If the graph of g is translated vertically upward by 5 units, it becomes the graph of
a function f. Find the expression of f(x).

Answer:

Y=1800+150x

Step-by-step explanation:

Answer:

4. Y = 150x + 1800  

Answer:

\(g'(y)=3y^2-4y-8\)

Step-by-step explanation:

start by foiling out the given function

\(g(y)=(y-4)(2y+y^2)\\=2y^2+y^3-8y-4y^2\\=y^3-2y^2-8y\)

next, use the power rule to find the derivative

power rule: To use the power rule, multiply the variable's exponent n, by its coefficient a, then subtract 1 from the exponent. If there's no coefficient (the coefficient is 1), then the exponent will become the new coefficient.

\(g'(y)=3y^2-4y-8\)

Answer:

95% confidence interval for the proportion of smokers who have tried to quit within the past year

(0.47956 ,0.50620)

Step-by-step explanation:

Step(i):-

Given that  National Center for Health Statistics interviewed 5409 adult smokers in 2015

Sample size 'n' = 5409

Given that 2666 of them said they had tried to quit smoking during the past year.

proportion

             \(P = \frac{x}{n} = \frac{2666}{5409} = 0.49288\)

             Q = 1 - P = 1 - 0.49288 = 0.50712

Step(ii):-

95% confidence interval for the proportion of smokers who have tried to quit within the past year

\(({P - Z_{0.05} \sqrt{\frac{PQ}{n} } , P + Z_{0.05} \sqrt{\frac{PQ}{n} )\)

\(({0.49288 - 1.96 \sqrt{\frac{0.49288 X 0.50712}{5409} } , 0.49288 + 1.96\sqrt{\frac{0.49288 X 0.50712}{5409} )\)

(0.49288 - 0.01332 , 0.49288+0.01332)

(0.47956 , 0.50620 )

Final answer:-

95% confidence interval for the proportion of smokers who have tried to quit within the past year

(0.47956 ,0.50620)

Answer:

650,000,000

Step-by-step explanation:

6.5x10^8

its 6.25

A=1/2bh

=1/2×5×2.5=6.25

Answer:

376,404 copies sold.

Step-by-step explanation:

To find this answer, divide 33,500 copies by the 8.9%:

33,500 divided by 8.9% = 376404.494382

Now, if we round this number to the nearest whole number, it would be:

376,404 copies sold.

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Answer: 7% at 6 years would best fit their payment option. They would then be paying $238.69 monthly and which is under $250, I hope this helps!

The age of Sadie is 6 years.

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

Let x be the age of Sadie

x+1 be the age of Guadalupe

The sum of the square of Sadie's age and 5 times Guadalupe's age is 71.

x² +5(x+1)=71

x² +5x+5=71

x² +5x-66=0

Factor out the expression.

x²+11x-6x-66=0

x(x+11)-6(x+11)=0

(x-6)(x+11)=0

x=6 and x=-11

Hence, the age of Sadie is 6 years.

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Answer:

Cost for each pound of jelly beans:  $2.75

Cost for each pound of almonds:  $3.75

Step-by-step explanation:

Let J be the cost of one pound of jelly beans.

Let A be the cost of one pound of almonds.

Using the given information, we can create a system of equations.

Given 3 pounds of jelly beans and 5 pounds of almonds cost $27:

\(\implies 3J + 5A = 27\)

Given 9 pounds of jelly beans and 7 pounds of almonds cost $51:

\(\implies 9J + 7A = 51\)

Therefore, the system of equations is:

\(\begin{cases}3J+5A=27\\9J+7A=51\end{cases}\)

To solve the system of equations, multiply the first equation by 3 to create a third equation:

\(3J \cdot 3+5A \cdot 3=27 \cdot 3\)

\(9J+15A=81\)

Subtract the second equation from the third equation to eliminate the J term.

\(\begin{array}{crcrcl}&9J & + & 15A & = & 81\\\vphantom{\dfrac12}- & (9J & + & 7A & = & 51)\\\cline{2-6}\vphantom{\dfrac12} &&&8A&=&30\end{array}\)

Solve the equation for A by dividing both sides by 8:

\(\dfrac{8A}{8}=\dfrac{30}{8}\)

\(A=3.75\)

Therefore, the cost of one pound of almonds is $3.75.

Now that we know the cost of one pound of almonds, we can substitute this value into one of the original equations to solve for J.

Using the first equation:

\(3J+5(3.75)=27\)

\(3J+18.75=27\)

\(3J+18.75-18/75=27-18.75\)

\(3J=8.25\)

\(\dfrac{3J}{3}=\dfrac{8.25}{3}\)

\(J=2.75\)

Therefore, the cost of one pound of jelly beans is $2.75.

Answer:

Step-by-step explanation:

Based on the calculations, the IQR of this data is equal to 2.

How to determine the IQR of this data?

IQR is an acronym for interquartile range and it is a measure of the middle 50% of data values when they are ordered from lowest to highest.

Next, we would order the data from lowest to highest and then determine the median as follows:

Data = {1, 4, 4,} 4, {4, 6, 5}

Median = 4.

For Q₁ of the lower half of the data, we have:

Lower half = {1, 4, 4,}

Q₁ = 4.

For Q₃ of the upper half of the data, we have:

Upper half = {4, 6, 5}

Q₃ = 6.

Mathematically, IQR is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

IQR = 6 - 4

IQR = 2.

Answer by

Lanuel

The results of those seven rolls that are shown shows that the range is 5.

The range is the size of the smallest interval which contains all the data and provides an indication of statistical dispersion. It is measured in the same units as the data.

Given that a six-sided die is rolled 7 times, to give 1, 4, 4, 4, 4, 6, 5, we need to find the range,

The numbers that are gotten include:

1, 4, 4, 4, 4, 6, 5.

It should be noted that range is calculated as:

R = Highest value - Lowest value

R = 6 - 1

R= 5

Therefore, the range from the numbers given is 5.

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Answer:

5/6 + 2 1/6 in simplest form, would be 3.

Answer:

3

Step-by-step explanation:

Answer:

can you pls clear your questions?

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

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The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

A scale factor is defined as the ratio between the scale of a given original object and a new object,

We have,

The actual dimensions of the patio are 20 feet by 16 feet.

The scale factor is 1 inch to 4 feet,

This means that 1 inch on the scale drawing represents 4 feet in reality.

So the dimensions of the scale drawing are:

20 feet x (1/4) = 5 inches (length on scale drawing)

16 feet x (1/4) = 4 inches (width on scale drawing)

The area of the actual patio is:

= 20 feet x  16 feet

= 320 square feet

The area of the scale drawing is:

= 5 inches x 4 inches

= 20 square inches

The ratio of the area of the scaled drawing to the actual area of the patio is: 20 square inches : 320 square feet

To simplify this ratio, we need to convert both values to the same units.

Converting the area of the scale drawing to square feet:

= 20 square inches x  (1/144) square feet/square inch

= 0.1389 square feet

So the ratio of the area of the scaled drawing to the actual area of the patio is:

0.1389 square feet : 320 square feet

Or, in simplified form:

1 : 2306.56

Thus,

The ratio of the scaled area to the actual area of the patio is 0.1389 square feet : 320 square feet or 1 : 2306.56

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Answer:

The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.

In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:

C = pi x d = 3.14 x 60 = 188.4 centimeters

When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:

distance = 35 x circumference = 35 x 188.4 = 6584 centimeters

We can convert centimeters to meters by dividing the distance by 100:

distance = 6584 ÷ 100 = 65.84 meters

Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.

Answer:

x = 5

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-9x+27=9x-63

-18x=-90

x=5

Step-by-step explanation:

Answer:

A or D i think..

Step-by-step explanation:

Answer:

i think that is 147

Step-by-step explanation:

Based on the calculations using unit pricing, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)

Saving money while shopping is one of the best ways to reduce your expenses and have more disposable income for other things. Unit pricing is a pricing system that displays prices in standard units, allowing customers to compare prices across different brands and package sizes and save money. To determine which toilet paper deal is better, we can use the unit price method, which divides the price by the number of units in the package. The toilet paper with the lower unit price is the better deal.
The formula for unit pricing is as follows:
Unit price = total price ÷ number of units
Using the above formula, we can calculate the unit price of toilet paper A and toilet paper B as follows:
For Toilet paper A:
Unit price = $4.59 ÷ 6 mega rolls
Unit price = $0.765 per mega roll
For Toilet paper B:
Unit price = $9.02 ÷ 12 mega rolls
Unit price = $0.751 per mega roll
Therefore, based on the calculations, Toilet paper B has a lower unit price and is the better deal between the two. Customers will save more money if they purchase toilet paper B rather than toilet paper A because the price per mega roll is lower. (option b)
Unit pricing is a great way to compare prices, and consumers should always use it to determine the better deal between two products, as this will help them save money and stick to their budget.

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Answer:

7/8

Step-by-step explanation:

Answer:

4/5

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

\(1+9+2^3+1+1 \\ \\ =10+8+2 \\ \\ =18+2 \\ \\ =20\)

Answer:

it will be 25 percent

Step-by-step explanation:

divide 2 by 8

Answer: 25 %

Step-by-step explanation:

2/8

on simplifing  we got 1/4 in fraction  that is equal to  0.25  that is equal tp 25 % in percentage form.

Hope this will help you

Answer:

Below

Step-by-step explanation:

a) they won 120 games out of 369 played  = 40/23=.325

b) they lost 248 out of 369 played = 248/369 = .672

c) Home games are 185 out of 369 = .501

d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389

Answer:

7 and -7

Step-by-step explanation:

Correct question

Which shows all the values of x that make the rational expression 2x^2-72/5x^2-245 undefined

For the expression to be undefined, the denominator must be equal to zero

Hence 5x² - 245 =0

Add 245 to both sides

5x²-245+245 = 0+245

5x² = 245

x² = 245/5

x² = 49

x = ±√49

x =7 and -7

Hence the values of x that will make the function undefined are 7 and -7

Answer:

the answer is

\(x = 13a {}^{2} \)

A mathematics topic that van be looked into is how linear algebra, graph theory and optimization can be used on the airline industry.

In this case, to solve the scheduling issues faced by airlines such as planning flights, assigning planes and crews to routes - mathematical techniques can be employed.

By leveraging Linear Algebra, operators can simulate the flow of aircrafts and passengers while Graph Theory can help model flight schedules and aircraft routes.

Simultaneously using Optimization techniques in the problem-solving process can work to streamline various operations resulting in reduced costs and improved efficiency which can increase profit margins.

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Answer: 16%

Step-by-step explanation: