develop a least squares estimated regression line. (round your numerical values to five decimal places.)

The unit rate for miles per gallon for each​ car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

You are running an efficiency study. One of the vehicles you find is blue. It can travel 45 ¹/₂ miles on 1 ¹/₄ gallon of fuel. Another vehicle is red. It can travel 24 ⁴/₅ on ⁴/₅ gallons of fuel.

The rate of blue cars is given as,

⇒ (45 ¹/₂) / (1 ¹/₄)

⇒ 45.5 / 1.25

⇒ 36.4 miles per gallon

The rate of red cars is given as,

⇒ (24 ⁴/₅) / (⁴/₅)

⇒ 24.8 / 0.8

⇒ 31 miles per hour

The unit rate for miles per gallon for each​ car will be 36.4 and 31. And the blue car can travel greater distances on 1 gallon of​ gasoline.

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Answer:

there was 30 people at her birthday party

The sampling method is independent as the rain samples were taken from two different locations. As the sample sizes are small, they can be approximately considered normal distributions and t-test can be used to check the hypothesis.

Used in inferential statistics, t test can be used when we need to compare two different sets value to check if their is a significant difference between them.

T tests can be paired and dependent, like measuring the weight of a same patient before and after a diet or they can be unpaired an independent. Unpaired datasets might sometime have the same variance or unequal variance. Different formular are used to calculate the t-tests involving different datasets. To prove a null or alternate hypothesis, the t values must be checked with t- test table.

As the following datasets measuring rain pH at different cities are indepent and have unequal variances, the following formula should be used for calculating the t-score and the degree of freedom:

T-value= [tex]\frac{Mean1-Mean2}{\sqrt(\frac{var1}{n1})+(\frac{var2}{n2})}[/tex]

Substituing the values of Mean1=4.77; Mean2=4.50, Var1=0.1366, Var2= 0.0242, n1= 12, n2= 14, we get the t value as 2.27

Now calculating degree of freedom, which comes around

Δ=14

At x=0.05, from the table, t value=2.145

Hence as the calculated t vale is more than critical t value, null hypothesis can be rejected and alternate hypothesis can be accepeted proving that their is a significant visible difference in pH in the rain of Chicago and Huston.

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Exactly one-ninth of the original water is left after 8 pourings.

Given data,

Model the container's remaining contents as follows;

After the first pour, 1⁄2 is left, after the second, half * two-thirds, etc.

This is the final result. 1/2 * 2/3 * 3/4 * . . . . 8/9 * 9/10

Because the terms cancel out, 9/10 remains.

The numerators form an arithmetic sequence with a common difference of 1 and endpoints (1, 8), thus all that is left to do is count the terms or pour.

Therefore, 8 pourings do exactly one-ninth of the original water remain.

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Answer:

Let's call the number of diners at the Italian restaurant x, and the number of diners at the Mexican restaurant y. We can set up the following system of equations to represent the problem:

Italian restaurant: $20 + 2x = $30 + $1y

Mexican restaurant: $30 + $1y = $20 + 2x

Subtracting $20 from both sides of the first equation and $30 from both sides of the second equation, we get:

Italian restaurant: 2x = $10 + $1y

Mexican restaurant: $1y = $10 + 2x

Multiplying both sides of the first equation by 1/2, we get:

x = $5 + $0.5y

Substituting this expression for x in the second equation, we get:

$1y = $10 + 2($5 + $0.5y)

Expanding the expression on the right side, we get:

$1y = $10 + $10 + $1y

Subtracting $1y from both sides, we get:

0 = $10

This equation is true, so the system of equations is consistent.

Since the total donations from each restaurant would be the same, we can set the total donations equal to each other and solve for the number of diners at each restaurant. The total donation from the Italian restaurant is $20 + 2x, and the total donation from the Mexican restaurant is $30 + $1y. Setting these expressions equal to each other, we get:

$20 + 2x = $30 + $1y

Subtracting $20 from both sides and $1 from both sides, we get:

2x - 2 = $10 + $1y - $1

Combining like terms on both sides, we get:

2x - 2 = $10 + $1y - $1

2x - 2 = $9 + $1y

2x - $9 - $1y = 2 - $9

2x - $1y = -$7

Dividing both sides by 2, we get:

x - $0.5y = -$3.5

Substituting this expression for x in the first equation, we get:

$20 + 2(-$3.5) = $30 + $1y

Simplifying the expression on the left side, we get:

$20 - $7 = $30 + $1y

Subtracting $20 from both sides, we get:

-$7 = $10 + $1y

Subtracting $10 from both sides, we get:

-$17 = $1y

Dividing both sides by -1, we get:

$17 = -$1y

Multiplying both sides by -1, we get:

-$17 = $1y

Dividing both sides by $1, we get:

-$17/$1 = $1y/$1

Simplifying the expression on the left side, we get:

-17 = y

Thus, the number of diners at the Mexican restaurant is -17, and the number of diners at the Italian restaurant is x = $5 + $0.5y = $5 + $0.5(-17) = $5 - $8.5 = -$3.5.

Since the number

People withe the appropriate clearance and a signed non-disclosure agreement may access classifies information within a company or organization.

People must have a favorable determination of eligibility at the proper level, have a "need-to-know", and have signed an appropriate non-disclosure agreement before accessing classified information. Any individual who falls to meet these requirements is not authorized to access classified information.

Classified information may be made available to a person only when the possessor of the information establishes that the person has a valid "need-to-know" and the access is essential to the accomplishment of official government duties.

Data classification is the process of organizing data into categories that make it easy to retrieve,sort and store for future use. A well-planned data classification system makes essential data easy to find and retrieve.

Given question is incomplete.

Who can access classified data?

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The types of angles include the supplementary, complementary, adjacent and vertical angles.

An angle is defined as the common point that is being formed when two straight lines meet at a common endpoint.

There are various types of angles that include the following:

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The t-statistic for these two sample is 3.80 with 73 df

T-value is a ratio of the difference between the mean of two samples sets an the variation exist within the sample sets .
The numerator value is difference of mean of two samples.

According to the question,

We have two different sample

Sample 1

n1 = 35 (sample size)

x1 = 13.6 (sample mean)

s1 = 5.8 (standard deviation)

Sample 2

n2 = 40

x2 = 10.1

s2 = 8.5

To calculate the t-value of difference of sample means

[tex]t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{\frac{s_1^2}{n_1} - \frac{s_2^2}{n_2}}}[/tex]

Substituting all the values

=> [tex]t = \frac{13.6-10.1}{\sqrt{\frac{5.8^2}{35} - \frac{8.5^2}{40}}}[/tex]

Solving ,

=> t = 3.5 / 0.9192

=> t = 3.807

With degree of freedom = n1 + n2 - 2

=> df =73

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Answer:

$5809.17

Step-by-step explanation:

Using the formula for continuous compound interest [tex]P(t)=Pe^{rt}[/tex] We can plug in our values [tex]P(t)=5000e^{0.03*5}[/tex] and solve.

The length of the other leg can't be found because the length of hypotenuse can't be smaller than the length of any of the sides.

What is Pythagoras theorem ?

The three sides of a right-angled triangle are explained by Pythagoras' theorem, also referred to as the Pythagorean theorem. The hypotenuse square of a right-angled triangle is equal to the sum of the squares of the other two sides, according to the Pythagoras theorem.

Given, hypotenuse = 2 cm

          one leg = 3 cm

Let the other leg to be ' x'

By Pythagoras theorem :

hypotenuse^2 = base^2 + perpendicular^2

                 2^2  =  3^2+ perpendicular^2

               perpendicular^2 = 4 - 9 = -5 which is not possible.

Here, The length of hypotenuse is smaller than the length of other side which clearly indicates that the given right triangle can't exist.

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"Fail to reject the null hypothesis" is the correct conclusion for the test.

We have given that,

a P-value of 1.018943 is calculated on a hypothesis test with significance level set at 0.01.

That means p-value is greater that significance level.

And we know that if p-value is greater than significance level then the effect is statistically not significant. There is no enough evidence to reject the null hypothesis.

A p-value greater than 0.01 means that deviation from the null hypothesis is not statistically significant, and the null hypothesis is not rejected.

High p-value indicates that your evidence is not strong enough to suggest an effect exist in the population. An effect might exist but it's possible that the effect size is too small, that sample size is too small or there is too much variability for the hypothesis test to detect it.

Therefore "Fail to reject the null hypothesis" is the correct conclusion for the given test.

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Answer:

[tex] \frac{17}{36} [/tex]

Step-by-step explanation:

- 1 and 3/4 can be made into an improper fraction, 7/4

- 7/4 = 3x + 1/3, where x is equal to the amount of liters in each cup, 7/4 represents the total amount of lemonade in both the pitcher and cups, and 1/3 represents the amount of lemonade left over.

- Solve for x:

7/4 - 1/3 = 3x

21/12 - 4/12 = 3x

17/12 = 3x

x = 17/36

The linear feet of fencing in the rectangular garden s 692 feet

From the question, we have the following parameters that can be used in our computation:

Length  = 204 feet

Width = 142 feet

To calculate the amount of linear feet of fencing that is required, we make use of the following perimeter equation

Linear feet of fencing = 2 * (Length + Width)

Substitute the known values in the above equation, so, we have the following representation

Linear feet of fencing = 2 * (204 + 142)

Evaluate

Linear feet of fencing = 692

Hence, the linear feet of fencing is 692 feet

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The measure of the angle Q in degrees is 90° if angles Q and R form a right angle.

A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.

Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.

Q and R create a right angle given.

Therefore, the angle formed by either Q or R is 90 degrees.

Angle R is doubled by the given angle Q.

From there, Q must have an angle of 90 degrees.

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By using the concept of midpoint of a line, it can be concluded that-

F is the midpoint of AA' because EG bisects AA'

First option is correct

What is midpoint of a line?

Midpoint of a line is the point which divides the line into two equal parts.

ΔA'B'C' is the reflection of  ΔABC

E is the midpoint of BB'

F is the midpoint of AA'

G is the midpoint of CC'

EG is the bisector of BB', AA', CC'

F is the midpoint of AA' because EG bisects AA'

First option is correct

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Complete Question

The figure has been attached

Answer: D

Step-by-step explanation: trust

Answer:One fourth

Step-by-step explanation:

In Experiment 1 the probability of each outcome is always the same. The probability of landing on each color of the spinner is always one fourth.

Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

First, work out parenthesis 5*5/5(1)

Then, Multiply/divide from left to right 25/5(1) -> 5(1) = 5

Answer:

angle A = 124 degrees, angle D = 124 degrees, angle C = 56 degrees

Step-by-step explanation:

1. apply that opposite angles in a parallelogram are congruent

measure of angle A = measure of angle C

measure of angle B = measure of angle D

2. given the measure of angle A = 56 degrees, angle C is also 56 degrees

angle A = angle C = 56 degrees

3. calculate the measure of angle A

measure of angle A + 56 degrees = 180 degrees

4. subtract 56 from both sides

measure of angle A = 124 degrees

5. measure of angle A = measure of angle D

angle A = angle D = 124 degrees

answer:

angle A = 124 degrees

angle D = 124 degrees

angle C = 56 degrees

Answer:

A

Step-by-step explanation:

2p - 5p < 8 + 4

- 3p < 12

-3/-3 p > 12/-3

p  > -4

-2, - 3

Hence, the measure of the angles are

∠q = 65°

∠r = 65°

∠s = 50°

∠t = 65°

∠b = 64°

From the question, we are to determine the measure of the angles.

Calculating the measure of angle q

∠q + 65° + (180° - 130°) = 180° (Sum of angles in a triangle)

∠q + 65° + 50° = 180°

∠q + 115° = 180°

∠q = 180° - 115°

∠q = 65°

Calculating the measure of angle r

∠r = ∠q (Corresponding angles)

Therefore,

∠r = 65°

Calculating the measure of angle s

∠s + ∠r + 65° = 180° (Sum of angles on a straight line)

∠s + 65° + 65° = 180°

∠s + 130° = 180°

∠s = 180° - 130°

∠s = 50°

Calculating the measure of angle t

∠t = ∠r (Vertically opposite angles)

Therefore,

∠t = 65°

Second diagram

Calculating the measure of angle b

∠b = ∠a (Corresponding angles)

Therefore,

∠b = 64°

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The solution of the corresponding system of linear equations is: (X1, X2, X3, X4) = (-9s, 10s, -4s, t).

The reduced row echelon form of the matrix is:

1 0 0 -9

0 1 0 10

0 0 1 -4

0 0 0 0

This tells us that the system of linear equations has the following solution:

X1 = -9X4

X2 = 10X4

X3 = -4X4

The system is dependent, so we assign the free variables the parameters s and t:

X1 = -9s

X2 = 10s

X3 = -4s

X4 = t

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Refer to the photos taken.

Answer:

98

Step-by-step explanation:

Using Poisson distribution to calculate the probability distribution of the event, the probability is 0.2084

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty.

A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a particular value or set of values. It is used to describe the behavior of random variables, either discrete (e.g. coin flips) or continuous (e.g. temperatures), and is often used in the field of statistics to predict the behavior of a system or process.

Using Poisson distribution;

P(X ≥ 5) = 1 - P(X ≤ 4)

P= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

P= 1 - (e^(-4.615) + (4.615*e^(-4.615))/1! + (4.615^2*e^(-4.615))/2! + (4.615^3*e^(-4.615))/3! + (4.615^4*e^(-4.615))/4!)

P = 0.2084

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Answer:

they ran the same speed as each other c

Answer:

47. 18

48. 13

49. Candy A

Step-by-step explanation:

47. To find the number of groups of 25 people, you can divide the total number of employees by the size of each group. In this case, you would divide 425 employees by 25 people per group to get 17 groups. However, since you can't have a fraction of a group, you would need to round up to the nearest whole number. In this case, you would have 18 groups of 25 people.

48. he average number of customers contacted each day can be calculated by adding the total number of customers contacted during the week and dividing by the number of days in the week. In this case, the total number of customers contacted during the week is 15 + 12 + 14 + 11 + 13 = 65. Dividing this by the number of days in the week, which is 5, gives an average of 13 customers per day.

The method used to calculate the average in this case is the mean, which is the sum of all the values divided by the number of values. The mean is the most commonly used measure of central tendency and is a good choice for finding the average when the data is evenly distributed and there are no extreme values (outliers).

49. the question is cut off but if its ....the most popular and should be included in the most number of kits?

Candy A is the most popular candy, as it is sold in the greatest quantity on an average day. It should be included in the most number of kits in order to maximize sales.

Injective function is a type of function which relates an element of a given set with a distinct element of another set. An injective function is also referred to as a one-one function.

Let's start by listing supposition and their respective reasons.

Suppose,

g О f is injective then f : A → B is also injective.

As we are dealing with injective functions, we can rightly proceed.

The functions f(x) = f(y) when x,y ∈ A

g(f(x)) = g(f(y))

Given the fact that g О f ,then x = y

Thus, we can say that since g О f , f : A is an injective function too (one to one function)

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Answer:

13

Step-by-step explanation:

-11+2/3x(-12)+4/1/8 Identify the sign

-11-\\\2/3x12+4/1/8 multiplying and inverting

-11-2/3x12+4x8 Simplify

-11 -2x4+4x8

-11-8+32

13

Answer:

y=-4/3x+13

Step-by-step explanation:

formula:y=mx+b

you need to add 9 on both sides of the equation

so it's look like this:y-9=-4/3x+5

                                  +9          +9

so combine the like terms

y=-4/3x+13

Dimensions of the rectangle of maximum area will be [3, 12]

Area of Rectangular?

The formula for the area of a rectangle is multiply length x width.

The given equation represents an ellipse centered at the origin with semi-major axis 12 and semi-minor axis 3. The semi-major axis is the longer axis of the ellipse, and the semi-minor axis is the shorter axis.

unitsize(1.5 cm);

draw((-12,0)--(12,0));

draw((0,-3)--(0,3));

draw(shift((0,0))*xscale(12)*yscale(3)*unitcircle);

To find the dimensions of the rectangle with maximum area that can be inscribed in the ellipse, we should look for a rectangle with sides parallel to the coordinate axes and with one side coinciding with a semi-axis of the ellipse. This is because the semi-axes are the longest lines that can be drawn within the ellipse, and the rectangle will have the maximum area if it coincides with one of these lines.

In this case, we can see that the semi-minor axis of the ellipse is 3, so we can inscribe a rectangle with sides parallel to the coordinate axes and with one side of length 3 within the ellipse. The other side of the rectangle will be the semi-major axis of the ellipse, which is 12. Therefore, the dimensions of the rectangle with maximum area that can be inscribed in the ellipse are 3 and 12, and the maximum area of the rectangle is 3 * 12 = 36.

Answer: [3, 12]

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