Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( 20 , 6 ) b. If an American is randomly chosen, find the probability that this American will receive no more than 24 Christmas cards this year. 0.7486 c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 66% of all Americans receive at most how many Christmas cards? (Please enter a whole number)

Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

The best way to solve this problem is to simplify each factorial one by one!

Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.

At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.

To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]

Just simply multiply and then divide, and we are given 1/18

Answer:

(0,11)

Step-by-step explanation:

If we let x=0, then -y = -11, and so y=11.

Thus, (0,11) is a solution to the linear equation.

The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have a scatter plot shown in the table:

1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:

Standard deviation = SD

6SD(x) = 40

SD(x) = 40/6 = 6.67

6SD(y) = 20

SD(y) = 20/6 = 3.37

2) Slope of the line:

= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5

3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.

Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

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Answer:

X = ABC+ AB+ ABC

X = AB(C+1+C)

X = AB(2C+1)

The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.

To solve the problem, we must:

Know how many 30-minutes have passed during the time period.

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.

Friday = 48 × [tex]\frac{1}{2}[/tex] = 24

Saturday = 48

Sunday = 48

Monday = 48 × [tex]\frac{3}{4}[/tex] = 36

TOTAL = 24 + 48 + 48 + 36 = 156

Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.

Divide the number of total seconds late by the number of 30-minutes passed.

That is, the number of total seconds late= 468 seconds ÷ 156

= 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

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The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right

Figure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)

Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?

From the attached figure, we can see that:

ABCD and A'B'C'D' are on either sides of the y-axis.

This means that ABCD is first reflected across the y-axis.

ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.

This means that the reflection is followed by a translation.

The unit of translation is:

Unit = 2 - 1

Evaluate

Unit = 1

1 represents a right translation

Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right

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The standard error will be equal to 0.75.

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.

The standard error will be calculated by using the formula:-

SE = [tex]\sigma[/tex] / √n

Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.

SE = 6.5 / √75

SE = 0.75

Therefore the standard error will be equal to 0.75.

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The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

We have

(x₁, y₁) ⇒ (-4, -5)

(x₂, y₂) ⇒ (3, -3)

(x₃, y₃) ⇒ (3, -7)

Then the area will be

Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]

Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]

Area = 1/2[-18 + 4]

Area = 1/2 × 14

Area = 7 square units

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Answer:

l

Step-by-step explanation:

Answer:

Lines L and n are parallel

Explanation -

In the question it is given that angle 7 and angle 5 are supplementary.

which means that sum of this angle is 180°

so line L and n are parallel

Answer:

Step-by-step explanation:

Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.

Point-slope form into y-intercept form.

Answer:

For finding slope

we have the formula

m = y2 - y1/ x2 - x1

x1 = (-2)

x2. = ( 8)

y1. = (-1)

y2 =(-3)

putting the value of this in the formula we get,

m = (-3)-(-1)/8-(-2)

m = (-3+1)/8 + 2.

m = (-2)/10

m = (-1)/5.

m = (-1)/5

Answer:

18

Step-by-step explanation:

Using order of operations:

[tex] \frac{15 - 9}{3} (19 - 10)[/tex]

[tex] \frac{6}{3} (9)[/tex]

[tex]2(9) = 18[/tex]

Answer:

56x² + 8x

(second option listed)

Step-by-step explanation:

area: length × width

length: 7x + 1

width: 8x

(8x)(7x + 1)

{distribute 8x}:

(8x)(7x):  8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²

(8x)(1) = 8x

area = 56x² + 8x

so, the area of this rectangle is 56x² + 8x

Answer:

56x² + 8x

[answer B]

The equation would be  y+ 3/8x+9/4.

Lets try to explain in the further steps to calculate the equation,

Slope formula: (y₂ - y₁) / (x₂ - x₁)

First, plug in these values of the two given points.

[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]

Slope = -3/8

To find the equation of the line, (y- y1) = m* (x-x1)

So by putting the values into the above equation we get,

[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]

Hence the equation is [tex]y+ 3/8x+9/4.[/tex]

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Step-by-step explanation:

Very easy the value are given apply the value for X and y

From the given study, we can tell that the conclusion is; The frequency of eating breakfast is associated with lower BMI in adolescent girls.

From the study in the question, we see that a national institute is trying to examine the association of breakfast intake and body mass index (BMI).

Now, in the research we saw that the frequency is being counted about the type of foods being eaten by those surveyed to find out the impact on BMI.

From the study, we see that girls who ate breakfast more often tended to have a lower BMI. Thus, we can say that the conclusion is that The frequency of eating breakfast is associated with lower BMI in adolescent girls.

The missing options are;

A. The frequency of eating breakfast is associated with lower BMI in adolescent girls.

B. There is no relationship between eating breakfast and BMI in adolescent girls.

C. Eating breakfast makes adolescent girls thinner.

D. Skipping breakfast can contribute to obesity in adolescent girls.

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We conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

Remember that two lines are perpendicular only if the slope of one of the lines is equal to the opposite of the inverse of the slope of the other line.

So, if line l has the slope 2/3.

Then the perpendicular lines have a slope equal to -3/2.

Now, remember that if a line goes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is:

[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

So here we just need to find two points (x₁, y₁) and (x₂, y₂) such that the slope is equal to -3/2.

If we define (x₁, y₁) = (0, 0), then the other point must be:

[tex]a = \frac{y_2 - 0}{x_2 - 0} = -3/2\\\\y_2/x_2 = -3/2[/tex]

Then we can write the other point as (2, -3).

So we conclude that the line that passes through (0, 0) and (2, -3) is perpendicular to line l.

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In logarithmic form, we get In(2e^9)= ln(2)+9.

We are given,

 ln(2[tex]e^{9}[/tex])

We know that, ln(ab) = ln(a) + ln(b)

So we get,

 ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])

Since ln(m^n)=n ln(m)  

And ln(e)= 1, we will get,

ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)

          = ln(2) +9

Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.

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Answer:

the answer is L

Step-by-step explanation:

rounding up to any number/decimal requires the digit before the specified digit to be 5 or greater.
rounding down requires the digit to be 4 or less.
if the estimated time to the nearest 0.01 of a second is 35.20 then the actual race time could be from 35.195 to 35.205 since any number between could be rounded to 35.20

Step-by-step explanation:

Easy buddy....

_________________________________

Remember, from now on, wherever the function domain is asked

They mean the same inputs or xs of the function.

Now you can answer them yourself but I like to help you to do it buddy.

_________________________________

The first function's domain is :

D = { -6 , -1 , 0 , 3 }

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

The second function's domain is :

D = { -7 , -6 , -2 , -1 , 0 , 1 , 3 , 9 }

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

The domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

In any given function, all x-values (input) make up the domain of the function, while corresponding y-values (output) make up the range of the function.

In the table given, the x-values (input) are -6, -1, 0, and 3.

Therefore, the domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

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Answer:

60°

Step-by-step explanation:

since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there

Answer:

Step-by-step explanation:

Plan

7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.

Solution

7y + 5y = 180 degrees               Combine the left

12y = 180 degrees                      Divide by 12

12y/12 = 180/12

y = 15

3y + 5y + x = 180                         Combine the left side

8y + x = 180                                  Substitute 15 for y

8*15 + x = 180                               Combine

120 + x = 180                                Subtract 120 from both sides

120 -120 +x =180 - 120                 Combine

x  = 60

Answer

s = 60 degrees

<TRS = 5y = 75

When h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2 for the given expression.

The missing expression is  f(x) = x² + 2x.

f(x+h)-f(x)/h is called the formula of difference quotient.

When h---> 0 ,

the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line

Here the the expression is

f(x) = x² + 2x

Determining f(x + h) by substituting x = x + h on both sides of the given f(x).

Then f(x + h) = (x + h)² + 2(x + h)

= x² + 2xh + h² + 2x + 2h

the difference f(x + h) - f(x).

f(x + h) - f(x) = [x²  + 2xh + h²  + 2x + 2h] - [x² + 2x]

= 2xh + h² + 2h

Divide the difference from h as in the formula of difference coefficient

[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h

= 2x + h + 2

So, when h = 0 ,  [f(x + h) - f(x)]/h  = 2x +2

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Answer: It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate.

A function assigns the values. The correct option is C, x=-6.

A function assigns the value of each element of one set to the other specific element of another set.

A.) When the value of x is -12,

f(-12) = 2/3(-12) + 7 = -1

g(-12) = 2(-12) + 15 = -9

B.) When the value of x is -9,

f(-9) = 2/3(-9) + 7 = 1

g(-9) = 2(-9) + 15 = -3

C.) When the value of x is -6,

f(-6) = 2/3(-6) + 7 = 3

g(-6) = 2(-6) + 15 = 3

D.) When the value of x is -3,

f(-9) = 2/3(-3) + 7 = 5

g(-9) = 2(-2) + 15 = 11

Hence, the correct option is C, x=-6.

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Answer:

C

Step-by-step explanation:

James receives a pay increase of 100% per month and has a starting salary of $500.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the rate of pay increase and a represent the initial pay.

Let us assume that he had received 128000 after the 8 months. hence:

128000 = ab⁸   (1)

Also in the 10th month, he had received 512000, hence:

512000 = ab¹⁰    (2)

From the both equations:

a = 500, b = 2

rate of increase = 200% - 100% = 100%

James receives a pay increase of 100% per month and has a starting salary of $500.

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Answer:

Line LM

Step-by-step explanation:

First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.

Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.

To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.

Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]

Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]

Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.

If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.

The true option about the system of linear equation is that the system can only be independent and consistent.

It should be noted that the system is consistent as it can illustrate more than a solution.

Also, it can't be independent and dependent at the same time as depicted in some of the option given.

In this case, true option about the system is that the system can only be independent and consistent.

The complete question is:

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

The system can be either inconsistent or consistent.

The system can be either independent or dependent.

The system can only be independent and consistent.

The system can only be dependent and inconsistent.

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Answer:

3x²-2x+1=?

3(4²)-2(4)+1=?

3(16)-8+1=?

48-8+1=?

40+1=41

Answer:

the answer is 24

Step-by-step explanation:

6x - 48 = 4x

6x - 4x - 48 = 0

2x - 48 = 0

2x = 0 + 48

2x = 48

x = 24