A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50 and 52 minutes. Find the probability that a given class period runs between 51.5and 51.75 minutes.

Using the Empirical Rule, the percentages are given as follows:

a) 99.7%.

b) 32%.

c) 16%.

It states that, for a normally distributed random variable:

Item a:

61 and 139 is within 3 standard deviations of the mean, hence the percentage is of 99.7%.

Item b:

87 and 113 is within one standard deviation of the mean, hence 68% of the data is within this interval and 100 - 68 = 32% of the data is outside this interval.

Item c:

Considering that the normal distribution is symmetric, and item b, this percentage is of 32%/2 = 16%.

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Answer:

x = 35.537677791974°

y = 63.434948822922°

Step-by-step explanation:

let x be the measure of the angle of elevation of the sun.

tan(x) = 10/14

Then

x = tan⁻¹ (10÷14) = 35.537677791974°

………………………………………………

let y be the measure of the angle of elevation of the sun

where the shadow decreases to 5m.

tan(y) = 10/5 = 2

Then

y = tan⁻¹ (2) = 63.434948822922°

Answer:

a) 35.54°

b) 63.43°

Given following:

Determining, the shadow is adjacent side and length of the pole is the opposite side. Hence, use the tan rule. Let the angle be x.

(a)

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{14}[/tex]

[tex]\sf x = tan^{-1}(\dfrac{10}{14} )[/tex]

[tex]\sf x = 35.54^{\circ \:} \quad (rounded \ to \ nearest \ hundredth )[/tex]

(b) If the shadow decreases to 5 meter.

[tex]\sf tan(x) = \dfrac{opposite}{adjacent}[/tex]

[tex]\sf tan(x) = \dfrac{10}{5}[/tex]

[tex]\sf x = tan^{-1} (\dfrac{10}{5})[/tex]

[tex]\sf x = 63.43 ^\circ \quad (rounded \ to \ nearest \ hundredth)[/tex]

The measure of both the interior angles are 70 and 110 degree.

Lines they never intersect with each other and the distance between them always remains same are called parallel lines.

It is given that

Line l and m are parallel lines and are intersected by a transversal ,n

Interior angles of the same side are (2x−8) degree and (3x−7) degree

Applying the property of interior angles of parallel lines

2x -8 + 3x - 7 = 180 degree

5x -15 = 180

5x = 195

x = 39 degree

Both the angles have measure of

2 * 39 - 8 = 70 degree

3 * 39 -7 = 110 degree

Therefore the measure of both the angles are 70 and 110 degree.

The complete question is

Two parallel lines l and m are cut by a transversal  n . If the interior angles of the same side of n are (2x−8) degree and (3x−7) degree  , find the measure of each of these angles.

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Answer:

a) $74.62

Step-by-step explanation:

Cost of both clothes = 28+35 = $63

Tax = 0.08*63 = $5.04

Shipping: $6.54

Add: 63+5.04+6.58 = 74.62

The volume of the cone to nearest tenth is 247. 12 cm ^3

Note that the shape is a cone

Volume for a cone =

[tex]\pi \: { {r}^{2} \frac{h}{3} } [/tex]

Given that radius = 5.3cm

height = 8.4cm

Substitute into the formula, we have

Volume = 3.142 × 5.3 × 5.3 × (8.4/3)

Volume = 3. 142× 28.09 × 2.8

Volume = 247. 12 cm ^3

Thus, the volume of the cone to nearest tenth is 247. 12 cm ^3

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Answer:

?

Step-by-step explanation:

Please explain-WHAT TRACKS?

Answer:

5.275

Step-by-step explanation:

Got the answer from Emma on Gauth Math

Answer:

A) 10

Step-by-step explanation:

Votes for Marcus: 420/2 = 210 votes

Votes for Mary: 420/3 = 140 votes

Votes for Edward: 420/7 = 60 votes

Total number of votes: 210+140+60 = 410 votes

people who didn't vote: 420-410 = 10 people

There are 7,315 different combinations, thus, the correct option is c

If we have a set of N elements, the number of different combinations of K elements (such that K ≤ N) of these N elements that we can make is:

[tex]C(N, K) = \frac{N!}{(N - K)!K!}[/tex]

In this case we have K = 4 and N = 22, replacing that, we get:

[tex]C(22, 4) = \frac{22!}{(22 - 4)!*4!} = \frac{22*21*20*19}{4*3*2*1} = 7,315[/tex]

So there are 7,315 different combinations, thus, the correct option is c.

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Answer:

370,000 centimeters

Step-by-step explanation:

1. There are 1000 meters in a kilometer.

2. 3.7 kilometers x 1000 = 3,700 meters

3. There are 100 centimeters in a meter

4. 3,700 x 100 = 370,000 centimeters

5.7099 is the margin of error.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean.

Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

According to the question,

The standard sampling error of the sample mean is σₓ ,

The sampling distribution is: N (u,σₓ/n)

Therefore,

By using the standard deviation formula:

σₓ = √∑(xi -μ)/N

Where,

∑= population standard deviation

N= the size of the population

xi= each value from the population

μ =the population mean

So ,

σₓ = [tex]\frac{20.6}{\sqrt{50} }[/tex] = 2.913

Since, a = 1- 95% = 0.05

therefore [tex]Z\frac{a}{2}[/tex] = (1-0.005 x 2) = 1.959964

Here, the margin of error for a 95% confidence interval for this sample is given by:

[tex]Z\frac{a}{2}[/tex] * σₓ = 1.959964 x 2.913    

           = 5.7099

5.7099 is the margin of error for a 95% confidence interval for this sample.

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Probability sampling simply illustrates a scenario where the subjects of the population have an equal opportunity.

Probability simply means the likelihood of the occurence of an event.

In this case, in probability sampling, the subjects of the population have an equal opportunity.

In non-sampling, an equal opportunity isn't given.

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Using it's concept, the average rate of change of the function over the interval 10 < x < 22 is given by:

[tex]r = \frac{f(22) - f(10)}{12}[/tex]

It is given by the change in the output divided by the change in input.

Over the interval 10 < x < 22, the outputs are f(10) and f(22), hence the rate of change is given by:

[tex]r = \frac{f(22) - f(10)}{12}[/tex]

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Two more examples of relationship patterns found in mathematics are Geometric sequences and Fibonacci numbers.

Mathematical patterns are a sequence of repeated arrangements of numbers, shapes, colors, letters, etc.

Mathematical patterns are usually abstract.

A geometric sequence is a sequence of non-zero numbers.  The first number is the product of multiplying a previous number by a fixed, non-zero number, called the common ratio.

A Geometric sequence may look like: 2, 4, 8, 16, 32, 64, 128, ..., where the common ratio is 2.

A Fibonacci number starts with a zero, followed by a one, then by another one, and then by a series of steadily increasing numbers.

The rule of the Fibonacci sequence is that each number is equal to the sum of the preceding two numbers, for example, 0, 1, 1, 2, 3, 5, 8, 13.

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Answer:

19

Step-by-step explanation:

fx=16+4

fx=20

gx= 20-1

gx=19

19

Answer:

  15.4 years

Step-by-step explanation:

An investment is doubled when it is twice its initial value. The equation can be solved for the value of t that makes this true.

In the exponential equation for investment value, the factor y₀ is the initial value of the investment. We want to find t when y = 2y₀.

  2y₀ = y₀·e^(0.045t)

Dividing by y₀ gives ...

  2 = e^(0.045t)

Taking natural logarithms, we have ...

  ln(2) = 0.045t

Dividing by the coefficient of t gives its value:

  t = ln(2)/0.045 ≈ 15.4

The investment will be doubled after 15.4 years.

__

Additional comment

The continuously compounded interest rate for this investment is 4.5%. The doubling time is 0.693 divided by this: 0.693/0.045 ≈ 15.4. This relationship holds for any sort of continuous compounding.

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

The given statement is "The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx".

The point where the reference axes in a coordinate system meet. The values of coordinates are normally defined as zero.

The equation of the line is y = mx + b.

If the line goes through the origin, then b = 0, so y = mx + b is y = mx + 0 or y = mx.

The equations are the same when the line goes through the origin. y = mx + b is a more general form of y = mx. Therefore, Renee is correct.

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An equation is formed of two equal expressions. The value of 'a' in the given equation is 6.452.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The given equation can be solved for 'a' as shown below,

[tex]\dfrac{(3-0)}{4a} = (10-0.8a)\\\\\dfrac{3}{4a} = (10-0.8a)\\\\[/tex]

0.75a = 10 - 0.8a

0.75a + 0.8a = 10

1.55a = 10

a = 6.452

Hence, the value of 'a' in the given equation is 6.452.

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Answer:

76 sqcm.

Step-by-step explanation:

2(5 x 2) + 2(5 x 4) + 2(4 x 2) = 2(10) + 2(20) + 2(8)
                                             =  20 + 40 + 16
                                             =  76

Answer: -211/76

Step-by-step explanation:

to solve this word problem equation, we need to first convert the words to numbers and variables we can solve for:

we can replace "a number" for a variable such as x

this gives:

-76·x-61=x+89

now all you have to do is solve the equation and you're done!

Answer:

a = -17/30

Step-by-step explanation:

So the first step is to distribute the negative sign, if that's a bit confusing think of the negative sign as a -1 instead of just a negative sign, and then think of distributing that negative 1 to the 23a and -13.

Original Equation:

-(23a - 13) + 53a

Distribute negative sign

-23a + 13 + 53a

Group like terms:

(-23a + 53a) + 13

Simplify

30a + 13 = -4

Subtract 13 from both sides

30a = -17

Divide both sides by 30

a = -17/30

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Example: x²+3x+5 is a polynomial.

The polynomial whose factors are (a²-6) and (a²+4) is,

P(x) =  (a²-6)(a²+4)

      = a⁴ + 4a² - 6a² - 24

      = a⁴ - 2a² - 24

Hence, The polynomial whose factors are (a²-6) and (a²+4) is a⁴ - 2a² - 24.

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[tex]5x - 7 \leqslant 13 \\ add \: 7 \: on \: both \: sides \\ 5x - 7 + 7 \leqslant 13 + 7 \\ 5x \leqslant 20 \\ divide \: both \: sides \: by \: 5 \\ \frac{5x}{5} \leqslant \frac{20}{5} \\ x \leqslant 4[/tex]

Answer:

-42

Step-by-step explanation:

You have to To subtract the fractions, then find the Least common denominator (LCD) and then combine.

pls brainliest Hope this helps have a nice day :>

[tex]\boldsymbol{(-1-3^{2})-\dfrac{4^{3} }{2} }[/tex]

Calculates 3 to the power of 2 and gets 9.

[tex]\boldsymbol{-1-9-\dfrac{4^{3} }{2} }[/tex]

Subtract 9 from −1 to get −10.

[tex]\boldsymbol{-10-\dfrac{4^{3} }{2} }[/tex]

Calculates 4 to the power of 3 and gets 64.

[tex]\boldsymbol{-10-\dfrac{64}{2} }[/tex]

Divide 64 by 2 to get 32.

[tex]\bf{-10-32 }[/tex]

Subtract 32 from −10 to get −42.

[tex]\bf{-42 \ \ \to \ \ \ Answer}[/tex]

Answer:

The distance is √17.

Step-by-step explanation:

the step is provided in the image....

I hope it was helpful

Answer:

10√2

Step-by-step explanation:

The square root of 200 in its simplest radical form is 10√2.

If we know the prime factorization of a number, we can write the radical form of the square root of that number. As a result, the prime factorization of 200 is 2 × 2 × 2 × 5 × 5.

As a result, the square root of 200 in the simplest radical form should be 10√2.

[tex]f(x) = x {}^{3} - 2 \\ f(3) = 3 {}^{3} - 2 = 27 - 2 = 25[/tex]

[tex]f(3) = 25[/tex]

The equation which is a function of x is x²=y.

Given an equation that is a function of x.

A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.

If we input a value of x then we get the output f(x) = y, which is the function of x.

We are given four options out of which we are to pick the one which may be a function of 'x'.

The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.

The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.

The third option is x²=y in which y contains power 1. So, option 3 is correct.

The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.

Hence, the equation which is a function of x is x²=y.

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Answer:

there 32 students and 20 have pets so you take 20 over 30 divide by 2 to get 10/16 then divide by 2 to get 5/8and that is the answer