Mathematics College

Please help me with this word problem thank you

Answers

Answer 1

Answer:

10 miles per hour

Step-by-step explanation:

122-52= 70

70 miles/ 7 hours

10 miles per hour

Related Questions

Find the axis of symmetry:
Picture is below.

Answers

Answer:

x = -3

Step-by-step explanation:

Axis of symmetry:

Axis of symmetry is the vertical line that divides the parabola into two equal halves and it passes through the vertex of the parabola.

From the graph, Vertex (-3, 4)

Axis of symmetry: x = -3

A company's cost formula for its salaries and wages cost is $2,850 per month plus $317 per job. For the
month of February, the company planned for activity of 16 jobs, but the actual level of activity was 14
jobs. The actual salaries and wages cost for the month was $7,640. The spending variance for salaries
and wages cost in February would be closest to:
$352 F
$352 U
O $282 F
$282 U

Answers

The spending variance for salaries and wages cost in February would be closest to; $282 F.

What is the spending variance in February?

The spending variance as the name implies is the difference between the budgeted cost and actual cost paid for an item. It therefore follows from the definition above that for the month of February;

Spending variance = $7,640 - (2850 + (16×317))

Spending variance = $7,640 - (7922)

Spending variance is therefore; $282 F.

Answers

The price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.

Profit

Given that a furniture store can sell 40 chairs per week at a price of $80 each, and the manager estimates that for each and $5 price reduction, she can sell five more chairs per week, and the chairs cost the store $30 each, to determine the price of the chairs and the quantity that maximize profit, the following calculation must be made:

40 x (80-30) = 200045 x (75-30) = 202550 x (70-30) = 200055 x (65-30) = 1925

Therefore, the price of the chairs and the quantity that maximizes profit is to sell 45 chairs at $75 each.

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The following data show the height, in inches, of 11 different plants in a garden:

9

4

10

9

5

2

22

10

3

3

5

After removing the outlier, what does the mean absolute deviation of this data set represent?
On average, the height of a plant varies 2.8 inches from the mean of 6 inches.
On average, the height of a plant varies 3.2 inches from the mean of 5 inches.
On average, the height of a plant varies 2.8 inches from the mean of 5 inches.
On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

Answers

On average, the height of a plant varies 3.2 inches from the mean of 6 inches.

What does the mean absolute deviation represent?

An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier is 22.

Mean absolute deviation = (1/n) x ∑ l x - m(x) l

Mean without the outlier : (9 + 4 + 10 + 9 + 5+ 2 + 10 + 3 + 3+ 5) / 10 = 6

(1/10) x ∑ l (9 - 6) + (4 - 6) + (10 - 6) + (9 - 6) + (5 - 6) + (2 - 6) + (10 - 6) + (3 - 6) + (3 - 6) + ( 5 - 6) = 3.2

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Find the equation of the line through point (−2,−1) and perpendicular to 5x+6y=−6

Answers

Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

6x-5y=-7

BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

B.) (1, -5)

Given, equation:

[tex]\sf \dfrac{(x-1)^2}{25} -\dfrac{(y+5)^2}{49} =1[/tex]

Comparing it with standard formula of hyperbola:

[tex]\sf \dfrac{(x-h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]

where (h, k) is center

The given equation in standard form:

[tex]\sf \dfrac{(x-1)^2}{5^2} -\dfrac{(y-(-5))^2}{7^2} =1[/tex]

Determined:

(h, k) = (1, -5)

a = 5, b = 7

So, here (1, -5) is the center of the given hyperbola.

If n = 140 and X = 112, construct a 95% confidence interval for the population proportion, p.

Give your answers to three decimals

Answers

The confidence interval for the population proportion, p is (0.766, 0.833)

Confidence interval

The formula for calculating the confidence interval for proportion is expressed as:

CI = p±√pq/n

Given the following

p = 112/140 = 0.8

q = 1-p = 0.2

Substitute

CI = 0.8±√(0.8)(0.2)/140

CI = 0.8±0.0338

CI = (0.766, 0.833)

Hence the confidence interval for the population proportion, p is (0.766, 0.833)

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Linear functions f(x) and g(x) have been combined by addition and multiplication. The table shows values for the sum, s(x), and product, p(x).

Which statements correctly compare the sum and product? Check all that apply.
Both functions have a constant rate of change.
The sum is linear and the product is quadratic.
The x-intercepts are the same.
The sum has one y-intercept and the product has two x-intercepts.
Both functions decrease for x ≥ 2.

Answers

The statements that correctly compare the sum and product of the function are:

The sum is linear and the product is quadratic.The sum has one y-intercept and the product has two x-intercepts.

What is a linear function?

A linear function simply means a function that represents a straight line on the coordinate plane.

In this case, the sum is linear and the product is quadratic while the sum has one y-intercept and the product has two x-intercepts.

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You get a raise of 3.5% each year.

a. What is the approximate doubling time of your salary?

b. If you are currently 25 years old and are making $40,000 per year, use the approximate doubling time to find your annual salary when you retire at the age of 65.

Answers

Using an exponential function, it is found that:

a) The doubling time of the salary is of approximately 20 years.

b) The salary will be of $160,000.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

A(0) is the initial value.r is the growth rate, as a decimal.

The growth rate for this problem is:

r = 0.035.

The doubling time is t for which A(t) = 2A(0), hence:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]2A(0) = A(0)(1.035)^t[/tex]

[tex](1.035)^t = 2[/tex]

[tex]\log{(1.035)^t} = \log{2}[/tex]

[tex]t\log{1.035} = \log{2}[/tex]

[tex]t = \frac{\log{2}}{\log{1.035}}[/tex]

t = 20 years.

You retire in 40 years, which is 2 doubling periods, hence the salary will be of:

40000 x 2 x 2 = $160,000.

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Solve the logarithmic equation by writing in exponential form or by
graphing.
log (5-2x) = 0

Answers

Answer:

Hello,

Step-by-step explanation:

[tex]log(5-2x)=0\\\\\ \Longleftrightarrow\ 10^{log(5-2x)}=10^0\\\\\\\Longleftrightarrow\ 5-2x=1\\\\\Longleftrightarrow\ 2x=5-1\\\\\\\Longleftrightarrow\ x=\dfrac{4}{2}\\\\\\\Longleftrightarrow\ \boxed{x=2}\\[/tex]

In the year 2000, The U.S. Budgeted $25,003 million for Natural Resources and Environment. In 2014, they budgeted $40,156 million. What was the absolute and relative change in environmental spending from 2000 to 2014?

Answers

Using it's concepts, we have that:

The absolute change was of $15,153 million.The relative change was of 60.60%.

What is the absolute change of two values?

The absolute change between two values is given by the absolute value of the difference between two values.

In this problem, the values are of $40,156 million, which is the final value, and $25,003 million, which is the initial value, hence the absolute change is:

A = 40,156 - 25,003 = $15,153 million.

What is the relative change?

The relative change is the absolute change multiplied by 100% and divided by the initial value, hence:

(15,153/25,003) x 100% = 60.60%.

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A national chain of department stores ranks its 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile. Brian's sales
are at the 33rd percentile.
(If necessary, consult a list of formulas.)

(a) Which of the following must be true about Karen's sales?
The value of Karen's sales were about 26% of the chain's total.
O The value of Karen's sales was in the top half of all of the salespeople.
O Karen sold $2600 in merchandise.
O Karen had sales lower in value than about 74% of the salespeople.

(b) Which of the following must be
true about Karen's and Brian's sales?
The value of Brian's sales were $700 more than Karen's.
O The value of Karen's sales were $700 more than Brian's.
O Both Karen and Brian had sales higher in value than the median.
O Both Karen and Brian had sales lower in value than the median.

Answers

(a) The truth about Karen's sales is that Karen had sales lower in value than about 74% of the salespeople. So, the correct option is D.

(b) The truth about Karen's and Brian's sales is that both Karen and Brian had lower sales in value than the median. So, the correct option is D.

Given that department stores rank their 1,000,000 salespeople by the monetary value of their sales. Karen's sales are at the 26th percentile and brian's sales are at the 33rd percentile.

A percentile is a measure used in statistics that indicates the value below which a certain percentage of observations in a group of observations falls.

(a) Karen had sales lower in value than about 74% of the salespeople because the 26% percentile represents his relative position among all the employees in terms of sales.

(b) Both Karen and Brian had sales lower in value than the median because the Median represents the 50th percentile. Since Karen's sales are at the 26th percentile and Brian's sales are at the 33rd percentile it implies their sales are less than the median value.

Hence, the truth about Karen's sales is Karen had sales lower in value than about 74% of the salespeople, and true about Karen's and Brian's sales is both Karen and Brian had lower sales in value than the median.

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If cot theta = 3/2, what is the value of csc theta?

Answers

The value of csc theta is [tex]\frac{3. 61}{2}[/tex]

How to determine the value

It is important to note that the ratio for cot is given as;

Cot theta = adjacent/opposite

cosec theta = hypotenuse/opposite

If cot theta = 3/2, then

Adjacent = 3

Opposite = 2

Using Pythagoras theorem, we have

Hypotenuse square = opposite + adjacent square

[tex]H = \sqrt{2^2 + 3^2}[/tex]

[tex]H = \sqrt{4 + 9}[/tex]

[tex]H = 3. 61[/tex]

Cosec theta = [tex]\frac{3. 61}{2}[/tex]

Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]

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Answer:

3.16/2

Step-by-step explanation:

Have a great day

32) Find the cost of linoleum flooring for a floor that is 15 feet by 10 feet if it costs $9.00 to cover 12 square feet.
O a.) $110.50
Ob.) $132.50
Oc.) $122.50
Od.) $112.50

Answers

Answer:

d.) $112.50

Step-by-step explanation:

Area of floor:

15 ft × 10 ft = 150 ft²

150 ft² is how many times 12 ft²?

It is 150 ft² / 12 ft² = 12.5.

150 ft² is 12.5 times 12 ft².

12 ft² cost $9.00, so 12.5 times 12 ft² costs 12.5 times $9.00.

12.5 × $9.00 = $112.5

Answer: d.) $112.50

D.) 112.50

The Square foot flooring is calculated by doing 15ft x 10ft = 150ft^2. Since it cost $9.00 to cover 12ft^2, you would do 150ft^2/12ft^2 to find out how many times you have to pay 9 dollars. This gives you 12.5 times you have to pay 9 dollars. Therefore, you do $9.00x12.5 which gives you $112.50

The median household in the United States increased by a rate of 0.25% each year between 1980 and 1985. If the median household income was $42,050 in 1980, what was the median household income after 5 years? Round answer to the nearest whole dollar.

Answers

Using an exponential function, the median household income after 5 years was of $42,578.

What is an exponential function?

An increasing exponential function is modeled by:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

A(0) is the initial value.r is the growth rate, as a decimal.

For this problem, the parameters are:

A(0) = 42050, t = 5, r = 0.0025[/tex]

Hence:

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]A(t) = 42050(1.0025)^t[/tex]

[tex]A(5) = 42050(1.0025)^5 = 42578[/tex]

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Express the confidence interval (0.065,0.143) in the form of p - E

Answers

The confidence interval expressed in the form p - E is:

(0.104 - 0.039, 0.104 + 0.039).

What are the mean and the margin of error of a confidence interval?

The mean is the mean of the bounds, hence:

p = (0.065 + 0.143)/2 = 0.104.

The margin of error is the difference between the bounds and the mean, hence:

E = 0.104 - 0.065 = 0.143 - 0.104 = 0.039.

Hence the interval in the desired format is:

(0.104 - 0.039, 0.104 + 0.039).

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Students at a high school were polled to determine the type of music they preferred. There were students who completed the poll. Their responses are represented in the circle graph.
What percent of students preferred music?
A circle graph titled Music Preferences consists of a circle divided into 6 regions with labels and sizes as follows: rap, 945; alternative, 462; rock and roll, 275; country, 168; jazz, 15; other, 85.
Music Preferences
Rap 945
Alternative 462
Rock and Roll 275
Country 168
Jazz 15
Other 85

Answers

The percent of students that preferred alternative music is 23.7%

How to determine the percentage?

The music type and the preference are given as:

Music Preferences

Rap 945

Alternative 462

Rock and Roll 275

Country 168

Jazz 15

Other 85

From the above table, we have:

Alternative = 462

Total = 945 + 462 + 275 + 168 + 15 + 85

Total = 1950

The percentage is then calculated as:

Percentage = Alternative/Total * 100%

This gives

Percentage = 462/1950 * 100%

Evaluate

Percentage = 23.7%

Hence, the percent of students that preferred alternative music is 23.7%

Answers

The equations that can be used to find the lengths of the legs of the triangle are as follows:

100 = (x + 2)² + x²24 = 0.5 × (x + 2)(x)x² + 2x - 48 = 0How to find the equation of a right triangle?

The equation that can be used to find the length of the leg of the right triangle uses Pythagoras theorem,

Therefore,

c² = a² + b²

where

c = hypotenuse sidea and b are the other legs

Therefore,

10² = (x + 2)² + x²

100 = (x + 2)² + x²

Therefore, using the area of a triangle,

area of a triangle = 1 / 2 bh

where

b = baseh = height

Therefore,

area of the triangle = 1 / 2 × (x + 2)(x)

24 = 0.5 × (x + 2)(x)

24 = x² + 2x / 2

cross multiply

48 = x² + 2x

x² + 2x - 48 = 0

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SKETCHPAD
Question 5
Given AABC shown on the coordinate plane below.
AA"B"C" = Ro (T(-4,3)(ABC))
90°
Draw AA'B'C'' if
You may use different colors for the separate transformations. Indicate your final
answer. Feel free to use the Dynamic Geometry Tool to complete the
transformations.

Answers

The attached figure represents the image of A"B"C" after the transformation

How to transform the triangle?

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

Answers

Answer:

40 ml of water must be added.

Step-by-step explanation:

Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.

First, let's find the volume of each component.

If the oil is x then water is 4x according to ratio and their sum is 100 ml:

x + 4x = 1005x = 100x = 20

So, we have 20 ml of oil and 80 ml of water.

Now, let's added volume of oil be y. Then we have the ratio:

(20 + y)/80 = 1/220 + y = 40y = 20

So, we have 40 ml of oil and 80 ml of water.

Lastly, let's added water be z. Then we have the ratio:

40/(80 + z) = 1/380 + z = 120z = 40

We must add 40 ml of water.

What is the y-intercept of the liner function? (y=3x-2)

Answers

The y-intercept of the linear function y = 3x - 2 is -2

How to determine the y-intercept?

The function is given as

y = 3x - 2

The above function is a linear function, and the y-intercept is the point on the graph, where x = 0 i.e. the point (0, y)

As a general rule, linear functions are those functions that have constant rates or slopes

Next, we set x to 0, and calculate y to determine the value of the y-intercept

y = 3(0) - 2

Remove the bracket in the above equation

y = 3 * 0 - 2

Evaluate the product of 3 and 0 i.e. multiply 3 and 0

y = 0 - 2

Evaluate the difference of 0 and -2 i.e. subtract 0 from 2

y = -2

The above means that the value of y when x is 0 is -2

Hence, the y-intercept of the linear function y = 3x - 2 is -2

Answers

I hope this helpssssss:)

What is the domain of the function given below

Answers

Answer:

c. [-1, infinity)

Step-by-step explanation:

the domain the interval or set of valid x values (while the range is the same for the valid y values).

what is the smallest value of x we see for the graph ?

for x values we need to look left and right.

and the more left the value, the smaller it is.

so, in other words, what is the left-most x value e can find ?

x = -1

that is the "starting point" of the function. there is no functional value for any smaller x.

and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.

therefore the answer.

keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).

10 - 13x + 2 in words

Answers

The simplification of the equation above in words is = Twelve minus thirteen X.

Simplification of an equation

In mathematics, coefficients are those numbers that multiplies a variable. For example in 13x, the coefficient is 13 which multiplies a variable known as X.

The equation given is,

10 - 13x + 2

Arrange the digits without a coefficient together.

That is ,

10+2 -13x

12 - 13x

Therefore the simplification of the given equation in words is Twelve minus thirteen X.

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How many fewer people live in Elmira than White Plains

Answers

Population density implies the number of an object, items, or people that can be found in a unit area at a particular time. Therefore, the number of fewer people that live in Elmira than in White Plains is 27,653.

Population density implies the total number of objects, items, or people that exist in a unit area or a place at a particular time. So that the number of people that exist in a place, area, city, or country can be referred to as population, in a particular period.

Thus in the given question, it can be deduced that;

The population of people living in White Plains =56,853

The population of people living in Elmira = 29,200

So, the difference in the population between the two cities can be determined as;

= 56,853 - 29,200

= 27,653

Thus, the number of fewer people living in Elmira than in White Plains is 27,653

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What are the fourth roots of -3+3√3i?
Enter your answer by filling in the boxes. Enter the roots in order of increasing angle measure in simplest form.

Answers

By De Moivre's formula, we have the following four roots: [tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex], [tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex], [tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex] and [tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex].

How to determine a fourth root of a complex number

According to complex analysis, the fourth roots of a complex number can be found by De Moivre's formula:

[tex]\sqrt[n]{z} = \sqrt[n]{r}\cdot \left[\cos \left(\frac{\theta + 2\pi\cdot i}{n} \right)+ i\,\sin \left(\frac{\theta + 2\pi\cdot i}{n} \right)\right][/tex], for [tex]i = \{0, 1, ..., n - 1\}[/tex] (1)

Where:

r - Magnitude of the complex number.θ - Direction of the complex number, in radians.

First, we find the magnitude and direction of the complex number:

[tex]r = \sqrt{(-3)^{2}+(3\sqrt{3})^{2}}[/tex]

r = 6

[tex]\theta = \tan^{-1} \left(\frac{3\sqrt{3}}{-3} \right)[/tex]

[tex]\theta = \frac{2\pi}{3} \,rad[/tex]

Now we find the four quartic roots of the complex number:

[tex]z_{1} = 1.565 \cdot \left(\cos \frac{\pi}{6} + i\,\sin \frac{\pi}{6} \right)[/tex]

[tex]z_{2} = 1.565\cdot \left(\cos \frac{2\pi}{3} + i\,\sin \frac{2\pi}{3} \right)[/tex]

[tex]z_{3} = 1.565\cdot \left(\cos \frac{7\pi}{6}+i\,\sin \frac{7\pi}{6} \right)[/tex]

[tex]z_{4} = 1.565\cdot \left(\cos \frac{5\pi}{3} + i\,\sin \frac{5\pi}{3} \right)[/tex]

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Find the area of the figure.

Answers

i hope this helpssss :))

What is an equation of the line that passes through the points (6, 4) and(6,−6)?

Answers

Answer:

Step-by-step explanation:

Need help with that I don’t understand it

Answers

The answer is no. b.

Step-by-step explanation:

The answer is no b. u just take common

the set of all months that contain less than 31 years

Answers

The set of all months that contains less than 31 days is; {February, April, June, September, November}.

What is the set of all months that contain less than 31 days?

It follows from the task content that the set whose elements are to be determined is characterized by containing less than 31 days.

On this note, it follows that the elements of the set are; February (28/29 days), April (30 days), September (30 days), June (30 days) and November (30 days).