5. Mr. Q's class is having a give-
away where his students can
receive 100 classroom credits.
He will pull names out of a hat
and select two winners. Once a
student wins, they are not
eligible to win a second time. If
there are 40 total people in the
class, including you and your
best friend.

What is the probability that both you and your best friend get the 100 classroom
credits? (Show work please)

In a symmetric, unimodal distribution, about two-thirds of the observations are within one standard deviation of the mean. Option A is correct.

GIven that,
To determine the appropriate options that complete the statement "In a symmetric, unimodal distribution, about two-thirds of the observations are where".

The statistic is the study of mathematics that deal with relations between comprehensive data.

Here,
From the definition of symmetric and unimodal distribution,
At least one standard deviation of the mean is two-thirds of the observation.

Thus, In a symmetric, unimodal distribution, about two-thirds of the observations are within one standard deviation of the mean. Option A is correct.

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Answer:

D

Step-by-step explanation:

The value of the missing side lengths x and y are 5√2 and 5 respectively.

The figure in the image is a right triangle.

Angle θ = 45 degree

Hypotenuse = x

Opposite to angle θ = y

Adjacent to angle θ = 5

To solve for side x and side y, we use the trigonometric ratio.

Note that:

Cosine = adjacent / hypotenuse

tangent = opposite / adjacent

Solving for x:

Cosine = adjacent / hypotenuse

Plug in the values

cos( 45 ) = 5/x

x = 5 / cos( 45 )

x = 5√2

Solving for side y:

tangent = opposite / adjacent

Plug in the values

tan( 45 ) = y/5

y = tan( 45 ) × 5

y = 5

Therefore, the value of side length x is 5 units.

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Answer:

\(x\approx 267\ miles\)

Step-by-step explanation:

Linear Modeling

Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.

The linear function can be expressed in the slope-intercept format:

\(f(x)=mx+b\)

For the problem at hand, we must pick the adequate variables according to the data provided.

The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:

c = the charge for renting a car in dollars

x = the distance driven by the businessman in miles

Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:

\(c = mx+b\)

We must find the values of m and b with the data provided. Substituting the first point:

\(79 = 150m+b\)

Substituting the second point:

\(63.70 = 65m+b\)

Both equations form the following system:

\(\left\{\begin{matrix}150m+b=79\\ 65m+b=63.70 \end{matrix}\right.\)

Subtracting both equations:

\(150m-65m=79-63.70\)

Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:

\(85m=15.3\)

Solving:

\(m=15.3/85=0.18\)

From the first equation

\(79 = 150m+b\)

Solving for b:

\(b=79-150m=79-150(0.18) = 52.\)

The model for the problem is:

\(c=0.18x+52\)

Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100

\(100=0.18x+52\)

Solve for x:

\(0.18x+52=100\)

\(0.18x=100-52=48\)

\(x=48/0.18=266.67\)

Rounding to the closest integer:

\(\boxed{x\approx 267\ miles}\)

To conduct a hypothesis test for the difference between two population proportions under independent sampling is,

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5.

What is population proportion?

In statistics, a population proportion is a parameter that describes a percentage value connected to a population. It is typically denoted by P or the Greek letter π.

As per central limit theorem sample size needs to be greater than 30.

So required conditions are Only if n1 ≥ 30 and n2 ≥ 30.

Also for normal approximation we need the condition

\(np \geq 5 and\)  n(1 - p) ≥ 5

So one more condition is Only if

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5

Hence,  to conduct a hypothesis test for the difference between two population proportions under independent sampling is

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5

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Answer:

1. 26

2. x = 1.5

Step-by-step explanation:

1. C(0.7) means to plug in 0.7 into the equation

here, C(x) = 30x + 5. replace x with 0.7 to get

C(0.7) = 30*0.7 + 5= 26

2. C(x) = 30x + 5 = 50

30x+5 = 50

subtract 5 from both sides to isolate x and its coefficient

30x = 45

divide both sides by 30 to find x

x = 1.5

The equation that represents the total number of black and white squares on the chess board is 8 * 2² = 32

From the question, we have the following parameters that can be used in our computation:

The chess board

From the chess board, we have

Black squares = 32

White squares = 32

When factorized, we have

Black squares = 32 = 8 * 2²

White squared = 32 = 8 * 2²

Hence, the equation that represents the squares on the chess board is 8 * 2² = 32

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Answer:

It's D

Step-by-step explanation:

Answer:

3 feet 11 inches

Step-by-step explanation:

Answer:

ok is that supposed to be on top of the number because if so it is 8'10-4'11=

Step-by-step explanation:

1069547520 but I am not sure if that could be the slightest bit correct you could try it thought :D

Answer:

a.) After using the coupon the total comes out to 32.75

b.) It shows a different way buy adding 10 with the number of hours times the price per hour minus the discount.

Step-by-step explanation:

Expression A: 18x dollars (Before coupon)

Expression B: 18x dollars (Before coupon)

To use the coupon, subtract 1.5 with 8 giving you 7.5 per hour replacing the 8's with 7.5

For example: [A] (10+7.5h)

Answer:

0 = 0 means that there are infinite solutions.

Step-by-step explanation:

Equation is -5(-4+2n)=-10(n-2)

1. Distribute the -5 and -10

20 -10n = -10n + 20

2. Subtract 20 from one side to the other to get only 1 variable on 1 side.

-10n = -10n

3. divide -10 to separate the variable from the constant.

n = n

This means there are infinite solutions.

Answer:

Step-by-step explanation:

Mass of the planet:

The water's mass:

Mass of the planet's water:

To beat the school long jump record, John must jump an additional 5 1/4 inches

From the given question, we are to determine how farther John must jump in order to break the record

From the given information,

"A high school track team's long jump record is 23 ft 1 3/4 in"

and

"John's best long jump is 22 ft 8 1/2 in"

First, we will convert the distances to inches

NOTE: 1 ft = 12 inches

23 ft 1 3/4 in = 276 + 1 3/4 in = 277 3/4 in

22 ft 8 1/2 in = 264 + 8 1/2 in = 272 1/2 in

Now, to determine how farther John must jump, we will subtract the distances

277 3/4 in - 272 1/2 in = 5 1/4 in

Hence, he must jump 5 1/4 in farther

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Answer: Convert the mixed numbers to improper fractions, then find the LCD and combine them.

Exact Form:

188

5

Decimal Form:

37.6

Mixed Number Form:

37

3

5

hope this helped have a nice day! :)

Answer:

Step-by-step explanation:

(124+64) /5

= 188/5

Answer is = 37.5

Answer:

Step-by-step explanation:

Josslyn burns 7 calories per minute while swimming and 5 calories per minute while practicing yoga. Let x be the number of minutes she spends swimming and y be the number of minutes she spends practicing yoga.

The total number of calories burned, C, is given by:

C = 7x + 5y

To burn at least 500 calories each day, we can write the inequality:

7x + 5y ≥ 500

This inequality states that the total number of calories burned from swimming and practicing yoga, 7x + 5y, must be greater than or equal to 500. Josslyn can achieve this goal by spending a combination of x minutes swimming and y minutes practicing yoga.

Answer:

some ppl got summer school

Step-by-step explanation:

Answer:

oc,2

Step-by-step explanation:

(__(_+)£)£(£886++17+£7+

\(\frac{25-17}{25}\)×\(100%\)%

\(=32\)%

∴ 32% is left to be plant.

9514 1404 393

Answer:

  x + 3y = 9

Step-by-step explanation:

The parallel line will have the same x- and y-coefficients. The new constant can be found by using the (x, y) values of the given point.

  x + 3y = (6 +3(1)) = 9

The equation of the parallel line is ...

  x + 3y = 9

Answer:

Step-by-step explanation:

Answer: 36

Step-by-step explanation: Gail needs 9 yards of fabric for a quilt. How many different patterns of fabric does she need if she buys

1

4

of a yard of each pat

patterns

Step-by-step explanation:

5+4m=21

4m=21-5

4m=16

m=16/4

m=4

Answer:

m=6

Step-by-step explanation:

(6)+4m(-1)=21<subtract 6-1

(-5)+4m=(21)<subtract 5 to both sides

(4m)=(26)<divide

Answer:

-23

Step-by-step explanation:

Any number multiplied by 1 is the same

*17-(-30)x1+1-71

=17+30+1-71

=47+1-71

=48-71

=-23

Step-by-step explanation:

17-(-13)1+1-71=

17+13×1+1-71=

17+13+1-71=

30+1-71=

31-71=

=-40

Jennifer and Charlie took 6.16 days.

According to the question, to complete the painting job by Jennifer in 11 days and same job with Charlie in 14 days. Using time and work concept, the given expression can be written as:

Jennifer one day work (A)= 1/11

Charlie one day work (B) = 1/14

Now, when both of them working together, then add both the values:

A + B = 1/11 + 1/14 = (14 + 11)/(154) = 25/154

So, the time taken by Jennifer and Charlie together is: 154/25 = 6.16 days.

Hence, the correct answer is 6.16 days.

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Answer:

-20r + 40

Step-by-step explanation:

-10(2r - 4)

-20r +40

Nestor, this is the solution to the problem:

Step 1: Let's isolate x in the first equation, this way:

2x + 3y = -15

2x = -15 - 3y

Dividing by 2 at both sides:

2x/2 = (-15 - 3y)/2

x = (-15 - 3y)/2

Step 2: Let's substitute x and solve for y in the second equation, as follows:

-7x - 4y = -6

-7 (-15 - 3y)/2 - 4y = -6

Solving parenthesis:

105 +21y/2 - 4y = -6

Multiplying by 2 at both sides:

105 + 21y - 8y = -12

Like terms:

13y = -12 - 105

13y = -117

y = -9

Step 3: Let's solve for x in the first equation, this way:

2x + 3y = -15

2x + 3 * -9 = -15

2x -27 = -15

Adding 27 at both sides:

2x - 27 + 27 = -15 + 27

2x = 12

Dividing by 2 at both sides:

2x/2 = 12/2

x = 6

Answer:

x=10

Step-by-step explanation:

add al the numbers that are alike so xes with xes blah blah

17x+10=180

-10 both sides

17x=170

divide 17 both sides

check

5(10)=50-1=49

80+5=85

40+6=46

49+85+46=180