The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.5 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)

Answer:

x<3

Step-by-step explanation:

Answer:

[tex]\boxed{x\leq 3}[/tex]

Step-by-step explanation:

[tex]4x \leq 12[/tex]

[tex]\sf Divide \ both \ parts \ by \ 4.[/tex]

[tex]\displaystyle \frac{4x}{4} \leq \frac{12}{4}[/tex]

[tex]x\leq 3[/tex]

Answer:

3¾

Step-by-step explanation:

Geometric sequence also known as geometric progression, can be said to be a sequence with a constant ratio between the terms.

Formula for geometric sequence:

[tex] a^n = a ( n-1 ) * r [/tex]

Given:

First term, a1 = 30

ratio, r = ½

Required:

Find the fourth term

Where, the first term, a¹ = 30

Second term: a² = 30 * ½ = 15

Third term: a³ = 15 * ½ = 7.5

Fourth term: a⁴ = 7.5 * ½ = 3.75 = 3¾

Therfore the fourth term of the geometric sequence is 3¾

Answer:

a) 12 ft/s  (12 feet per second is the rate at which she runs)

b) the tables is completed as follows:

for column 1: 12

for column 2: 24

for column 3: 36

for column 4: 48

Step-by-step explanation:

Notice that since she did 60 feet in 5 seconds, then her speed (which is defined as distance divided by the time it took to cover that distance) is: 60/5 feet/second = 12 ft/s

Now this means that for every second she runs, she covers 12 feet

Then in the first second running she covered 12 ft, after 2 seconds running, she covered 24 ft, after 3 seconds running, she covered 36 ft, after 4 seconds running, she covered 48 ft. And these values complete the requested table.

Answer:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Step-by-step explanation:

First thing to understand is that we will be producing a sine or cosine function to solve this one. I'll use a cosine function for the sake of the problem, since it's most easily represented by a cosine wave flipped over. If you're interested in seeing a visualization of how a circle's height converts to one of these waves, you may find the Better Explained article Intuitive Understanding of Sine Waves helpful.

Now let's get started on the problem. Cosine functions generally take the form

[tex]y=a\cos(b(x-c))+d[/tex]

Where:

[tex]|a|[/tex] is the amplitude

[tex]\frac{2\pi}{b}[/tex] is the period, or the time it takes to go one full rotation around the circle (ferris wheel)

[tex]c[/tex] is the horizontal displacement

[tex]d[/tex] is the vertical shift

Step one, find the period of the function. To do this, we know that it takes six minutes to do three revolutions on the ferris wheel, so it takes 2 minutes to do one full revolution. Now, let's find [tex]b[/tex] to put into our function:

[tex]\frac{2\pi}{b}=2[/tex]

[tex]2\pi=2b[/tex]

[tex]\pi=b[/tex]

I skipped some of the basic algebra to shorten the solution, but we have found our b. Next, we'll get the amplitude of the wave by using the maximum and minimum height of the wheel. Remember, it's 4 meters at its lowest point, meaning its highest point is 54 meters in the air rather than 50. Using the formula for amplitude:

[tex]\frac{\max-\min}{2}[/tex]

[tex]\frac{54-4}{2}[/tex]

[tex]\frac{50}{2}=25=a[/tex]

Our vertical transformation is given by [tex]\min+a[/tex] or [tex]\max-a[/tex], which is the height of the center of the ferris wheel, [tex]4+25=29=d[/tex]

Because cosine starts at the minimum, [tex]c=0[/tex].

The last thing to point out is that a cosine wave starts at its maximum. For that reason, we need to flip the entire function by making the amplitude negative in our final equation. Therefore our equation ends up being:

[tex]h(t)=-25\cos(\pi t)+29[/tex]

Answer:

The answers for:

Step-by-step explanation:

In order to find the value of expression, you have to apply gradient formula :

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

So for Question 1,

[tex]let \: (3,2) \: be \: (x1,y1) \\ let \: (4,j) \: be \: (x2,y2) \\ let \: m = 1[/tex]

[tex] \frac{j - 2}{4 - 3} = 1[/tex]

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

[tex]j - 2 = 1[/tex]

[tex]j = 1 + 2 = 3[/tex]

Question 2,

[tex]let \: (5,0) \: be \: (x1,y1) \\ let \: (1,k) \: be \: (x2,y2) \\ let \: m = \frac{1}{2} [/tex]

[tex] \frac{k - 0}{1 - 5} = \frac{1}{2} [/tex]

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

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

Question 3,

[tex]let \: (x,2) \: be \: (x1,y1) \\ let \: (3, - 4) \: be \: (x2,y2) \\ let \: m = 2[/tex]

[tex] \frac{ - 4 - 2}{3 - x} = 2[/tex]

[tex] \frac{ - 6}{3 - x } = 2[/tex]

[tex] - 6 = 2(3 - x)[/tex]

[tex] - 6 = 6 - 2x[/tex]

[tex] - 6 - 6 = - 2x[/tex]

[tex] - 2x = - 12[/tex]

[tex]x = - 12 \div - 2 = 6[/tex]

Question 4,

[tex]let \: (12, - 4) \: be \: (x1,y1) \\ let \: (r,2) \: be \: (x2,y2) \\ let \: m = - \frac{1}{2} [/tex]

[tex] \frac{2 - ( - 4)}{r - 12} = - \frac{1}{2} [/tex]

[tex] \frac{6}{r - 12} = - \frac{1}{2} [/tex]

[tex] - 1(r - 12) = 2(6)[/tex]

[tex] - r + 12 = 12[/tex]

[tex]r = (12 - 12) \div - 1 = 0[/tex]

Complete Question

If w'(t) is the rate of growth of a child in pounds per year, what does

[tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  represent?

a) The change in the child's weight (in pounds) between the ages of 4 and 7.

b) The change in the child's age (in years) between the ages of 4 and 7.

c) The child's weight at age 7.

d) The child's weight at age 4. The child's initial weight at birth.

Answer:

The correct option is  option a

Step-by-step explanation:

From the question we are told that

       [tex]w'(t)[/tex] represents the rate of growth of a child in   [tex]\frac{pounds}{year}[/tex]

So      [tex]{w'(t)} \, dt[/tex]  will be in  [tex]pounds[/tex]

Which then mean that this  [tex]\int\limits^{7}_{4} {w'(t)} \, dt[/tex]  the change in the weight of the child between the ages of  [tex]4 \to 7[/tex] years

Answer:

4 : 5

Step-by-step explanation:

you can divide 120 and 150 by 30 and 8 and 10 by 2.

120/30 = 4

150/30 = 5

8/2 = 4

10/2=5

Answer: 4:5

Step-by-step explanation:

Answer:

Step-by-step explanation:

cot (x)=2/3

we know csc^2(x)-cot^2(x)=1

csc^2(x)=1+cot^2(x)=1+4/9=13/9

csc (x)=±√13/3

Answer:

[tex]h'(1) = 23[/tex]

Step-by-step explanation:

Let be [tex]h(x) = (x^{2}+8)\cdot g(x)[/tex], where [tex]r(x) = x^{2} + 8[/tex]. If both [tex]r(x)[/tex] and [tex]g(x)[/tex] are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:

[tex]h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)[/tex]

[tex]r'(x) = 2\cdot x[/tex]

[tex]h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)[/tex]

Given that [tex]x = 1[/tex], [tex]g (1) = -2[/tex] and [tex]g'(1) = 3[/tex], the derivative of [tex]h(x)[/tex] evaluated in [tex]x = 1[/tex] is:

[tex]h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)[/tex]

[tex]h'(1) = 23[/tex]

Answer:

Graph A

So it has two distinct real roots.

Graph B

It has one repeated real root

Graph C

So it has two complex roots.

Graph D

One real root and one complex root

Step-by-step explanation:

For graph A

The value of the roots is x= 1 and x= 3

And the minimum value = -3

It's a positive graph

So it has two distinct real roots.

For graph B

The value of the roots is x = 2 and x= 2

That is x= 2 twice

Has a maximum value of 0

It's an inverse graph

It has one repeated real root

For graph C

It's a positive graph but on the negative of x

Has a minimum value of 1

It didn't touch x at y = 0

And it's root will be negative

So it has two complex roots.

For Graph D

Value of the roots is x= 2 and x= -2

It's a positive graph

Minimum value of -4

One real root and one complex root

Answer:

1). (0, 1)

2). (1, a)

3). Above

Step-by-step explanation:

This question is not complete; here is the complete question.

The graph of an exponential function of the form y = f(x) = [tex]a^{x}[/tex] passes through the points 1).               and 2).              . The graph lies 3).             x-axis.

1). (0.a), (0,1), (0,2), (0,-1)

2). (1,0), (1,1), (1,a), (1,-2)

3). (above), (below), (on the)

Given exponential function is f(x) = [tex]a^{x}[/tex]

1). For x = 0,

  f(0) = [tex]a^{0}[/tex] = 1

  Therefore, the given exponential function passes through a point (0, 1).

2). For x = 1,

  f(1) = [tex]a^{1}[/tex]

  f(1) = a

  Therefore, graph of the exponential function passes through (1, a)

3).For y = 0

  0 = [tex]a^{x}[/tex]

  But for any value of 'x', f(x) will never be zero. Therefore, there is no x-intercept.

  The graph lies above the x-axis.

Answer:

No Factors

Step-by-step explanation:

[tex]x^3-12x^2-19x+20 = 0\\Let \ p(x) = x^3-12x^2-19x+20[/tex]

Factors of 20 = ±1, ±2 , ±4 , ±5 , ±10 and ±20

±1, ±2 and ±3 are not the factors of given polynomial.

Putting x = 4 in the given polynomial

[tex]p(4) = (4)^3+12(4)^2-19(4)+20\\p(4) = 64+192-76+20\\p(4) = 200[/tex]

So, x = 4 is not a factor of p(x)

Putting x = -4 in the given equation

[tex]p(-4) = (-4)^3+12(-4)^2-19(4)+20\\p(-4) = -64+192-76+20\\p(-4) = 73[/tex]

So, x = -4 in the given equation

Putting x = 5 in the given equation

[tex]p(5) = (5)^3+12(5)^2-19(5)+20\\p(5) = 125+300-95+20\\p(5) = 350[/tex]

So, x = 5 is not a factor of p(x)

Putting x = -5 in the given equation

[tex]p(-5) = (-5)^3+12(-5)^2-19(-5)+20\\p(-5) = -125+300+95+20\\p(-5) = 290[/tex]

So, x = -5 is not a factor of p(x)

Putting x = 10 in the given equation

[tex]p(10) = (10)^3+12(10)^2-19(10)+20\\p(10) = 1000+1200-190+20\\p(10) = 2030[/tex]

So, x = 10 is not a factor of p(x)

Putting x = -10 in the given equation

[tex]p(-10) = (-10)^3+12(-10)^2-19(-10)+20\\p(-10) = -1000+1200+190+20\\p(-10) = 410[/tex]

So, x = -10 is not a factor of p(x)

Putting x = 20 in the given equation

[tex]p(20) = (20)^3+12(20)^2-19(20)+20\\p(20) = 8000+4800-380+20\\p(20) = 12440[/tex]

So, x = 20 is not a factor of p(x)

Putting x = -20 in the given equation

[tex]p(-20) = (-20)^3+12(-20)^2-19(-20)+20\\p(-20) = -8000+4800+380+20\\p(-20) = -2800[/tex]

So, x = -20 is not a factor of p(x)

From the above solution, we conclude that the given equation can not be factorized and thus, has no factors.

Answer:

[tex]\boxed{\mathrm{No \: factors}}[/tex]

Step-by-step explanation:

[tex]x^3 +12x^2 -19x= -20[/tex]

Add 20 on both sides.

[tex]x^3 +12x^2 -19x+20= 0[/tex]

Add 67x and 44 on both sides.

[tex]x^3 +12x^2 +48x+64= 67x + 44[/tex]

Factor left side of the equation.

[tex](x+4)(x+4)(x+4)= 67x + 44[/tex]

[tex](x+4)^3=67x+44[/tex]

Subtract 67x and 44 on both sides.

[tex](x+4)^3-67x-44=0[/tex]

Cannot be factored further.

This is a prime expression. A prime expression cannot be factored.

We cannot factor out x from the expression, there are no factors.

Answer:

the drop in the level of water in the container is 2.03 cm

Step-by-step explanation:

The volume of a cylinder can be written as;

[tex]V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter[/tex]

the change in height when the volume changes can be derived by differentiating the equation.

[tex]dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}[/tex]

substituting the given values;

[tex]\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.[/tex]

[tex]dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm[/tex]

the drop in the level of water in the container is 2.03 cm

Answer:

Equation: S(W) = 60W + 350

After 19 weeks, total accumulated = S(19) = 1490

Step-by-step explanation:

The interest rate is not indicated, so cannot take that into account.

Each week, he adds 60$, with initial value of 350$

So the equation is

S(W) = 60W + 350

for W = 19,

S = 60*19 + 350

S(19) = 1490

Answer:

$1490

Step-by-step explanation:

Answer:

Since we are talking annual interest and, I assume a time period of 1 year:

The interest earned is the sum of the interest earned on the two loans separately

Let x = amount loaned at 14%

18,500-x = amount loaned at 12%

I = prt

p = x and 18500-x

r = 0.14 and 0.12

t = 1

2390 = 0.14x + 0.1(18500-x)

2390 = .14x + 1850 - 0.1x

x = 13500

x = $13,500 loaned at 14%

18500-x = $5,000 loaned at 12%

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Step-by-step explanation:

Total loan: $18,500.

Part at 14%

Part at 12%

Let the part at 14% = x.

Let the part at 12% = y.

Equation of amount of loan:

x + y = 18500

x amount at 14% earns 14% of x = 0.14x interest.

y amount at 12% earns 12% of y = 0.12y interest.

Equation of interest charged:

0.14x + 0.12y = 2390

We have a system of equations.

x + y = 18500

0.14x + 0.12y = 2390

Multiply both sides of the first equation by -0.12. Write the second equation below it, and add the equations.

     -0.12x - 0.12y = -2220

(+)    0.14x + 0.12x = 2390

-------------------------------------

      0.02x             = 170

x = 170/0.02

x = 8500

x + y = 18,500

8500 + y = 18,500

y = 10,000

Answer:

$8,500 was loaned at 14%, and

$10,000 was loaned at 12%.

Answer:

Y =4

Step-by-step explanation:

Hope it helps

Answer:

1650 yards

Step-by-step explanation:

Here, we have to find the minimal spanning tree required to span the neighborhood.

We start from house 1. The minimum distance from house 1 to house 2 is 250 yards. Now from 2, we can go to house 3,4 or 5 all having the equal distances  of 400 yard from house 2. So we go to from house 2 to house 3. Now from 3, we go to house 5 which is at a minimum  distance of 350 yards. Now from house 5 we go to house 4 with 300 yards and then from house 4 we go to house 6 which is at 350 yards from 4.

Thus the network is complete and the total distance covered is

= 250 + 400 + 350 + 300 + 350

= 1650 yards

This is the minimum distance by which the neighborhood can be wired.

And the tree is

[tex]$1\rightarrow2\rightarrow3\rightarrow5\rightarrow4\rightarrow6$[/tex]    

Answer:

The train must travel at 50 km/hr to make it on time.

Step-by-step explanation:

distance to be covered = 55 km

time to cover this distance = 1 hr 20 min

1 hr 20 min = 1.33 hrs (20 min = 20/60 hrs = 0.33 hrs)

The train travels the first 30 km distance at a speed of 36 km/hr

and we know that time taken = distance/speed

therefore the time taken to run this 30 km will be

time = 30/36 = 0.83 hr

The train still has 55 - 30 = 25 km to cover,

and the time left is 1.33 - 0.83 = 0.5 hrs left

to make it on time, the train must travel at

speed = distance/time = 25/0.5 = 50 km/hr

Answer:

1.75 miles

Step-by-step explanation:

Zeno's friend's house is two miles away. He travels half the distance in one hour.

0.5 × 2 = 1

The second hour, his horse travels half the remaining distance.

0.5 × 1 = 0.5

The third hour, his horse travels half the remaining distance.

0.5 × 0.5 = 0.25

1 + 0.5 + 0.25 = 1.75

Zeno travels 1.75 miles in three hours.

Hope this helps.

Answer:

a. 4.5 grams per cup

b. 3.2 ounces per week

c. 19.2 grams per cubic centimeters

d. $3.29 per gallon

Step-by-step explanation:

The unit rate is simply a ratio comparing 2 given quantities, whereby the denominator is 1.

The unit rate of the above given problems can be determined as shown below:

a. 18 grams of salt per 4 cups, to find the unit rate, calculate how many grams of salt you'd get in 1 cup by dividing 18 by 4

[tex] \frac{18}{4} = 4.5 [/tex]

Unit rate = 4.5 grams per cup

b. 19.2 ounces is gained by the baby in 6 weeks.

Unit rate is the amount of ounces gained in 1 week

Unit rate = [tex] \frac{19.2}{6} = 3.2 [/tex]

Unit rate = 3.2 ounces per week

c. Unit rate = [tex] \frac{76.8}{4} = 19.2 [/tex]

Unit rate = 19.2 grams per cubic centimeters

d. Unit rate = [tex] \frac{23.03}{7} = 3.23 [/tex]

Unit rate = $3.29 per gallon

Answer: new Q = (-4, 5)

Step-by-step explanation:

Given: Q = (-4, 1)

Reflected across y = -2:    

Q is 3 units above y = -2 so a reflection is 3 units below y = -2 --> Q' = (-4, -5)

Reflected across x-axis:    

Q' is 5 units below x-axis so a reflection is 5 units above x-axis --> Q'' = (-4, 5)

Answer:

not rejecting the null hypothesis when it is false.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis.

For making the error, it should not reject the null hypothesis at the time when it should be false.

It is the level where the probability of rejecting the null hypothesis at the time when the null hypothesis should be true. It is relevant for making the incorrect decision. Also, it is the statistical test that measured the probability of type 1 error.

Therefore, For making the error, it should not reject the null hypothesis at the time when it should be false.

Learn more about error here: https://brainly.com/question/18831983

Answer:

B. 7.35 inches

Step-by-step explanation:

In the triangle:

Now we know that:

[tex]\angle A+\angle B+\angle C=180^\circ$ (Sum of angles in a \triangle)\\63^\circ+47^\circ+\angle C=180^\circ\\\angle C=180^\circ-(63^\circ+47^\circ)\\\angle C=70^\circ[/tex]

Using the Law of Sines

[tex]\dfrac{a}{\sin A} =\dfrac{c}{\sin C}\\\\\dfrac{a}{\sin 63^\circ} =\dfrac{7.75}{\sin 70^\circ} \\\\a=\dfrac{7.75}{\sin 70^\circ} \times \sin 63^\circ\\\\a=7.35$ inches (to the nearest hundredth of an inch)[/tex]

Answer:

B.  7.35 inches

Step-by-step explanation:

just use the law of sines

Answer:

The length is 5.5 inches

Step-by-step explanation:

The area of a rectangle is

A = lw

66 =  l * 12

Divide each side by 12

66/12 = l

5.5 = l

The length is 5.5 inches

Answer:

5.5 inches

Step-by-step explanation:

Length times width is the area so

12*width =66

same as

66/12=5.5 inches

Ask more questions in the comments if you are still confused.

Answer:

$705.30,  $837.67,  $994.89 Respectively

Step-by-step explanation:

Given

P= $500

r= 3.5%= 3.5/100= 0.035

Applying the compound interest formula we have

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

where

A = final amount

P = initial principal balance

r = interest rate

t = number of time periods elapsed

[tex]A= 500(1+0.035)^1^0\\\ A= 500(1.035)^1^0\\\\ A= 500*1.410598\\\ A=705.299[/tex]

A= $705.30

[tex]A= 500(1+0.035)^1^5\\\ A= 500(1.035)^15\\\\ A= 500*1.67534\\\ A=837.67[/tex]

A= $837.67

Answer:

A. Histogram.

Step-by-step explanation:

Histogram is a graphical display in the form of bars. The numerical data is displayed through graph to understand easily. Skewness measure frequency distribution of histogram. The histogram is skewed in a way that its right side tail is greater than its left side tail. They are skewed to right. The histogram are positively skewed which means their most of data falls to right side. The mean of positively skewed histogram is greater than its median.

Answer:

Margin of error is 9.8

Step-by-step explanation:

Using the formular for the margin of error

The margin of error = z* (sd/√n)

Where z is the z score for the desired confidence level = 1.96, sd is the population standard deviation = 50 and n is the sample size = 100

Thus

Margin of error = 1.96 (50/√100)

= 1.96 (50/10)

= 1.96 (5)

= 9.8

Margin of error is 9.8

Answer:

x = {9, -3}

Step-by-step explanation:

Or it can be shown as:

Step-by-step explanation:

a) The Roughly shape of the probability model is bell shaped or symmetric

( normal )

(b) Roughly, guess the center (mean) of the probability model

The mean is 5/10 =0.5

Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .

(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.

Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .

Answer:

a) Mean = 4.55

   Median = 4.7

   Mode = 1.9

b) S =  2.3952

   CV = 52.64 %

   Range = 6.3

c) Yes, since the average and median values are both over "acceptable" ranges.

Step-by-step explanation:

Explanation is provided in the attached document.