On a test that has a normal distribution, a score of 30 falls three standard deviations below the mean, and a score of 60 falls three standard deviations above the mean. Determine the mean of this test.

Answers

Answer 1

Answer:

45

Step-by-step explanation:

Let μ - mean, σ - standard deviation.

Given:

A score of 30 falls three standard deviations below the mean:

μ - 3σ = 30

A score of 60 falls three standard deviations above the mean:

μ + 3σ = 60

Add up the two expressions and find the value of μ:

μ - 3σ + μ + 3σ = 30 + 602μ = 90μ = 45

The mean is 45


Related Questions

is 0.9999 really the same as 1

Answers

Answer:

No but on a calculator it will just be rounded up. If 0.99999 was 1, maths would be pretty much useless.

Answer:

no the value tends to go to 1 but it is not exactly one.

Can someone help me with geometry

Answers

Applying the circle theorems, we have:

4. y = 120°

x = 45°

5. x = 90°

y = 32°

6. x = 40°

y = 20°

7. x = 116°

y = 98°

8. x = 100°

y = 60°

9. x = 54°

y = 75°

What is the Angle of Intersecting Secants Theorem?

The angle formed outside a circle by the intersection of two secants equals half the positive difference of the measures of the intercepted arcs, based on the angle of intersecting secants theorem.

What is the Angle of Intersecting Chords Theorem?

The angle formed when two chords of a circle intersect, equals the half the sum of the measures of the intercepted arcs, based on the angle of intersecting chords theorem.

4. y = 360 - 95 - 30 - 115 = 120°

x = 1/2(120 - 30) [angle of intersecting secants theorem]

x = 45°

5. x = 90° [based on the tangent theorem]

y = 180 - 90 - 58 [triangle sum theorem]

y = 32°

6. x = 360 - 160 - 160 [central angle theorem]

x = 40°

y = 1/2(40) [inscribed angle theorem]

y = 20°

7. x = 180 - 2(32)

x = 116°

y = 1/2[132 + 2(32)] [angle of intersecting chords theorem]

y = 98°

8. x = 180 - 80 [opposite angles of an inscribed quadrilateral are supplementary]

x = 100°

y = 1/2[(2(80) - 90) + 50] [inscribed angle theorem]

y = 1/2[70 + 50]

y = 60°

9. 40 = 1/2(134 - x) [angle of intersecting secants theorem]

2(40) = 134 - x

80 = 134 - x

80 - 134 = - x

-54 = -x

x = 54°

y = 360 - 134 - 54 - 97

y = 75°

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what is 3/7 divided by 3/7 equal to and simplified

Answers

Answer:

1

Step-by-step explanation:

3/7 divided by 3/7 is nothing but

3/7 times 7/3 because of the keep, change, flip rule.

3/7 times 7/3 is nothing but 21/21

21/21 simplifies to 1/1

1/1 = 1

give brainliest please!

hope this helps :)

Is this relation a function? Explain.
(-2, -1), (4, 2), (-8, -4), (6, 3) ​

Answers

Answer:

Yes

Step-by-step explanation:

Functions are relations that express a rule between the x-values and the y-values.

What Makes a Function

Functions are types of relations, specifically, where the x-values do not repeat. This means that each x-value has exactly one y-value. So, if the x-values do not repeat in a relation, then it must be a function.

How To Find a Function From Coordinates

In the question, we are given 4 different coordinate points. The points have 4 x-values, none of which repeat. This means that the relationship must be a function.

To find a function from points, all you need to do is check that the x-values do not repeat.

How To Find a Function From a Graph

If you are given a continuous graph, another way to figure out if it is the vertical line test. The vertical line test is when you draw vertical lines across the graph. If you are able to draw a vertical line everywhere on the graph without the line intersecting with the graph more than once, then it is a function. However, if the line intersects with the graph more than once at any point, then it is not a function.

What is the first step in constructing an incenter to triangle xyz?

Answers

The first step is constructing an angle bisector for one of the angles of the triangle.

We have to find the first step for the constructing an inscribed circle

What is the incenter triangle?

The incenter of a triangle is the point from which the distances to the sides are equal, in this point we can start to construct the inscribed circle in the triangle because the incenter would also be the center of the circumference.

Therefore the first step in constructing an angle bisector for one of the angles of the triangle.

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Answer:

Construct the angle bisector of angle Y.

Step-by-step explanation:

I just took the test and got the answer correct :)

Solve PV = nRT for R.

Answers

Answer:

[tex] R = \dfrac{PV}{nT} [/tex]

Step-by-step explanation:

[tex] PV = nRT [/tex]

[tex] nRT = PV [/tex]

[tex] R = \dfrac{PV}{nT} [/tex]

Ben believe the orioles will win only 40% of their games this year if they play 160 games how many games does Ben predict they will win (use equivalent ratios)

Answers

The number of games Ben predict Orioles will win this year is 64 games

How to find percentage?

Percentage of games Ben believe the orioles will win = 40%Number of games Orioles played = 160

Number of games Ben predict they will win = 40% of 160

= 40/100 × 160

= 0.4 × 160

= 64

Therefore, the total number of games Ben predict they will win is 64 games

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i need help it’s due at the end of class

Answers

It is the 3rd option

Roll of the Dice Are the chances of rolling a 3 with one die the same as the chances of rolling a total of 6 with two dice? If not, which has the higher probability ?

Answers

Answer:

The probability is the same.

Step-by-step explanation:

The chances of rolling a 3 with one die is 1/6. The chances of rolling a 6 with 2 dice is 2/12.

If you replace the outlier of 113°F with 100°F, what happens to the range? Why do you think this occurs?

Answers

If you replace the outlier of 113°F with 100°F, the the range changes from 42 degrees to 29 degrees.

What is the outlier about?

In the case above, by  replace the outlier of 113°F with 100°F, IQR will not change due to the fact that the q1 and q3 values are not influence by the outlier.

But the range will change from 42 degrees to 29 due to the fact that

113 - 71 = 42 and

100 - 71 =  29

Therefore, If you replace the outlier of 113°F with 100°F, the the range changes from 42 degrees to 29 degrees .

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Rational number of 2.3

Answers

[tex]Rational \: numbers \: can \: be \: written \: in \: the \: form \: of \: \frac{a}{b} \\ 2.3 = \frac{23}{10} = > answer[/tex]

Hope this helps :)

An aquarium holds 11.1 cubic feet of water and is 2.8 feet long and is 1.2 feet wide.what is the depth?

Answers

Step-by-step explanation:

the volume of any cube or prism is

length × width × height (or depth)

11.1 = 2.8 × 1.2 × depth

depth = 11.1 / (2.8 × 1.2) = 11.1 / 3.36 = 3.303571429 ft

≈ 3.3 ft

Using the Vertical Line Test
Which graph does not represent a function?

Answers

Using the Vertical Line Test, the graph does not represent a function is  ellipse, the third graph.

What is vertical line test?

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function. It is done by visually examining the number of intersections of the curve with vertical lines.

Any vertical line in the x y plane must intersect the graph of a function at most once.

In the given graphs, the graph of a function intersects the y axis twice. So, it is not a function.

From the given graphs, the third graph which is of ellipse crosses the vertical line twice.

Thus, the graph does not represent a function is ellipse.

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Sybil can put a total mass of 950 g in her bag. she buys a book that weighs 450 g and a notebook that weighs 210 g. write an equation to represent how much more mass, m, her bag can hold. then, solve for the answer and include an explanation of how you solved the equation

Answers

Answer:

M =290

Step-by-step explanation:

Subtraction of numbers

Harry works in a local computer store and he kept a record of the number of computers sold each month for the past year. How many more computers were sold in the month of February than in the month of September? A. 20
B. 17
C. 15
D. 10

Answers

Answer:

A.) 20

Step-by-step explanation:

According to the bar graph, in February, the store sold 50 computers. In September, it seems like the store sold 30 computers. Therefore, if 50 - 30 = 20, the store sold 20 more computers in February than in September.

Answer:

A) 20

Step-by-step explanation:

Computers sold in Feb: 50

Computers sold in Sept: 30

50 - 30 = 20

Write each expression as a single number:
a)2°+2raise to the power -1 + 2 raise to the power -2
b)10 raise to the power -1 +10°+10 raise to the power 3

Please explain it all I can’t understand it

Answers

Answer:

B) 2º+2=4

raise ^that 4 to the power of -1+2 like this

4-1+2=5

raise ^to the power -2 like this

5-2=3 <Awnser

Which expression is equivalent to 6(4
+ 9)?

Answers

Answer: 78

Step-by-step explanation:

6(4+9)

use foil to distribute the 6 to the 4 and 9

6×4 + 6×9

24 + 54

⇒ 78

The answer is 6x13 Hope this helps

which ordered pair is a solution of y= 2x + 5?

Answers

Answer: (-2, 1)

Step-by-step explanation:

The 1st value in a pair is x, the 2nd is y.

▪︎ (-2, 1)

1 = 2(-2)+5

1 = -4+5

1 = 1 ✅

▪︎ (-1, 4)

4 = 2(-1)+5

4 = -2 + 5

4 = 3❌

▪︎ (1, 6)

6 = 2*1+5

6 = 2 + 5

6 = 7❌

▪︎ (3, 10)

10 = 2*3+5

10 = 6 + 5

10 = 11❌

(-2, 1) is an ordered pair bro

began doing his homework at 3:30 p.m. to stop at 4 p.m. how many degrees does the minute hand turn during rick's walk.explain how you found your answer

Answers

At 3:30 pm

the minute hand was at 6 and hour hand was in between 3 and 4

At 4 pm

the minute hand is at 12 and hour hand is at 4

Total numbers travelled by minute hand

12-66

Total degrees turn

6(30)180° clockwise turn

What is the area of this rectangle? 10units 20units 24units 48 units

Answers

Answer:

24 units ^2

Step-by-step explanation:

The base runs from 3 to 7 so the base is 7-3 = 4 units

The height runs from 2 to 8  so the height is 8-2 = 6 units

The area is

A = bh

   = 6*4 = 24 units ^2

The volume of a cone is 736.853 cubic
inches. The height is 11 inches. Calculate the
diameter of the cone.

Answers

diameter of the cone=15.8inches


Write the square or cube for each number.
1) 19³=
2) 16² =
3) 15³ =
4) 20² =____
5) 10³ =_

Answers

Answer:

1) 19³=6859

2) 16² =256

3) 15³ =3375

4) 20² =400

5) 10³ =1000

Step-by-step explanation:

using your calculator to (square = number times itself) or (cube = number times itself times itself again)

Simplify the following.
a) 3×a×2× b​

Answers

Answer:

first multiply numbrrs3*2=6ab

Simplify 3xa2xb equals 6b

A carpenter has a board that is 8 feet long. He cuts off 2 pieces. One piece is 3 1/2 feet long and the other is 2 1/3 feet long. How much of the board is left? IM SO SORRY THIS QUESTION ISN’T MULTIPLE CHOICE PLS FORGIVE ME

Answers

Answer:

2 1/6

Step-by-step explanation:

The answer is 2 1/6 because you should start by adding 3 1/2 + 2 1/3. This equals 5 5/6 feet. You should then subtract 8 - 5 5/6 because you are figuring out how much is left. When you subtract 8 - 5 5/6, you get 2 1/6. So 2 1/6 feet of the board is left.

Hope this helps!

Find the equation of the axis of symmetry for the parabola y = x² + 4x + 5. Simplify any numbers and write them as proper fractions, improper fractions, or integers.​

Answers

the equation's squared variable is the "x", namely x², so we're looking at a vertical parabola, and thus its axis of symmetry will be a vertical line that runs through its vertex, so

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+5} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 5-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~5 - \cfrac{ 16 }{ 4 } \right)\implies (\stackrel{x}{-2}~~,~~1) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{axis of symmetry}}{x=-2}~\hfill[/tex]

Check the picture below.

Jacob sells stools with round seats. if
the radius of a seat is 34.2 cm, find the
surface area of the stool

Answers

The surface area of the stool is 3629.84 square cm

How to determine the surface area?

The radius is given as:

r = 34.2

The surface area is calculated using:

A = πr^2

So, we have:

A = 3.14 * 34^2

Evaluate

A = 3629.84

Hence, the surface area of the stool is 3629.84 square cm

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Which of the following is most likely the next step in the series?

Answers

Answer:

C

Step-by-step explanation:

Option C is correct, the polygon in c option is the next step in the series

What is Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.

In the first step we can see a triangle

The triangle has three sides

In the second step there is a rectangle which has four sides

The third step has pentagon which has five sides

So in next step the polygon should have six sides

Hexagon is the next step in the series

Hence, option C is correct, the polygon in c option is the next step in the series

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What is the surface area of a half sphere with a diameter of 16?

Answers

Answer:

603.185789 m2

Step-by-step explanation:

603.185789 m2 or 192 π m2

formula is  [tex]3\pi r^2[/tex]:

3 x  pi x 8^2 = 603.185789489

Which of the following shows how to calculate the probability of randomly selecting a cat or dog?
P(cat) + P(dog)
P(cat) − P(dog)
P(cat) · P(dog)
P(cat) ÷ P(dog)

Answers

The probability of randomly selecting a cat or dog is P(cat or dog) = P(cat) + P(dog)

Since we cannot select a cat and dog at the same time, their probabilities are mutually exclusive

Probability of mutually exclusive events

If we have events a and b which are mutually exclusive with probabilities P(a) and P(b) respectively, the probability of a or b is P(a or b) = P(a) + P(b)

Probability of randomly selecting a cat or dog

Let

P(cat) = probability of selecting a cat and P(dog) = probability of selecting a dog

So, probability of randomly selecting a cat or dog is

P(cat or dog) = P(cat) + P(dog)

So, probability of randomly selecting a cat or dog is P(cat or dog) = P(cat) + P(dog)

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3 less than the square of a number

Answers

Answer:

  n² -3

Step-by-step explanation:

The square of a number is found by multiplying it by itself. The square of a number in an algebraic expression is shown using an exponent of 2. For a number represented by n, the square of the number is n².

3 less than a number is found by subtracting 3 from the number. Equivalently, it is found by adding -3 to the number. The addition can be done in any order. For a number represented by n, 3 less than the number is either of ...

  -3 +n

  n -3

__

given expression

The expression for "3 less than the square of a number" is ...

  n² -3 . . . . . where n represents the number

It can also be written ...

  -3 +n²

We generally prefer the first form, with variable exponents decreasing left-to-right.

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