In a report prepared by the Economic Research Department of a major bank the Department manager maintains that the average annual family income on Metropolis is $48,432. What do you conclude about the validity of the report if a random sample of 400 families shows and average income of $48,574 with a standard deviation of 2000?

Answer:

The travel time to work that separates the 8% of people with the shortest travel times from the other 92% with longer travel times is 10.6 minutes.

Step-by-step explanation:

We are given that the average travel time to work for a person living and working in Kokomo, Indiana is 17 minutes.

Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.

Let X = the distribution of travel time

The z-score probability distribution for the normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = average travel time = 17 minutes

            [tex]\sigma[/tex] = standard deviation = 4.5 minutes

So, X ~ Normal([tex]\mu=17, \sigma^{2} =4.5^{2}[/tex])

Now, we have to find the travel time to work that separates the 8% of people with the shortest travel times from the other 92% with longer travel times, that means;

            P(X < x) = 0.08      {where x is the required travel time}

            P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-17}{4.5}[/tex] ) = 0.08

            P(Z < [tex]\frac{x-17}{4.5}[/tex] ) = 0.08

In the z table the critical value of z that represents the below 8% of the area is given by -1.43, that is;

                         [tex]\frac{x-17}{4.5}=-1.43[/tex]

                         [tex]{x-17}{}=-1.43\times 4.5[/tex]

                         x = 17 - 6.435 = 10.6 minutes

Hence, the travel time to work that separates the 8% of people with the shortest travel times from the other 92% with longer travel times is 10.6 minutes.

Answer:

I pretty sure its 2 a^ 2 + 6 a^ 3 + 9 a^ 2 + 8 a

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

A.

Let's split the integral into two parts, by the Sum Rule.

[tex]\int\limits {x-4x^3} \, dx[/tex]                              [split into 2 integrals]

[tex]\int\limits {x} \, dx -\int\limits {4x^3} \, dx[/tex]                      [solve integral for each part]

[tex]\frac{1}{2} x^2-x^4+C[/tex]                            [Remember, we need to add C for constant]

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B.

[tex]\int\limits {\frac{1+x}{\sqrt{x} } } \, dx[/tex]                                    [expand into 2 integrals]

[tex]\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\frac{x}{\sqrt{x} } } \, dx[/tex]                    [simplify second integral]

[tex]\int\limits {\frac{1}{\sqrt{x} } } \, dx +\int\limits {\sqrt{x} } \, dx[/tex]                    [solve integral for each part]

[tex]2\sqrt{x} +\frac{2}{3}x^3^/^2+C[/tex]

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C.

[tex]\int\limits^4_0 {z(z^1^/^2-z^-^1^/^2)} \, dz[/tex]                [distribute]

[tex]\int\limits^4_0 {z^3^/^2-z^1^/^2} \, dz[/tex]                       [split into 2 integrals]

[tex]\int\limits^4_0 {z^3^/^2} \, dz -\int\limits^4_0 {z^1^/^2} \, dxz[/tex]              [solve integral for each part]

[tex]\frac{64}{5} -\frac{16}{3}[/tex]                                     [solve]

[tex]\frac{112}{15}[/tex]

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D. *Note: I can't put -1 for the interval, but know that the 1 on the bottom is supposed to be -1.

[tex]\int\limits^1_1 {(1+u)(1-u)} \, du[/tex]                  [expand]

[tex]\int\limits^1_1 {1-u^2} \, du[/tex]                              [split into 2 integrals]

[tex]\int\limits^1_1 {1} \, du-\int\limits^1_1 {u^2} \, du[/tex]                      [solve integral for each part]

[tex]2-\frac{2}{3}[/tex]                                      [solve]

[tex]\frac{4}{3}[/tex]

Answer: x=2 and y=4/3

Step-by-step explanation:

To solve by substitution method, you want to solve for one variable, and plug it into the other equation.

Let's solve for y in 2x+3y=8.

[tex]2x+3y=8[/tex]                          [subtract both sides by 2x]

[tex]3y=8-2x[/tex]                           [divide both sides by 3]

[tex]y=\frac{8-2x}{3}[/tex]

Now that we have y, we can plug it into the second equation.

[tex]9x-3y=14[/tex]                         [plug in y]

[tex]9x-3(\frac{8-2x}{3} )=14[/tex]                 [multiply 3 and y to cancel out the 3]

[tex]9x-(8-2x)=14[/tex]                [distribute -1 to 8-2x]

[tex]9x-8+2x=14[/tex]                   [combine like terms]

[tex]11x-8=14[/tex]                          [add both sides by 8]

[tex]11x=22[/tex]                                [divide both sides by 11]

[tex]x=2[/tex]

Since we know the value of x, we can substitute it back into any of the 2 equations to find y.

[tex]2x+3y=8[/tex]                           [plug in x=2]

[tex]2(2)+3y=8[/tex]                        [multiply 2 and 2]

[tex]4+3y=8[/tex]                            [subtract both sides by 4]

[tex]3y=4[/tex]                                  [divide both sides by 3]

[tex]y=\frac{4}{3}[/tex]

Our final answer is x=2 and y=4/3.

Answer:

-83

Step-by-step explanation:

25-(4-1)*(3-9)^2  [tex]\sqrt{16} =4[/tex]

25-(3)*(-6)^2   4-1=3   3-9=-6

25-3*36  -6*-6=36

25-108   3*36=108

-83

Answer:

|-49| < |-52|

Step-by-step explanation:

|-49| = 49

|-52| = 52

49 < 52

--> |-49| < |-52|

Answer:

|-49|<|-52|

Step-by-step explanation:

Absolute Values

|-49|=49

|-52|=52

49<52 so

|-49|<|-52|

Answer:

[tex]\huge\boxed{42.9 \%}[/tex]

Step-by-step explanation:

=> [tex]\frac{3}{7}[/tex]

To make it a percentage, we need to multiply and divide it by 100

=> [tex]\frac{3}{7} * \frac{100}{100}[/tex]

=> [tex]\frac{300}{700}[/tex]

To make the denominator 100, we'll divide the numerator and denominator by 7

=> [tex]\frac{300/7}{700/7}[/tex]

=> [tex]\frac{42.9}{100}[/tex]

Percentage means out of hundred, so it becomes

=> 42.9 %

Answer:

[tex] - 2n + 1 = 3n + 6 \\ - 2n - 3n = - 1 + 6 \\ - 5n = 5 \\ n = \frac{5}{ - 5} \\ n = - 1[/tex]

Answer:

n = -1

Step-by-step explanation:

Solve for n:

1 - 2 n = 3 (n + 2)

Expand out terms of the right-hand side:

1 - 2 n = 3 n + 6

Subtract 3 n from both sides:

1 + (-2 n - 3 n) = (3 n - 3 n) + 6

-2 n - 3 n = -5 n:

-5 n + 1 = (3 n - 3 n) + 6

3 n - 3 n = 0:

1 - 5 n = 6

Subtract 1 from both sides:

(1 - 1) - 5 n = 6 - 1

1 - 1 = 0:

-5 n = 6 - 1

6 - 1 = 5:

-5 n = 5

Divide both sides of -5 n = 5 by -5:

(-5 n)/(-5) = 5/(-5)

(-5)/(-5) = 1:

n = 5/(-5)

The gcd of 5 and -5 is 5, so 5/(-5) = (5×1)/(5 (-1)) = 5/5×1/(-1) = 1/(-1):

n = 1/(-1)

1/(-1) = -1:

Answer: n = -1

Answer:

Distributive Property

Step-by-step explanation:

I think it's because the bracket was expanded.

Answer:

Natalie is 13 years old

Step-by-step explanation:

7+6=13

Answer:13

Step-by-step explanation: 7 + 6 = 13

Answer:

  30)  25x^2 +28x +16

  31)  (15/2)x +15

  32)  18x^3 -21x^2 -52x -20

Step-by-step explanation:

For a shape with a cutout, the shaded area is the difference between the area of the enclosing shape and the area of the cutout. The applicable area formulas are ...

  area of rectangle: A = bh

  area of triangle: A = (1/2)bh

Here, the dimensions are given as binomials (2-term polynomials), so you have to multiply those to find the areas. The distributive property is helpful for that.

__

30) shaded area = (5x+8)(6x+2) -(5x)(x+6)

  = (5x)(6x+2) +8(6x+2) -5x^2 -30x

  = 30x^2 +10x +48x +16 -5x^2 -30x

  shaded area = 25x^2 +28x +16

__

31) shaded area = (1/2)(x+6)(2x+5) -x(x+1)

  = (1/2)(x(2x+5) +6(2x+5)) -x^2 -x

  = (1/2)(2x^2 +5x +12x +30) -x^2 -x

  = x^2 +(17/2)x +15 -x^2 -x

  shaded area = (15/2)x +15

__

32) volume = lwh = (2x -5)(3x +2)(3x +2)

  = (2x -5)(3x(3x +2) +2(3x +2))

  = (2x -5)(9x^2 +6x +6x +4)

  = (2x -5)(9x^2 +12x +4)

  = 2x(9x^2 +12x +4) -5(9x^2 +12x +4)

  = 18x^3 +24x^2 +8x -45x^2 -60x -20

  volume = 18x^3 -21x^2 -52x -20

Answer: It lost $6.75 in the first year.

Step-by-step explanation: Using the graph, first determine the function of loss in value and years, by calculating:

Slope: m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex] and then, substitute in: [tex]y-y_{0}=m(x-x_{0})[/tex]

The equation is:

[tex]y-y_{0}=(\frac{y_{a}-y_{b}}{x_{a}-x_{b}} )(x-x_{0})[/tex]

Assuming y is value and x is years.

From the graph, in year 0, loss is 10 and in year 4, loss is 7, i.e.:

[tex]y-10=(\frac{7-10}{4-0} )(x-0)[/tex]

[tex]y=\frac{-3}{4}x+10[/tex]

For the first year, loss in value will be:

[tex]y=\frac{-3}{4}.1+10[/tex]

y = 6.75

During the first year, the loss in value is $6.75

Answer: 1,000

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

I don't know how to use it using a number line sorry

-1/3 - (-1/2)

Two minuses give us a plus

so:

-1/3 + 1/2

make the denominators the same and what you multiply at the bottom you multiply at the top (check online about adding fractions if you don't understand)

so:

-2/6 + 3/6 = 1/6

Answer:

[tex]11n-1=120[/tex]

Step-by-step explanation:

It is given that,

Length of each brick = 10 inches

Mortar between between each brick = 1 inch

For 2 bricks, we need mortar once.

For 3 bricks, we need mortar 2 times.

For 4 bricks, we need mortar 3 times.

Similarly,

For n bricks, we need mortar (n-1) times.

Total length of n bricks = 10n inches

Total length of (n-1) times mortar = 1(n-1) = n-1 inches

Total length of wall = 10n + (n-1) inches.

1 feet  = 12 inches

10 feet = 120 inches

The equation to model the number of bricks,n, nikki needs in each layer to build a wall 10 feet long.

[tex]10n+(n-1)=120[/tex]

[tex]11n-1=120[/tex]

Therefore, the required equation is [tex]11n-1=120[/tex].

Answer:

-2.4+3.2t

Step-by-step explanation:

[tex]-3.6-1.9t+1.2+5.1t\\\\=(-3.6+1.2)+(-1.9+5.1)t\\\\=-2.4+3.2t[/tex]

Answer:

-2.4+3.2t

Step-by-step explanation:

Khan

Step-by-step explanation:

It is given that,

[tex]u{\cdot}v=4\\\\|u|=5\\\\|v|=3[/tex]

We need to find the value of [tex]4u{\cdot} (4u-7v)[/tex]

Firstly, we should simplify [tex]4u{\cdot} (4u-7v)[/tex]

[tex]4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v[/tex]

Now using distributive property : x(y-z)=xy-yz

So,

[tex]4u{\cdot} (4u-7v)=4u{\cdot} 4u-4u{\cdot} 7v\\\\=16u{\cdot}u-28{u{\cdot} v}\\\\=16|u|^2-28(u{\cdot}v)\\\\=16\times 5^2-28\times 4\\\\=288[/tex]

So, the value of  [tex]4u{\cdot} (4u-7v)[/tex] is 288.

Answer:

m

Step-by-step explanation:

If all points are plotted on a graph, we'd see that (3, 5) and (10, 5), would be on the same horizontal level. Both points have the same y coordinate of 5.

Invariably, (0, 1) would be on the same horizontal level with (m, n). The coordinate of n, which is the y value on the y-axis would be same as 1.

The coordinate of m, which is the x-value on the x-axis would certainly be greater than 1.

Therefore, coordinate m represents a greater number.

Answer:

5

Step-by-step explanation:

If all points are plotted on a graph, we'd see that (3, 5) and (10, 5), would be on the same horizontal level. Both points have the same y coordinate of 5.

Invariably, (0, 1) would be on the same horizontal level with (m, n). The coordinate of n, which is the y value on the y-axis would be same as 1.

The coordinate of m, which is the x-value on the x-axis would certainly be greater than 1.

Therefore, coordinate m represents a greater number.

Answer:

3.5 lbs of jellybeans

Step-by-step explanation:

2.5 x 3.40

8.5

13.75 - 8.5 = 5. 25

5. 25 divided by 1.50 =

3.5

Answer:

3.5

Step-by-step explanation:

Answer: 75

Step-by-step explanation:

Answer:

slope = -5/2

the y-intercept is the point (0, 3)

Step-by-step explanation:

Notice the equation is given to you already in slope-intercept form, o you can extract those values directly:

Slope is the factor accompanying the variable x , that is the fraction -5/2 and the y value of the y-intercept is the "+3" that follows.

So the slope = -5/2

and the y-intercept is the point (0, 3) because x must be always  zero when the line intersects the y-axis.

Answer:

0.183

Step-by-step explanation:

This is a question on Binomial Probability

Formula =nCx × p^x × q^n - x

p = 0.72

q = 1 - p

= 1 - 0.72

= 0.28

x = number of successes = 9

n = 10

The probability that at least nine out of ten people used an online travel website when they booked their airline ticket

At least 9 out of 10 means

x ≥ 9 = x = 9 and x = 10

Hence,

P(x ≥ 9) = 10C9 × (0.72^9 × 0.28^10 - 9) + 10C10 × ( 0.72^10 × 0.28^10 - 10)

P(x ≥ 9) = 0.14559635388 + 0.0374390623

= 0.18303541631

≈ 0.183

Answer: 11

Step-by-step explanation:

Let x = the number

6x-3=52+x

   6x=55+x

   5x=55

     x=11

Hope this helps!! :)

Please let me know if you have any questions

Answer:

21 boys

Step-by-step explanation:

 Girls            Boys

     6                  7            <= reflects the 6:7 ratio mentioned in the problem

----------   =    ----------

     18                 x

Cross multiply to determine x:  

6x = 7(18), or x = 7(3), or x = 21

There are 21 boys when we have 18 girls.

Answer:

[tex]\boxed{x=5}[/tex]

Step-by-step explanation:

First, you need to combine like terms in order to begin simplifying. This is done by subtracting 2x from 6x. Also, add 7 to 23.

6x + 10 - 2x = 7 + 23

4x + 10 = 7 + 23

4x + 10 = 30

Now, you have a two-step equation. Subtract 10 from both sides, and then divide by 4.

4x + 10 = 30

4x = 20

x = 5 is the final answer.

Answer:

o.ooo7

Step-by-step explanation:

The square root of 49/10,000 is 0.0007.

Hope this helps

please mark as brainlist

Answer:

True

Step-by-step explanation:

2.54 centimeters = 1 inch

1 x 10 = 10 inches

2.54 x 10 = 25.4 centimeters

Good luck mate :)

Answer:  2240

Step-by-step explanation: Simplify the expression.

I hope this helps you out.

Here, 2 x 3 x 2 x 5 x 7 is the prime factorization of 420.

Given that,
To determine the number that is this prime factorization 2 x 3 2 x 5 x 7 belongs to.

Factors can be defined by splitting the value into multipliable values.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Prime factors of the number are the factors that consist of only prime numbers,
i.e.
2 x 3 x 2 x 5 x 7 =  420

Thus, 2 x 3 x 2 x 5 x 7 is the prime factorization of 420.

Learn more about Factors here:
https://brainly.com/question/24182713

#SPJ2

Answer:

12

Step-by-step explanation: Given:1st no. is 3

3×8=24

24+6=30

30/2=15

15-3=12

therefore,ans is 12

Answer:

The result is 12.

Step-by-step explanation:

3×8=24

24+6=30

30÷2=15

15-3=12

Hope it helps :)

Answer:$132.70

Just believe it

Answer: 125.7

Step-by-step explanation: