 54080

Since the first number cannot be 0 or 1, there would be only 8 possible numbers for the first number. For the second number, we can now have all 10 numbers.

The number of different combinations of numbers would then be:

Then, for the first letter, we have 26 possible letters, as well as the second letter. The number of different combinations of letters would then be:

So, for a license plate that has 2 numbers and 2 letters, where the first number cannot be 0 or 1, there would be:

4) -1/2

1) Rewriting the expression:

2) As a power we can write this way, considering that we can rewrite any radical as a power and that when we have a radical on the denominator we can rewrite it as a negative rational exponent. So we can write it out:

3) Hence, the answer is 4) -1/2

Using the concept of Fraction, the weekly rate of Jake eating the cake is 11.2.

Fraction represents parts of a whole or group of objects. A fraction consists of two parts. The numerator is the number at the beginning of the line. It specifies the number of equal parts taken from the whole or collection. The number below the line is the denominator. It shows the total number of equal parts into which the whole is divided or the total number of identical objects in a collection.

We know that,

The cake is cut into 12 equal slices.

After 3 days Jake eats 5 slices then,

For 1 day = [tex]\frac{5}{3}[/tex]

= 1.6

Then for 7 days,

1.6 × 7 = 11.2

Hence, Jake's weekly rate of eating the cake is 11.2.

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The complete question would be

'A cake is cut into 12 equal slices. After 3 days Jake has eaten 5 slices. What is his weekly rate of eating the cake?'

To solve the inequality we need to find the x-values that are the roots of the quadratic equation, let's use the quadratic formula:

Now, let's try values less or greater than these roots:

If x=-1:

Now let's try x=3:

Then, the graph of the inequality is:

The red-shaded area are the solution to the inequality, then in interval notation we have:

In builder notation it would be:

If the maximum vertical length of pool is 40 feet, and the maximum horizontal width of pool is 18 feet , then the equation that represent the pool is x/81 + y/400 = 1 , the correct is option is (B) .

In the question ,

it is given that

the shape of the pool is ellipse .

the maximum vertical length is 40 feet

the maximum horizontal length is 18 feet .

the general equation of the ellipse , is given by x/a + y/b = 1 ,

where a is the length of horizontal axis from origin

and b is the length of the vertical axis from the origin ,

So , the equation that represents the pool is x/81 + y/400 = 1

Therefore , if the pool is in the shape of ellipse , then the equation of the pool is x/81 + y/400 = 1  .

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We are given two similar triangles which are;

Note that the sides are not equal, but similar in the sense that the ratio of two sides in one triangle is equal to that of the two corresponding sides in the other triangle.

To calculate the length of side BC, we can use any of the following ratios (proportions);

Using the first ratio as stated above, we shall have;

Next we cross multiply and we have;

ANSWER:

Answer:

Area= 24π.

Explanation:

The area of a sector is calculated using the formula below:

From the diagram:

• The central angle, θ = 60°

Diameter of the circle = 24

• Therefore, Radius, r = 24/2 = 12

Substitute these values into the formula:

The area of the sector in terms of pi is 24π square units.

The binomial probability of x successes is 0.302.

Since we are dealing with a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . p^r . q^n-r

Given: n=10, p=0.2, x=2

The failures can be calculated using q = 1 - p = 1 - 0.2 = 0.8

P(x = 2) =  10C2 x 0.2²  x 0.8¹⁰⁻²

            = 10!/(10-2)! 2!  x 0.2² x 0.8⁸

            = 10!/(8!2!)  x 0.2² x 0.8^8

            = 10x9x8!/(8!2!)  x 0.2² x 0.8⁸

            = 45 x 0.2² x 0.8⁸

           = 0.302

Therefore, the probability of x successes in 10 trials is 0.302

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Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,

Solving for s,

Thus, the result of the cross multiplication is 3s=30 and the answer is s=10

The distance between the two points is [tex]2\sqrt{13} units[/tex]

What is distance formula?

Distance formula is the measurement of distance between 2 points. It calculates the straight line distance between the given points. The formula can be given as [tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} }[/tex] Where A(a, b) B(c, d) Are the coordinates.

We are given the coordinates as (-2, 1) and (4, -3)

We substitute the values in the distance formula we get

[tex]distance=\sqrt{(c-a)^{2} +(d-b)^{2} } \\distance=\sqrt{(4+2)^{2} +(-3-1)^{2} }\\ distance=\sqrt{36+16 } \\distance=\sqrt{52 } \\distance =2\sqrt{13}[/tex]

Hence the distance between two points is [tex]2\sqrt{13} units[/tex]

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A appears to be the only correct answer

a^2+b^2=c^2

you are solving for c when finding distance, so (a^2 + b^2) must be square rooted, as a whole, not separately

and a = (x1-x2)

and b = (y1-y2)

you can flip the 1 and 2 but you have to flip for both x and y

like x1-x2 means you have to do y1-y2

like x2-x1 means you have to do y2-y1

so both above are correct as long as the order of 1 and 2 stays the same for both x and y