Four buses carrying 150 football fans from the same school arrive at a football stadium. The buses carry, respectively, 20, 45, 35, and 50 students. One of the fans is randomly selected. Let X denote the number of fans that were on the bus carrying the randomly selected person. One of the 4 bus drivers is also randomly selected. Let Y denote the fans of students on his bus. Compute E(X) and Var(X)

Answer:

um hi?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given points:

Slope is:

Use formula y = mx + b, substitute x = -2, y = 1, m = -3/5, find y-intercept b:

Correct option is B.

Step-by-step explanation:

\( m \: = \: -3/5 \: and \: b \: = \: -1/5\)

The slοpe οf the line that gοes thrοugh (-3,-5) and (-3,-6) is undefined.

Slοpe is a measure οf the steepness οr incline οf a line. It represents the rate at which the line is rising οr falling, and is defined as the change in the y-cοοrdinate (vertical change) divided by the change in the x-cοοrdinate (hοrizοntal change) between twο pοints οn the line.

The slope of the line that goes through (-3,-5) and (-3,-6) is:

\($ \rm m = \frac{y_2 - y_1}{x_2 - x_1}\)

y2 - y1 = m(x2 - x1)

-6 - (-5)= m(-3 - (-3))

-6 + 5 = m(-3 + 3)

-1 = m0

m = -1/0

Thus, The slope of the line that goes through (-3,-5) and (-3,-6) is undefined.

This is because the x-coordinates of the two points are the same, which means that the line is vertical and has no defined slope. In other words, the line is parallel to the y-axis and does not have a rate of change with respect to x.

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To determine how much of the variation in average annual energy expenditures is explained by the least-squares regression line, we can look at the coefficient of determination (R-squared) for the regression model.

R-squared is the proportion of the variance in the dependent variable (in this case, average annual energy expenditures) that is explained by the independent variable(s) (in this case, the variable(s) used in the regression model).

The formula for R-squared is:

R-squared = 1 - (SSres / SStot)

where SSres is the sum of squared residuals (i.e., the sum of the squared differences between the actual values and the predicted values) and SStot is the total sum of squares (i.e., the sum of the squared differences between the actual values and the mean value of the dependent variable).

Since the question does not provide any data or regression model, we cannot calculate the exact value of R-squared. However, if you have the data and the regression model, you can calculate R-squared using the above formula and round the answer to at least one decimal place.

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Answer:

5

Step-by-step explanation:

AB=

\( \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ \sqrt{ {4}^{2} + {3}^{2} } = 5\)

Answer:

I think 5

Step-by-step explanation:

no of horizontal blocks = 4

number of vertical blocks = 3

using Pythagoras theorem

c^2 = 4^2 + 3 ^2

= 16 + 9

= 25

c = 5

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

B. SAS

Step-by-step explanation:

the line that joins the 2 triangles is considered a side, if you put an angle in between 2 sides its SAS.

The data collected from the customers in restaurants about the quality of food is an example of a(n); Observational Study

There are four types of statistical studies namely;

Observational studies

Surveys

Experiments

Meta-analytical studies.

1) An observational study involves observing and recording data on some variable(s) of interest.

2) A (sample) survey uses questioning to gather data.

3) An experiment also referred to as experimental study attempts to give an answer to a statistical question by manipulating all or part of the sample.

Now, we are told that some data was collected from the customers in restaurants about the quality of food.

This is a type of observational study because it involves observing and recording data on an interest which is quality of food

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The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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Answer:

C

Step-by-step explanation:

area for the rectangle is 5x6=30

area for the triangle is 5x2/2=5

30+5=35

Answer:

35

Step-by-step explanation:

A=b*h

30=5*6

A=.5*b*h

5=.5*2*5

30+5=35

Answer:

The surface area of one face of the cube is 100 square centimeters.

Step-by-step explanation:

From the given diagram, we can conclude that a cube has 6 faces. To get the surface area of one face, we take the total surface area and divide it by 6, as following:

This way, we can conclude that the surface area of one face of the cube is 100 square centimeters.

The value of ∫20 x⋅f′(x)dx is 3, thus the answer is not listed among the options (A) 3, (B) 6, (C) 10, or (D) 17.

To find the value of ∫20 x⋅f′(x)dx, we can use integration by parts. Let's denote F(x) as the antiderivative of f(x), so F'(x) = f(x).

Using integration by parts, we have:

∫ x⋅f′(x)dx = x⋅F(x) - ∫ F(x)dx

Now, we need to evaluate this expression over the interval [0, 2]:

∫20 x⋅f′(x)dx = [x⋅F(x)]20 - ∫20 F(x)dx

Plugging in the given values f(0) = 1 and f(2) = 5, we can determine the expression for x⋅F(x) over the interval [0, 2]:

x⋅F(x) = x⋅[F(x) - F(0)] = x⋅[F(x) - F(0)] = x⋅[∫0x f(t)dt - 1]

Now, let's evaluate the expression:

∫20 x⋅f′(x)dx = [x⋅[∫0x f(t)dt - 1]]20 - ∫20 F(x)dx

Applying the Fundamental Theorem of Calculus, we know that ∫20 F(x)dx = F(2) - F(0).

Therefore:

∫20 x⋅f′(x)dx = [x⋅[∫0x f(t)dt - 1]]20 - (F(2) - F(0))

Now, we are given that ∫20 f(x)dx = 7, so we can rewrite the expression as:

∫20 x⋅f′(x)dx = [x⋅[∫0x f(t)dt - 1]]20 - (F(2) - F(0)) = [x⋅[7 - 1]]20 - (F(2) - F(0))

Simplifying further:

∫20 x⋅f′(x)dx = [x⋅[6]]20 - (F(2) - F(0)) = 6 - (F(2) - F(0))

Now, plugging in the values f(0) = 1 and f(2) = 5, we can evaluate F(2) - F(0):

∫20 x⋅f′(x)dx = 6 - (F(2) - F(0)) = 6 - (5 - 1) = 6 - 4 = 2

Therefore, ∫20 x⋅f′(x)dx equals 2.

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Answer:

let

hypotenuse[h]=60ft

base[b]=36ft

perpendicular [p]=48ft

by using Pythagoras law

p²+b²=h²

48²+36²=60²

2896≠3600

since p²+b²≠ h²[so the stage is not in a right angled triangle]but it is scalene triangle

Answer:

see below

Step-by-step explanation:

road 1 100km/h x hrs

road 2 80km/hr y hrs

total 6hours

total 530 km

100x+80y=530

x+y=6

x=6-y

100(6-y) + 80y =530

600-100y+80y =530

20y=70

y=3.5

x =6-3.5 =2.5

Answer: x =2.5 y= 3.5

Step-by-step explanation:

The range of the exponential function y = bx is all real numbers except 0.

The exponential function y = bx is defined as the equation where b is the base and x is the exponent. The range of this equation is all real numbers except 0. This is because when x is negative, the value of y will be a fraction (or a decimal) which is always a real number except for 0. When x is positive, the value of y will be a multiple of b which is also always a real number except for 0.

Therefore, the range of the exponential function y = bx is all real numbers except 0.

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The largest area that the farmer can enclose is 32metres²

Since, we have the farmer wants to build a rectangular pen, means that opposite  sides are of equal length.

So, let suppose the length of rectangular pen be x meters and width of rectangular pen as y meters.

We know that perimeter of rectangle is =2×(length + breadth)

Therefore, perimeter of rectangular pen =2x+y,and we are given the perimeter of rectangular pen in form of length of electric fence,

So,2x+y=16-------(eq1)

We know that area of rectangle=length × breadth

∴A=x × y

Now putting values of y from (eq1),we get

=>A=x×(16-2x)

For largest  area, we need to differentiate the area with respect to x and equate to it to equal to zero.

∴d(A)/dx=16-4x

=>16-4x=0

=>x=4metres

Therefore, y=16-2×4=8metres

Now, area of rectangular pen will be =x × y=4×8=32metres².

Hence, the largest area of rectangular pen  which will be bounded on one side by a river and on the other three sides by a single-strand electric fence is 32metres².

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Olivia's solution is not a reasonable prediction based on the survey data.

Hence the correct answer is given as follows:

490 people.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

70% spend an average of $100 per week on groceries, hence the constant is given as follows:

k = 0.7.

Hence the equation is:

y = 0.7x.

Hence, out of 700 people, we have that:

y = 0.7 x 700

y = 490 people.

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The formula for v(x) is v(x) = 2x - 3, and its domain is all real numbers. The formula for w(x) is w(x) = 5x + 4, and its domain is also all real numbers.

To find the formulas and domains for v(x) = s(x) / t(x) and w(x) = t(x) / s(x), we will substitute the given expressions for s(x) and t(x) into the respective formulas.

Let's start with v(x) = s(x) / t(x):

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

To simplify the expression, we need to find a common denominator for the numerator and denominator:

v(x) = (2x - 3) / (5x + 4) * (1 / 1)

Now, we can multiply the numerator and denominator by the conjugate of the denominator, which is (5x + 4):

v(x) = (2x - 3) * (1 / (5x + 4)) * ((5x + 4) / (5x + 4))

Expanding the expression, we have:

v(x) = (2x - 3) * (5x + 4) / (5x + 4)

Canceling out the common factor of (5x + 4), we get:

v(x) = (2x - 3)

Therefore, the formula for v(x) is v(x) = 2x - 3.

To determine the domain of v(x), we need to consider any values of x that would make the denominator (5x + 4) equal to zero. However, in this case, there is no such value since the denominator is a linear function that never equals zero. Therefore, the domain of v(x) is all real numbers.

Now, let's find w(x) = t(x) / s(x):

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

Following a similar process, we can simplify the expression:

w(x) = (5x + 4) / (2x - 3) * (1 / 1)

Multiplying the numerator and denominator by the conjugate of the denominator, which is (2x - 3):

w(x) = (5x + 4) * (1 / (2x - 3)) * ((2x - 3) / (2x - 3))

Expanding the expression, we have:

w(x) = (5x + 4) * (2x - 3) / (2x - 3)

Canceling out the common factor of (2x - 3), we get:

w(x) = 5x + 4

Therefore, the formula for w(x) is w(x) = 5x + 4.

Similar to v(x), the domain of w(x) is all real numbers since there are no values of x that would make the denominator (2x - 3) equal to zero.

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SOLUTION;

Sold for 5/6 of the original price.

The original price was $90.

The sale price of the baseball glove is;

The sale price of the baseball glove is $75.

Answer:

10. 108

11. 1,100

12.

-11 + 13 = 2

35 + -5 = 30

6 + (-3) +4 + 6 + (-5) = 8

5 + (-4) + (-9) + 8 = 0

(6) (8) = 48

(-2) (9) = -18

(-11) (-4) = 44

-256 divided by 0 = 0

-96 divided by +3 = -32

-36 divided by 3 = -12

Step-by-step explanation:

Step-by-step explanation:

\(volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100\)

For a hypothesis testing by considering two samples related to rate of people who exercise and who do not exercise, the observed t-value < standard so, null hypothesis does not rejected and there is no evidence to support the claim.

We have a researcher who was interested in making a comparison of resting pulse rate of people who exercise regularly and who do not exercise regularly. There is two independent samples. In 1ˢᵗ sample, sample size, n₁= 16

Sample mean, \(\bar X_1\) = 72.3

Standard deviations, s₁ = 10.3

In case of second sample, sample size, n₂ = 12

Sample mean, \( \bar X_2\) = 69.0

Standard deviations, s₂ = 8.9

Level of significance = 2.5% = 0.25

Consider the null and alternative hypothesis for the test hypothesis are defined as \(H_0 : μ_1 =μ_2\)

\(H_a : μ_1 >μ_2\)

The test statistic : using t-test formula

\(t = \frac{ \bar X_1 - \bar X_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}}}\)

\(= \frac{72.3- 69}{ \sqrt{ \frac {10.3^2}{16} + \frac{8.9^2}{12}}}\)

= 0.91

Degree of freedom, df = n1 + n2 - 2

= 16 + 12 -2 = 26

Using the t-distribution table, the critical value for t(0.025, df = 26) is equals to the 2.06. Now, the observed t-value = 0.91 is less than 2.06 ( standard t value), so, we do not reject H₀ . Hence, no evidence to support the researcher claim.

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Step-by-step explanation:

x^2 - 2x - 3 = 0

(x - 3)(x + 1) = 0

x = 3 (or) x = -1

Increasing the sample size while keeping the same confidence level decreases the margin of error and, hence, increases the accuracy of estimating a population mean by a sample mean.

This is because a larger sample size reduces the variability in the data, resulting in a smaller standard error of the mean and a narrower confidence interval.

As a result, the estimate of the population mean based on the sample mean becomes more precise and closer to the true value of the population mean.

Sample size refers to the number of individuals or items selected from a population to be included in a statistical sample.

The margin of error (MOE) is the amount of random sampling error that is expected in a statistical survey's results.

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a) Median will be an appropriate measure for the distribution. b) Mean will be an approprate measure for the distribution.

Here we already have the data available to us. From the data, we can clearly see that

Mode < Mean < Median

Hence this is a negatively skewed distribution.

Therefore the appropriate measure of central tendency for this distribution will be the median. The median will tell us the point at which the frequency is divided by 50%.

Hence we can say that the median will a more appropriate measure.

Now if the data has another aspect of sex included, then the frequency column would be divided into separate columns with each gender identity taking up its own column.

Since now this will become multivariate data, the best measure of central tendency will be Mean.

The difference in the measure of central tendency will depend upon how skewed the data for every sex will be. For example, if in a country, men preferred to be educated over women, then the mean for men will be a lot higher than that of women. On the other hand, the EDUC for women will be a lot lower.

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