One batch of trail mix can be made by mixing 3 cups of granola with 0.75 cup of raisins. Hamid needs to make a bigger batch of trail mix. He makes a graph to be sure the mixture will be correct. On a coordinate plane, the point (3, 0.75) is plotted. How can he use the graph to find an equivalent ratio?

Answer:

7.1349 * 102

Step-by-step explanation:

Hope this helps. Have a great day!

the approximate probability that a randomly selected fast male cross-country runner completes a 5K in less than 17 minutes is 0.68.

To approximate the probability that a randomly selected fast male cross-country runner completes a 5K in less than 17 minutes, we can use the 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule.

According to this rule, for a normal distribution:

- Approximately 68% of the data falls within one standard deviation of the mean.

- Approximately 95% of the data falls within two standard deviations of the mean.

- Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean is 16.5 minutes and the standard deviation is 0.5 minutes.

To find the probability of completing the 5K in less than 17 minutes, we need to calculate the z-score, which measures the number of standard deviations a particular value is from the mean.

The z-score can be calculated using the formula:

z = (x - μ) / σ

where x is the value we want to calculate the probability for, μ is the mean, and σ is the standard deviation.

For our case, x = 17, μ = 16.5, and σ = 0.5.

Plugging these values into the formula, we get:

z = (17 - 16.5) / 0.5 = 1

Now, we can use the z-score to estimate the probability. Since we want the probability of completing the 5K in less than 17 minutes, we need to find the area under the normal curve to the left of the z-score.

Using the 68-95-99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean. Since our z-score is 1, which is within one standard deviation, we can approximate the probability to be around 68%.

Therefore, the approximate probability that a randomly selected fast male cross-country runner completes a 5K in less than 17 minutes is 0.68.

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The given number 314,609 is rounded to:

The nearest hundred thousand: 300,000

The nearest ten thousand: 310,000

The nearest thousand: 315,000

To round the place values of a number to the nearest place values following rules are considered:

The given number is 314,609

The number name for 314,609 is " Three hundred and fourteen thousand, six hundred and nine "

The order of the places is Hth(Hundred thousand), Tth(Ten thousand), Th(Thousands), H(Hundreds), T(Tens), O(Ones)

Rounding to the nearest hundred thousand:

Hth  Tth  Th  H  T  O

3       1      4    6  0  9

The digit in the hundreds of thousands place is "3". The digit next/after this place is "1" in ten thousand's place. Since 1 < 5, the digits after 3 are rounded as zeros. I.e., 300,000.

Thus, the nearest hundred thousand for the given number is 300,000.

Rounding to the nearest ten thousand:

Hth  Tth  Th  H  T  O

3       1      4    6  0  9

The digit in the ten thousand places is "1". The digit after this place is "4" in the thousands place. Since 4 < 5, the digits after 1 are rounded as zeros. I.e., 310,000.

Thus, the nearest ten thousand for the given number is 310,000.

Rounding to the nearest thousand:

Hth  Tth  Th  H  T  O

3       1      4    6  0  9

The digit in the thousand's place is "4". The digit after this place is "6" in the hundreds place. Since 6 > 5, the digit in the thousands place is added by 1, and the digits after it are made as zeros. I.e., 4 + 1 = 5 and the rounded number is 315,000.

Thus, the nearest thousand for the given number is 315,000.

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If we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

Given,

The total amount = $60

The ratio = 3:1

Then the amount given to first person = 3x

The amount given to the second person = x

Given that the total amount is 60

Then  the equation will become

x+3x=60

4x=60

x=\(\frac{60}{4}\)

x=15

The amount given to the first person = 3x

Substitute the value of x in the equation

The amount given to the first person =3x

=3×15

= $45

The amount given to the second person =x

= $15

Hence, if we share $60 in the ratio 3:1, then each person will get is $45 and $15 respectively

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Answer:

184 boxes

Step-by-step explanation:

8648/47 = 184

Answer:

84.53%

Step-by-step explanation:

total=293

completed=247.7

percentage=247.7/293. ×100%

=84.539%

Answer:

The class sociologist Max Weber formulated a three-component theory of stratification that saw political power as an interplay between “class”, “status” and “group power. ” Weber theorized that class position was determined by a person’s skills and education, rather than by their relationship to the means of production

Therefore, the rank of matrix 'a' in this case would be 5.

To find the rank of a matrix, we need to perform row reduction to obtain its row echelon form (REF) or reduced row echelon form (RREF). However, since the matrix 'a' is not provided, I cannot perform the calculations or determine its rank.

The rank of a matrix is equal to the number of non-zero rows in its row echelon form or reduced row echelon form. If the system of equations 'ax = 0' has a two-dimensional solution space, it means that the rank of matrix 'a' is less than the number of columns (6) but greater than 4 (since the solution space is two-dimensional).

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Answer: 30

Step-by-step explanation:

1 yard is 3 foot so meaning 10 yards will be 30, always multiply your given yard number by 3 to find the feet

Answer:

504 ft^3

Step-by-step explanation:

Ok, so we have the equation for the cylinder as well as the rectangular prism. Basically we're just going to find the volume of each of them separately and then add them together.

Let's start with the cylinder:

V(cylinder) = pi*r^2*h

pi = 3

d = 4ft

r = d/2 = 4/2 = 2ft

h = 12ft

V(cylinder) = (3)*(2^2)*(12)

V(cylinder) = 3*4*12

V(cylinder) = 144 ft^3

Now the rectangular prism:

V(rectangular prism) = l*w*h

l = 10ft

w = 6ft

h = 6ft

V(rectangular prism) = 10*6*6

V(rectangular prism) = 360 ft^3

Now we can add them together:

V(total) = 360 + 144

V(total) = 504 ft^3

Answer:

m<2= 48

m<3= 52

m<4= 48

Step-by-step explanation:

the opposite of 1 is 3 so 3 is 52 bc  opposite angles have the same degree

to find angle 4 you subtract 90 by 52 bc 90 is the total for angle 1 and 4

to find angle 2. u find the opposite of it which is 42 and like i said opposite angles have the same degree

hope this helps

Answer:

D. 23/27

Step-by-step explanation:

The good news is, they wrote out all the possible options for you.

There are 27 possibilities in all, so that's our denominator.

They want to know which possibilities have a W in there OR an R comes first. So we'll count up the possibilities that start with R. There are 9.

Then, of the remaining 18, 14 include a W somewhere in there.

9 + 14 = 23 out of 27.

We are not counting the Ws in the possibilities that start with R, because of the OR in the sentence.

Please let me know if you have questions about this.

Answer:

It would be B

Step-by-step explanation:

24 and 36 greatest common factor is 12 and  its least is 72

With the thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters.

a) 40% of the flanges exceeds 1.01 millimeters.

b) 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of flange thickness is 1 millimeters and the variance of flange thickness is 0.01 millimeters^2.

a) To determine the proportion of flanges that exceeds 1.01 millimeters, we need to find the area under the probability density function (pdf) of the thickness that is greater than 1.01 millimeters.

Let's call the random variable X representing the thickness of the flange. The pdf of X is uniform, so it has constant value over the interval [0.95, 1.05]. Therefore, the proportion of flanges that exceeds 1.01 millimeters can be found as follows:

P(X > 1.01) = (1.05 - 1.01) / (1.05 - 0.95) = (1.05 - 1.01) / 0.1 = 0.04 / 0.1 = 0.4

So, 40% of the flanges exceed 1.01 millimeters.

b) To find the thickness that is exceeded by 90% of the flanges, we need to solve for X in the following equation:

P(X > X) = 0.9

Substituting the values for the pdf, we get:

(X - 0.95) / (1.05 - 0.95) = 0.9

Solving for X, we get:

X = 0.95 + 0.9 * (1.05 - 0.95) = 0.95 + 0.9 * 0.1 = 0.95 + 0.09 = 1.04

So, 1.04 millimeters is the thickness that is exceeded by 90% of the flanges.

c) The mean of X can be calculated as follows:

Mean = (0.95 + 1.05) / 2 = 1

The variance of X can be calculated as follows:

Variance = (1.05 - 0.95)^2 / 12 = 0.01

So, the mean and variance of flange thickness are:

Mean = 1 millimeters

Variance = 0.01 millimeters^2

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Option A is the correct answer. Ellora wants to accumulate 150,000 in an RRSP by making annual contributions of 5,000 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

First, we have to find the interest rate per quarter, which will be
\(5.5% / 4\)= 1.375%.
The formula for the future value of an annuity is: 
\(FV = (C * [(1 + r)^n - 1] / r)\),

For Ellora, \(FV = $150,000, C = $5,000, and r = 1.375%.\)
Substituting these values into the formula gives:
\(150,000 = 5,000 * [(1 + 0.01375)^n - 1] / 0.01375\)
Simplifying this equation gives:
\(30 = [(1.01375)^n - 1]\)

We can solve this using logarithms:
\(ln 30 = ln [(1.01375)^n - 1]\)
\(ln 30 = n * ln 1.01375 - ln 1.01375e^(ln 30) / e^(-ln 1.01375) = n18.202125 = n\)

Therefore, it will take Ellora 18.202125 years to accumulate 150,000 in her RRSP through \($5,000\)annual contributions made at the beginning of each year with interest of \(5.5%\) compounded quarterly.

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Step-by-step explanation:

131.58 --> 130.00

130.00 ÷ 10 = 13

13 = 10% of 130

13 x 2 = 26 (20% of 130)

The tip would be $26

Answer:

$27.93

Step-by-step explanation:

First we divided 4 from 15.96 and got 3.99, so now we know that $3.99 is how much each ounce of jellybeans costs so now we multiply 3.99 times 7 to get our answer of 27.93.

Answer:

1 is true

2 is true

3 is true

4 is false

5 is true

6 is true

The Probability of a pregnancy lasting less than 250 days is 0.1151.

Probability: - It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed  from 0 to 1.

Let the length of human pregnancy be denoted by X. We obtain the probability associated with this value by converting it to be standard normal ( z) score and then consulting a Z- table to find the corresponding probability.

P(x< 250) = P( x-μ /σ < 250 - 268 /15)

                = P( z < -1.2)

                = 0.1151

∴ The probability of a pregnancy lasting less than 250 days is 0.1151.

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Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Equation of regression line : y^ = 60.7 + 0.139x

x = payroll (in millions of dollars) and y = number of wins for Major League Baseball teams in 2016.

From the general regression equation:

y = mx + c

Where m = slope of regression line.

The slope (m) of the equation given is 0.139

The slope could be interpreted as ; for every per unit change in y (every win a major league baseball team has in 2016), the payroll in million dollar increases by a product of 0.139

The slope of a regression line is the average rate of change of the line.

The interpretation of the slope is: the rate of wins per payroll is 13.9%

From the question, we have:

\(\mathbf{\bar y= 60.7 + 0.139x}\)

The equation of a linear regression is:

\(\mathbf{\bar y= c + mx}\)

Where m represents the slope

So, by comparison:

\(\mathbf{m = 0.139}\)

\(\mathbf{m = 13.9\%}\)

This means that, the rate of wins per payroll is 13.9%

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The scale structure being used in a question that asks the respondent to write in his or her age on the survey is Ratio. Option C is correct.

The ratio scale allows for the measurement of quantities with a meaningful zero point and consistent intervals between values. Age is a variable that can be measured on a ratio scale because it possesses these characteristics. It has a meaningful zero point (birth), and the intervals between ages are consistent (each year represents an equal interval).

Thus, the required, scale structure being used in a question that asks the respondent to write in his or her age on the survey is Ratio.

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The question seems to be incomplete, the complete question is:

What type of scale structure is being used in a question that asks the respondent to write in his or her age on the survey?

A. Nominal

B. Ordinal

C. Ratio

D. Interval

E. Likert

The average time required for a passenger to pass through security screening is found to be approximately 0.0612 minutes.

(a) The operating characteristics for the screening facility with two screening stations open are as follows:

P0 = 0.0196

Lq = 0.3922

L = 0.4902

Wq = 0.0490 min

W = 0.0612 min

Pw = 0.0909

(b) The two-screening-station system will not be able to meet the facility manager's goal of limiting the average number of passengers waiting in line to 10 or fewer.

The operating characteristics for the screening facility with two screening stations open are calculated as follows:

P0 = 0.0196, Lq = 0.3922, L = 0.4902, Wq = 0.0490 min, W = 0.0612 min, Pw = 0.0909.

Based on these calculations, the two-screening-station system will not be able to meet the facility manager's goal of limiting the average number of passengers waiting in line to 10 or fewer.

(c) The average time required for a passenger to pass through security screening is 0.0612 minutes.

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Answer: 76 meters

Step-by-step explanation:

top side left blank = 18 because it is congruent to the bottom

left side blank is 4 + 4 + 4 (right side lengths added)

left side blank is 12

add all side lengths together for perimeter

12 + 18 + 4 + 8 + 4 + 8 + 4 + 18 = 76

76 meters

Step-by-step explanation:

Hey there!!

It 's so simple.

You remember common property of triangle. (i.e sum of interior angle of a triangle is 180°)

So,

77° + 31° + x = 180°

x + 108° = 180°

x = 180° - 108°

Therefore the measure of angle x is 72°.

Hope it helps....

Step-by-step explanation:

1. find P of semicircle

perimeter of a semicircle = pi×r+d

=3.14×5+10

=25.7

2.find P of rectangle

P=10×4=40cm

3. add P of semicircle and P of rectangle

25.7+40=65.7cm

Answer:

its true or 0

Step-by-step explanation:

Answer:

B it seems like it's the most suitable answer

Cartesian equation is\(4y^2 = x\ or\ y^2 = x/4\)We know that the polar equation of the form \(r = f(\Theta)\)can be obtained by converting the Cartesian equation x = g(y) into polar coordinates.

To convert the equation, \(x = 4y^2\) into polar coordinates, we need to replace x and y with their respective polar coordinates.

We know that \(x = r\ cos\ \Theta\) and \(y = r\ sin\ \Theta\), where r is the radial distance and θ is the polar angle.

So, the Cartesian equation can be expressed as follows:\(4(r\ sin\ \theta)^2 = r\ sin\ \theta\⇒\\\ 4r^2 sin^2 \theta = r\ cos\ \theta\⇒ \\r = 4\ cos\ \theta sin^2 \theta\)

Therefore, the polar equation for the curve represented by the given Cartesian equation is \(r = 4\ cos\ \theta\ sin^2\ \theta\).The polar equation for the curve represented by the given Cartesian equation \(x = 4y^2\ is\ r = 4\ cos\ \theta\ sin\ \theta\).

To convert the given Cartesian equation\(r = 4 \cos\ \theta \sin^2 \theta\)\(x = 4y^2\) into polar coordinates, we need to replace x and y with their respective polar coordinates.

Using the equation \(x = r\ cos\ \theta\)and \(y = r\ sin\ \theta\), we get \(4(r\ sin\ \theta)^2 = r\ cos\ \theta\), which simplifies to \(r = 4\ cos\ \theta \sin^2 \theta\).

Hence, the polar equation for the curve represented by the given Cartesian equation is r = 4 cos θ sin² θ.

Therefore, the polar equation for the given Cartesian equation \(x = 4y^2\)is \(r = 4\ cos \ \theta\ sin^2 \theta\).

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