At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 31 years old, with a standard deviation of 10 years. If you were to take a sampling of 10 employees, what is the probability your mean age will be at least 28? Round to the nearest percent.

Answer:

114°

Step-by-step explanation:

The angle which represents 2/5 of a circle is 144 degree.

A figure known as an angle is created when two rays, referred to as the angle's sides and vertices, share a single terminal. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Given:

Shaded portion= 2/5

and, the complete angle= 360

So, the 2/5 portion of the angle

= 360 x 2/5

= 720/5

= 144

Hence, the angle of portion 2/8 is 144 degree.

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Answer: Option B

[tex]y = 0.75cos(2\phi)[/tex]

Step-by-step explanation:

The general cosine function has the following form  

[tex]y = Acos(b\phi) + k[/tex]

Where A is the amplitude: half the vertical distance between the highest peak and the lowest peak of the wave.  

[tex]\frac{2\pi}{b}[/tex] is the period: time it takes the wave to complete a cycle.

k is the vertical displacement.

The maximum value of y is is 0.75 and the minimum is -0.75. Then the amplitude A is:  

[tex]A =\frac{0.75-(-0.75)}{2}\\\\A= 0.75[/tex]

Then [tex]k=0[/tex]

The cycle is repeated every [tex]\pi[/tex] units  

So the period is [tex]\pi[/tex]

Thus:

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

The function is:

[tex]y = 0.75cos(2\phi)[/tex]

when [tex]\phi=0[/tex] y is maximum therefore [tex]y=0.75[/tex] As shown in the graph

Answer:

[tex]2x^3-3x^2-4x+3[/tex]

Step-by-step explanation:

Use FOILing to get the answer.  Distribute x into 2x^2, to get 2x^3, then into x to get - x^2, then into -3 to get -3x.  Then distribute the -1 into the 2x^2 to get -2x^2, then into the x to get -x, then into the -3 to get 3.  Combine like terms to get the solution above.

Answer:

2x^3-x^2-4x+3

Step-by-step explanation:

First of all, the negative sign means that we will turn clockwise.

Since [tex]\frac{\pi}{4}[/tex] is half a quarter, we have:

So, option A is correct.

To draw the angle -3pi/4 in standard position, we measure 135 degrees clockwise from the positive x-axis.

To draw the angle below in standard position, -3pi/4, you begin from the positive x-axis (which is usually referred rightward).

In standard position, positive angles are measured counterclockwise and negative angles are measured clockwise. Since we're dealing with a negative angle of -3pi/4, we will measure this clockwise.

The angle -3pi/4 corresponds to 135 degrees (because -3pi/4 is -3 * 180 degrees/2 = -135 degrees). You would measure 135 degrees clockwise from the positive x-axis to draw this angle in standard position.

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Answer:

so where the points are on the triangles is where you would go side to side and up and down

Step-by-step explanation:

Find the lengths of the sides:

BA = 4, this would be y1

BC = 6, this would be x1

CD = 2, this would be y2

DE = 3, this would be x2

The slope is the Y over X

Slope of ABC = 4 / 6

Slope of CDE = 2 / 3

Answer A equals both of those:

6-2 / 9-3 = 4/6

8-6 = 12-9 = 2/3

25 I think I hope I’m right

Answer:

Because we knew that the function rule for the input/output table is to multiply by 6, just multiply 7 by 6 and we get y = 42

For the second question, we also knew that the function rule for the input/output table is to divide by 3, just divide 6 by 3 and we get y = 2

Since we already knew that the charge for downloading a movie is $3, then we can also predict that x is number of movies downloaded, and the total fee for downloading x movies should be 3x, plus the monthly fee, we have the equation: y = 3x + 6.50

*I could be wrong though

I think your correct answer is C. Please don’t be mad if I am wrong!❤️❤️

Answer:

Step-by-step explanation:

Look at the first picture.

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (1, 4) and (2, 1). Substitute:

[tex]m=\dfrac{1-4}{2-1}=\dfrac{-3}{1}=-3[/tex]

Look at the second picture.

The slope m:

[tex]m=\dfrac{rise}{run}[/tex]

[tex]rise=-3\\run=1[/tex]

Substitute:

[tex]m=\dfrac{-3}{1}=-3[/tex]

ANSWER

D) sin Y

EXPLANATION

The given triangle is a right triangle.

This implies that that:

[tex]x + y = 90 \degree[/tex]

Then we have

[tex]y= 90 - x[/tex]

Recall that

[tex] \cos(x) = \sin(90 - x) [/tex]

But

[tex]90 - x = y[/tex]

When we do the substitution, we get,

[tex] \cos(x) = \sin(y) [/tex]

Therefore cos(x) is a equivalent to sin(y).

The correct answer is D.

Answer A isometry

Step-by-step explanation:

Isometry is a mapping that does not change the size of the original figure. Isometry can be things like translation and rotation, both of which don't change size or shape!

Hope this helps!

You did not specify the brother's age, so I make a expression, b as the variable.

(3b + 5) - 11

Now do that with the brother age instead of the variable.

(3b + 5) - 11 = 3

you first add 3 and 5 which equals 8 ten you subtract 11 and 8 which equals 3, so jane is 3 years old

the answer would be 36

Answer:

36

Step-by-step explanation:

Cross a number out once on each side. That is, cross out 10 and 78, then 15 and 56, on and on until you get the last number that isn't crossed out. In this case, 36.

Answer:

24

Step-by-step explanation:

12 * 2 = 24

The value of x² is 144.

Just multiply an integer by itself to square it. For instance, "4 squared" equals 4 4 = 16. frequently displayed with a tiny 2 in the corner as follows: 42 = 16. "4 squared equals 16" is a common expression. The result of multiplying an integer (not a fraction) by itself is a square number.

Given

x = 12

x² = x * x = 12*12 = 144

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Answer:

Step-by-step explanation:

The center tells you how to handle the left side of a circle's equation.

(x - 2)^2 + (x - 1)^2 = r^2

The point (5,2) gives you enough information to find r^2

x = 5

y = 2

(5 - 2)^2 + (2 - 1)^2 = r^2

(3)^2 + 1^2 = r^2

9 + 1 = r^2

r^2 = 10

Complete equation

(x - 2)^2 + (y - 1)^2 = 10

Answer: (x-2)^2+(y-1)^2=10

Step-by-step explanation:

r=√(x-h)^2+(y-k)^2

r=√(5-2)^2+(2-1)^2

r=√3^2+1^2

r=√9+1

r=√10

X^2+y^2=r^2

(x-2)^2+(y-1)^2=(√10)^2

(x-2)^2+(y-1)^2=10

The insufficient evidence found in your test indicates that there's not ample proof to reject the claim regarding the standard deviation of time women spend washing their hair in the morning being 15 seconds.

In the realm of statistics, we are testing a claim about the standard deviation. In this case, you've tested a claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds. If your test does not reject the null hypothesis, that means you've found insufficient evidence to say the standard deviation differs from your claim. Thus, your final conclusion in this instance would be: 'There is not sufficient evidence to reject the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds.'

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The final conclusion is: There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.

The final conclusion is: There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds. When the initial test fails to reject the null hypothesis, it means that there is not enough evidence to support the alternative hypothesis. In this case, it suggests that there is not enough evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.

To reach this conclusion, you would have conducted a hypothesis test using a significance level (alpha). If the p-value from the test is greater than alpha, you would fail to reject the null hypothesis. This means there is not enough evidence to support the alternative hypothesis, which implies that the claim of the standard deviation not being 15 seconds is not supported.

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Answer:

3f³/g²

Step-by-step explanation:

√(900f^6/100g^4) =√(9f^6/g^4)=3f³/g²

Answer:

[tex][3f^{3}g^{-2}][/tex]

Step-by-step explanation:

The given expression is [tex]\sqrt{\frac{900f^{6} }{100g^{4}}}[/tex]

We can rewrite the expression as [tex]\sqrt{\frac{(30f^{3})^{2}}{(10g^{2})^{2}}}[/tex]

Now we can remove the radical of the expression =  [tex]\frac{30f^{3} }{10g^{2} }[/tex]

= [tex][\frac{3f^{3} }{g^{2}}][/tex]

= [tex][3f^{3}g^{-2}][/tex]

= [tex][3f^{3}g^{-2}][/tex] is the answer.

First, we have to find the ratio of quarters to the ratio of total coins:

15/15+8+27 = 15/50

Then, multiply the ratios:

15/50 * 14/49

(14/49 since one quarter has already been removed)

210/2450

21/245 = 0.0857

The probability is about 9 percent.

Answer: Alright get ready for a long explanation

he would have 820.00$ in his savings account after the 5 years

Step-by-step explanation:

if he earns 12% interest then you would have to multiply 100 by the 12/100 which is .12 in decimal form.

100 TIMES .12 = $12.00

because we are doing this in months you need to multiply the amount he makes per month by the amount of months that the 100 dollars is in the bank account.

Alright so now that thats over, he makes 12 dollars every month

thers 12 months in a year, so you would have to do 12 (the number of moths) times 5 (the amount of years) that equals 60.  

60 TIMES the amount he makes per month ($12) equals $720.00

LASTLY! add the amount he made to the original amount and you get the answer of $820.00

i hope this helps :)

ANSWER

3 square units

EXPLANATION

The given formula is

[tex]A=12s^2[/tex]

But

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

We substitute the value of s into the formula to get;

[tex]A=12( \frac{1}{2} )^2[/tex]

[tex]A=12 \times \frac{1}{4}[/tex]

[tex]A=3 {units}^{2} [/tex]

The value of A in square units is

3

Answer: n divided by 43

Step-by-step explanation: You always take the last number of the equation and divide it by the answer and you should get the first number.

Circumference = diameter x PI

Circumference = 3.14 x 68 yards = 213.52 yards.

Area = PI x r^2

r = 1/2 the diameter = 1/2 x 68 = 34 yards.

Area = 3.14 x 34^2 = 3.14 x 1156 = 3629.84 yards^2

Answer:

0.0000135

Step-by-step explanation:

Answer:

Width = x-1

Step-by-step explanation:

Given

Area of rectangle=A= x^4+4x^3+3x^2-4x-4

Length of Rectangle=L= x^3+5x^2+8x+4

We have to find width

Width of rectangle=W= ?

We know that the formula for the area of triangle is:

Area of Rectangle=Length*Width

A=L*W

Since we need the value of width, length will be moved to the left of equals to.

A/L=W

W= (x^4+4x^3+3x^2-4x-4)/(x^3+5x^2+8x+4)

After long division, we will get

Width=W=x-1

Answer:

Never. (Not viable)

Step-by-step explanation:

3% of 500=15

5% of 300=15

Since both of them would get $15 a year, then they would stay the same amount apart. For example, when the first account reached 515 dollars, the second one would be at 315 dollars. Thus, they'd always be 200 dollars apart.

However!

Since it is a compound interest, and if there is the original 7% a year, the formula we'll use for this is the simple interest formula, or:  

I=Pxrxt

Where:

P is the principal amount, $500.00.

r is the interest rate, 3% per year, or in decimal form, 3/100=0.03.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 500 × 0.03 × 5 to get that:  

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),  

or 500.00 + 75.00 = 575.00. For example:

If you borrowed the $500.00, you would now owe $575.00

If you loaned someone $500.00, you would now be due $575.00

If owned something, like a $500.00 bond, it would be worth $575.00 now.

You want to calculate the interest on $300 at 5% interest per year after 5 year(s).

The formula we'll use for this is the simple interest formula, or:  

I=Pxrxt

Where:

P is the principal amount, $300.00.

r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.

t is the time involved, 5....year(s) time periods.

So, t is 5....year time periods.

To find the simple interest, we multiply 300 × 0.05 × 5 to get that:  

The interest is: $75.00

Usually now, the interest is added onto the principal to figure some new amount after 5 year(s),  

or 300.00 + 75.00 = 375.00. For example:

If you borrowed the $300.00, you would now owe $375.00

If you loaned someone $300.00, you would now be due $375.00

If owned something, like a $300.00 bond, it would be worth $375.00 now.

Answer: there is only one solution and it is viable . ( answer on PLATO)

Step-by-step explanation:

what's the equation to find x

Answer:

The correct answer is: a= -32

Answer:

The graph in the attached figure

Step-by-step explanation:

we know that

The graph represent a vertical parabola open up

The vertex is the minimum value of the parabola

The vertex is the point (3,-4)

The x-intercepts are the points (1,0) and (5,0)

The x-intercepts are the values of x when the value of y is equal to zero

The y-intercept is the point (0,5)

The y-intercept is the value of y when the value of x is equal to zero

The domain is the interval -----> (-∞,∞)  All real numbers

The range is the interval -----> [-4, ∞)  All real numbers greater than or equal to -4

see the attached figure to better understand the problem

Answer:

Solution 5,0

Vertex 3,-4

Y-intercept 0,5

Step-by-step explanation:

Just finished on math nation

Let [tex]x[/tex] be the length of the shorter leg.

The other leg is 1m longer, so its length is [tex]x+1[/tex]

The hypothenuse is 9m longer, so its length is [tex]x+9[/tex]

The pythagorean theorem states that the sum of the squares of the legs is the square of the hypothenuse, so we have

[tex]x^2+(x+1)^2=(x+9)^2[/tex]

Expanding the squares gives

[tex]x^2+x^2+2x+1=x^2+18x+81[/tex]

Move all to the left hand side:

[tex]x^2-16x-80=0[/tex]

This equation has solutions [tex]x=-4[/tex] and [tex]x=20[/tex]

We can't accept the first solution, because it would lead to the side lengths

[tex]x=-4,\quad x+1=-3,\quad x+9=5[/tex]

And we can't have negative side lengths.

The other solution is fine, because it leads to the side lengths

[tex]x=20,\quad x+1=21,\quad x+9=29[/tex]

So, the side lengths are 20 (shorter leg), 21 (longer leg), 29 (hypothenuse)

Answer:

20 m , 21 m and 29 m.

Step-by-step explanation:

Let the length of the shorter leg be x m. Then the longer leg = x + 1 m and the hypotenuse =  x + 9 m. So, by Pythagoras:

(x + 9)^2 = x^2 + (x + 1)^2

x^2 + 18x + 81  = x^2 + x^2 + 2x + 1

18x + 81 = x^2 + 2x + 1

x^2 - 16x - 80 = 0

(x - 20)(x + 4) = 0

x = 20, -4  (as we are dealing with lengths of sides we ignore the negative root).

So the sides have length 20, 21 and 29 (answer).

Answer:

4z-(3z) z

Step-by-step explanation:

I hope that helps

Answer:

D) y = 4x - 13

Step-by-step explanation:

Slope: the change in y over the change in x

In a equation in slope-intercept form is in y = mx + d, where m is the slope.

The slope can be found by its definition. As y goes up by 4, x goes up by 1, so the slope is 4/1 = 4.

The only option with 4 as the slope is D.