Use interval notation or set notation to answer the following questions.
The domain of this function is ?
The range of this function is?

Answer:

$134.71

Step-by-step explanation:

A = P(1 + rt)

A = Amount after t months or years

P = Principal or amount saved

r = interest rate = 5.18% = 0.0518

t = time.in years = 18 months

= 1 year and 6 month

= 1.5 year

A = $125( 1 + 0.0518 × 1.5)

A = $125 ( 1 + 0.0777)

A = $125(1.0777)

A = $134.71

Answer:

y=2x

Step-by-step explanation:

From (0,0) to (3,6), it is 3 units to the left and 6 units left, divide that so you can have 1 unit to the left and 2 units up.  Therefore, the answer is y = 2x.

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, \(\mu\) = \(n \times p\) = \(200 \times 0.11\) = 22

and the new standard deviation of X, \(\sigma\) = \(\sqrt{n \times p \times (1-p)}\)

                                                                  = \(\sqrt{200 \times 0.11 \times (1-0.11)}\)

                                                                  = 4.42

So, X ~ Normal(\(\mu =22, \sigma^{2} = 4.42^{2}\))

(a) The probability that X is at most 30 is given by = P(X < 30.5)  {using continuity correction}

        P(X < 30.5) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{30.5-22}{4.42}\) ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X \(\leq\) 29.5)    {using continuity correction}

        P(X \(\leq\) 29.5) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{29.5-22}{4.42}\) ) = P(Z \(\leq\) 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 \(\leq\) X \(\leq\) 25) = P(X < 25.5) - P(X \(\leq\) 14.5)   {using continuity correction}

       P(X < 25.5) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{25.5-22}{4.42}\) ) = P(Z < 0.79) = 0.7852

       P(X \(\leq\) 14.5) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{14.5-22}{4.42}\) ) = P(Z \(\leq\) -1.70) = 1 - P(Z < 1.70)

                                                          = 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 \(\leq\) X \(\leq\) 25) = 0.7852 - 0.0446 = 0.7406.

Answer:

In a nutshell, \(f(x)\) is obtained by applying an horizontal translation on \(g(x)\), followed by a vertical translation.

Step-by-step explanation:

Let be \(g(x) = x^{3}\) the parent function, \(f(x)\) is obtained by applying an horizontal translation on \(g(x)\), followed by a vertical translation, that is:

\(f(x) = g(x-a)-b,\,a,b\in\mathbb{R}\) (1)

If \(a > 0\), then translation is rightwards.

If \(b > 0\), then translation in downwars.

If \(a = 2\) and \(b = 1\), then the resulting function is:

\(f(x) = g(x-2)-1\)

\(f(x) = (x-2)^{3}-1\) (2)

In a nutshell, \(f(x)\) is obtained by applying an horizontal translation on \(g(x)\), followed by a vertical translation.

The value that each term can be multiplied by to eliminate the decimals in the equation is 4

The equation is given as

0.5x + 1 = 0.75x

Represent the terms as a fraction

So, we have

1/2x + 1 = 3/4x

The denominators in th​e above fractions are

2 and 4

The LCM of 2 and 4 is 4

Hence, the value that each term can be multiplied by to eliminate the decimals in the equation is 4

Read more about equations at

https://brainly.com/question/13763238

#SPJ1

Answer:

x=100 degree's

Step-by-step explanation:

Its 100 degrees because you add 80 and 20 degrees and because I think they might be called congruent angles.

Answer:

pretty sure it's just 100, just add 80 and 20, angles are opposite of each other.

Answer:

2.5%

Step-by-step explanation:

Eli borrowed $9500 to buy a jet ski if he pays $218 each month for the next 48 months then the interest rate is, 2.53%

Simple interest is a amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider principle amount(P), rate(R) and time(T).

Every time we calculate simple interest the principle values will be same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

Given that,

P = $9500

R = ?

T =  48 months = 4 year

I  =  Total amount paid - Principle amount

  =   ( 48 × 218 ) - 9500

  =   10464 - 9500

  =   964

964  = 9500 × R × 4/100

R = 2.53

Hence, The interest rate is 2.53%

To know more about Interest check:

brainly.com/question/29480777

#SPJ1

Answer:

2/14, 4/28, 5/35, 7/49

Answer:

it is 5/35 and 4/28 , 2.14, and 7/49

Step-by-step explanation:

Hopes this helps you out

have a nice day

Answer:

A =  225 π  c m \(x^{2}\)

Step-by-step explanation:

the area of a circle formula with radius  

A  =  π r\(x^{2}\)  

in this case

A = π ×  15\(x^{2}\)  

A  =  225 π  c m\(x^{2}\)

Answer:

Step-by-step explanation:

Area of a circle = π r²        you are given the r  radius =  15cm

   area = π 15² cm

Answer:

you have to show the diagram ...

Step-by-step explanation:

Theres an easy way to calculate this called factorial number

factorial number gives the numberof combinations

its calculated taking the major jumber( in this case 8 ) and multiplying by the rest of the minor numbers

thar means N = 8x7x6x5x4x3x2x1

its a big number

Answer:

B

Step-by-step explanation:

Divide y by x for each ordered pair:

2/4 = 1/2

3/6 = 1/2

5/10 = 1/2

7/14 = 1/2

All ratios are equal, so it is proportional.

Answer: B

Answer:

b

Step-by-step explanation:

mark brainliest

Answer:

  27π/2

Step-by-step explanation:

The differential of volume is the product of a differential of area and the circumference of the revolution of that area about the given axis. The limits of integration in the x-direction are where y=28 crosses the curve, at x=4 and x=7.

   \(dV=2\pi(x-4)(y-28)\,dx\\\\dV=2\pi(x-4)(-x^2+11x-28)\,dx=2\pi(-x^3+15x^2-72x+112)\,dx\\\\\displaystyle V=\int_4^7{dV}=2\pi\int_4^7{(-x^3+15x^2-72x+112)}\,dx\\\\=2\pi\left(\dfrac{4^4-7^4}{4}+15\dfrac{7^3-4^3}{3}-72\dfrac{7^2-4^2}{2}+112(7-4)\right)=2\pi\dfrac{27}{4}\\\\\boxed{V=\dfrac{27\pi}{2}}\)

_____

Check

The parabola's vertex is (5.5, 30.25), so its area above the line y=28 is ...

  A = (2/3)(7 -4)(30.25 -28) = 4.5 . . . square units

The centroid of that area lies on the line x=5.5, a distance of 1.5 from the axis of rotation. So, the volume of revolution is ...

  V = 2π(1.5)(4.5) = 27π/2 . . . matches the above

Answer:

70%

Step-by-step explanation:

you do it

The store will loose $100 if the man did not return amount to the register, but the store will loose only $70 amount of the if the man returns the change of 30 dollars.

From the $100 amount of money stolen from the register, the man spent only $70 to buy his goods

He got the change of 30 dollars which we are not told if he returned it back to the store register.

Now if the man does not return the change of 30 dollars to the store register, then the store have lost the whole money which is $100

but if he returned the change of $30 to the store register, then the store would have lost $70 of the amount of money used to buy his goods.

Therefore, the store will loose $100 if the man did not return amount to the register, but the store will loose only $70 amount of the if the man returns the change of 30 dollars.

Know more about dollars here: https://brainly.com/question/23103804

#SPJ1

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

Learn more on puzzle: https://brainly.com/question/27645967

#SPJ1

Answer:

y = -3x + 8.3

Step-by-step explanation:

You need to rearrange 9x + 3y = 22 in the form y = mx +c.

9x+3y = 22

3y = -9x +22

y = -3x + 7.3

As long as the gradient is the same, the lines will be parallel. So you can give any number to the intercept (in this case I gave 8.3) and you will have parallel equations.

The top graph is your answer.

Note that pink = cherry, and yellow = lemon. The question states that for every 4 cherry sold, one lemon is, therefore making the ratio 4 cherry: 1 lemon.

The next question is asking that how much in total is sold if there are 30 more cherry cones sold.

Let the amount of lemon cones sold be denoted by the variable, x.

The amount of cherry cones would still sold would be 4:1, but the amount is 30 more then x.

Multiply both sides of the ratio given by 10:

4 x 10 = 40

1 x 10 = 10

The result will give you 30 more cherry cones, and also give you the total of 50 cones in all.

50.

~

Answer:

Step-by-step explanation:

The distance between Toby and Meg are approximately 95 feet apart.

We can solve this problem using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.

The distance between Toby and Meg is the hypotenuse of a right triangle with legs 57 feet and 76 feet.

So we can use the Pythagorean theorem to find this distance:

distance^2 = 57^2 + 76^2

distance^2 = 3249 + 5776

distance^2 = 9025

distance = sqrt(9025)

distance = 95

Learn more about Pythagoras theorem at

https://brainly.com/question/231802

#SPJ1

Answer:

48 miles

Step-by-step explanation:

i think thats it.

Answer: 4.

Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.

                                Hope this helps!

The six different classifications are :

BASED ON SIDES:

• Isosceles triangle: This type of triangle has 2 equal adjacent sides, while one side is different

• Scalene triangle : All three sides are different in measurement

• Equivalent triangle : All three sides measure the same, meaning the measurement of sides are equal

BASED ON ANGLES:

• Obtuse angle triangle: One obtuse angle present (more than 90)

• Acute angle triangle: Has all three acute angles (less than 90)

• Right angle triangle: Has one angle which is 90° and the other two are acute

Hope it helps!

The quotient of the expressions −48.132 and −0.84 will be 57.30. Then the correct option is C.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Given −48.132 ÷ −0.84.

Then the value of the expression will be

⇒ −48.132 / −0.84

If in the numerator and the denomination, the negative sign is present, then both will cancel out each other.

⇒ 48.132 / 0.84

⇒ 57.30

The quotient of the expressions −48.132 and −0.84 will be 57.30.

Then the correct option is C.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

The solution to the equation 3x = 8 - 2x is x = 1.6.

To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:

Express the equation in the form of y = f(x). Rearrange the equation:

3x + 2x = 8

5x = 8

x = 8/5 or 1.6

Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.

Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.

The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).

Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.

for such more question on equation

https://brainly.com/question/27870704

#SPJ8

The bug population whose growth shows geometric sequence ,on Week 26 the value is approximately 9,461.01.

What is a geometric sequence, and how can we use it to predict the growth of a population?

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio. Mathematically, a geometric sequence can be expressed as:

\(a, ar, ar^2, ar^3, ...\)

where a is the first term, r is the common ratio, and each subsequent term is obtained by multiplying the previous term by r.

Calculation of  the bug population on week 26 -

To solve this problem, we can use the formula for a geometric sequence:

\(a_n = a_1 \times r^{n-1}\)

Where:

\(a_n\) = the nth term in the sequence

\(a_1\) = the first term in the sequence

r = the common ratio between terms

n = the term number

We are given that the bug population follows a geometric sequence, with a first term of 500 and a second term of 600. To find the common ratio, we can divide the second term by the first term:

\(r = 600 / 500 = 1.2\)

Now we can use the formula to find the population on Week 26:

\(a_{26} = 500 \times 1.2^{(26-1)}\)

\(a_{26} = 500 \times 1.2^{25}\)

Evaluate this expression to get:

\(a_{26}\) ≈ \(9,461.01\)

Therefore, the bug population on Week 26 is approximately 9,461.01.

To know more about geometric sequence visit :

brainly.com/question/21961097

#SPJ9

Using correlation and it's value of coefficient , The answer is b. 0.50

A statistical method called regression links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether changes in one or more of the explanatory variables are related to changes in the dependent variable.

A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.

we have 25% variance confidence.

\(r ^ {2} = 0.25\)

\(r=\sqrt {0.25}\)

\(r=0.50\)

The answer is b.0.50

To learn more about correlation and regression visit:

https://brainly.com/question/14313391

#SPJ4

If a linear regression equation predicts more than 25% of the variance in the Y scores, then the correlation between X and Y must be greater than (c) r = 0.35.

Correlation (r) quantifies the strength and direction of the linear relationship between two variables. A correlation of 0.35 indicates a moderate positive linear association, suggesting that as X increases, Y tends to increase as well, and vice versa.

When the correlation surpasses this threshold, it implies that a substantial portion of the variability in Y can be explained by changes in X. However, it's important to interpret the correlation value within the context of the specific data and the field of study.

Other factors like sample size and potential outliers can also influence the significance of the correlation. In summary, a correlation greater than (c) 0.35 signifies a meaningful connection between X and Y, contributing to the prediction of Y scores using the linear regression equation.

To know more about linear regression equation refer here :    

https://brainly.com/question/28285612#

#SPJ11  

\(f^(-1)(2) = 6\), which is consistent with our earlier result.

A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.

Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?

Solution:

To find f^(-1)(2), we need to find the value of x such that  \(f(x) = 2\) . We can set up an equation:

\(f(x) = \sqrt(2x - 8) = 2\)

Squaring both sides, we get:

\(2x - 8 = 4\)

\(2x = 12\)

\(x = 6\)

Therefore, \(f^(-1)(2) = 6.\)

We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:

\(f(f^(-1)(x)) = x\)

We can substitute x = 2 and solve for f^(-1)(2):

\(f(f^(-1)(2)) = 2\)

\(f^(-1)(2) = (f(6))^(-1)\)

f(6) = √(2(6) - 8) = √4 = 2

Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.

Learn more about function here:

https://brainly.com/question/2541698

#SPJ1

Answer:

y = 4/3x - 5

Step-by-step explanation:

y-intercept will be (0,-5)

so m = (y2-y1)/(x2-x1)

m = (-5 -7)/(0 - 9) = (-12)/(-9) = 4/3

Using m = 4/3, y = 7, x = 9

y = mx + b

7 = 4/3(9) + b

7 = 12 + b

b = -5

so

y = 4/3x - 5

Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

We have ,

Net income considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.

The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.

Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.

Hence, Walton's actual check average is $9.52

The actual food cost is lower than the flexible budget by $5020

Read more about net income here:

brainly.com/question/28390284

#SPJ1

complete question:

A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?

b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?

d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?

e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?

f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?

g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?

h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?