Finding Slope

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Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:

D. 19 miles.

Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.

Their coordinates in this problem are as follows:

Each unit on the plane represents a mile, hence their distance is given as follows:

[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]

D = 19.2 miles.

Rounded to 19 miles, hence option D is correct.

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Step-by-step explanation:

the midpoint coordinates between 2 points A and B are

((xa + xb)/2, (ya + yb)/2)

xa = 3

ya = 0

and so we get

(3 + xb)/2 = 0

3 + xb = 0

xb = -3

(0 + yb)/2 = 5

yb = 10

therefore, S = (-3, 10)

Yes, the number of scoops proportional.

Define Proportional

A linear relationship between two amounts or variables is indicated by proportionality. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

Hence, It is proportional. This is because as the number of people increases, the number of scoops also increase.

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The equation is, 4x - y = -5

The equation is, x + 2y = 6

The equation is, [tex][tex]y = -\frac{3}{4}x + \frac{29}{4}[/tex][/tex]

The equation is, y = -2x + 5

What is standard form of equation of line?

When A and B are not both zero, a line has the usual form Ax + By = C. The standard form of equation with slope and the point is,[tex][tex]y - y_{1} = m(x - x_1)[/tex][/tex] ...(1)

1. Given:[tex][tex]x_1 = -3, y_1 = -7, m = 4[/tex][/tex]

Plug these values in the above equation,

[tex][tex]y - (-7) = 4(x - (-3)\\ y + 7 = 4(x + 3)\\\\y + 7 = 4x + 12\\y = 4x + 5\\\\4x - y = -5[/tex][/tex]

This is the equation in standard form of line.

2. Given:

[tex][tex]x_1 = 10, y_1 = -2, m = -\frac{1}{2}[/tex][/tex]

Plug these values in the equation (1),

[tex][tex]y - (-2) = -\frac{1}{2} (x - 10)\\y + 2 = -\frac{1}{2} x + 5\\[/tex][/tex]

Multiply both sides by 2.2y + 4 = -x + 10x + 2y = 6

This is the equation in standard form of line.

3. Given:

[tex][tex]x_1 = -1, y_1 = 8, m = -\frac{3}{4}[/tex][/tex]

Plug these values in the equation (1),[tex][tex]y - 8 = -\frac{3}{4}(x - (-1))\\ y -8 = -\frac{3}{4}(x + 1)\\ y - 8 = -\frac{3}{4}x - \frac{3}{4}[/tex][tex]y = -\frac{3}{4}x -\frac{3}{4} + 8\\ y = -\frac{3}{4}x + \frac{29}{4} \\[/tex][/tex]

This is the equation in point slope form.

4. Given:[tex][tex](x_1, y_1) = (-3, 11), (x_2, y_2) = (6, -7)[/tex][/tex]

First to find the slope from the given two points.

[tex][tex]m = \frac{y_2 - y_1}{x_2 - x_1} \\m = \frac{-7-11}{6-(-3)}\\ m = \frac{-18}{9\\}\\ m = -2[/tex][/tex]

Now plug m = -2 and one of the given point in the equation (1), we ge[tex]t[tex]y - 11 = -2(x - (-3))\\y - 11 = -2(x + 3)\\y - 11 = -2x - 6\\y = -2x + 5[/tex][/tex]

This is the equation in slope intercept form.

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Equation (B) "y = 3x + 10" represents the growth of the puppy.

So, the equation that represents the situation:

Then:

For example, Salomon checks the weight for the 6th time then:

So, the equation is correct.

Therefore, equation (B) "y = 3x + 10" represents the growth of the puppy.

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The correct question is given below:
Salomon tracks the weight of his new puppy every 2 weeks. She weighs 10 lbs the day he brings her home. His list for her first 6 "weighs" is as follows: (10, 13, 16, 19, 22, 25}

Which equation represents the growth of the puppy? Select one:

A. y = x + 3

B. y = 3x + 10

C. y = 10x + 3

D. y = x + 10

Given

Points (4,2) and (2,1)

Find

Slope of the line

Explanation

Slope of line is given by

so ,

Final Answer

Hence , the slope of line is m = 1/2

Answer: 93°

Step-by-step explanation:

[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]

Answer: a b C D

Step-by-step explanation:

Answer:

Sum of angles in a triangle add up to 180°.

x = 180 - 64 - 40

= 76°

The greatest common factor is  5 .

If you factor it out, the expression becomes        5 (4x + 7y) .

Answer: 55x^1 y^1

Step-by-step explanation:
Add 20+35= 55
x & y can't stand by it's self, so x^1 and y^1
So you take those answers and you got 55x^1 y^1
You must keep it in letters in alphabetic order or it's considered wrong.

If equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

The equation of the height h = -16[tex]t^2[/tex]+150

Where h is the height

t is the time taken

We have to find the time taken for the object to be 6 feet above the valley floor

The height = -150+6

= -144

Substitute the values in the equation

-16[tex]t^2[/tex]+150 = -144

-16[tex]t^2[/tex] = -144-150

-16[tex]t^2[/tex] = -294

[tex]t^{2}[/tex] = 18.375

t = 4.28 seconds

Hence, if equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

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The probability the friend finds no one in the first spot is 60%.

Probability is the chance or likelihood that an expected event occurs when there are many possible outcomes or events.

For instance, the probability that when the counting friend goes to the hiding spot, they can or cannot find a friend there.

The two friends can only hide in 2 spots, leaving 3 spots with nobody.

The number of hiding spots = 5

The number of friends hiding = 2

The number of counting friends = 1

The number of spots they can hide = 2 out of 5

The probability of finding a person in a hiding spot = 2/5 or 40%

The probability of not finding a person in a hiding spot = 3/5 (1 - 2/5) or 60% (1 - 40%).

The chances that your friend finds anyone in the first spot are 60%.

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Given:

Total number of people surveyed = 205

a) Percentage of the survey respondents that do not like both hamburgers and burritos.

Number of people that do not like both = 54

To find the percentage of the respondents that do not like both, we have:

Therefore, the percentage of the survey respondents that do not like both hamburgers and burritos is 26.3%

b) Marginal relative frequency of all customers that like hambugers.

Given:

Number of customers that like hamburgers = 110

To find the marginal relative frequency, we have:

The marginal relative frequency of all customers that like hambugers is 54%

c) Conditional relative frequencies:

i) Conditional relative frequency that a person likes hamburgers given that the person does not like burritos:

ii) Conditional relative frequency that a person likes burritos, given that the person does not like hamburgers:

According to the given information, the reason for the second statement is definition of supplementary angles, this is because the definition of supplementary angles says that the sum of two supplements is 180°.

It means that the answer is B. Definition of supplementary angles.

Box plots present the shape of the distribution (density curve), Box plots can involve a categorical variable and a continuous numerical variable, Box plots show where the peak of the distribution is are the correct statement.

Instead of showing the raw data points, Box Plots takes the sample data and then present the ranges of values based on the quartiles and also display the asterisks for outliers that generally falls outside the whiskers.

Yes, the shape of distribution can be understood from a Box Plot. It can show whether a statistical data set is normally distributed or skewed.

A Box plot is a graph of the distribution that has Continuous variables. It is also applicable for Categorical variables.

Box Plot generally shows the below parameters: Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

A size can be determined by using these parameters but is not directly seen in a Box Plot

Generally a Standard Deviation is not visualized by Box Plot. It mainly visualizes Maximum, Minimum, Median, 75th Percentile, 25th Percentile and Interquartile Range.

Yes, the peak of the distribution can be analyzed from Box Plot

Generally for Normal Distribution, Mean = Median and this is the point where the peak is seen.

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ANSWER:

78.5 ft

STEP-BY-STEP EXPLANATION:

One trip equals the circumference of the circle.

The circumference of a circle is calculated by means of the following formula:

Therefore, we substitute and calculate the distance the pony would walk for a trip:

That is, the number of feet the pony walks is 78.5

The expression that represents the output value when the input is n is -4 - 2n

From the question, the input parameters are given as

Input 1,2,3,4,n

Similarly, the output parameters are given as

output: -6,-8,-10,-12

So, we have the following table of values

1,2,3,4,n

-6,-8,-10,-12

From the above table of values, we have the following parameters

The output value for the input n is then calculated as

Tn = a + (n - 1) * d

So, we have

Tn = -6 + (n - 1) * -2

Open brackets

Tn = -6 - 2n + 2

Evaluate the like terms

Tn = -4 - 2n

Hence, the output value for the input n is -4 - 2n

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f is 7. The process of composing small units into larger units that solve larger problems is known as composition.

Therefore,

f = 2 (-2)² - 1 : f = 7

Steps

f = 2 (-2)² - 1

2 (-2)² =2³

f = 2³-1

2³ = 8

f = 8-1

Subtract the numbers:

8 - 1 = 7

f = 7

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Answer:

The second graph (B: X?)

Step-by-step explanation:

The second graph (B?) is a function because the graphed line passes the vertical line test (no two points are vertically on top of each other).

Reason:

The diagram describes values between -1 and 3. We exclude -1 because of the open hole. We include 3 because of the closed endpoint.

Answer:

mA = 69 degrees

Step-by-step explanation:

A complementary angle has a measure of 90 degrees.

(2x + 27) + (2x - 21) = 90

Simplify

4x + 6 = 90

-6

4x = 84

/4

x = 21

mA: 2(21) + 27 = 69

Answer:

A = 69°

Step-by-step explanation:

Complementary angles sum 90°

A + B = 90°

(2x + 27) + (2x-21) = 90°

4x + 27 - 21 = 90°

4x + 6 = 90°

4x = 90 - 6

4x = 84°

x = 84°/4

x = 21

Then A:

A = 2x + 27

A = 2*21  +  27

A = 42 + 27

A = 69°

B = 2x - 21

B = 2(21)  + 27

B = 42 - 21

B = 21°

Check:

69 + 21 = 90

Sample space n(s)=2+2+5+7=16

Let P(E) be the probability of red beard or is only in the beard competition:

Total number of red beard=2+5=7

P(red beard)=2/7

Use 1-Prop Z Int to create a 95% confidence interval.

Z test should be employed because there is only one set of samples collected and the sample size is huge.

An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:

z = (p-p0) / √(p0(1-p0)/n)

where:

p = observed sample proportion

p0 = hypothesized population proportion

n = sample size

You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).

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The location on the number line to plot the sum of the given number is shown in the image attached below.

In Mathematics, a number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Note: Each interval on this number line represents 1/10.

Next, we would add the given numbers together as follows:

Number = −1 3/10 + 2/5

Number = −13/10 + 2/5

Number = (-13 + 4)/10

Number = -9/10 or -0.9.

Therefore, the sum would be located between -4/5 and -1.

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The cost of the jam Elmo uses to make the sandwiches =$1.65

What is the cost of the jam Elmo uses to make the sandwiches?

B globs of Peanut butter at 4 cents = 4B

J blobs of Jam at 5 cents = 5J

The number of sandwiches is given by the linear equation,

N(4B + 5J ) =$ 2.53

N(4B + 5J ) = 253 cents    ---(1)

The factors of 253 = 1, 11, 23, 253.

Since N > 1 , N is 11 or 23

Considering N = 11

11(4B + 5J ) = 253

4B + 5J  = 23   ---(2)

The possible values of B and J to satisfy the linear equation:

B = 2 and J = 3

Substituting B and J in (2)

4B + 5J  = 23

4 (2) + 5(3) = 23

8 + 15 = 23

23 = 23

The linear equation is verified.

The cost of jam Elmo uses to make the sandwiches =N( 5J)

                                                                                       =11 (5*3)

                                                                                       = 11 *15

                                                                                        = 165 cents or $1.65

The complete question is:

elmo makes N sandwiches for a fundraiser. for each sandwich he uses B globs of peanut butter at 4 cents per glob and J blobs of jam at 5 cents per blob. the cost of the peanut butter and jam to make all the sandwiches is $2.53. assume that B, J, and N are positive integers with N>1. what is the cost of the jam elmo uses to make the sandwiches?

What is a linear equation?

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Domain are the inputs of the function. They are the x values of the function

The function gives a parabola. This means the values of x will be from negative infinty to positve infinity

Plotting the graph:

Range are the outputs of the function. They are the y values of the function

From the graph, we see tip of the parabola starts at y = -50 and extends upwards

The y value will be from -50 to positive infinity

Scatter plot with x axis labeled variable x and y axis labeled variable y. Points go from lower left to upper right.

To make a poster you have to keep the ratio between lenght and height (otherwise it will look weird)

This is:

For a random day with the standard deviation, the probability that there are less than 200 shoppers on a random day, is 0.0039.

The average total number of shoppers on a  grocery store in 1 day is 506; the standard deviation is 115.

The number of shoppers is normally distributed.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 506 and standard deviation of 115.

Then, we can say that,

Z=(X-506)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P(X<200)

[tex]=P(Z < \frac{200-506}{115})[/tex]

=P(Z<-2.66)

Where, Z is the standard normal variate.

ρ = -0.266

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.0039

For a random day, the probability that there are less than 200 shoppers on a random day, is 0.0039.

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[tex] \frac{ - 1(15 + 4 - 27)}{16} \\ = \frac{ - 1(19- 27)}{16} \\ = \frac{ - 1( - 8)}{16} \\ = \frac{8}{16} \\ = 0.5[/tex]

ATTACHED IS THE SOLUTION

Answer:

= - 19 + 16^27