Suppose the commute times for employees of a large company follow anormal distribution. If the mean time is 24 minutes and the standarddeviation is 5 minutes, 95% of the employees will have a travel time within which range?

Percentage of the student body exists at least 21 years old exists 50%.

A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

As one moves away from the center, values start to taper off and the majority of values are concentrated in this area. In a normal distribution, the mean, mode, and median are identical measures of central tendency.

When given a normal or Symmetric distribution, the mean of the distribution exists at the center with 0.5 or 50% of the distribution to either side (right and left) of the distribution.

Therefore, if the mean = 21 ; then the percentage of student body with at least 21 years is the percentage to the left of the distribution, which exists 50%.

P(x ≤ 21) = 0.5 = 50%

Therefore, 50 percentage of the student body exists at least 21 years old

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Answer:

option a is the right answer .

Step-by-step explanation:

Cos theta = B/h = 8/21

theta = 67.6 °

Step-by-step explanation:

imagine the triangle being flipped upwards around DE, so that F is on top instead of on the bottom.

then you see clearly that

DF (21) is the radius of the trigonometric circle,

DE is cos(angle D)×radius,

EF (8) is sin(angle D)×radius.

so,

8 = sin(angle D)×21

sin(angle D) = 8/21 = 0.380952381...

angle D = 22.39268781...° ≈ 22.4°

and so, something is wrong with your problem definition.

the answer options seem to aim for angle F, for which EF (8) is the cosine × radius.

but for angle D EF is clearly the sine × radius.

and for answer option b (20.9°) EF would have to be about 7.5 units long (with the radius DF still being 21). that is all too much off.

your teacher made a mistake. send him/ her my regards.

Equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .

As given in the question,

For the function f(x):

Standard form of the equation with solution x =a and x=b is:

f(x) = k(x-a)(x-b)

Solutions for the given function f(x) is x =-4 and x=3 and a point (0,-60)

is given by:

f(x) = k(x-(-4))(x-3)

     = k(x+4)(x-3)

Point at (0,-60) we get,

-60 = k ( 0+4)(0 -3)

⇒-60 = -12k

⇒ k =5

Required equation is :

f(x) = 5(x+4)(x-3)

Therefore, equation in the form of f(x) for the solutions of x=-4 and x=3 and a point (0,-60) is equal to f(x) = 5(x+4)(x-3) .

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Which property is demonstrated below?

a(b + c) = (a*b) + (a*c)

O Inverse property

O Distributive property

O Communitive property

O Identity property

Answer:

Hope this helps!!

The sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

First we will convert the mixed fractions into improper fractions.

-1 and 3/4 = -7/4

2 and 1/2 = 5/2

Sum of -1 and 3/4 and 2 and 1/2 = -7/4 + 5/2 = -7/4 + 10/4 = 3/4

Difference between  2 and 1/2 and 1 and 3/4 = 5/2 - 7/4 = 10/4 - 7/4 = 3/4

As both the values equal to 3/4 , we can say that the sum of  -1  and 3/4 and 2 and 1/2 is the same as the difference between 2 and 1/2 and 1 and 3/4.

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It is not possible to write a linear inequality such that the solution contains only positive values of x and y.

This happens because every line on the coordinate plane must have a y-intercept and/or an x-intercept. When the line crosses an axis, either the variable x or y changes its sign.

The value of g(a) + h(a) is a²-3a-2 or (a-2)(a-1) using addition of functions.

Given a collection of inputs X (domain) and a set of potential outputs Y (codomain), a function is more technically defined as a set of ordered pairings (x,y) where x belongs to X  and y belongs to Y, with the caveat that there can only be one ordered pair with the same value of x. The function notation f:XY can be used to express that f is a function from X to Y

Adding two functions-

g(a) = a²- 2

h(a) = -3a

Let h(a) be g(a) + h(a)

So h(a) = a² - 2 - 3a.

We can factorize the function into (a-2)(a-1).

So we get h(a) = (a-2)(a-1).

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The relation that represents a function is given as follows:

B. The second graph.

A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.

For a point in the standard format (x,y), we have that:

In a graph, the equivalent to this is that there can be no vertically aligned points.

Then, for the options in this problem, we have that:

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Among the given statements The equation c = 0.4w is correctly represented by the graph is correct.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

By given the equation c = 0.4w, where c represents the total cost and w represents weight in ounces.

Given that graph with x axis labeled weight in ounces and y axis labeled cost

Let us construct a table

Weight(x)   1          2

Cost (Y)     0.4      0.8    

As given graph with x axis labeled weight in ounces and y axis labeled cost in dollars, with a line from 0 comma 0 going through 2 comma 0.8

The equation c = 0.4w is correctly represented by the graph.

Hence among the given statements The equation c = 0.4w is correctly represented by the graph is correct.

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Answer:

sin2x = 16/65

cos2x = -63/65

tan2x = -16/63

Explanation:

the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:

Therefore, we can calculate the value of the hypotenuse as:

With the hypotenuse, we can calculate sin(x) and cos(x) as follows:

We type the negative sign because the question says that sin(x) is negative.

Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)

Therefore, replacing the values, we get:

So, the answers are:

sin2x = 16/65

cos2x = -63/65

tan2x = -16/63

If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3,-2), B'(-2,-1), C'(10,-1) and D'(3,0)

The coordinates of the quadrilateral ABCD is

A (-6,2) , B(-5,3), C(7,3) and D(0,4)

The quadrilateral is translated 4 units down and 3 units right

After translation

A(x, y)⇒ A(x + a, y +b)

The value of a and b will be positive if the shift is right and up.

The value of a and b will be negative if the shift is left and down.

Therefore

a = 3, b = -4

The coordinates of A' =(-6+3,2-4)=(-3,-2)

The coordinates of B' =(-5+3,3-4)=(-2,-1)

The coordinates of C' =(7+3,3-4)=(10,-1)

The coordinates of D' =(0+3,4-4)=(3,0)

Hence, If the coordinates of quadrilateral ABCD are A (-6,2) B (-5,3) C (7,3) D (0,4) and it is translated 4 units down and 3 units right, then the coordinates of the image is A'(-3, -2), B'(-2, -1), C'(10, -1) and D'(3, 0)

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In terms of the calculation, the answer is 39/4 in improper fraction.

An improper fraction has a denominator that is greater than or equal to the numerator. Based on the numerator and denominator values, proper fractions and improper fractions are the two main types of fractions in mathematics.

A mixed fraction is a fraction formed by combining a natural number and a proper fraction. It is a shortened version of an improper fraction.

The given equation is [tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] .

Taking 4 as LCM from the above equation.

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13/4) + (13/2)

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = (13+26)/4

[tex]3\frac{1}{4}[/tex] + [tex]6\frac{1}{2}[/tex] = 39/4

Now, since the solution must be proffered in an improper fraction.

Therefore, the obtained improper fraction is 39/4.

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The coordinates of the vertices of the image of the square are S'(x, y) = (- 1, - 4), T'(x, y) = (- 1, 1), U'(x, y) = (4, 1) and V'(x, y) = (4, - 4).

In this problem we need to make use of a translation on a geometric locus on a Cartesian plane, which is generated by four points representing the vertices of the square. The translation is a kind of rigid transformation, whose formula is shown below:

P'(x, y) = P(x, y) + t(x, y)

Where:

If we know that S(x, y) = (- 6, - 5), T(x, y) = (- 6, 0), U(x, y) = (- 1, 0) and V(x, y) = (- 1, - 5) and t(x, y) = (5, 1), then the locations of the vertices of the triangle are:

S'(x, y) = (- 6, - 5) + (5, 1)

S'(x, y) = (- 1, - 4)

T'(x, y) = (- 6, 0) + (5, 1)

T'(x, y) = (- 1, 1)

U'(x, y) = (- 1, 0) + (5, 1)

U'(x, y) = (4, 1)

V'(x, y) = (- 1, - 5) + (5, 1)

V'(x, y) = (4, - 4)

The location of the image of the square is shown below.

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Answer:

x = 32

Step-by-step explanation:

-6(x-18) = -84

Divide both sides by -6

x - 18 = 14

Add 18 to both sides

x = 32

The correct option regarding the error in the proportional relationship is given as follows:

Row 2 should show 6 feet is equivalent to 182.88 centimeters.

A direct proportional relationship is a function in which the output variable y is calculated by the multiplication of the input variable x and the constant of proportionality k, as follows:

y = kx.

In the context of this problem, the input and the output are given as follows:

The constant is calculated dividing the output by the input of each of the lengths, hence:

Due to the different ratio, the mistake is in Row 2, and the correct value should be of:

6 x 30.48 =182.88 centimeters.

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Each midpoint's coordinate is given by the mean of the respective coordinates of the two endpoints of the segment. Then, if we say M is the midpoint of that segment, we have:

Mx = (-4 + 4)/2 = 0/2 = 0

My = [6 + (-2)]/2 = (6 - 2)/2 = 4/2 = 2

Therefore, writing those coordinates as an ordered pair, we have:

M = (0, 2)

The volume of the sphere is 4/3 times the volume of the cylinder.

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

The volume of the cone is 1/3 the volume of a cylinder.

The volume of a cone is given as:

V = (1/3)πr²h ____(1)

The volume of a cylinder is given as:

V = πr²h _____(2)

From (1) and (2) we get,

(1/3)πr²h = 1/3 πr²h

The volume of a sphere:

V = 4/3 πr³

Since the height of the sphere and the radius is the same we can have

V = 4/3πr²h

So,

Volume of sphere = 4/3 x πr²h

The volume of the sphere = 4/3 x the Volume of the cylinder.

Thus,

The volume of the sphere is 4/3 times the volume of the cylinder.

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The probability that Gary will get exactly 3 text messages in a 2-hour portion of his work day using the Poisson distribution, what is the time interval of interest: 2 hours

Gary will get calls according to Poisson distribution with an average # of calls per hour = 15.

Let x be the Poisson random Variable Such that X ~Poisson (15).

We need to find P(x≤3) in 2 hours.

Thus, the time interval of interest is 2 hours.

Probability is the likelihood  of an event occurring. It can range from an impossible event  to a probability to an absolute certainty. In mathematics, probability is on a scale of 0-1. Zero means the event is impossible, like rolling  seven dice with only the numbers 1-6. One is an event that will happen, that's for sure. An example of a specific event is tomorrow is Friday if today is Thursday. It will definitely  happen. The median is 0.5 or half and these events are equally likely. A good example of half probability  is tossing a coin. It gets straight heads or tails.

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If a rectangle has an area of A and sides b and h, then:

Solving for the base:

Basically, the sides b and h could have any value provided that b*h=A.

Nevertheless, this problem seems to want from us to factorize the expression:

So that each side is a binomial.

Part a)

To factorize that expression, find two numbers so that if they are added up, the sum is equal to -5, and if they are multiplied, the product is equal to -300.

Since the product is negative, one number must be negative. Since the sum is negative, the biggest number should be the negative one.

Consider the factors of 300:

Using those factors, we can find pairs of numbers that give 300 as a result from multiplying.

After a bit of trial and error, notice that 15*20=300. If we choose 20 as the negative number, then 15*(-20)=-300 and 15+(-20)=-5. Therefore:

So, we can choose the width and the height to be those factors. Since (x+15) is greater then (x-20), then:

Part b)

If x=45, then:

To find the number we can create the following equation and solve for x:

Let x be the missing number, use inverse operations to solve the equation:

The number is 40.

Answer:

y=2x+0

Step-by-step explanation:

This is slope intercept form. The slope is 2 you can tell by the two points on the graph at (0,0) and (1,2). The points move up 2 and over 1. That makes the slope 2/1 but since the bottom half is just a one it can be simplified to 2.

And the +0 just means that its y intercept is 0,0

however it is not required to put +0 at the end

Answer:y=2x+0

Step-by-step explanation:

Given:

1. The sum of X and 96 equals half of X.

To determine the algebraic equation, we note that the sum of x and 96 would be:

x+96

Next, half of x must be like this:

x/2

Then, the phrase equals means we set x+96 equals to x/2.

Therefore, the answer is:

Answer:

A. 2.25 feet.

Explanation:

We know the following equation:

Where v is the speed, g is the gravity and h is the height. So, replacing v by 12 feet per second and g by 32 feet per second square, we get:

So, solving for h, we get:

Therefore, the answer is A. 2.25 feet.

The result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]

The first number = 3.0×[tex]10^{15}[/tex]

The second number = 5.0×[tex]10^6[/tex]

3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] means we have to divide the first number by the second number

The scientific notation is the a method of representing the a very large number or a very small number in a simple way. The general from of the scientific notation is when a number from 1 to 10 is multiplied by the power of 10.

Here we have to divide 3.0×[tex]10^{15}[/tex] by 5.0×[tex]10^6[/tex]

3.0×[tex]10^{15}[/tex]  ÷ 5.0×[tex]10^6[/tex] = (3/5) × [tex]10^{15-6}[/tex]

= 0.6×[tex]10^9[/tex]

= 6×[tex]10^8[/tex]

Hence, the result of 3.0×[tex]10^{15}[/tex] over 5.0×[tex]10^6[/tex] in scientific notation is 6×[tex]10^8[/tex]

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We are given a jar that contains 22 red marble( 1 to 20) and 52 blue marbles (1 to 52). We can proceed to find the solution for each part of the question.

PART 1

Let the probability that the marble is red be P(r).

Therefore,

This gives,

Therefore, the probability that the marble is red is:

ANSWER= 0.297

PART 2:

Let the probability of picking odd-numbered balls be P(o)

Therefore,

We already know that the total number of balls is 72 for the previous question. Therefore, the total number of oddballs will be the sum of odd red balls and odd blue balls. This consists of 11 odd red balls and 26 odd blue balls.

Therefore,

The probability of picking odd-numbered balls is

ANSWER = 0.5

PART 3:

Let the probability of picking a red or odd-numbered ball be P(r U o)

Since we already have the values of P(r) and P(o), therefore we only need to find p(r n o).

p(r n o) is the probability of the ball being red and odd. The number of the red and oddball is 11.

Therefore,

This implies that,

Hence, the probability of picking a red or odd-numbered ball is

ANSWER = 0.648

PART 4:

Let the probability of picking a blue or even-numbered ball be P(b U e)

Therefore,

From the above formula, we would need to figure out all the parts. p(b) represents the probability of blue marble. This gives,

p(e) represents the probability of even balls. The total number of even balls will be the sum of the even red balls and even blue balls.

p(b n e) represents the probability of blue and even balls. We have 26 blue and even balls

Therefore,

Therefore, the probability of picking a blue or an even ball is:

ANSWER = 0.852

The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

Total amount to spend = $720

Cost of bicycle = $401.83

Cost of bicycle reflector = $12.85 ( 4 reflector bought )

Cost of bike cloves = $23.83

Cost of biking outfits = $40.49

The number of possible biking outfits:

401.83 + 4 x 12.85 + 23.83 + M40.49 ≤ 720

401.83 + 51.4 + 23.83 + M40.49 ≤ 720

477.06 + M40.49 ≤ 720

M40.49 ≤ 720 - 477.06

M40.49 ≤ 242.94

M ≤ 242.94 / 40.49

M ≤ 6

M = Number of possible outfits

Thus,

The inequality that represents the number of outfits he can buy while staying within his budget is M ≤ 6.

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Given:

Evelyn sells beauty supplies. She gets 5% commission for selling beauty products.

Required:

To find the commission she receive if she sells $1,648 worth of beauty products.

Explanation:

The commission she receive if she sells $1,648 worth of beauty products is

Final Answer:

$82.4