1. A random sample of 64 customers at a drive-through bank window is observed, and it is found that the teller spends an average of 2.8 minutes with each customer, with a standard deviation of 1.2 minutes. Is there sufficient evidence to conclude that the teller spends less than 3 minutes with each customer slader

Answer:

The plant is 2.5 inches above the ground!

Step-by-step explanation:

i just did it

Answer:

Could you please rephrase this?

Answer:

A. 19 years old

Step-by-step explanation:

A  person at the age of 19 is probably still in college . He/She is probably investing more time and finance in his/her education. A person at age 19 is still building his or her career . He/she is  likely to have limited working experience. He/she has more years ahead of him to invest his little income(that is if he has any) for a longer term plan like owning a house and building a business.  

In fact at age 19 a person is more concern in his/her career development and studies. Buying a house is most likely a long time goal for a person of 19 years old because he has so many year ahead of him to gather or create wealth for himself.

The other ages 59, 79 and 69 years are individuals who have probably amassed wealth . They probably have over 3 decades of working experience and this working years will reflect in their savings. people at this age have shorter time to work or are probably even retired.

Answer:

A. 19 years old

Step-by-step explanation:

19 years old because usually by the time someone between the ages of 59 and 79 should already own or be renting a house if they have set their financial goals correctly.

Answer:

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

And replacing we got:

[tex] V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3[/tex]

And the best option would be:

65.42 Inches cubed

Step-by-step explanation:

For this case we have the following info given:

[tex] h =2.5 in[/tex] represent the height of the cone

[tex] r = 5 in[/tex] represent the radius

And the volume of the cone is given by;

[tex] V =\frac{1}{3} \pi r^2 h[/tex]

And replacing we got:

[tex] V = \frac{1}{3} (3.14) (5in)^2 (2.5in) = 65.42 in^3[/tex]

And the best option would be:

65.42 Inches cubed

Answer:

32.71 Inches cubed

Step-by-step explanation:

Let's recall the volume of the cone to be = 1/3πr³h

So using the formula.

r= 5

h = 2.5

I = 3.14

Volume = 1/3 * 3.14 * 5³ * 2.5

Volume = 327.1 in³

Answer:

57.45% increase

Step-by-step explanation:

The formula for percent change is (new - old)/new x 100.

The new value is $282 and the old value is $120.

Plug that into the formula:

(282 - 120)/282 x 100

= 57.45%

I hope this helped!

Answer:

the answer is c.

Answer:

Let x represent the variety of tickets sold, and y represent the total amount of cash raised. Since each price tag is $2.50, the total amount of money raised is identical to $2.50 instances the wide variety of tickets. The equation would be y = 2.50x.

Step-by-step explanation:

The x variable represents the number of tickets sold.

The y variable represents the total amount of money raised from ticket sales.

The equation for the scenario is y = 2.50x.

Answer:

325 mph and 420 mph

Step-by-step explanation:

If the speed of the slower plane is x, then the speed of the faster plane is x + 95.

The distance traveled by the slower plane is 3x.

The distance traveled by the faster plane is 3(x + 95).

The total distance is 2235 miles.

3x + 3(x + 95) = 2235

3x + 3x + 285 = 2235

6x = 1950

x = 325

x + 95 = 420

The speed of the planes is 325 mph and 420 mph.

Answer:

[tex]S=\frac{C}{2}[/tex]

Step-by-step explanation:

From the graph B,

Let the equation of the line representing the relation between hours spent in studying 'S' and hours spent in class 'C' is,

S = mC + b

Where m = Slope of the line

b = y-intercept of the line

We choose two points (2, 1), and (4, 2) lying on the line.

Slope 'm' = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

m = [tex]\frac{2-1}{4-2}[/tex]

m = [tex]\frac{1}{2}[/tex]

y-intercept 'b' = 0

Equation of the line will be

S = [tex]\frac{1}{2}C[/tex]

Answer:

Option B. 36

Step-by-step explanation:

From the figure attached,

ΔLMN ~ ΔPON

Therefore, corresponding sides of these similar triangles will be in the same ratio.

[tex]\frac{LM}{OP}=\frac{MN}{ON}=\frac{LN}{PN}[/tex]

[tex]\frac{LM}{OP}=\frac{MN}{ON}[/tex]

[tex]\frac{42}{14}=\frac{x}{12}[/tex]

x = [tex]\frac{42\times 12}{14}[/tex]

x = 36

Therefore, measure of side MN = x = 36 units

Option B. will be answer.

Answer:

x=0 or x=3 or x= -3⅘

Step-by-step explanation:

Please see attached picture for full solution.

Another way to solve it is to factorise x out from the equation from the beginning. This would leave you with

x(5x² +4x -57x)=0

Then you can factorise the quadratic equation.

x(x -3)(5x +19)= 0

And solve it just like we did above.

x=0 or x-3=0 or 5x+19=0

x=3 or 5x= -19

x= -3⅘

In the picture, I used synthetic division but long division works too!

Answer:

scale

Step-by-step explanation:

scales are used to measure weight

The tool that Caroline can use to Measure the mass of a dictionary is; Pan Balance.

When discussing measurements, there are different tools and equipment's that can be used such as  Ruler, Pan balance, Stopwatch, Liter container.

Now, the tools above can be used for measuring different things but our question wants the one that would be used to measure the mass of a dictionary and the correct tool is a Pan Balance.

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Answer:

x=-0.4

Step-by-step explanation:

We have the equation:

[tex]-9x+0.4=4[/tex]

First, the operation to move all the constants to the right side is subtraction since we would have to subtract 0.4 from each side, let's see this:

[tex]-9x+0.4=4\\-9x+0.4-0.4=4-0.4\\-9x=3.6[/tex]

Now, we have all the constants on the right side of the equation.

Now, the operation we need to perform to isolate the variable is division (since the x has a -9 that is being multiplied by x) we need to do the opposite operation:

[tex]-9x=3.6\\\frac{-9x}{-9} =\frac{3.6}{-9} \\x=-0.4[/tex]

Thus, the answer to this equation is x= -0.4

Answer:

a)

Subtract 0.4 from both side.

-9x +0.4 = 4

-9x + 0.4 - 0.4 = 4 - 0.4

-9x = 3.6

b)

divide by -9 both side

-9x/-9 = 3.6/-9

x = -0.4

Step-by-step explanation:

-9x+0.4=4

    -0.4  -0.4

_______________

-9x=3.6

__    __

-9     -9

________________

x=-0.4

AM really good !

Step-by-step explanation:

Answer:

0.3950

Step-by-step explanation:

Any team team will win the championship with probability 63% that is

P(W)=0.63

when teams win the championship, they win the first game of the series 72% of the time that is

P(F|W)=0.72

When they lose the championship, they win the first game 27% of the time.

P(F|W')=0.27

The probability that they will win the World Series when the first game is over and your team has lost that is

P(W|F')

Now, By Bayes theorem

[tex]\begin{array}{l}

P\left(W | F^{\prime}\right)=\frac{P\left(F^{\prime} | W\right) P(W)}{P\left(F^{\prime} | W\right) P(W)+P\left(F^{\prime} | W^{\prime}\right) P\left(W^{\prime}\right)} \\

\quad=\frac{[1-P(F | W)] P(W)}{[1-P(F | W)] P(W)+\left[1-P\left(F | W^{\prime}\right)\right][1-P(W)]} \\

\quad=\frac{[1-0.72] \times 0.63}{[1-0.72] \times 0.63+[1-0.27][1-0.63]} \\

\quad=\frac{0.28\times 0.63}{0.28\times 0.63+0.73 \times 0.37} \\

=0.3950\end{array}[/tex]

Answer:

  c, d.  see attached

  e. about 2.96 miles; about $1.63 million

Step-by-step explanation:

e. The x-coordinates of points A and B are 1/3 and 2/3 of the x-coordinate of "Downtown", respectively. The y-coordinates of A and B are 2/3 and 1/3 of the y-coordinate of "Town pool", respectively. Then the distances from A and B to the Mall can be found using the Pythagorean theorem:

  A to Mall = √(4² +(10/3)²) = √(244/9) ≈ 5.20683 . . . miles

  B to Mall = √(8² +(5/3)²) = √(601/9) ≈ 8.17177 . . . miles

The difference in distance is ...

  (BM -AM) = 8.17177 -5.20683 = 2.96493 . . . miles

The mall is about 2.96 miles farther from point B than from point A.

The additional cost is the difference in miles multiplied by the cost per mile:

  (2.96 mi)($0.550 M/mi) = $1.63 M

The additional cost of the longer road is about $1.63 million.

Answer:

h(n+1) = -⅓ h(n), h(0) = 63

Step-by-step explanation:

h(n) = 63 (-⅓)ⁿ

This is a geometric series where the first term is 63 and the common ratio is -⅓.

Therefore, each term is -⅓ of the previous term.

h(n+1) = -⅓ h(n), h(0) = 63.

Answer:

Measure of the acute angle = 84°

Step-by-step explanation:

In the figure attached,

ABDE is a swimming pool having length 'AB' = 65 feet

Depth of one end of the pool is BE = 4 feet

And depth of the other end AD = 11 feet

Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.

Now from ΔCDE,

tanx = [tex]\frac{EC}{DC}[/tex]

tanx = [tex]\frac{7}{65}[/tex]

x = [tex]\text{tan}^{-1}(\frac{7}{65})[/tex]

x = 6.15°

Now measure of acute angle the bottom of the pool makes with wall at he deep end,

m∠ADE = (90 - 6.15)°

             = 83.85°

             ≈ 84°

Answer:

A,B,D,F

Step-by-step explanation:

The angle measures that are true are:

m∠1 = 60

m∠13 = 80

m∠5 = 60

m∠14 = 100

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

m∠3 = 120

m∠12 = 80

Now,

1)

m∠1 = 60 (true)

m∠1 + m∠3 = 180

So,

m∠1 = 180 - 120 = 60

2)

m∠13 = 80 (true)

m∠12 and m∠13 are alternate angles.

So,

m∠13 = 80

3)

m∠6 = 80 ( false)

m∠6 and m∠3 are alternate angles.

So,

m∠6 = 120

4)

m∠5 = 60 (true)

m∠5 + m∠3 = 180

m∠5 = 180 - 120 = 60

5)

m∠10= 120 (false)

m∠10 + m∠12 = 180

m∠10 = 180 - 80 = 100

6)

m∠14 = 100 (true)

m∠14 + m∠12  = 180

m∠12 = 180 - 80 = 100

Thus,

The angle measures that are true are:

m∠1 = 60

m∠13 = 80

m∠5 = 60

m∠14 = 100

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Answer: See below

The line goes through -4 on the x-axis (horizontal line) and 0 on the y-axis. Therefore the x-intercept is (-4, 0)

The line goes through -8 on the y-axis (vertical line) and 0 on the x-axis. Therefore the y-intercept is (0, -8)

Answer:

D

Step-by-step explanation:

The equations are similar and so if we compute the vertex we would see they are the same..

Let's try computing the maximum or minimum point of y= -3(x+2)^2 - 4 and y= 3(x+2)^2 - 4 ;

For y= 3(x+2)^2 - 4 ;

to compute the maximum or minimum point we find dy/dx of the expression equating it to 0; the value of x is determined and we substitute to the original expression for y.

If y is -ve we know it's a minimum graph and if y is +be it's a maximum graph.

From the foregoing;

For y= 3(x+2)^2 - 4 ;

dy/dx = 2× 3 ( x+2) ×1 = 6(x+2) = 6x + 12= 0

6x= -12=>x= -12/6= -2;

We substitute x= -2 in y =3(x+2)^2 - 4; y = 3(-2+2)^2-4 = -4

Since y = -4 is a hence y= 3(x+2)^2 - 4 is a minimum graph.

For y= -3(x+2)^2 - 4 ;

dy/dx = 2× -3 ( x+2) ×1 = -6(x+2) = -6x - 12= 0

-6x= 12=>x= -12/6= -2;

Substituting in the y= -3(x+2)^2 - 4 ;

We have;

We substitute x= -2 in y =-3(x+2)^2 - 4; y = -3(-2+2)^2-4 = -4

y= -4 ;

Since both graphs look like they are minimum that is the vertex is y= -4;

Let's explore a further step

The derivative of the previous derivative;

For y= 3(x+2)^2 - 4;

We means d/dy × [dx/dy] = d/dy [ 6x + 12 ] = 6

Hence y= 3(x+2)^2 - 4 is a maximum graph;

Similarly for y= -3(x+2)^2 - 4 ;

d/dy × [dx/dy]

d/dy [-6x-12 ] = -6

Hence y= -3(x+2)^2 - 4 is a minimum graph;

Conclusion: y= 3(x+2)^2 - 4 is a maximum graph and y= -3(x+2)^2 - 4 is a minimum graph;

Answer: rotated 90 degrees counterclockwise and shifted 2 units up.

Step-by-step explanation:

Answer:

[tex]\boxed{\sf \ C \ is \ the \ correct \ answer \ ! \ }[/tex]

Step-by-step explanation:

fog(x)=f(g(x))

so it comes

[tex]f(g(x))=f(x+1)=4(x+1)^2[/tex]

so C is the correct answer

Answer:

Option B

Step-by-step explanation:

[tex]f(x) = 4x^2\\g(x) = x+1[/tex]

Multiplying both will give us:

[tex](fg)(x) = 4x^2(x+1)[/tex]

=> [tex](fg)(x) = 4x^3+4x^2[/tex]

Answer:

About 25.1 cubic meters

Step-by-step explanation:

The diameter of a circle is twice the radius, meaning that the radius of the base of this cone is 4/2=2 meters. The formula for the volume of a cone is:

[tex]V=\dfrac{1}{3} \pi r^2 h=\\\\\dfrac{1}{3} \cdot \pi \cdot 2^2 \cdot 6\approx 25.1[/tex]

Hope this helps!

Answer:

About 75 in²; Aubrey found the surface area of the cone and included the base.

Complete question:

Aubrey is making cone-shaped hats for a birthday party. She mistakenly thinks that she will need about 104 square inches of paper for each hat.Cone with diameter six inches and slant height eight inches.What is the correct amount of paper Aubrey will need per hat? Explain Aubrey’s mistake. Use 3.14 for π and round to the nearest inch.

Step-by-step explanation:

Lateral surface area of a cone = Paper required to for each hat

Lateral surface area = πrl

where, r is radius of the cone and l is lateral height of the cone

Lateral surface area = π(3)(8)

                                = 75.36 square inches

                                ≈ 75 square inches

Therefore, total paper required for each cap is about 75 square inches.

Total surface area of the cone (Lateral area + Area of the base)

                                 = πr(r + l)

                                 = 3.14(3)(3 + 8)

                                 = 103.62

                                 ≈ 104 square inches.

Aubrey did a mistake by finding the total surface area (including base area) of the cone instead of lateral surface area.

Answer:

~75 in

Step-by-step explanation:

Answer:

Step-by-step explanation:

2, 4, 12, 12, 17, 18, 28, 29, 33

(17+18)/2

35/2= 17.5 is the median

The median is 17 for the data. 12,33,18,28,29,12,17,4,2 which is a mid value of the data.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

We have data:

12, 33, 18, 28, 29, 12, 17, 4, 2

After arranging in accending orde:

2, 4, 12, 12, 17, 18, 28, 29, 33

As we can see the mid-value is 17

Median = 17

Thus, the median is 17 for the data. 12,33,18,28,29,12,17,4,2 which is a mid value of the data.

Learn more about the median here:

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Answer:

-19

Step-by-step explanation:

2*(-2)+3(-5)=-4+(-15)= -19

Answer:

68.11% probability that the firm involved is firm B

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Cost overrun

Event B: Agency B used.

A certain federal agency employs three consulting firms (A, B and C) with probabilities 0.40, 0.45 and 0.15.

This means that [tex]P(B) = 0.45[/tex]

From past experiences, it is known that the probability of cost overruns for the firms are 0.01, 0.14, and 0.17, respectively.

This means that [tex]P(A|B) = 0.14[/tex]

Probability of cost overrun.

Firm A is used 40% of the time, with 1% of these having cost overrun. B is used 45%, with 14% of these having cost overruns. C is used 15% of the time, with 17% of these having cost overruns.

So

[tex]P(A) = 0.4*0.01 + 0.45*0.14 + 0.15*0.17 = 0.0925[/tex]

What is the probability that the firm involved is firm B

[tex]P(B|A) = \frac{0.45*0.14}{0.0925} = 0.6811[/tex]

68.11% probability that the firm involved is firm B

Answer:

102

Step-by-step explanation:

We have the mean (m) 128.5 and the standard deviation (sd) 8.2, we must calculate the value of z for each one and determine whether or not it is an outlier:

z = (x - m) / sd

In the first case x = 148:

z = (148 - 128.5) /8.2

z = 2.37

In the second case x = 102:

z = (102 - 128.5) /8.2

z = -3.23

In the first case x = 152:

z = (152 - 128.5) /8.2

z = 2.86

The value of this is usually between -3 and 3, therefore when x is 102 it goes outside the range of the value of z, which means that this is the outlier.

Answer:

4x+8 or 4 (x) + 4 (2)

Step-by-step explanation:

Hope it helps.

Answer:

B

Step-by-step explanation:

4(x+2).

By expanding the expression we have;

4(x+2) = 4× x + 4× 2 = 4(x) + 4(2)

Answer: 4

Step-by-step explanation:

Given

[tex]F(x)=2x+4[/tex]

[tex]R(x)=x[/tex]

We need to find [tex]R(F(x))[/tex] at [tex]x=0[/tex]

[tex]R(F(x))=[2x+4][/tex]

[tex]R(F(x))=2x+4[/tex]

[tex]R(F(0))=2\times 1+4=4[/tex]

[tex]R(F(0))=4[/tex]

Answer:

x = 3

Step-by-step explanation:

-3 + 4x = 9 .... add the 3 over

4x = 12 .... divide by 4

x = 3

Answer:

Step-by-step explanation:

The following statement is either true (in all cases) or false (for at least one example). if false, construct a specific example to show that the statement is not always true. such an example is called a counterexample to the statement. if the statement is true, give a justification. if v_1, v_2, v_3 are in ropf^3 and v_3 is not a linear combination of v_1, v_2, then {v_1, v_2, v_3} is linearly independent. fill in the blanks below. the statement is take v_1 and v_2 to be multiples of one vector and take v_3 to be not a multiple of that vector. for example, v_1 = [1 1 1], v_2 = [2 2 2], v_3 = [1 0 0] since at least one of the vectors is a linear combination of the other two, the three vectors are linearly