Suppose that 2 ≤ f ' ( x ) ≤ 3 for all values of x . What are the minimum and maximum possible values of f ( 7 ) − f ( 2 ) ? ≤ f ( 7 ) − f ( 2 ) ≤

Answer:

A

Step-by-step explanation:

For point-slope form, you need a point and the slope.

y - y₁ = m(x - x₁)

Looking at the graph, the points you have are (4, 0) and (-4, -4).  You can use these points to find the slope.  Divide the difference of the y's by the difference of the x's/

-4 - 0 = -4

-4 - 4 = -8

-4/-8 = 1/2

The slope is 1/2.  This cancels out choices C and D.

With the point (-4, -4), A is the answer.

the equation of the line in slope-intercept form is:

y = (1/2)x - 2

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.

From the graph, two points on the line are (-4, -4) and (4,0),

The formula for the slope of a line is:

m = (y₂ - y₁) / (x₁ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the given points (-4, -4) and (4, 0), we can calculate the slope:

m = (0 - (-4)) / (4 - (-4))

m = 4 / 8

m = 1/2

Now that we know the slope, we can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):

y = mx + b

-4 = (1/2)(-4) + b

-4 = -2 + b

b = -2

Therefore, the slope-intercept form of the line is y = (1/2)x - 2.

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Answer:

The principal amount is $10160

Step-by-step explanation:

Given; Simple interest, I = 7620

Rate, R = 6.25

Time, T = 12

Principal, P =?

The formula for simple interest, I is;

[tex]I = \frac{PRT}{100}[/tex]

Making P the subject of formula;

[tex]P = \frac{I100}{RT}[/tex]

[tex]P = \frac{7620 *100}{6.25*12}[/tex]

[tex]P = \frac{762000}{75}\\P = 10160[/tex]

Therefore, the principal amount is $10160

Answer:

10000

Step-by-step explanation:

If an amount of money, P, called the principal, is invested for a period of t years at an annual interest rate r, the amount of simple interest, I, earned is given by

I=PrtwhereIPrt=interest=principal=rate=time

The following information is given.

Irt=$7,620=0.0635=12 years

Substituting the given information into the simple interest formula and solving for P gives

7,6207,620=(P)(0.0635)(12)=0.762P

Dividing both sides by 0.762, we have

P=7,6200.762=10,000

Thus, the principal amount of the bond was $10,000.

Answer:

c. there might not be any causal relationship between x and y.

Step-by-step explanation:

A correlation can be defined as a numerical measure of the relationship between existing between two variables (x and y).

In Mathematics and Statistics, a group of data can either be negatively correlated, positively correlated or not correlated at all.

1. For a negative correlation: a set of values in a data increases, when the other set begins to decrease. Here, the correlation coefficient is less than zero (0).

2. For a positive correlation: a set of values in a data increases, when the other set also increases. Here, the correlation coefficient is greater than zero (0).

3. For no or zero correlation: a set of values in a data has no effect on the other set. Here, the correlation coefficient is equal to zero (0).

If two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

A causal relation exists between two variables (x and y), if the occurrence of the first causes the other; where, the first variable (x) is referred to as the cause while the second variable (y) is the effect.

A strong linear relationship exists between two variables (x and y), if they both increases or decreases at the same time. It usually has a correlation coefficient greater than zero or a slope of 1.

Hence, if two variables, x and y, have a very strong linear relationship, then there might not be any causal relationship between x and y.

Answer:

4

Step-by-step explanation:

25% of 25

0.25 × 25 = 6.25

15% of 15​

0.15 × 15 = 2.25

Find the difference.

6.25 - 2.25

= 4

Answer:

5 4/5

Step-by-step explanation:

29 ÷ 5 = 5

29 - 25 = 4

Since 5x5 is 25 and we have 4 as a remainder we put it over the original denominator 5.

I really hope this helps.

29/5 as a mixed number is 5 and 4/5.

To convert the indecorous bit29/5 into a mixed number.

First, divide the numerator( 29) by the denominator( 5) and express the result as a whole number and a bit.

Now, 29 divided by 5 equals 5 with a remainder of 4.

The quotient( 5) becomes the whole number part of the mixed number, and the remainder( 4) becomes the numerator of the bit part, while the denominator remains the same.

Thus, 29/5 as a mixed number is 5 and 4/5.

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Answer: a) P(1&2 =defect)= 1/800

b)  P(1&2 =defect)= 1/780

Step-by-step explanation:

a) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

So if we replace it by the not defective the number of defective fuses is 1 and total number is 40.

So the probability that 2-nd selected fuse is defective as well is 1/40

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/40=2/1600=1/800

b) The probability that 1st of the selected fuses is defective is   2/40=1/20 =0.05

SO residual amount of the fuses is 39. 1 of them is defective.

So the probability that 2-nd selected fuse is defective as well is 1/39

The probability both fuses are defective is

P(1&2 =defect)= 2/40*1/39=2/1560=1/780

Answer:

2

Step-by-step explanation:

Answer:

I hope it will help you....

Answer:

Yes.

Step-by-step explanation:

In the future, simply plug both equations into Desmos.

Answer: 136

Step-by-step explanation:

An= A1+(n-1)d

A1=16, d=8, and n=16

A16= 16 +(16-1)(8)

A16= 16(15)(8)

A16= 16+120

A16=136

Hey there! :)

Answer:

f(16) = 136 seats.

Step-by-step explanation:

This situation can be expressed as an explicit function where 'n' is the row number.

The question also states that the number of seats increases by 8. Use this in the equation:

f(n) = 16 + 8(n-1)

Solve for the number of seats in the 16th row by plugging in 16 for n:

f(16) = 16 + 8(16-1)

f(16) = 16 + 8(15)

f(16) = 16 + 120

f(16) = 136 seats.

Answer:

D. A=(9)(4)

Step-by-step explanation:

area= length x width = 9x4

=============================================================

How I got that answer:

We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.

Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.

----------

You could use the slope formula to get the job done. This is because the slope represents the rise over run

slope = rise/run

The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...

In a more written out way, the steps would be

slope = rise/run

slope = (y2-y1)/(x2-x1)

slope = (793 - 54)/(2004 - 1995)

slope = 739/9

slope = 82.111....

Answer:

The transformation is rigid because the corresponding side lengths and angles are congruent.

Step-by-step explanation:

Since we have congruent triangles (not similar triangles), they will have to have the same length and angles throughout your transformation. Therefore, our answer is the 1st Option.

Answer:

B) The transformation is rigid because the corresponding side lengths and angles are congruent.

Step-by-step explanation:

Answer:

Hope this helps you

Answer:

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

Step-by-step explanation:

Given A=  [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B

Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.

so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]

Now multiply and add the separate elements of the matrix A*B=

[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]

A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]

b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.

c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785

Total cost of benefits for all employees at the food truck= 121 + 14= 135

Answer:

Step-by-step explanation:

A=2(3.14)rh+2(3.14)r^2

A=2(3.14)(4.5)(19)+2(3.14)(4.5)^2

A=536.94+127.17

A=664.11

Might want to double the math but the formula is right!

Answer:

13

Step-by-step explanation:

p^2 -6p +6

Let p=-1

(-1)^2 -6(-1) +6

1 +6+6

13

Answer:

The width = 38 yard

Step-by-step explanation:

Given

Dimension of Park = 32 by 24 yard

Area = 1748 yd²

Required

Find the width of the park

Given that the park is surrounded by a trail;

Let the distance between the park and the trail be represented with y;

Such that, the dimension of the park becomes (32 + y + y) by (24 + y + y) because it is surrounded on all sides

Area of rectangle is calculated as thus;

Area = Length * Width

Substitute 1748 for area; 32 + 2y and 24 + 2y for length and width

The formula becomes

[tex]1748 = (32 + 2y) * (24 +2y)[/tex]

Open Bracket

[tex]1748 = 32(24 + 2y) + 2y(24 + 2y)[/tex]

[tex]1748 = 768 + 64y + 48y + 4y^2[/tex]

[tex]1748 = 768 + 112y + 4y^2[/tex]

Subtract 1748 from both sides

[tex]1748 -1748 = 768 -1748 + 112y + 4y^2[/tex]

[tex]0 = 768 -1748 + 112y + 4y^2[/tex]

[tex]0 = -980 + 112y + 4y^2[/tex]

Rearrange

[tex]4y^2 + 112y -980 = 0[/tex]

Divide through by 4

[tex]y^2 + 28y - 245 = 0[/tex]

Expand

[tex]y^2 + 35y -7y - 245 = 0[/tex]

Factorize

[tex]y(y+35) - 7(y + 35) = 0[/tex]

[tex](y-7)(y+35) = 0[/tex]

Split the above into two

[tex]y - 7 = 0\ or\ y + 35 = 0[/tex]

[tex]y = 7\ or\ y = -35[/tex]

But y can't be less than 0;

[tex]So,\ y = 7[/tex]

Recall that the dimension of the park is 32 + 2y by 24 + 2y

So, the dimension becomes 32 + 2*7 by 24 + 2*7

Dimension = 32 + 14 yard by 24 + 14 yard

Dimension = 46 yard by 38 yard

Hence, the width = 38 yard

Answer:

Option B - There is at least some difference in the average times spent by the two groups in the mall.

Step-by-step explanation:

A null hypothesis is a hypothesis that states that there is no statistical significance between the two variables. Thus, It is usually the hypothesis that a researcher or experimenter will try to disprove or discredit. While an alternative hypothesis is one that states there is a statistically significant relationship between two variables.

Now, applying these definitions to the question, we can see that;

Null Hypothesis is;

H0; There is no difference in the average times spent by the two groups in the mall

While the alternative hypothesis is;

Ha; There is at least some difference in the average times spent by the two groups in the mall

Thus, correct answer is option B

Answer:

It is option b

Step-by-step explanation:

Answer:

x = 4.5 ft

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{18}{x}[/tex] = [tex]\frac{8}{2}[/tex] ( cross- multiply )

8x = 36 ( divide both sides by 8 )

x = 4.5

Answer:

The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=0.15[/tex]

The standard deviation of this sampling distribution of sample proportion is:

 [tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.

Compute the mean and standard deviation as follows:

[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]

So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]

In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.

Then,

                                  P (µ-σ < X < µ+σ) ≈ 0.68

                                  P (µ-2σ <X < µ+2σ) ≈ 0.95

                                  P (µ-3σ <X < µ+3σ) ≈ 0.997

Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.

That is:

[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]

Answer:

  33 units²

Step-by-step explanation:

A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...

  A = (1/2)(8 + 8.5)(4) = 33

__

If you do the integration, it gets a bit messy.

  [tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]

The appropriate answer choice is 33 square units.

Answer:

Step-by-step explanation:

3x2−5x−2=0

For this equation: a=3, b=-5, c=-2

3x2+−5x+−2=0

Step 1: Use quadratic formula with a=3, b=-5, c=-2.

x= (−b±√b2−4ac )2a

x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)

x= (5±√49 )/6

x=2 or x= −1 /3

Answer:

x=2 or x= −1/ 3

The solutions to the equation are x = -1/3 and x = 2.

Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:

First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Next, we set each factor equal to 0 and solve for x.

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

3x + 1 = 0

3x = -1

x = -1/3

x - 2 = 0

x = 2

Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.

Here is the explanation for each of the steps:

Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).

Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.

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Answer:

The product of 5/ 12 and –420 should have been the value of x.

Answer: D

Step-by-step explanation:

Took the test

Answer:

Step-by-step explanation:

[tex]\frac{14}{x} =14/x[/tex]

Thus, we can multiply both sides by x to get 14=0.  Because 14 does not equal 0, the equation has no solutions.  A value of x that makes the equation false is 541, which makes the simplified equation turn into 14=0.

Another value of x that makes the equation false is 7, which makes the simplified equation turn into 14=0.

Hope it helps <3

Answer:

1. V = 15.95 (to 2 decimal places)

2. V = 107.23 (to 2 decimal places)

3. V = 560.25 (to 2 decimal places)

Step-by-step explanation:

1. y = ln 5x, y = 2, y = 3, x = 0; about the y-axis

Find volume using the disk method.

First find inverse of y=ln(5x)

5x = exp(y)

x(y)=exp(y)/5

Width of each strip = dy

length of each strip = x(y)

volume of each disk by rotation of strip about y=axis

dV = 2*pi*x(y)dy

total volume  

V = integral (dV) for y=2 to 3

= integral (2*pi*e^y/5) for y=2 to 3

= 2*pi*(e^y/5) for y=2 to 3

= 2pi(e^3-e^2)/5

= 15.95 (to 2 decimal places)

2. y2 = 2x, x = 2y; about the y-axis

Find point of intersection between  

solve y^2/2 = 2y  =>  y=4, x=2y=8, therefore

intersection is at (8,4), which is the upper integration limit

Using the disk method again

Volume of each disk

dV(y) = pi((2y)^2-(y^2/2)^2)dy

Total volume of solid  

V = integral(pi((2y)^2-(y^2/2)^2)dy) for y=0 to 4

= pi (4y^3/3 - y^5/20)  for y = 0,4

= pi (256/3 - 1024/20)

= 512pi/15

= 107.23 (to 2 decimal places)

3. y = x, y = 0, x = 2, x = 7; about x = 1

Use the shell method.

volume of each shell formed by roatation of a vertical strip about the axis of rotation (x=1)

dV = 2*pi*(x-1)*(y*dx)

Total volume of rotation

V = integral(2*pi*(x-1)*y dx for x=2 to 7

= 535pi/3

= 560.25 (to 2 decimal places)

Answer:

A and B are independent because P(A) * P(B) = P(A and B).

Step-by-step explanation:

If A and B are independent, then P(A) * P(B) = P(A and B)

since

P(A)*P(B) = (2/3*1/4) = 2/12 = 1 / 6 = P(A and B)

A and B are independent.

Answer:

YES THANKS FOR 30

Step-by-step explanation:

Answer:

It's written as

[tex]6.83 \times {10}^{ - 2} [/tex]

Hope this helps you

Answer:

6.83 × 10 -2

hopefully this helped :3

Answer:

y - 2 = (3/2)(x + 1)

Step-by-step explanation:

Start with the point-slope formula y - k = m(x - h).  With m = 3/2, h = -1 and k = 2, we get:

y - 2 = (3/2)(x + 1)