Biking at 10 mph, it takes Kristen 1/4 hour to reach the train station to go to work. Kristen then takes the train to work, and it takes another 1/4 hour for her to get to work when the train travels 28 mph. How far does Kristen travel to work?

a- 37.5
b- 8.5
c- 19.5
d- 9.5

Answer: 464

Step-by-step explanation: First you multiply by 580 times .20 and subtract the answer of that by 580

In order to run a successful charity event for 6 people, it is important to ensure that everyone has something to enjoy.

Number is a mathematical entity used to represent a computer magnitude it can be symbol or a combination of simple you should in order to take quantity such as the two, five, seven, three or eight number are used to verify the context including counting measuring and computing.


One way to do this is to provide cupcakes to one out of every three people. This will ensure that some people get a special treat while the others still have a chance to get one if they come to the event again. It also allows for a sense of fairness and equality, as everyone has an equal chance of receiving a cupcake. Additionally, it helps to build a sense of community and fellowship among the participants, as they can share the cupcakes and enjoy the experience together. It is also a great way to raise awareness about the charity and its cause, as people can talk about it while enjoying the cupcakes. To make sure that the event runs smoothly, it is important to have plenty of cupcakes on hand and to make sure that everyone is aware of the rules for receiving one.

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Answer:

28.6 grams

Step-by-step explanation:

Percentage of cocoa in the chocolate bar = 54%

Weight of the chocolate = 53 grams

Weight of the cocoa = 54% of 53 = 28.62 grams

Rounding off to nearest tenth = 30 grams

Answer:6

Step-by-step explanation: because the 2 feet already has four pieces and if you add two more pieces to it there will be six in total.

Answer:

19. x = 60

20. x= 27

Step-by-step explanation:

19. Given 2 triangles are congruent

so BQ/BC = BR/BD

30/84 = x/168

84x = 30(168)

84x = 5040

x = 5040/84 = 60

20. Given 2 triangles are congruent

QS/QP = ST/PR

18/x = 10/15

10x = 18(15)

10x = 270

x = 270/10 = 27

Reflection across x=3 is a transformation that involves reflecting a figure across a vertical line of symmetry at x=3.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.


This transformation produces a mirror image of the original figure. Reflection across x=3 can be represented in the form of a matrix equation,

A= [[-1, 0],
   [ 0, 1]]

This matrix equation demonstrates that the x coordinates of a point will be multiplied by -1, while the y coordinates will remain unchanged. This transformation is also known as a reflection over the y-axis.

Reflection across x=3 can be used to change the orientation of a figure in a 2-dimensional coordinate plane. For example, if a triangle is located at the position (2,4) and the coordinates need to be changed so the triangle is reflected across x=3, the coordinates would be transformed to (-2,4).

Reflection across x=3 can also be used to solve various types of mathematical problems. For example, if a problem asks for the coordinates of a point that is the reflection of a point across x=3, the coordinates of the reflected point can be calculated by multiplying the original x coordinate by -1 and leaving the y coordinate unchanged.

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1. The probability the project will be finished in 62 weeks or less is 0.6915. 2.The probability the project will be finished in longer than 65 days is 0.8944.

The standard score in statistics is the amount of standard deviations that a raw score (i.e., an observed value or data point) deviates from or exceeds the mean of the thing being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.

It is determined by deducting the population mean from a given raw score, then dividing the result by the population standard deviation. Standardizing or normalising is the process of transforming a raw score into a standard score.

Given that,

mean = 60 weeks

SD = 4 weeks

1. P (p ≤ 62) = P(z ≤ 62)

The z-score is given by:

z-score = x - mean / SD

Substituting the values we have:

z-score = 62 - 60/4 = 2/4 = 0.5

P(z ≤ 0.5) = 0.6915 (Using the z -table)

Hence, the probability the project will be finished in 62 weeks or less is 0.6915.

Similarly,

2. P(z > 65) = P(z > 1.25) = 0.8944

Hence, the probability the project will be finished in longer than 65 days is 0.8944.

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Answer:

7/5, 3/2, 11/4, 15/4, 13/3.

Step-by-step explanation:

Convert all to decimal then arrange from lowest to highest

Answer:

Step-by-step explanation:

Answer:21 dimes and 28 quarters

Step-by-step explanation:

Mr. Finn's rent in the next 3 years will be £ 833.49

To find the rent, calculate how much it will increase in the first and in the second year by using calculating percentages individually or using the compound interest formula. From the find total rent for next years. Using the total rent in the second year find the rent in 3rd year.

Here we have

The rent paid by Mr. Finn is £700 per month in rent.

His landlord informed him that rent will increase by 5% for the next two years and by 8% after that.

The rent in the 1st year = 700 + 5% of 700

= 700 + (5/100) 700

= 700 + 35 = 735  

In the second year again the rent will increase by 5%

The total rent in the second year = 735 + 5% of 735

= 735 + 36.75 = 771.75

After 2 years, the increment will be 8%

So, The total rent in the 3rd year year = 771.75 + 8% of 771.75

= 771.75 + (8/100) 771.75

= 833.49

Therefore,

Mr. Finn's rent in the next 3 years will be £ 833.49

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The total earnings for the first month are given as follows:

R370,256.

The series in this problem is a geometric sequence, as there is a common ratio between consecutive terms.

Each day, the amount paid to you by the company is doubled, hence the common ratio of the geometric sequence is given as follows:

r = 2.

The amount paid on the first day is given as follows:

a(1) = 0.01.

The sum of the first n terms of a geometric sequence is given as follows:

S = [a1(1 - r^n)]/(1 - r).

Hence the sum for the first 30 days is given as follows:

S = [0.01(1 - 2^30)]/(1 - 30)

S = 370,256.

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For given coordinates of a linear equation, the slope will be 3/4 i.e. B.

What is a linear equation, exactly?

When the greatest power of a variable is 1, the equation is said to be linear. Other term used for it is a one-degree equation. The standard form of a linear equation with one variable is Ax + B = 0. There are three variables in this equation: x, A, and B. A denotes a coefficient. A linear equation with only two variables is commonly written as Ax + By = C. There is three more constants added to the constant C: the variables x and y, the coefficients A and B, and the variables.

and general equation of line is y=mx+c

where m=slope=y2-y1/x2-x1

Now,

Here given coordinates are , (-3,4) and (1/7)

then (x1,y1) and (x2,y2) are  (-3,4) and (1/7) respectively

so slope=m=7-4/1-(-3)=3/4

Hence,

          For given coordinates of a linear equation, the slope will be 3/4.

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The domain where fx) is 1-to-1 is x ≥1 , and the inverse there is:

f⁻¹(x) =  √x + 1

Here we have the quadratic function:

f(x) = (x - 1)^2

If we look from the vertex to the right (or the left, is the same) we will have an one to one function.

Here the vertex is at x = 1

f(1) = (1 - 1)^2 = 0

Then for x ≥1 we have an one to one function.

Noe let's find the inverse, if the inverse is f⁻¹(x), then we must have that:

f( f⁻¹(x) ) = x

Solving that:

(f⁻¹(x)  - 1)^2 = x

(f⁻¹(x)  - 1) = √x    (here we only take the positive square root)

f⁻¹(x) =  √x + 1

That is the inverse.

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A function that represents the height of Elmer's carriage is,

h(x) = 52cosx + 77.

The adjacent side to hypotenuse ratio is known as the cos function. It aids in determining the triangle's side lengths regardless of the provided angle. If the angle between the adjacent side and the hypotenuse of a right triangle is, we may write this using the cosine function. Adjacent Side/Hypotenuse = Cos.

Given:
Elmer is on a Ferris wheel which has a diameter of 104 ft and whose center is 129 ft off the ground.

That means the radius of the Ferris wheel is r = 104/2 = 52 feet.

The wheel is 129 - 52 = 77 feet off the ground.

Elmer's carriage makes an angle of x radians in a horizontal way.

So, the height of Elmer's carriage is,

= rcosx + a

Here, r = 52 and a = 77

So, we get,

h(x) = 52cosx + 77.

Therefore, the function is h(x) = 52cosx + 77.

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Answer:

Step-by-step explanation:

I believe its

(-2,-6)

The dimensions of this rectangular swimming pool include the following:

Width = 10 meters.

Length = 21 meters.

Mathematically, the perimeter of a rectangular shape can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

From the information about the width, we have:

Width, W = L - 11

Substituting the given parameters into the perimeter of a rectangle formula, we have the following expressions;

62 = 2(L + L - 11)

62 = 4L - 22

4L = 84

Length, L = 21 meters.

For the width, we have:

Width, W = L - 11

Width, W = 21 - 11

Width, W = 10 meters.

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Answer:

y=5

Step-by-step explanation:

i think it is ahhhh&hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

{x = -1, 3}

Step-by-step explanation:

See picture below :)

The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.

What is a bar graph?

Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.

We are given a graph showing grasshopper numbers before and after blue jays preyed on them.

From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.

Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.

Hence, the statement A and statement B are supported by the data in the table.

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The complete question has been attached below

Answer:

Step-by-step explanation:

No.

The number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Numbers that divide an original number evenly or precisely are known as its factors. A factor is a whole number that can divide a larger number in two equal parts. A factor is a number that divides another number, leaving no remainder

Given data ,

Let the number be represented as n

Now , the number can be said to be a multiple of 4 if the last two digits of the number is a multiple of 4

Let the value of the number n be n = 3240

Now , the last two digits of the number is 40

And , the number 40 is a multiple of 4 , so the number 3240 is also a multiple of 4

where n / 4 = 810

Hence , the factors of the number 4 is a multiple of 4

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The mean and the variance of the poisson distribution are;

Mean = 2.66

Variance = 1.277

The formula for the PMF of a Poisson distribution is;

p(x:λ) = [e^(-λ) * λ^(x)]/x! for x = 0, 1, 2......

Thus;

p(x = 0) =  [e^(-λ) * λ^(0)]/0!

e^(-λ) = 0.07

λ = - In 0.07

λ = 2.66

That is the mean

Variance is square root of standard deviation;

Variance = √√(2.66)

Variance = 1.277

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Answer:

2.65926003693 for mean and variance.

Step-by-step explanation:

First of all, when it comes to Poisson distributions, the mean and variance equal the same thing. Here we can find the mean using e^-(lambda)=0.07 therefore lambda= -ln(0.07) which equals 2.65926003693 for both.

Answer:

2h

Step-by-step explanation:

You can still divide 6h by 3 even if its not 3h

Imagine there are 6 h's:

H H H H H H

now divide them by 3:

     1                   2

  HHH            HHH

Now you have 2 groups of H so:

2H

The slope of this graph​ is equal to 0.375 or 3/8.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (35 - 20)/(40 - 0)

Slope, m = 15/40

Slope, m = 0.375 or 3/8.

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Answer:

Please Mark Brainlaiest Answer

Step-by-step explanation:

The best linear approximation for f(x) = cos(x) near x = pi/2 is given by the equation:

y = -(x - pi/2) + 1

This is because the linear approximation should have the same value and slope as the original function at x = pi/2.

At x = pi/2, the value of f(x) = cos(pi/2) = 0. The value of the linear approximation at x = pi/2 is:

y = -(pi/2 - pi/2) + 1 = 1

So, the value of the linear approximation matches the value of the original function at x = pi/2.

The slope of the original function at x = pi/2 is -sin(pi/2) = -1. The slope of the linear approximation is:

y' = -1

So, the slope of the linear approximation also matches the slope of the original function at x = pi/2.

Therefore, the best linear approximation for f(x) = cos(x) near x = pi/2 is:

y = -(x - pi/2) + 1

Hence, the correct option is "y equals negative x plus pi over 2 plus 1".

Answered By Unish ©

Verified Answer ✅

The direct distance between the White House and the Pentagon is approximately 3.067 miles.

Distance is a measure of how far apart two objects or points are from each other. It is a fundamental concept in mathematics, physics, and other scientific disciplines, and plays a crucial role in our everyday lives.

Distance can be measured in various units, such as meters, kilometers, miles, feet, and inches, depending on the context and application. In mathematics, the distance between two points in a plane can be found using the Pythagorean theorem, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula:

distance = √((x2-x1)² + (y2-y1)²)

In this formula, the square of the difference in the x-coordinates and the y-coordinates of the two points are added and then the square root of the sum is taken to obtain the distance.

Using the distance formula, the direct distance between the two buildings is:

d = sqrt[(x2 - x1)^2 + (y2 - y1)^2]

where (x1, y1) = (-8,-6) and (x2, y2) = (-1,10)

d = sqrt[(-1 - (-8))^2 + (10 - (-6))^2]

d = sqrt[7^2 + 16^2]

d = sqrt(49 + 256)

d = sqrt(305)

Since each unit on the grid represents 0.125 miles, we can convert the answer to miles by multiplying by 0.125:

d = sqrt(305) * 0.125

d = 3.067 miles (rounded to 3 decimal places)

Therefore, the direct distance between the White House and the Pentagon is approximately 3.067 miles.

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Yes, they are statistically different.

Statistical significance is a term used to indicate that a result from a statistical test is likely to be reliable and reproducible. It is the probability that a result is caused by something other than random chance. Statistical significance is usually determined by calculating the probability, or p-value, that the result occurred by chance. A result is deemed to be statistically significant if the p-value is below a certain threshold. This threshold is typically set at 0.05, but can be adjusted depending on the study.

A p-value below 0.05 is generally considered to be statistically significant, indicating that the differences observed between the two groups are unlikely to have occurred by chance. In this case, a p-value of 0.03 is well below the threshold, indicating that the two groups are statistically different

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We have discussed what is skewed distribution and how to deal with skewed data as mentioned below.

What is a skewed distribution?

When one tail is longer than the other, the distribution is said to be skewed. The asymmetry of a distribution is defined by skewness. These distributions are asymmetric, in contrast to the well-known normal distribution and its bell-shaped curve. Because the data are not equally distributed on both sides of the distribution peak, the two parts of the distribution are not mirror images.

A) The direction of outliers is revealed by skewness. A distribution curve's tail is longer on the right side when there is a positive skew. As a result, the distribution curve's outliers are more extreme to the right and closer to the mean to the left. Skewness simply conveys the direction of outliers; it does not convey the number of outliers.

B) Lower or upper boundaries on the data frequently cause skewed data. In other words, data with a lower bound are frequently skewed right, whereas data with an upper bound are typically skewed left.

C) One popular method for handling skewed outcome data is to logarithmically transform each observation before conducting the analysis with the resulting values.

D) It is likely that the income distribution curve you plot on a graph will be positively skewed to the right. If the majority of people earn normal earnings and a smaller proportion earn high incomes, then this would happen.

Therefore this is what skewed distribution is and the above mentioned ways are how one deals with skewed data in research.

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the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

How to determine?

To find the equation of the line perpendicular to the line 5x - 4y = 10 and passing through the point (5,12), we need to first find the slope of the given line.

Rewriting the equation of the given line in slope-intercept form (y = mx + b), we get:

5x - 4y = 10

-4y = -5x + 10

y = (5/4)x - 5/2

The slope of this line is (5/4), so the slope of any line perpendicular to it is the negative reciprocal of (5/4), which is -(4/5).

Now we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line and m is the slope.

Plugging in the values we have, we get:

y - 12 = -(4/5)(x - 5)

Expanding and simplifying, we get:

y - 12 = -(4/5)x + 4

y = -(4/5)x + 16

Therefore, the equation of the line perpendicular to 5x - 4y = 10 and passing through the point (5,12) is y = -(4/5)x + 16.

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[tex]\dfrac{x^2-15x+36}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5x-60}[/tex]

[tex]= \dfrac{(x-3)(x-12)}{5(x-12)}[/tex]

[tex]= \dfrac{(x-3)}{5}\\= \dfrac{x-3}{5}[/tex]

[tex]\dfrac{x-3}{5}[/tex], [tex]x\neq12[/tex]