Suppose that shoe sizes of american women have a bell shaped distribution with a mean of 8.21 and a standard deviation of 1.49. using the empirical rule what percentage of american women have shoe sizes that are less than 11.19

Answer:

The vector which has a greater magnitude.

Solution:

We know that, magnitude of a vector represents the length of it.

The first vector that is 2 meters long has a magnitude 2.

The second vector that is 4 meters long has a magnitude 4.

Clearly, 4 is greater that 2, i.e., 4 > 2. So, magnitude of second vector is greater.

Therefore, the vector that is 4 meters long has greater magnitude.

Step-by-step explanation:

The store has 16 board games

What are equivalent ratios?

The ratios that are same when compared are called equivalent ratios. The equivalentity of two or more ratios can be determined by comparing them to one another. For instance, 1:2 and 2:4 have the same ratio.

Let x = number of legos

Let y =  number of board games

Given ratio: 9:6= 9/6

x/y = 9/6

substitute x=24

24/y=9/6

Do cross multiplication

(6*24)/9=y

16=y

or

y=16

So, the store has 16 board games

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Rajiv chose to make a cardboard box of length 7 cm from the given cardboard available.

It is given that the amount of cardboard available is 245 cm.  Therefore, the box's surface area will be less than or equal to 245 cm².

We are given that the box does not have any lid. Hence, the box is made up of 5 squares.

Let the length of one side of the box be x cm.

We know, that the surface of the area of a regular cube is

6a².

That means,

no. of squares X square of the length.

Hence, the surface area of the box is 5x².

Therefore from the given problem, we get that

5x² ≤ 245

or, x² ≤ 245/5

or, x² ≤ 49

49 is a perfect square of 7. Hence assuming Rajiv makes the largest possible box,

the length of the side he chose is 7 cm.

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Answer:

Two points A(x,y) B(x₂,y₂) or One point A(x,y) and gradient(slope).

Step-by-step explanation:

Answer:

v=53 degrees

Step-by-step explanation:

So since 180 degrees in tri, v-23+2v+v-9=180

Plus 23 and 9: 4v=212

v=53 degrees

The.maximum number of gigabytes Meena can use while staying within her budget is 5 gigabytes

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal.

They are denoted by the symbols ≥ < > ≤.

Let the maximum gigabytes be x.

The inequality to illustrate the information will be:

38 + 3x < 55

Collect like terms

3x < 55 - 38

3x < 17

Divide

x < 17/3

x < 5 2/3

The maximum gigabytes is 5.

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The age of Jane based on the information is 10 3/10 years.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

In this case, Dan is 12 4/5 years old, Karina is 1 1/6 years younger than Sarah and Jane is 1 1/3 years younger than Greg

The age of Jane will be:

= 12 4/5 - 1 1/6 - 1 1/3

= 12 24/30 - 1 5/30 - 1 10/30

= 12 24/30 - 2 15/30

= 10 9/30

= 10 3/10

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The required line is y = 1.5·x + 2 which represents line K.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The given coordinate of two points on the line are;

(-2, 5) and (0, 2)

Line K is the line about which line L is reflected.

The coordinates of the point's image (x, y) after a reflection about

the y-axis is the point (-x, y).

Therefore, the coordinates of the points on the line K are;

(-2, 5) → (2, 5)

(0, 2) → (0, 2)

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 2, y₁ = 5

x₂ = 0, y₂ = 2

⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute values in the equation, we get

⇒ y - 5 = (5 - 2)/(0 -2)[x -2]

⇒ y - 5 = -3/2(x-2)

⇒ y = 1.5·x + 2

Therefore, the required line is y = 1.5·x + 2 which represents line K.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-7}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-7}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-3)}}} \implies \cfrac{-7 +2}{1 +3} \implies \cfrac{ -5 }{ 4 } \implies {\Large \begin{array}{llll} - \cfrac{5 }{ 4 } \end{array}}[/tex]

Answer:

The answer is -256

Step-by-step explanation:

-4+-4=-8

-8+-8=-16

-16+-16=-32

-32+-32=-64

-64+-64=-128

-128+-128=-256

Hope this helps :)

Answer:

One Solution

Step-by-step explanation:

5(3x+2)-2=4(4x-3)

15x + 10 - 2 = 16x - 12

15x + 8 = 16x - 12

15x = 16x - 20

-x = -20

x = 20

Answer: 4

Step-by-step explanation:

100/8 = 12 golf balls in each box

8*12 = 96 golf balls are used

100-96= 4 gold balls left

The points on the ellipse 5x² + y² = 5 that are farthest away from (1, 0) are (-0.25, ±√4.6875).

The square of the distance from a point on the ellipse to the point (1, 0) is ...

 d^2 = (x -1)^2 +y^2

Using the equation of the ellipse to write an expression for y^2, we have ...

 d^2 = (x -1)^2 +5 -5x^2

 d^2 = -4x^2 -2x +6

The expression on the right is that of a downward-opening parabola with ...

 a = -4, b = -2, c = 6

The maximum is located at ...

 x = -b/(2a) = -(-2)/(2(-4)) = -1/4

The value of y there is ...

 y^2 = 5 -5(-1/4)^2 = 4 11/16

 y = √4.6875

Hence the points on the ellipse farthest from (1, 0) are (-0.25,±√4.6875).

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Answer:

1/4b

Step-by-step explanation:

The measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees

What are isosceles triangles?

Isosceles triangles are triangles that have two sides equal in measurement.

Main Body:

From the given diagram;

∠BAC = 18 degrees

∠BDC = 48 degrees

Required angle  : ∠ABD

From the diagram, ∠DAB = ∠BAC = 18 degrees

Also, ∠ADC + ∠ACD + ∠DAC = 180

Since triangles ACD is isosceles, hence ∠ADC = ∠ACD. The expression above becomes

∠ADC + ∠ADC + ∠DAC = 180

2∠ADC + ∠DAC = 180

2∠ADC  = 180 - 36

2∠ADC = 144

∠ADC = 144/2

∠ADC = 72 degrees

This means that ∠ADB = 72 - ∠BDC

∠ADB = 72 - 48

∠ADB = 24 degrees

Get the required angle ABD

From triangle ADB, ∠ABD + ∠ADB + ∠DAB = 180

∠ABD + 24 + 18 = 180

∠ABD + 42 = 180

∠ABD = 180 - 42

∠ABD = 138 degrees

Hence the measure of angle ABD if triangles ACD and BCD are isosceles is 138 degrees.

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Answer:

$8551.56

Step-by-step explanation:

In the equation

[tex]A=P(1+\frac{r}{n})^(nt)[/tex],

P is the principal (in this case, the amount loaned to Erica), r is the interest rate, n is the number of times compounded per year (12 in the problem since there are 12 months in a year), and t is the time in years.

By plugging in our principal, rate (converted to a decimal), compounding periods and time, we have:

[tex]A=5300(1+\frac{0.08}{12})^(12*6)\\ A=5300(\frac{151}{150})^(72)\\ A=8551.561=8551.56[/tex]

Y in the expression represents the range of the function. Option A is correct.

Given that,
In the expression y = 12- 4x, what y = 3 represents in the function, is to be determined.

Range, it is the set of values that come out to an outcome for a certain mathematical operation.

here,
y = 12 - 4x
where, 12 = intercept , -4 = rate,
when y = 3 implies that, at the value of x, the outcome of the equation is 3 or it is said to be range.

Thus, Y in the expression represents the range of the function. Option A is correct.

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The probability of an event {a or b} is 0.7

Probability: It is the branch of mathematics concerning numerical, descriptions of how likely an event is to occur or how likely it is that a proposition is true. the probability of an event is a number between

0 and 1.

if the two events a and b are mutually exclusive then the addition rule of probability is:

P( a or b) = P(a) + P(b) - P(a∩ b)

Given that,

P(a) = 0.6                    P(b) = 0.5

               P(a ∩ b)= 0.4

According to probability methods, if two events are mutually exclusive, then the probability of either occurring is denoted as P (a ∪ b).

Now, we know that,

P( a ∪ b) = P(a) + P(b) - P( a ∩ b)

              = 0.6 + 0.5 - 0.4

              = 0.7

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The cost of one knife is £ 5.52.

Given, one knife is equal to three times spoon.

Let the cost of knife be x, and cost of spoon be y.

x=3y. ------(1)

9 spoons and 12 knives costs £82. 80, which can be written as

9(spoons)+12(knife)=£82. 80

9y+12x=£82. 80

9y+12(3y)=£82. 80

9y+36y=£82. 80

45y=£82. 80

y=£82. 80/45

y=£ 1.84

The cost of one spoon is £1.84.

We have to find the cost of one knife, we can substitute the value of y in equation 1 to get the cost of one knife.

x=3(1.84)

x=5.52.

Therefore, the cost of one knife is £5.52.

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Corrected Question

A knife is three times the cost of a spoon.  9 spoon and 12 knives cost £82. 80 work out the cost of one knife.

If Netflix would like to estimate the proportion of their current subscribers who would pay extra for a premium membership including access to more movies and tv shows. The number of  subscribers they must  sample to obtain this interval is: b) 385.

Using this formula to find the number of  subscribers  they must sample to obtain this interval

n≥ (zσ/2 ÷ 2ME)²

Where:

n= Sample =?

zσ = Z-score for 95% confidence interval = 1.96

ME = margin of error = 0.05

Let plug in the formula

n≥ [1.96 / 2(0.05)]²

n≥ [1.96 / 0.1]²

= (19.6)²

= 384.16

=385 (Rounded)

Therefore the correct option is B.

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The complete question is:

Netflix would like to estimate the proportion of their current subscribers who would pay

extra for a premium membership including access to more movies and TV shows. To do

this, they plan to calculate a 95% confidence interval to estimate the proportion. They

would like a margin of error of .05. How many subscribers must they sample to obtain this

interval?

a) 1537

b) 385

c) 192

d) 10

[tex]\tan \theta=\frac{7}{16} \\ \\ \theta=\arctan(7/16) \approx 24^{\circ}[/tex]

The 99 percent confidence interval for the mean score of all subjects lies greater than 63.464 and less than 78.936.

Given:

No. of samples (n)= 16

df = n-1 = 16 -1 = 15

The mean score is 71.2

The standard deviation = 10.5.

So, from the t-distribution of critical values table through the above-mentioned details. We get the values:

Alpha / 2 = 0.005

z = 99/100 + 0.005 = .99 + .005 = .995

Sample mean = xbar = 76.2

t = 2.947

The formula for standard error = E = value of t (at z, and df) / S.D./sqrt(n)

i.e. E = 2.947 x 10.5 / sqrt 16 = 7.736

I = 71.2 +/- E =  71.2 +/-  7.736

99 percent confidence interval - 71.2 +/- 7.736

Adding both sides 7.736 for range. We get,

63.464 < u < 78.936

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The answer to the question probability of randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

What is standard deviation?

A measure of a group of values' variance or dispersion in statistics is called the standard deviation. When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

The lowercase Greek letter sigma, which stands for the population standard deviation, or the Latin letter s, which stands for the sample standard deviation, are most frequently used in mathematical equations and texts to represent standard deviation. Standard deviation is also sometimes referred to as SD.

The mean blood pressure for people in china is 128 mmHg.

The standard deviation of 23 mmHg.

For blood pressure of 182.6 mmHg

=p(x> 182.6)

=p(z> 182.6-128/23)

=p(z> 2.37)

=0.0088

Hence the probability of a randomly selected person has a blood pressure of 182.6 mmHg is 0.0088.

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From given report, on average college women gain more weight than college men during their first year of college.

In this question, we ahve been given a study is conducted to show that college women, on average, gain more weight than college men during their first year of college.

The study is completed and reports a p-value of 0.001

We need to write the conclusion for above situation.

We can see that the results are statistically significant.

And from given p-value, we can say that on average college women gain more weight than college men during their first year of college.

Therefore, on average college women gain more weight than college men.

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The equation to represent total amount of money that she receives for the tee shirts in terms of number of machines is  2800*n*(200 - n)  .

In the question ,

it is given that

the cost of 1 tee - shirt = $14

total days required to deliver the tee shirt = 20

number of tee - shirts that a machine can produce = 200 per day

let the number of machines = n

so the number of days require to set up the machines = n

hence all the machine will work for = (20 - n) days  

1  machines will produce 200(200 - n) tee shirts

n machines will produce = 200n(200 - n) tee shirts in the remaining (20 - n) days .

the selling price of 1 tee shirt is = $14

So, the total money M that she will receive is = 14*200*n*(200 - n)

= 2800*n*(200 - n)

Therefore , The equation to represent total amount of money that she receives for the shirts in terms of number of machines is  2800*n*(200 - n)  .

The given question is incomplete , the complete question is

A manufacturer wishes to make tee-shirts for the band dixie chicks. They sell for $14 each. She must deliver all the tee-shirts in 20 days time. The manufacturer will first set up some machines. Once all machines are set up she will turn them on. Each machine takes one day to set up. A machine produces 200 shirts in one day. All the machines must be set up before any of them are turned on. Express the total amount of money( M ) she will receive for the shirts in terms of the number of machines she decides to set up (assuming she sells all the shirts she makes).

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Mr. Patrick instructs 15 students in math. He discovered that Payton had received a 95 on the test while grading them from average.

There are 15 kids in Mr. Patrick's class. The average score on his most recent exam was 80 for 14 candidates (not including Payton).

I'm going to use x to represent the unknowable sum of the 14 test scores. Average is computed by adding all the numbers in the set (whose average you're trying to get) together, then dividing by the total number of numbers in that set.

This was the total of their scores: x=1120.

Adding Payton's score now (I'll use the letter p to stand in for her score):

1120+p /15=81→ Her test score was included in the fifteen students' average, which was 81 1120+p=1215

P=95.

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Answer:

343

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

D   the premium you pay is your bill for insurance

When  you transform row score into a set of z- score, you are able to compare the score of both distribution. When you compare the scores you can allow one to have a mean of 0 and standard deviation 01. A z- score let us see how many standard deviation away from the mean an element lies.

Z- score: It is a numerical measurement that describes a value's relationship to the mean of a group of values and is measured in terms of standard deviation from mean.

Raw score: A raw score is unaltered measured. For example:- if there is a test in a class and someone for 75 out of 100, 75 would be there raw score.

Transform a set a raw scores into  a set of z score:

Lets understand the importance of transforming  raw scores into  a set of z score with the help of an example.

For admission in PG program students need to appear  in the entrance exam which held in two batches. John appeared in both the exams and he scored 160 out of 200 in paper A and 145 out of 185 on paper B.

Solution: we needs to find the z score corresponding to each paper in order to compare them.

paper A: Score obtained : 160

              Average score: 155

              Standard Deviation: 10

Paper B: Score obtained: 145

               Average obtained: 135

                Standard deviation: 08

Using the Z- score formula:

             Z = (x - μ) /α

Using the above Z score formula to calculate z score for given raw score values:

z score for Paper A =  ( 160-155)÷ 10    

Z score for paper B = ( 145 - 135 ) ÷ 1.25

While Evaluating based on z score, we can say that John performed relatively better in paper B as compared to paper A.

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The number of hours Jason needs to work to earn $294.50 is 19 days which was found by using the given data.

Given: Jason's pay is directly proportionate to the number of hours he works at his job. Jason works 12 hours a day and makes $186.

Number of hours he needs to work to earn $294.50 is given as

= (12 × 294.50)/186

= 19

Therefore, the number of hours Jason needs to work to earn $294.50 is 19 days.

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