A manufacturer knows that their items have a normally distributed length, with a mean of 14.2 inches, and standard deviation of 1.9 inches. If one item is chosen at random, what is the probability that it is less than 11.9 inches long? Round your answer to 4 decimal places.

Answer:

X = 15

Step-by-step explanation:

We can tell that the two sides that show the degrees are equal because of the arc. We can set up a simple equation:

x + 45 = 60

x = 15

Answer:

x = 15°

Explanation:

The two marked angles are equal as they are vertically opposite angles.

∴ x + 45°  =  60°

⇒ x =  60° - 45°

⇒ x = 15°

Josephine's sales in dollar is $1500.

The first step is to determine the percentage commission earned by Daphne.

Percentage commission : ($80 / $1600) x 100 = 5%

Percentage commission of Josephine: 5% x 2 = 10%

Josephine's sales = dollar commission / percentage commission

$150 / 0.1 = $1500

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The linear equation formed is y = 200 +5x  and 60 weeks will be required to finish the project.

A statement that relates two mathematical expressions by an equal sign is called an Equation.

It is given that

No. of phones Per week  installed in the office = 5

Let the no. of phones installed at the present week is given by y

and let x weeks have passed by before that

then the linear equation is formed as

y = 200 +5x

If the company wants to replace all the phones

Total phones = 500

No. of week required = ?

500 = 200+5x

300 = 5x

x = 60

Therefore 60 weeks will be required to finish the project.

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Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.

Here we have:

[tex]f(x) = \sqrt{x}[/tex]

first we want to evaluate it in x = 0, 1, 4, 9.

Doing that we get:

[tex]f(0) = \sqrt{0} = 0\\f(1) = \sqrt{1} = 1\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]

The other function is:

[tex]g(x) = \sqrt{x} -3[/tex]

Evaluating in the same values of x.

[tex]g(0) = \sqrt{0} -3 = -3\\g(1) = \sqrt{1} -3 = -2\\g(4) = \sqrt{4} -3 = -1\\g(9) = \sqrt{9} -3 = 0[/tex]

Then we can see that for all the values of x, g(x) is 3 units less than f(x).

Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.

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Answer:

10 years

Step-by-step explanation:

the average or mean value is the sum of all data points divided by the number of data points.

x = the unknown age of the 5th student.

average = 9 = (5 + 7 + 8 + 15 + x)/5

45 = 5 + 7 + 8 + 15 + x = 35 + x

x = 45 - 35 = 10

the 5th student is 10 years old.

Answer:

Hello i am here to give the answer of the above question................................................................................................................................

Solution:Here

Given,

Volume of a cube is 27 so.

Length of a side of the cube =?

So I think the correct answer of this question is 3

Thank you......... ..................

The annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

Monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%.

Value of annuity as of September 1 calculation:

From the table:

For Jan:

Jan 0 $75.00 1.07214 $80.41

For Feb

Feb 1 $75.00 1.06152 $79.61

And on September 1, the value of the annuity will be:    =

= $621.43

Thus, the annuity on September 1 will be $621.43 if the monthly payments of $75 are paid into an annuity beginning on January 31, with a yearly interest rate of 3%

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Answer:

14/24 are ill so

58 percent

if you add 5 it does not get more complicated you just add 5 so 14/29

Hope This Helps!!!

Answer:

$49,553.54

Explanation:

[tex]\sf Continuously \ compound \ interest : {A = P e^{rt}[/tex]

[tex][\sf where \ A \ is \ final \ amount, \ P \ is \ principal \ amount, \ r \ is \ interest \ rate, \ n \ is \ years][/tex]

Here given following:

Inserting these values in formula:

[tex]\rightarrow {A = 24000e^{7.25\% (10)}[/tex]

simplify following

[tex]\rightarrow {A = 49553.54[/tex]

Answer:

-3/4

Step-by-step explanation:

So you have the equation: [tex]y=\frac{4}{3}x-\frac{5}{3}[/tex]. For a perpendicular line, the only thing that matters is the slope. The slope of the perpendicular line can be defined as: [tex]\frac{a}{b} = > -\frac{b}{a}[/tex]. It's the reciprocal with the sign being the opposite. So if the sign of the original line was negative it's now positive, and if it's positive, it's not negative. The fraction is also flipped, even if it's an integer, it can be defined as a fraction e.g ([tex]6 = > -\frac{1}{6}[/tex] (sign also changed too))

So in this case the slope is 4/3x, since it's given in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept. So we flip it to get 3/4 and change the sign to negative to get -3/4

Answer:

B

Step-by-step explanation:

Hope it helps :)

Answer:

y=886000(1.04)^t

t=1 year so answer is 886000*1.04 = 921440

It sounds like you're saying

[tex]z = \dfrac38 \left(\cos\left(\dfrac\pi8\right) + i \sin\left(\dfrac\pi8\right)\right)[/tex]

[tex]w = 2 \left(\cos\left(\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi{16}\right)\right)[/tex]

The product [tex]zw[/tex] is obtained by multiplying the moduli and adding the arguments. In other words

[tex]z = |z| e^{i\arg(z)} \text{ and } w = |w| e^{i\arg(w)} \implies zw = |z||w| e^{i(\arg(z)+\arg(w))}[/tex]

where [tex]e^{it}=\cos(t)+i\sin(t)[/tex], so that

[tex]zw = \dfrac38\times2 \left(\cos\left(\dfrac\pi8+\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi8 + \dfrac\pi{16}\right)\right) = \boxed{\dfrac34 \left(\cos\left(\dfrac{3\pi}{16}\right) + i \sin\left(\dfrac{3\pi}{16}\right)\right)}[/tex]

The final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697

The formula for calculating the compound interest is given as:

A = P(1+r/n)^nt

Given the following parameters

A = 10000(1+0.04/4)^4(6)

A = 10000(1+0.01)^24

A = 10000(1.01)^24

A = 1.2697(10,000)

A = $12,697

Hence the final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697

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The original selling price of the garden hoses is $19.99

Using the given formula,

M = S - N

where

Hence,

M = $12.35.

N = $7.64

Therefore,

S = M + N

S = 12.35 + 7.64

S = $19.99

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Answer:

0/6

Step-by-step explanation:

There are 6 numbers on the die: 1, 2, 3, 4, 5, 6

As you can see there is no 7, so the possibility is 0/6.

The solution of the unknown equation n + 6 = 13 will be n = 7.

A linear equation is an equation that has the variable of the highest power of 1.

The standard form of a linear equation is of the form Ax + B = 0.

The given equation is

n +6=13

To solve for n

Subtract 6 on both sides;

n +6=13

n = 13- 6

n = 7

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If you bought 20 pounds of cashews, your bottom line would remain the same.

Cashew and peanut butter together represent a linear relationship. Twenty pounds of cashews would have no impact on profits.

Cashews are represented here by the letter c and peanuts by the letter p.

U-4.00

Up=1.50

Um=2.00

p-40  pounds of peanuts that have not been sold.

m=40+c -when 40 pounds of peanuts are combined with cashews, the resulting combination

Generally, the equation for c is  mathematically given as

Ue x c+Up xp=Um x m

Therefore

4.00 x c+1.50 x 40 2.00 x (40+c)

4c+60-80+2c

2c= 20

c=10

In conclusion, If you bought 20 pounds of cashews, your bottom line would remain the same.

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Answer:

Step-by-step explanation:

Just put -2 in,where X is and get your answer that way

Using it's concepts, it is found that for the function [tex]f(x) = \frac{5x}{x - 25}[/tex]:

In this problem, the function is:

[tex]f(x) = \frac{5x}{x - 25}[/tex]

For the vertical asymptote, it is given by:

x - 25 = 0 -> x = 25.

The horizontal asymptote is given by:

[tex]y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{5x}{x - 25} = \lim_{x \rightarrow \infty} \frac{5x}{x} = 5[/tex]

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Answer:

(3, 25)

Step-by-step explanation:

The symmetry of a parabola means that if you have two y coordinates which are the same, the axis of symmetry is going to be in the middle of the x-coordinates. So in this case it's the middle number of -2 and 8. So to find the midpoint of these two numbers, you simply add them together and divide it by 2. This gives you the equation: [tex]\frac{-2+8}{2}=\frac{6}{2}=3[/tex]. This means that the axis of symmetry is at: [tex]x=3[/tex], and as you may know, this axis of symmetry passes through the vertex. So this means the x-axis of the vertex is 3, so to find the y-value simply plug in 3 as x

y = (-2-3)(3-8)

y = (-5)(-5)

y = 25

So this means the vertex is at (3, 25)

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

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\[/tex]

Segment AB is exactly [tex]\sqrt{17}[/tex] units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

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

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\[/tex]

Segment AB has a slope of 1/4.

Do the same for BC

[tex]B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\[/tex]

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a rhombus.

Answer:

  Rhombus

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. That is, they have the same midpoint. If they are the same length, that parallelogram is a rectangle. If they cross at right angles, it is a rhombus. If it is a rectangle and rhombus, then it is a square.

The midpoints of AC and BD are ...

  (A+C)/2 and (B+D)/2

To determine if the midpoints are the same, we can skip the division by 2 and simply look at the sums:

  A +C = (3, 5) +(6, 2) = (9, 7)

  B +D = (7, 6) +(2, 1) = (9, 7)

The midpoints of the diagonals are the same, so the figure is at least a parallelogram.

The diagonal vectors will be the same length if the figure is a rectangle. They will be perpendicular if the figure is a rhombus. The vectors are ...

  AC = C -A = (6, 2) -(3, 5) = (3, -3)

  BD = D -B = (2, 1) -(7, 6) = (-5, -5)

The length of each of these is the root of the sum of squares of its components. These are obviously different lengths (3√2 vs 5√2).

The dot-product of these will be zero if they are perpendicular:

  AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

The diagonals are different length and mutual perpendicular bisectors, so the figure is a rhombus.

__

Additional comment

Looking at the dot-product is a simple way to check that the slopes are opposite reciprocals. The slope of a vector with components (x, y) is m = y/x.

The requirement that slopes be opposite reciprocals means ...

  y1/x1 = -1/(y2/x2) . . . . . . . . slope relationship

  (y1)(y2)/((x1)(x2)) = -1 . . . . . multiply by y2/x2

  y1·y2 = -x1·x2 . . . . . . . . . . multiply by (x1·x2)

  x1·x2 +y1·y2 = 0 . . . . . . . . add x1·x2

This shows the vector dot product being zero is equivalent to the slopes being opposite reciprocals. The vectors are perpendicular in this case.

Answer:

2.73 million people per year

Step-by-step explanation:

Turn sentences into coordinates/points:

In 2000, 281.4 million people

In 2010, 308.7 million people

Rate of population per year:

[tex]\sf \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf \dfrac{308.7-281.4}{2010-2000}[/tex]

[tex]\rightarrow \sf 2.73 \ million \ people[/tex]

Answer:

P = 4x+10

Step-by-step explanation:

So a parallelogram has 2 set of sides which are parallel and equal. So if you're given two adjacent sides, that means you're given a side from each set of sides, which are equal. This means the perimeter is simply: 2(x+3) + 2(x+2). This can be further simplified by distributing the 2 which gives you the equation: 2x+6+2x+4, which further simplifies to 4x+10.

Answer:

Sin M= opposite/hypotenuse, cos M= adjacent/Hypotenuse, tan M= opposite/adjacent

Step-by-step explanation:

Answer:

sinM= [tex]\frac{opposite}{hypotenuse}[/tex]

cosM= [tex]\frac{adjacent}{hypotenuse}[/tex]

tanM= [tex]\frac{opposite}{adjacent}[/tex]