Delilah babysits a fixed number of hours per week. Her friend Laura babysits
5 hours more per week than Delilah. Write an equation that models the tota
number of hours Laura babysits.

Part A. An explicit expression for the function A(n), the final amount (future value) after n years is 1,500 x 1.0235^n.

Part B. The function for determining the future value of the CD at 2.35% annual compounded interest rate is derived by comparing the present value and the future value and using the difference to calculate the compound interest rate.

The future value is the present value compounded at an interest rate.

The future value formula or function is as follows:

FV = PV(1+r)^{n}

FV = future value

PV = present value

r = annual interest rate

{n} = number of periods interest held

Initial deposit in a ten-year certificate of deposit (CD) = $1,500

Deposit period = 10 years

Amount after 1 year = $1,535.25

Compound interest rate = 2.35% annually ($1,535.25 - $1,500)/$1,500 x 100)

Function for A(n) = 1,500 x 1.0235^n

Thus, from the future value after 1 year, we can derive the compound interest rate.

Learn more about the future value function or formula at https://brainly.com/question/29008543.

#SPJ1

The domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.

A function is composite when the co- domain of the first mapping is the domain of the second mapping

We shall evaluate the domain of the function f(-6) - f(9) as follows:

f(-6) = 2(-6) + 15 {put -6 for x }

f(-6) = -12 + 15

f(-6) = 3

f(9) = 2(9) + 15 {put 9 for x }

f(9) = 18 + 15

f(9) = 33

f(-6) - f(9) = 3 - 33

f(-6) - f(9) = -30

Therefore, the domain of the composite function f(-6) - f(9) for the function f(x) = 2x + 15 is equal to -30.

Know more about composite function here:https://brainly.com/question/10687170

#SPJ1

Possible question:

Given the function f(x) = 2x + 15. What is f(-6) - f(9)?

The trigonometric function equation obtained for the graph is y = 4 sec (πx) - 2.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The upper waver have a value of y = 2 and the lower waves have a value of  y = -6.

Add the points and divide by 2 -

[2 + (-6)] / 2

(2 - 6) / 2

-4 / 2

-2

Therefore, the midline is y = -2.

The vertical asymptotes are drawn and they intersect the midline at certain points.

Then the sinusoidal function is drawn using the intersection point.

There is one period of sinusoidal function that is starting from x = 0 and goes upto x = 2.

This pattern tells that the function is of cosine.

Then the graph will be of trigonometric function secant .

The value of C = -2 , A = 4, D = 0

Here C is the midline value, A is the points above and below the midline, D is the horizontal shift and 2π/B is the period.

Now, 2π/B = 2

2B = 2π

B = π

Now, use the formula -

y = A cos (B(x - D)) + C

y = 4 cos (π(x - 0)) - 2

y = 4 cos (πx) - 2

y = 4 sec (πx) - 2

Now plot the graph for the obtained function.

The graph is same as given in the question.

Therefore, the function is y = 4 sec (πx) - 2.

To learn more about trigonometric function from the given link

https://brainly.com/question/25618616

#SPJ1

The shaded set of numbers shown on the y-axis on the graph can be expressed in interval notation as interval notation as

{y∣-11≤y<∞} or [-11,∞). This set represents the function's range.

Endpoints that are part of an interval are indicated by square brackets. Endpoints that are not part of an interval are indicated by parentheses. When using or, parentheses are always used.

As a result, the set of shaded numerals displayed on the interval notation can be used to express the y-axis as {y∣-11≤y<∞} or [-11,∞)

This set displays the functional domain.

Learn more about functions on:

https://brainly.com/question/10439235

#SPJ1

Answer: 42

Step-by-step explanation: 165 x .25 = 42

Answer:

42

Step-by-step explanation:

If Naomi has 168 apps, then 100% is equal to 168 (since that's all her apps)

If 25% of these apps are games, then 25% is equal to x

If we multiply the number of total apps by the percentage of games, we'll find the total number of game apps

First change the percentage into a decimal:

25% = 0.25

Then multiply:

168 * 0.25 = x

Simplify:

x = 42

Another way you can do this is by realizing that 0.25 is equal to 1/4. If 168 is multiplied by 1/4, then that means the resulting equation is:

168/4 = x

x results in the same answer as the previous way:

x = 42

Answer:

14.8

Step-by-step explanation:

Answer: Anita gave $14.80 to the cashier.

Step-by-step explanation:

Add $10.04 and $4.76 together to find your total.

$10.04 + $4.76 = $14.80

Meaning, Anita gave $14.80 to the cashier.

The constant of proportionality is the ratio between two quantities that are in proportion. If two quantities are proportional, their ratio is always the same, and this constant ratio is called the constant of proportionality.

Given the two quantities 1.5 and 3.9, the constant of proportionality can be found by dividing one by the other:

k = 3.9 / 1.5

k = 2.6

So the constant of proportionality between 1.5 and 3.9 is 2.6.

Answer: All angles of the regular polygon in the image are 90 degrees

Step-by-step explanation: Hello!

All interior angles of a four-sided polygon add up to 360 degrees.  Since this is a square, all interior angles are congruent.  There are four interior angles that are congruent and they all add up to 360 degrees.  This can be represented by the equation:

s (side) x 4 = 360

Divide each side by 4 by the division property of equality.

s x 4/4 = 360/4

s = 90 degrees.

Each angle of the polygon is 90 degrees.

"The common property for all [] four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees."
-https://byjus.com/maths/interior-angles-of-a-polygon/#:~:text=The%20common%20property%20for%20all%20the%20above%20four-sided,will%20be%20equal%20to%3A%20360%2F4%20%3D%2090%20degrees.

Answer:

The measure of each interior angle of the regular polygon pictured below is 151.7°. This can be calculated using the formula 180n - 360, where n is the number of sides of the polygon. In this case, n = 8, so the measure of each interior angle is 180(8) - 360 = 151.7°.

Answer:

[tex]\dfrac{9\pm \sqrt{33}}{4} \longrightarrow \boxed {2x^2\:-\:9x+6=0}}[/tex]

[tex]\dfrac{4\pm \sqrt{6}}{2} \longrightarrow \boxed{2x^2 - 8x +5=0}[/tex]

[tex]\dfrac{9\pm\sqrt{89}}{4} \longrightarrow \boxed{2x^2\:-\:9x-1=0 }[/tex]

[tex]\dfrac{4\pm \sqrt{22}}{2} \longrightarrow \boxed{2x^2\:-\:8x-\:3=0}[/tex]

Step-by-step explanation:

Use a quadratic equation solver calculator

Here are the roots for each equation

Equation                          Roots

[tex]2x^2 - 8x +5=0\quad\quad\quad \quad \dfrac{4\pm \sqrt{6}}{2}[/tex]

[tex]2x^2\:-\:10x-\:3=0\quad\quad\quad \dfrac{5\pm \sqrt{31}}{2}[/tex]    

[tex]2x^2\:-\:8x-\:3=0\quad\quad\quad \dfrac{4\pm \sqrt{22}}{2}[/tex]

[tex]2x^2\:-\:9x-1=0 \quad\quad\quad \dfrac{9\pm\sqrt{89}}{4}[/tex]

[tex]2x^2\:-\:9x+6=0\quad\quad\quad \dfrac{9\pm \sqrt{33}}{4}[/tex]

The quadratic equations are solved and the tiles are matched with the following equations

a) 2x²- 8x + 5 = 0 → x = ( 4 ± √6 ) / 2

b) 2x² - 8x - 3 = 0 → x = ( 4 ± √22 ) / 2

c) 2x² - 9x - 1 = 0 → x = ( 9 ± √89 ) / 4

d) 2x² - 9x + 6 = 0 → x = ( 9 ± √33 ) / 4

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

a)

2x²- 8x + 5 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 4 ± √6 ) / 2

b)

2x² - 8x - 3 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 4 ± √22 ) / 2

c)

2x² - 9x - 1 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 9 ± √89 ) / 4

d)

2x² - 9x + 6 = 0

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

x = ( 9 ± √33 ) / 4

Hence , the quadratic equations are solved

To learn more about quadratic equations click :

https://brainly.com/question/25652857

#SPJ5

Kareem has $22, Raina has $28, Eric has $88.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Raina, Kareem, and Eric have a total of $138 in their wallets.

let Kareem has x dollar.

Then Raina has (x+6) dollar

and, Eric has 4x dollar

So, x+ 4x + x + 6 = 138

6x + 6 = 138

6x = 132

x= 22

Thus, Kareem has $22.

Raina has = 22 +6 = $28

and, Eric has =4x = $88

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ1

The expected phenotypes for the offspring is All tall.

Mendel came to the conclusion that some features predominated over other inherited traits when he noticed that a heterozygote offspring might exhibit the same phenotype as the parent homozygote. However, the connection between genotype and phenotype is rarely as straightforward as Mendel's descriptions of dominant and recessive patterns.

Given:

One is short and one is tall, Tall is dominant.

When two plants that are tall and short are crossed. They would all produce tall plants as a result, T.

The first crossing produced these children.

As a result of their parents' TT and SS genes, they all now have TS genes.

There will be some towering and some short off springs when these off springs are crossed. TS and TS will cross at this location. Given that they are all genetically tall and short.

So, The ratio of tall to short children they would have according to Mendel is 3:1.

Hence, almost All are tall.

Learn more about Phenotype here:

https://brainly.com/question/20730322

#SPJ1

The solution of the Jordan's system is 3/2 and -1.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y = 2x² + 3..............(1)

y – x = 6

y= 6 +x ..............(2)

Put the value from (2) in equation (1) we get

y = 2x² + 3

6+ x  = 2x² + 3

2x² + 3 -6 -x = 0

2x² - x - 3 = 0

2x² -3x + 2x -3= 0

x( 2x-3) +1 (2x-3)= 0

(2x- 3)(x+1)= 0

x= 3/2, -1.

Hence, the value is 3/2, -1.

Learn more about Equation here:

https://brainly.com/question/29657992

#SPJ1

The Question you have attaches seems to incomplete/ inappropriate.

the complete question is

Jordan is solving this system of equations: y = 2x2 + 3 and y – x = 6. Which statements are true about Jordan’s system? Check all that apply.

3.1 ft more fabric should be produced to make pillows versus a rug.

A fraction is a number expressed in the form of {x/y}, where y ≠ 0.

Given is that 1[tex]\frac{6}{11}[/tex] ft of fabric is needed to make a rug while 4[tex]\frac{1}{2}[/tex] ft of fabric is required to make pillows. Producing a rug is 2[tex]\frac{2}{7}[/tex] times faster than pillows.

We can write -

1[tex]\frac{6}{11}[/tex] x 4[tex]\frac{1}{2}[/tex] = 2[tex]\frac{2}{7}[/tex] x {y}

{17/11 x 9/2} = {16/7 y}

{y} = {6.96 x 7}/16

{y} = 3.1

Therefore, 3.1 ft more fabric should be produced to make pillows versus a rug.

To solve more questions on fractions, visit the link below-

brainly.com/question/1041084

#SPJ1

The degrees of freedom for this test are (3 - 1) = 2. With a 5% significance level and 2 degrees of freedom, the critical value for a chi-squared distribution is 5.991.

To determine whether customer preferences have changed, the analyst can conduct a hypothesis test. The null hypothesis is that customer preferences have not changed, and the alternative hypothesis is that customer preferences have changed.

The test statistic used to test this hypothesis is a chi-squared statistic. The formula for the chi-squared statistic is:

X² = ∑((O - E)² / E)

where O is the observed frequency, and E is the expected frequency based on the null hypothesis.

The expected frequency for Apple is 200 * 0.45 = 90, for Samsung is 200 * 0.40 = 80, and for others is 200 * 0.15 = 30.

Calculating the chi-squared statistic:

X² = ∑((102 - 90)² / 90) + ((82 - 80)² / 80) + ((16 - 30)² / 30) = (12² / 90) + (2² / 80) + (14² / 30) = 144 / 90 + 4 / 80 + 196 / 30 = 2.56 + 0.05 + 6.53 = 9.14

The degrees of freedom for this test are (3 - 1) = 2. With a 5% significance level and 2 degrees of freedom, the critical value for a chi-squared distribution is 5.991.

Since 9.14 > 5.991, the analyst can reject the null hypothesis and conclude that customer preferences have changed from their levels before the advertising campaigns were launched.

Learn more about chi-squared statistic in brainly.com/question/23879950

#SPJ1

Answer:

working on a answer one second

Step-by-step explanation:

The monthly payments over a period of 5 years is $214.05.

A fixed-rate mortgage is a home loan option with a specific interest rate for the entire term of the loan. Essentially, the interest rate on the mortgage will not change over the lifetime of the loan and the borrower's interest and principal payments will remain the same each month.

Given that, a family borrows $12,843 for an addition to their home.

The loan is to be paid off in monthly payments over a period of 5 years

We know that, 5 years = 60 months

Now, monthly payment = Total money/Number of months

= 12,843/60

= $214.05

Therefore, the monthly payments over a period of 5 years is $214.05.

To learn more about the mortgage payments visit:

https://brainly.com/question/17329729.

#SPJ1

Answer:

A.  y = -3x + 2

Step-by-step explanation:

Slope of a line perpendicular to another line is the negative reciprocal of the slope of the other line.

1/3 → -3/1

All the correct points lie on line f (x) = - 3x - 5 are (3, - 14)

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The equation of line is,

⇒ f (x) = - 3x - 5

Now, All the correct points that lie on line are satisfy the line.

For point (5, - 21);

⇒ f (x) = - 3x - 5

⇒ - 21 = - 3 × 5 - 5

⇒ - 21 = - 15 - 5

⇒ - 21 ≠ - 20

For point (3, - 14);

⇒ f (x) = - 3x - 5

⇒ - 14 = - 3 × 3 - 5

⇒ - 14 = - 9 - 5

⇒ - 14 = - 14

For point (0, - 6);

⇒ f (x) = - 3x - 5

⇒ - 6 = - 3 × 0 - 5

⇒ - 6 = - 0 - 5

⇒ - 6 ≠ - 5

For point (-5, 8);

⇒ f (x) = - 3x - 5

⇒ 8 = - 3 × - 5 - 5

⇒ 8 = 15 - 5

⇒ 8 ≠ 10

For point (-3, 5);

⇒ f (x) = - 3x - 5

⇒ 5 = - 3 × - 3 - 5

⇒ - 5 = 9 - 5

⇒ - 5 ≠ 4

Thus, Point (3, - 14) lie on the line.

Learn more about the coordinate visit:

https://brainly.com/question/24394007

#SPJ1

The statement that explains how mental math can be used to find how much farther Josh rode than Claire is that to round 11.4 to 11. Round 6.8 to 7. Then subtract 7 from 11 to get 4. Josh rode 4 miles farther than Claire. That is option A.

The use of metal maths is simply the calculation of a given mathematical problem without the use of an aid such as electronic devices.

The number of miles covered by Josh = 11.4 miles

The number of miles covered by Claire = 6.8 miles

To use mental maths, the values are rounded up to the nearest whole number and the difference between the two are gotten.

That is;

11.4 = 11

6.8 = 7

Therefore the difference in the distance between the two individuals = 11-7 = 4 miles.

Learn more about distance here:

https://brainly.com/question/26046491

#SPJ1!

Answer: pls see the analysis.

Step-by-step explanation:

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

Convert the ratio to a fraction, multiply it by a common factor, and divide it again to obtain the corresponding ratio of 6:4. Therefore, 12/8 is the same as 6:4.

Any two quantities can be compared using the ratio formula a: b a/b. The ratio, on the other hand, proportion formula is expressed as a:b::c:d⟶ab=cd a : b :: c : d ⟶ a b = c d

To know more about ratio visit:-

brainly.com/question/13419413

#SPJ1

The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Yolanda is building a fence around her garden.

For every 2 feet of fencing, the cost is 12.

The unit rate = 12/ 2 = $6 per feet

The complete table:

The fence → cost

3  → $18

5 → $30

7  → $42

Therefore, the complete table is given above.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ1

Answer: x = -4

Step-by-step explanation: Multiply both sides of the top equation by 2 so you can cancel the y's.

4x + 3x = -28.

7x = -28

x = -4

Answer:

f(x) = {

C(x) = 6, 0 < x ≤ 50

C(x) = 8, 50 < x ≤ 100

C(x) = 10, 100 < x ≤ 200

}

Step-by-step explanation:

Answer: [tex]6 \text{ m}^2[/tex]

Step-by-step explanation:

[tex]A=\frac{1}{2}bh=\frac{1}{2}(7.5)(1.6)=6 \text{ m}^2[/tex]

The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

To find an Equation that is parallel to 2x - y = 7 and passes through the point (10, 0)

Since, Both equations are parallel thus, the slope of the given equation will be the Same.

equation of the first line in slope intercept form: y = 2x - 7

Thus, Slope = 2

From the general formula of the linear equation in slope-intercept form:

y=mx+b,

where m is the slope

b is the y-intercept

in our case,

Slope = 2

So Line,

y = 2x + b

Since line passes through (10, 0)

b= -20

Thus,

Equation of line  y = 2x - 20

Therefore, The equation of the line that is parallel to  2x - y = 7 and passes through the point (10, 0) is  y = 2x - 20.

Learn more about Linear equations here:

https://brainly.com/question/11897796

#SPJ1

Answer:

The expression (6 × 10^7) × 0.007 simplified is 4.2 x 10^5.

Step-by-step explanation:

Answer:

15.25 - 5.75 h

this my be it but i'm not shore