1. What is the slope of a line Parallel to y=-2/3x - 7*3/2-3/2O 2/3-2/3

1) There exists a 3.82% probability that at least one right-handed student in this class is forced to utilize a seat designed for a left-hander.

2) There exists a 68.35% probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander.

The binomial probability exists the probability of exactly x successes on n repeated trials, and X can only contain two outcomes.

[tex]$P(X=x)=C_{n, x} \cdot \pi^x .(1-\pi)^{n-x}$$[/tex]

In which [tex]$C_{n, x}$[/tex] exists the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]$C_{n, x}=\frac{n !}{x !(n-x) !}[/tex]

And π exists the probability of X happening.

Given: 13 % of the students are left-handed and 100 - 13 = 87 % are right handed.

There are 220 sets. Of them, 25 exists designed for left handers and 220-25 = 195 for right handers.

There are 215 students, so n = 215.

In this case, a success is a student being right-handed. So [tex]$\pi=0.87$[/tex].

There are 195 seats for right handed students. If there are 196 or more right handed students, they will have to use a seat designed for a left hander. We have to find [tex]$P(X \geq 196)$[/tex]. Utilizing a binomial probability calculator, we find that [tex]$P(X \geq 196)=0.0382$[/tex]

So, there is a 3.82 % probability that at least one right-handed student in this class exists forced to utilize a seat designed for a left-hander.

There are 25 seats for left-handed students. If there exists 26 , or more, at least one exists going to be forced to utilize a seat designed for a right-hander.

In this case, a success is a student being left-handed. So [tex]$\pi=0.13$[/tex].

We have to find [tex]$P(X \geq 26)$[/tex].

Using a binomial probability calculator, we have that [tex]$P(X \geq 26)=0.6835$[/tex]

There exists a 68.35 % probability that at least one left-handed student in this class is forced to utilize a seat designed for a right-hander.

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To question 16, we see that for every change of plus 2 drinks, they pay an additional value of $2.50. It means that each drink does cost half of this value.

This way, the equation that will give the value of the total cost will be:

Where X stands for the number of drinks, and 1.25 is the value of a single drink.

From the solution presented above, we are able to conclude that the rate of change represents the value of a unitary drink, in the present situation.

Since the speed of the turbopropeller plane was 200 mph faster than the speed of the car, the speed of the turbopropeller plane is equal to 70 mph.

In order to solve this word problem, we would assign variables to the distance and speed of both Mattie's car and the turbopropeller plane, and then translate the word problem into algebraic equation as follows:

Translating the word problem into an algebraic equation, we have;

v₂ = v₁ + 200

Since Mattie and the turbopropeller plane travled at the same time, we have:

Time = distance/speed

Time = d₁/v₁ = d₂/v₂

Time = 140/v₁ = 540/v₁ + 200

Cross-multiplying, we have:

140(v₁ + 200) = 540v₁

140v₁ + 28,000 = 540v₁

Next, we would rearrange the equation by collecting like terms as follows:

540v₁ - 140v₁ = 28,000

400v₁ = 28,000

Speed of plane, v₁ = 28,000/400

Speed of plane, v₁ = 70 mph.

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The percentage of Rie's body that is Rie's legs is: 60%.

A percentage can be defined as an amount in each hundred or, simply put, a proportion of a quantity in relation of a whole.

To find the percentage of a quantity in a whole, divide the quantity by the whole quantity, then multiply the quotient by 100.

The "whole" in this problem is Rie's height, which is: 165 cm

The "quantity" in the context of this question is the length of Rie's leg, which is: 99 cm.

Therefore, to find the percentage of Rie's legs in Rie's body, we have the following:

99/165 × 100

= 0.6 × 100

= 60%.

Therefore, Rie's leg is 60% of Rie's body.

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1. The type of bias that the researcher would be making here based on the fact that the households were not that of single millennials is the sampling bias.

2. The voluntary response bias is the type of bias that is being done where the receipts of the website would be the bias that would occur from the company's website.

3. The under coverage bias is what would happen in this scenario given that the friend would not have to ask all of the persons that would be used for the study.

This is the term that is used to refer to the systematic error that would occur in research due to the researchers methods.

1. The answer is the sampling error due to the fact that the random generator was what was used. This would end up giving a sample that would not show the true representation of all of the population.

2. The voluntary response bias is what would be made here because those filling the form are doing it voluntarily.

3. The undercoverage bias is made here because the opinion of the entire school population is not well represented here.

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Statement Problem: Shane is a building engineer and is determining the length of an access ramp needed to reach a step 1.5 feet off the ground. He knows the length of the ramp, r, in feet, can be expressed with the equation below.

First, Shane finds that sin(4.5°) ≈ 0.08. Using his calculator, he then calculates the length of the ramp as shown below.

What could Shane do to make his calculation more accurate?

Solution:

The length of the ramp, r, in feet is expressed using the sine ratio;

Hence, Shane's calculation would be more accurate if he uses sin (4.5 degrees) in his calculator instead of 0.08

CORRECT OPTION: A

Answer: Cumulative frequency distribution

Step-by-step explanation: Not entirely sure but I believe you are looking for this definition based on the question. Hope this helps :)

The two equations that are true when x = -2 and x = 2 are x^2 - 4 = 0 and 4x^2 = 16.

We have given x = 2 and x = -2

Substitute the values in the given equations

Equation 1

x^2 - 4 = 0

Substitute x = 2 in LHS, we get

2^2-4 = 4 - 4 = 0 = RHS

Substitute x = -2 in LHS, we get

(-2)^2-4 = 4 - 4 = 0 = RHS

Equation 2

x^2 = -4

Substitute x = 2 in LHS, we get

2^2 = 4 ≠ RHS

Substitute x = -2 in LHS, we get

(-2)^2 = 4 ≠ RHS

Equation 3

3x^2 + 12 = 0

Substitute x = 2 in LHS, we get

3(2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Substitute x = -2 in LHS, we get

3(-2)^2 + 12 = 12 + 12 = 24 ≠ RHS

Equation 4

4x^2 = 16

Substitute x = 2 in LHS, we get

4(2)^2 = 4(4) = 16 = RHS

Substitute x = -2 in LHS, we get

4(-2)^2 = 4(4) = 16 = RHS

Equation 5

2(x-2)2 = 0

Substitute x = 2 in LHS, we get

2(2-2)2 = 2(0)(2) = 0 = RHS

Substitute x = -2 in LHS, we get

2(-2-2)2 = 2(-4)(2) = 16

Hence, we find that Equation 1 and Equation 2 are true for x = 2 and x = -2

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

Using the law of cosines, the missing angles are:

A = 34.1°, B = 44.4°, C = 101.5°

The law of cosines is used to solve a triangle when given the lengths of the three sides of a triangle, and it is expressed by the formula:

c² = a² + b² - 2ab × Cos C.

Given the following:

Find C by substituting the values into the law of cosines formula:

7² = 4² + 5² - 2 × 4 × 5 × Cos C

49 = 16 + 25 - 40 × Cos C

49 = 41 - 40Cos C

49 - 41 = -40Cos C

8/-40 = Cos C

-0.2 = Cos C

C = Cos^(-1)(-0.2)

C = 101.5°

Find B using the Law of Sines:

sin B/b = sin C/c

Substitute

sin B/5 = sin 101.5/7

(sin B)(7) = (sin 101.5)(5)

sin B = (sin 101.5)(5)/7

sin B = 0.69995

B = Sin^(-1)(0.69995)

B = 44.4°

Find the measure of angle A using the triangle sum theorem:

A = 180 - 101.5 - 44.4

A = 34.1°

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The expression that we can replace in the second equation is 4 - y, doing that, we will get the solutions:

x = -8 and y = 12

Here we have the system of equations:

x=4−y

3x+2y=15

Notice that x is already isolated on the first equation, so we can substitute that in the second equation. Then we will get:

3x+2y=15

3*(4 - y) + 2y = 0

So the expression that could be substituted for x in the second equation is 4 - y.

And now we get:

12 - 3y + 2y = 0

12  = y

And the value of x is:

x = 4 - y = 4 - 12 = -8

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Answer: 260 is greater than 53.46 times X +.13×350

Step-by-step explanation: You know you have to stay under $260 because that’s all she has so that’s where you get to 260 is greater than

And she knows she’s going to go about 350 miles so 260 is greater than $.13 times 350+5346 times you don’t know how many days so that your variable X

y = 2x - 12

SOLUTION

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Get the total number of visitors on saturday

STEP 2: Get the proportion/probability of the people who went to the Youth Wing on Saturday

STEP 3: Get the expected number of people to visit the Youth Wing on Sunday

Hence, the expected number of people to visit the Youth Wing on Sunday is approximately 382 people

We will solve as follows:

*First: We find out the value of the product:

Now, we find out from the other expressions:

*First:

[No]

*Second:

[Yes]

*Third:

[Yes]

*Fourth:

[No]

*Fifth:

[Yes]

Parallel lines has the same slope. In our case, the slope is -5. Then, the searched line has the form:

where b is the y-intercept.

We can find b by substituting the given point (3,2) into the las equation. Then, we have

which gives

Therefore, the parallel lines is given by

The probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Let the true proportion exists 0.07

number of samples exists 492 then we get

√(0.07)(1−0.07)/492 ≈ 0.01150291586

Since the true value of the population proportion exists 0.07, the value of p^ must fall between 0.04 and 0.10 in order for the error of estimation to be less than 0.03.

Therefore, the probability that the sample proportion will differ from the population proportion by less than 0.03 exists 0.9909.

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Step-by-step explanation:

100+14.75%

100+14=114

=114.75%

In general, the linear regression formula is shown below

The rate at which the base of the triangle is changing is equal to,

dB = -6.3 cm/minutes.

From the data given in the question.

The rate of increase in the area of the triangle, dA = 4.5 cm/minute

The rate of increase in the altitude of the triangle, dH = 3.5 cm/minute

The Area of the triangle, A = 87 square centimeters

The altitude of the triangle, H = 7.5 centimeters

The equation for the area of a triangle is equal to

A = 0.5×B×H

Plug in A and H to solve for B at that point:

87 = 0.5×B×7.5

B = 23.2

Differentiate the equation for the area of a triangle to find the rate of change of the area of a triangle (dA):

dA = 0.5× dB× H + 0.5×B × dH.

Plug in known variables to solve for the rate of change of the base dB

dA = 0.5 × dB × H + 0.5 × B × dH

4.5 = 0.5 × dB × 7.5 + 0.5 × 23.2 × 3.5

The rate at which the base of the triangle is changing is equal to,

dB = -6.3 cm/minutes.

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The percentage of the tax is 11.26%

Percentage:

Percentage is defined as the number or ratio that can be expressed as a fraction of 100. If you want to calculate percent of a number, divide the number by the whole and multiply by 100.

Given,

Two people dined at the la fiesta grill where the food cost was $36.54 to that a tax of 4.12 was added .

Here we need to find the tax in percentage.

Let us consider x be the percentage of tax has been added to the food.

The the given details, we have identified the following details,

Amount of the food = $36.54

Tax amount = $4.12

So, it can be written as,

x% of $36.54 = $4.12

Here we need the percentage value so we have to move the other to the right side, then we get,

x% = $4.12/36.54

x% = 0.1126

To convert it into percentage, then we have to multiply it by 100, then we get,

x = 11.26

Therefore, the tax percentage is 11.26%.

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Let x be the amount raised by each club member. Since there are 60 members, the amount raised by them would be

Now, we know the school contributed $1,000. Now, the amount raised is:

Since this amount has to be at least $5,000, we have that the inequality that shows the amount of money that each glee club member needs to raise to help pay for the trip is:

Answer: Option A

16) We know that the triangles are similar because the three angles are equal in both triangles:

The angles in K are opposite by the vertex, so they are equal.

We also know that angles L and N are equal too.

By the rule of the sum of the angles in a triangle, we know that the third angle has to be equal.

Also, the side opposite to the angle N and L in each triangle have the same measure, so we can conclude that the triangles are similar.

For the given figure, we will prove the triangles BGH and BDH are congruent.

So, the proof will be as follows:

Statement Reason

1) m∠F = m∠FEG = m∠FGE Given

2) ΔFGE is an equilateral triangle from (1), the definition of an equilateral Δ

3) FG = GE from (2), the definition of equilateral Δ

4) FG = ED Given

5) m∠ GEH = m∠DEH Given

6) EH = EH Reflexive property

7) ΔGEH ≅ Δ DEH SAS postulate

8) GH = DH from (7) CPCTC

9) m∠GHE = m∠DHE from (7) CPCTC

10) m∠GHB = m∠DHB Definition of supplementary angles

11) HB = HB Reflexive property

12) ΔBGH ≅ ΔBDH SAS postualte

13) ΔAGB is an isosceles Δ Given

14)AG = AB Definition of isosceles Δ

15) ΔBCD is an isosceles Δ Given

16) CB = CD Definition of isosceles Δ

17) CB = AG Given

18) m∠CDB = m∠CBD Definition of isosceles Δ

19) m∠ABG = m∠AGB Definition of isosceles Δ

20) m∠CDB = m∠AGB Given

21) m∠ABG = m∠CBD Transitive property

22) Δ AGB ≅ ΔCBD AAS postualte

For the right triangle shown in the picture, recall the trigonometric identity of the cosine function:

Isolate a from the equation:

Substitute for c=6.3 and B=43.8°:

Use a calculator to evaluate the expression:

Using first equation

y=x-6

substitute x = 5 into the equation

y = 5-6

y = -1

Or

Using second equation

-2x+3y=-13​

substitute x = 5 into the equation

-2(5) + 3y = -13

-10 + 3y = -13

3y = -13 + 10

3y = -3

y = -3/3

y = -1

The value of a in the equation (3x869)+(19x528)+428(3)(1049)=a is 1359555

From the question, the equation to evaluate is given as

(3x869)+(19x528)+428(3)(1049)=a

Rewrite the above equation to make it legible

So, we have the following equation

(3 x 869) + (19 x 528) + 428(3)(1049) = a

Evaluate the products in the expression

So, we have the following equation

2607 + (19 x 528) + 428(3)(1049) = a

Evaluate the other products in the expression

So, we have

2607 + 10032 + 428(3)(1049) = a

Remove the brackets in the equation

So, we have the following equation

2607 + 10032 + 1346916 = a

Evaluate the sum

1359555 = a

Rewrite as

a = 1359555

Hence, the solution to the equation is 1359555

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two lines are parallel if their slope is equal

equation of line is

y=mx+c

where m=slope

for y=2x-5

m=2

for -x+2y=-5

2y=-5+x

y=-5/2+x/2

m=1/2

lines are nor parallel becuase m (slope) is not equal

now we will test for perpendicularity

perpendicular lines have slopes that are reciprocal of each other

first line , m=2

second line, m=1/2

2 and 1/2 are reciprocals

therefore, the lines are perpendicular

Answer: 126

Step-by-step explanation:: 90 ÷ 10 = 9 (10%) 9 × 4 = 36 (40%) 90 + 36 = 126