Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x) = x , [0, 16]

Answers

Answer 1

Answer:

C = 4

Step-by-step explanation:

solution:

f(x) can be differentiated on (0,16)

By mean value theorem

= f(16) = 4

= f(0) = 0

= f(b) - f(a)/b - a

= f(4) - f(0)/ f(16) - f(0)

= f'(c) = 1/2√C

= 1/2√C = 4/16

= 1/2√C = 1/4

= 4 = 2√C

= √C = 4/2

we make c the subject of the formula and also eliminate the square root

= √C = 2

= C = 2²

= C = 4


Related Questions

88 feet/second = 60 miles/hour. How many feet per second is 1 mile/hour? (Hint: divide both sides of the equation
by the same amount.)
Round to the nearest thousandth.
One mile per hour is equivalent to
ao feet/second

Answers

Answer: 1ft/sec = 0.618 mi/hr

Explanation:

88 ft/sec = 60 mi/hr
88/88 ft/sec = 60/88 mi/hr (divide both sides by 88)
1 ft/sec = 60/88 mi/hr
1 ft/sec = 15/22 mi/hr
1 ft/sec = 0.681 mi/hr

Can any one help me with this

Answers

Answer: C

Step-by-step explanation:

Since this is an isosceles triangle as indicated by the markers on QP and PR, we know that QS and SR are equivalent.

To find the value of n, we set QS and SR equal to each other.

6n+3=4n+11                     [combine like terms]

2n=8                                 [divide both sides by 2]

n=4

Now that we know n=4, we know that A is incorrect. What we can do is use the value of n to solve for QS, SR, and QR.

QS

6(4)+3=13

Since the length of QS is 13, we know B is incorrect.

SR

4(4)+11=27

Since SR is 27, C is a correct answer.

QR

13+27=40

Since QR is 40, the only correct answer is C.

Combine like terms to simplify the expression: 2/5k - 3/5 +1/10k

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

1/2k - 3/5

▹ Step-by-Step Explanation

2/5k - 3/5 + 1/10k

Collect like terms:

2/5k + 1/10k = 1/2

Final Answer:

1/2k - 3/5

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1/2k - 3/5

Step-by-step explanation:

Hey there!

Well the only fraction needed to combine are,

2/5 and 1/10.

To add them we need to make 2/5 have a denominator of 10.

To do that we multiply 5 by 2.

5*2 = 10

What happens to the denominator happens to the denominator.

2*2 = 4

Fraction - 4/10

4/10 + 1/10 = 5/10

5/10

simplified

1/2

1/2k - 3/5

Hope this helps :)

Solve the system of equations. ​ 2y+7x=−5 5y−7x=12 ​

Answers

[tex]\text{Solve the systems of equations:}\\\\2y+7x=-5\\5y-7x=12\\\\\text{Solve by adding and subtracting}\\\\7y=7\\\\\text{Divide}\\\\y=1\\\\\text{To find x, plug 1 into y in one of the equations and solve:}\\\\2(1)+7x=-5\\\\2+7x=-5\\\\\text{Subtract 2 from both sides}\\\\7x=-7\\\\\text{Divide by 7}\\\\x=-1\\\\\boxed{y=1\,\,and\,\,x=-1}[/tex]

explain why the APR does not compare loans for different lengths of time

Answers

Answer:

APR does not tell you how long your rate is locked for. A 15-year loan may have a lower interest rate, but could have a higher APR, since the loan fees are amortized over a shorter period of time. It is not wise to compare a 30-year loan with a 15-year loan using their respective APRs.

Step-by-step explanation:

The parallelogram shown below has an area of 15 units^2.

Answers

Answer:

yes

Step-by-step explanation:

yes E

Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in accounting, economics, management information systems, public speaking, and statistics. The sizes of these classes are, respectively, 375, 35, 45, 25, and 60.Required:Find the mean and the median of the class sizes. What is a better measure of Lauren's "typical class size"—the mean or the median?

Answers

Answer:

Mean = 108

Median = 45

The better measure of Lauren's "typical class size" is the Mean

Step-by-step explanation:

1. Calculating mean and median.

The mean is an important measure of central tendency, and it is the average of the measurement of a given set of data. It is calculated as follows:

[tex]Mean\ (\overline {X}) &= \frac{\sum X}{N}[/tex]

where X = individual data sets

N = total number of data

[tex]Mean= \frac{375\; +\ 35\ +\ 45\ +\ 25\ +\ 60}{5} \\=\frac{540}{5} \\= 108[/tex]

The Median divides the measurements into two equal parts, and in order to calculate the median, the distribution has to first be arranged in ascending or descending order. Arranging this series in descending order:

375, 60, 45, 35, 25

The formula for calculating median is given by:

[tex]M_{d} = \frac{N\ +\ 1}{2} th\ data\\\\=\frac{5\ +\ 1}{2}th\ data\\\\=\frac{6}{2} th\ data\\= 3rd\ data\\M_{d} = 45[/tex]

from the list or arranged data in descending order (375, 60, 45, 35, 25), the third data is 45.

Therefore, Median = 45

2. The better measure of typical class size is Mean because the mean depends on all the values of the data sets, whereas the median does not. When there are extreme values (outliers) the effect on the median is very small, whereas it is effectively captured by the mean.

This need to be correct plzzzzzzzzzzzz I got this answer wrong so send the new one

Answers

Answer:

$215,892.50

Step-by-step explanation:

This is a problem of compound interest.

In compound interest Amount A for principal p charged at interest r% per annum is given by

A = p(1+r/100)^n

where n is the time period in years.

_____________________________

given

p = $100,000

r = 8%

t = 10 years

A= 100,000( 1+ 8/100)^10

A= 100,000( 1.08)^10

A = $215,892.50

So , you need to pay $215,892.50 in total to debt cleared of debt.

Bob cycles 5.4 km every morning.how many feet are in 5.4 km, given that 1 mile=1.609 km and 1 mile=5,280 feet?

Answers

Answer:

17,720 ft

Step-by-step explanation:

5.4 km * (1 mile)/(1.609 km) * (5280 ft)/(1 mile) = 17,720 ft

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°.

Answers

Answer:

[tex] \sqrt{4 {}^{2} + ( - 4) {}^{2} } [/tex]

[tex] \sqrt{32} [/tex]

and the angle

[tex] \tan( \alpha ) = - 4 \div 4 = - 1[/tex]

and since the sin component is -ve, we have our angle on 4th quadrant, which equals 315 degrees

Options:

Determine two pairs of polar coordinates for the point (-4, 4) with 0° ≤ θ < 360°. (5 points)

Group of answer choices

(4  , 135°), (-4  , 315°)

(4  , 45°), (-4  , 225°)

(4  , 315°), (-4  , 135°)

(4  , 225°), (-4  , 45°)

Step-by-step explanation:

The guy asking forgot to provide the options you can comment the awnswe in the comments just do it before brainly turns off comments to try and prevent people from learning

Excel:In cell B13, create a formula using the VLOOKUP function that looks up the value from cell A11 in the range A5:B7, returns the value in column 2, and specifies an exact match.

Answers

Answer:

=Vlookup'B13' A11' 7'false

Press enter.

Step-by-step explanation:

Vlookup is a technique in excel which enables users to search for criterion values. It is vertical lookup function in excel which return a value from a different column. The formula for Vlookup function is:

=Vlookup'select cell you want to look up in' select cell you want to lookup from' select column index number' true/false.

where true is approximate match and false is exact match.

Answer:=VLOOKUP(J2,A2:G23,2,FALSE)

Step-by-step explanation:

a. In cell J3, begin to enter a formula using the VLOOKUP function.

b. Use the Project ID (cell J2) as the lookup value.

c. Use the Projects table (range A2:G23) as the table_array.

d. Use the Project Name column (column 2) as the col_index_num.

e. Specify an exact match (FALSE) for the range_lookup.

is this correct if not which one?

Answers

Answer:

C.

Step-by-step explanation:

[tex]\frac{7x}{3y}+\frac{12x}{9y}[/tex]

We can reduce the second term:

[tex]\frac{7x}{3y} +\frac{4x}{3y}[/tex]

Since they now have a common denominator, we can add them:

[tex]=\frac{7x+4x}{3y}=11x/3y[/tex]

The answer is C.

So, yes, you're answer was correct!

Simplify: 9h-12h=54-23

A. 3h=-77

B.3h= 31

C.-3h= -31

D.-3h= 31

Answers

Answer:

c is the answer

Step-by-step explanation:

-3h = 31

-9h-12h = -3h

54-23= 31

Answer:

[tex]\boxed{C. -3h = 31}[/tex]

Step-by-step explanation:

Hey there!

9h - 12h = 54 - 23

Simplify

-3h = 31

C. -3h = 31

Hope this helps :)

A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.

Answers

Answer:

The exact distance is [tex]\sqrt{109}[/tex] miles.

The distance is approximately 10.4 miles.

Step-by-step explanation:

It is given that a rectangular city is 3 miles long and 10 miles wide. So,

Length = 3 miles

Width = 10 miles

We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.

Using Pythagoras theorem, the length of diagonal is

[tex]d=\sqrt{l^2+w^2}[/tex]

where, l is length and w is width.

Substitute l=3 and w=10.

[tex]d=\sqrt{(3)^2+(10)^2}[/tex]

[tex]d=\sqrt{9+100}[/tex]

[tex]d=\sqrt{109}[/tex]

The exact distance is [tex]\sqrt{109}[/tex] miles.

Now,

[tex]d=\sqrt{109}[/tex]

[tex]d=10.4403065[/tex]

[tex]d\approx 10.4[/tex]

The distance is approximately 10.4 miles.

Lester Hollar is vice president for human resources for a large manufacturing company. In recent years he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the last six months. Below are the results. At the .05 significance level, can he conclude that the number of absences has declined? Estimate the p-value.
Employee Before After
1 6 5
2 6 2
3 7 1
4 7 3
5 4 3
6 3 6
7 5 3
8 6 7

Answers

Answer:

t >± 1.895

t= 0.1705

Step-by-step explanation:

The null and alternative hypotheses are

H0: μd=0 Ha: μd>0

Significance level is set at ∝= 0.05

The critical region for  t  df=7       t >± 1.895

The test statistic under H0 is

t = d/ sd/ √n

Which has t distribution with n-1 degrees of freedom

Employee        After  Before         d = after - before        d²

1                          6         5               1                                  1

2                         6          2               4                               16

3                         7          1                6                               36

4                         7           3              4                               16

5                         4          3              1                                 1

6                         3          6              -3                               9

7                         5          3              2                               4

8                          6        7               -1                                1      

∑                                                    14                              84    

d`= ∑d/n= 14/8= 1.75

sd²= 1/8( 84- 14²/8) = 1/8 ( 84 - 24.5) = 59.5

sd= 7.7136

t= 3/ 7.7136/ √8

t= 0.1705

Since the calculated value of t= 0.1705 < ± 1.895  therefore reject the null hypothesis at 5 % significance level . On the basis of this we cannot conclude that the number of absences has declined.

The sum of triple a number
and nineteen.

Answers

Answer:

3x+19

Step-by-step explanation:

Let x be the unknown number

triple means 3 times

sum means add

3x+19

The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 229 customers on the number of hours cars are parked and the amount they are charged.

Number of Hours Frequency Amount Charged 1 16 $ 3 2 34 6 3 51 12 4 39 16 5 34 21 6 16 24 7 9 27 8 30 29 229

a. Convert the information on the number of hours parked to a probability distribution. (Round your answers to 3 decimal places.) Hours Probability 1 2 3 4 5 6 7 8

a-2. Is this a discrete or a continuous probability distribution?

b-1. Find the mean and the standard deviation of the number of hours parked. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

b-2. How long is a typical customer parked? (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

c. Find the mean and the standard deviation of the amount charged. (Do not round intermediate calculations. Round your final answers to 3 decimal places.)

Answers

Answer:

a

See in the explanation

a-2.

Discrete

b-1.

Mean = 4.201

Standard Deviation = 2.069

b-2.

4.201

c.

Mean = 16.153

Standard Deviation = 8.079

Step-by-step explanation:

Given Data:

Number of Hours         Frequency               Amount Charged  

          1                                 16                                $3        

          2                                34                                 6  

          3                                51                                  12  

          4                                39                                 16  

          5                                34                                 21

          6                                 16                                 24

          7                                  9                                  27

          8                                 30                                 29

                                       ∑f = 229

a. Convert the information on the number of hours parked to a probability distribution:

The probability is calculated by dividing each frequency by 229. For example probability of Hour 1 is calculated as:

16 / 229 = 0.06987

This way all the hours probabilities are computed. The probability distribution is given below

Hours          Probability

   1                0.06987

   2               0.14847

   3               0.2227

   4               0.1703

   5               0.1485

   6               0.0699

   7               0.0393

   8               0.1310

   ∑                    1

a-2. Is this a discrete or a continuous probability distribution?

This is a discrete probability distribution as the probability of each hour of between 0 and​ 1 and the sum of all the probabilities of hours is 1.

b-1. Find the mean and the standard deviation of the number of hours parked.

First multiply each value of Number of hours by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

Number of Hours Parked

fx

16

68

153

156

170

96

63

240

Now add the above computed products.

∑fx = 16+68+153+156+170+96+63+240  = 962

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 962 / 229

Mean = 4.201

Compute Standard Deviation:

Let x be the Number of hours.        

Let f be the frequency

First calculate (x-x_bar) where x is each number of hours and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 4.201

For example for the Hour = 1 , and mean = 4.201

Then (x-[tex]\frac{}{x}[/tex]) = 1 - 4.201 = -3.201

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-3.201

-2.201

-1.201

-0.201

0.799

1.799

2.799

3.799

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-3.201 )² = 10.246401

  (x-[tex]\frac{}{x}[/tex])²

10.246401

4.844401

1.442401

0.040401

0.638401

3.236401

7.834401

14.432401

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 10.246401  * 16 = 163.942416

(x-[tex]\frac{}{x}[/tex])² * f

163.942416

164.709634

73.562451

1.575639

21.705634

51.782416

70.509609

432.97203

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 980.759829

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

  = √980.759829  /  229

  = √4.2827940131004

  = 2.0694912449924

S = 2.069

b-2) How long is a typical customer parked?

That is the value of mean calculated in part b-1. Hence

Typical Customer Parked for 4.201 hours

c) Find the mean and the standard deviation of the amount charged.

First multiply each value of Amount Charged by the corresponding frequency. Let x represents the number of hours and f represents frequency. Then:

fx

48

204

612

624

714

384

243

870

Now add the above computed products.

∑fx = 48+204+612+624+714+384+243+870  = 3699

Compute Mean:

Now the formula to calculate mean:

Mean = Sum of the value / Number of value

         = ∑fx / ∑f

         = 3699 / 229

Mean = 16.153

Compute Standard Deviation:

Let x be the Amount Charged.        

Let f be the frequency.

First calculate (x-x_bar) where x is each value of Amount charged and x_bar is mean. The value of x_bar i.e. [tex]\frac{}{x}[/tex] = 16.153

For example for the Amount Charged = 3 , and mean = 16.153

Then (x-[tex]\frac{}{x}[/tex]) = 3 - 16.153 = -13.153

So calculating this for every number of hour we get:

(x-[tex]\frac{}{x}[/tex])

-13.153

-10.153

-4.153

-0.153

4.847

7.847

10.847

12.847

Next calculate (x-[tex]\frac{}{x}[/tex])². Just take the squares of the above column (x-[tex]\frac{}{x}[/tex])

For example the first entry of below calculation is computed by:

 (x-[tex]\frac{}{x}[/tex])² = (-13.153  )² = 173.001409

  (x-[tex]\frac{}{x}[/tex])²

173.001409

103.083409

17.247409

0.023409

23.493409

61.575409

117.657409

165.045409

Next multiply each entry of  (x-[tex]\frac{}{x}[/tex])² with frequency f. For example the first entry below is computed by:

(x-[tex]\frac{}{x}[/tex])² * f = 173.001409  * 16 =  

   (x-[tex]\frac{}{x}[/tex])² * f

2768.022544

3504.835906

879.617859

0.912951

798.775906

985.206544

1058.916681

4951.36227

∑(x-[tex]\frac{}{x}[/tex])² = 14947.65066

Now the formula to calculate standard deviation is:

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/n

Here

n = ∑f = 229

∑(x-[tex]\frac{}{x}[/tex])² * f  is the sum of all entries of (x-[tex]\frac{}{x}[/tex])² * f

∑(x-[tex]\frac{}{x}[/tex])² * f = 14947.65066

S = √∑(x-[tex]\frac{}{x}[/tex])² * f/ ∑f

  = √65.273583668122

  = 8.0792068712295

S = 8.079

Let $x=5$, $y=\frac{3}{4}$, and $z=-\frac{1}{7}$. What is $$\frac{xz}{y}?$$

Answers

Answer:

-20/21

Step-by-step explanation:

Given x = 5, y = 3/4 and z = -1/7, 2=we are to calculate [tex]\frac{xz}{y}[/tex]. Substituting the value of x, y and z into the expression will give;

[tex]= \frac{xz}{y}\\\\ \frac{5(-1/7)}{3/4} \\= \frac{-5/7}{3/4}\\\\= \frac{-5}{7} * \frac{4}{3}\\ \\ = \dfrac{-20}{21}\\[/tex]

Hence the value of the expression is -20/21

In a simple regression analysis with age as the only explanatory variable, the effects of other factors, such as faminc, are

Answers

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

How to convert 2cm to feet?

Answers

Answer:

Divide by 30.48: It would be 0.0656168 feet.

Step-by-step explanation:

Answer:

0.0656

Step-by-step explanation:

2.54 cm = 1 in

12 in = 1 ft

2.54 * 12 = 30.48

2/30.48 = 0.0656167979

An experimental probability is ______ likely to approach the theoretical probability if the number of trials simulated is larger. A. as B. more C. less D. not

Answers

Answer:

B. More

Step-by-step explanation:

This is according to the law of large numbers

An experimental probability is more likely to approach the theoretical probability if the number of trials simulated is larger.

What is an experimental probability and theoretical probability?

Experimental probability is an experimental outcome whereas theoretical probability is a possible or expected outcome.

An experimental probability is more likely to approach the theoretical probability if the number of trials increased because of the law of large numbers which states that the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed

Thus using the concept of the law of large numbers we can say that an experimental probability is more likely to approach the theoretical probability.

Learn more about probability here:

https://brainly.com/question/9627169

#SPJ5

The sides of a rectangle are in ratio 2:5,the longer side is 20 cm. Find the length of the shorter side​

Answers

Answer:

8 cm

Step-by-step explanation:

x:y= 2:5

x/y = 2/5

5x = 2y

y is the longer side

5x=2(20)

x=8 cm

The length of the shorter side is 8 cm.

What is rectangle?

A rectangle more generally than any quadrilateral whose axes of symmetry pass through each pair of opposite sides.This definition includes both right-angled rectangles and rectangles. Each has an axis of symmetry that is parallel and equidistant from a pair of opposite sides and a second that is a perpendicular bisector of those sides, but in the case of a crossed rectangle the first axis is not the axis of symmetry of either side. . that it divides.

Quadrilaterals that have two axes of symmetry, each passing through a pair of opposite sides, belong to the larger class of quadrilaterals that have at least one axis of symmetry through a pair of opposite sides. These quadrilaterals consist of isosceles trapezoids and crossed isosceles trapezoids (crossed quadrilaterals with the same arrangement of vertices as an isosceles trapezoid).

Given, sides of a rectangle are in ratio 2:5.

Let length of a rectangle be 5x cm and breadth of a rectangle be 2x cm.

We know length of a rectangle is longer than breadth.

So, length of the rectangle is 20 cm.

According to question,

[tex]5x = 20 \\ x = \frac{20}{5} \\ x = 4[/tex]

So, length of the rectangle (5×4) = 40 cm and breadth of the rectangle (2×4) = 8 cm.

Breath is shorter side of rectangle.

Therefore,The length of the shorter side is 8 cm.

Rectangle related one more question:

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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 4kg, the acceleration of the object is 15/ms2. If the same force acts upon another object whose mass is
10kg, what is this object's acceleration?

Answers

Answer:

[tex]a = 6m/s^2[/tex]

Step-by-step explanation:

Given

When mass = 4kg; Acceleration = 15m/s²

Required

Determine the acceleration when mass = 10kg, provided force is constant;

Represent mass with m and acceleration with a

The question says there's an inverse variation between acceleration and mass; This is represented as thus;

[tex]a\ \alpha\ \frac{1}{m}[/tex]

Convert variation to equality

[tex]a = \frac{F}{m}[/tex]; Where F is the constant of variation (Force)

Make F the subject of formula;

[tex]F = ma[/tex]

When mass = 4kg; Acceleration = 15m/s²

[tex]F = 4 * 15[/tex]

[tex]F = 60N[/tex]

When mass = 10kg; Substitute 60 for Force

[tex]F = ma[/tex]

[tex]60 = 10 * a[/tex]

[tex]60 = 10a[/tex]

Divide both sides by 10

[tex]\frac{60}{10} = \frac{10a}{10}[/tex]

[tex]a = 6m/s^2[/tex]

Hence, the acceleration is [tex]a = 6m/s^2[/tex]

An octagonal pyramid ... how many faces does it have, how many vertices and how many edges? A triangular prism ... how many faces does it have, how many vertices and how many edges? a triangular pyramid ... how many faces does it have, how many vertices and how many edges?

Answers

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

What is the slope of the line that passes through (2, 12) and (4, 20)?On the graph of the equation 3x + 2y = 18, what is the value of the y-intercept?

Answers

Answer: The slope of the line that passes through (2, 12) and (4, 20) is 4.

The value of the y-intercept is 9.

Step-by-step explanation:

Slope of line passing through (a,b) and (c,d) = [tex]\dfrac{d-b}{c-a}[/tex]

Then, the slope of the line that passes through (2, 12) and (4, 20) = [tex]\dfrac{20-12}{4-2}[/tex]

[tex]=\dfrac{8}{2}=4[/tex]

So, the slope of the line that passes through (2, 12) and (4, 20) is 4.

To find the y-intercept of 3x + 2y = 18, first write in slope intercept form y=mx+c ( where c= y-intercept ).

[tex]2y=-3x+18\\\\\Rightarrow\ y=-\dfrac{3}{2}x+9[/tex]

By comparison,  c= 9

Hence, the value of the y-intercept is 9.

a college entrance exam company determined that a score of 25 on the mathematics portion of the exam suggests that a student is ready for

Answers

Answer:

Student is ready for college level mathematics.

The null hypothesis will be H0 = 25

The alternative hypothesis is Ha > 25

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the z - score for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to  test a hypothesis.

Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.

Answers

Answer:

Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.

Step-by-step explanation:

Both functions have the same slope

The slope is m in the equation; y =mx+c which is the formula for a straight line.

m = change in Y/change in x

Using 2 points: (1,3/4) and ( 4,3) from the table;

= (3 - 3/4) / ( 4 - 1)

= 2.25/3

= 0.75 which is 3/4 which is the same as the slope of the function in the equation.

The origin is the y-intercept for the function expressed in the table.

Slope of function in table is known to be 0.75. Find c to complete equation.

3 = 0.75 ( 4) + c

3 = 3 + c

c = 0

c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.

The table and the graph express an equivalent function.

The function for the table as calculated is;

y = 0.75x + 0

y = 0.75x

This is the same as the function for the equation for the graph which is y = 3/4x.

Answer:Both functions have the same slope.

The origin is the y-intercept for the function expressed in the table.

The table and the graph express an equivalent function.

Step-by-step explanation:

Compare the linear functions expressed below by data in a table and by an equation.

A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.

Which of the following statements are true?  Select all that apply.

If the equation were graphed, it would be a horizontal line.

Both functions have the same slope.

The origin is the y-intercept for the function expressed in the table.

The linear equation does not have a y-intercept.

The table and the graph express an equivalent function.

(MG1) Convert 11,000 feet per second into
kilometers per hour.
A. 12070.08 kilometers per hour
B. 10000.00 kilometers per hour
C. 12000.08 kilometers per hour
D. 13000.08 kilometers per hour

Answers

Answer:

The answer is option A.

Step-by-step explanation:

To solve the question we use the following conversion

1 feet per second = 1.09728 kilometers per hour

Therefore 11 ,000 feet per second is

[tex]11000 \times 1.09728[/tex]

We have the final answer as

12070.08 kilometers per hour

Hope this helps you

Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major: Accounting 83 Management 68 Marketing 85 Economics 64 Total 300 Has there been any significant change in the number of students in each major between the last school year and this school year?

Answers

Answer:

There has been no significant change in the number of students in each major between the last school year and this school year.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: There has been no change in the number of students.

Hₐ: There has been a significant change in the number of students.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]

Here,

[tex]O_{i}[/tex] = Observed frequencies

[tex]E_{i}=N\times p_{i}[/tex] = Expected frequency.

The chi-square test statistic value is, 1.662.

The degrees of freedom is:

df = 4 - 1 = 4 - 1 = 3

Compute the p-value as follows:

[tex]p-value=P(\chi^{2}_{k-1} >1.662) =P(\chi^{2}_{3} >1.662) =0.645[/tex]

*Use a Chi-square table.

The  p-value is 0.645.

The p-value of the test is very large for all the commonly used significance level. The null hypothesis will not be rejected.

Thus, it can be concluded that the there has been no significant change in the number of students in each major between the last school year and this school year.

A particular salad contains 4 units of vitamin A, 5 units of vitamin B complex, and 2 mg of fat per serving. A nutritious soup contains 6 units of vitamin A, 2 units of vitamin B complex, and 3 mg of fat per serving. If a lunch consisting of these two foods is to have at least 10 units of vitamin A and at least 10 units of vitamin B complex, how many servings of each should be used to minimize the total number of milligrams of fat

Answers

Answer:

2 servings of salad and 1 serving of soup

Step-by-step explanation:

In the given scenario the aim is to minimise the fat content of the food combination.

Fat content of soup is 3mg while fat content of salad is 2 mg.

Using Soup as 0 and Salad as 2 will not give the required vitamin content

The logical step will be to keep servings of soup to the minimum.

Let's see some combinations of salad and soup. Keeping serving of soup to the minimum of 1

1. 1 serving of salad and one serving of soup will contain 10 mg of vitamin A, 7 mg of vitamin B complex, and 3 mg of fat.

This will not work because amount of vitamin B complex is not up to 10 mg

2. 2 servings of salad and 1 serving of soup. Will contain 14 mg of vitamin A, 12 mg of vitamin B, and 7 mg of fat

This is the best option as we have amount of vitamin A and vitamin B complex in adequate quantity.

Also fat is lowest in this combination because soup the food with highest fat content is at minimum amount of one serving

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