what do we mean by 16 1/4

Answer:

Option C, 13.7 cm

Step-by-step explanation:

Cos(31°) = [tex]\frac{x}{15}[/tex]

=> Multiply 15 on both sides of "="

Cos(31°) * 15 = x

13.7 = x

Hope this helps!

Answer:

Inferential study

Step-by-step explanation:

From the question, we understand that the professor concluded that majority of the class (of 198 students) preferred in class assessment based on the response from 67% of the sample size (i.e 30 students)

When decisions or conclusions are made about an overall population based on a survey carried out on a smaller sample, such study is referred to as an inferential study or inferential research.

Descriptive study on the other hand focuses on the features rather than the result of the experiment of the dataset.

The correct option regarding which of the sentences represents a trigonometric identity is given as follows:

b. None of the equations are identities.

A trigonometric identity is a relation that is true for all possible angle measures of [tex]\theta[/tex]

The first relation is given as follows:

[tex]4\cos{\theta}\tan{\theta}\sec{\theta} = 4[/tex]

The tangent and secant equations are given as follows:

Hence:

4cos(x)tan(x)sec(x) = 4cos(x) x sin(x)/cos(x) x 1/cos(x)

4cos(x)tan(x)sec(x) = 4sin(x)/cos(x)

4cos(x)tan(x)sec(x) = 4tan(x).

Meaning that the first statement is not an identity.

The second relation is given as follows:

[tex]\frac{9\sec^{2}{\theta}}{\cos^{2}{\theta}} - \frac{\tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

With a single denominator, we have that:

[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

The secant identity is given as follows:

[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]

Hence:

[tex]\frac{9\sec^{2}{\theta} - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

[tex]\frac{9(1 + \tan^2{\theta}) - \tan^{2}{\theta}}{\cos^{2}{\theta}} = 2[/tex]

[tex]\frac{9 + 8\tan^2{\theta}}{\cos^{2}{\theta}} = 2[/tex]

Is also a false statement, hence neither is an identity and option B is correct.

The statements are given by the image presented at the end of the answer.

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Answer:

It is not possible to find the greatest common factor of 3x.

Step-by-step explanation:

The greatest common factor (GCF) of a set of numbers is the largest number that divides into all of the numbers in the set.

In this case, you have provided a variable, 3x, and not a set of numbers. Therefore, it is not possible to find the greatest common factor of 3x.

If you have a set of numbers that you would like to find the greatest common factor of, please let me know and I will be happy to help.

Answer:

noseee  

Step-by-step explanation:

Answer:

theta =111°

hope it helps.

Answer:

69°

Step-by-step explanation:

Sum of angles in a triangle is 180°.

Moreover, because the marked lines are parallel, the third angle of the triangle (first two being 62° and Θ) is equal to 49°

That gives us:

[tex]\Theta = 180^\circ - 49^\circ - 62^\circ = 69^\circ[/tex]

Answer:

solution set must contain all numbers less than zero or greater than one

graph H illustrates this solution

Step-by-step explanation:

6x - 14 < -14

6x < 0

x < 0

3x + 10 > 13

3x > 3

x > 1

Answer:

Step-by-step explanation:

in the first triangle an angle is 60 degrees so it means that the triangle is half of a equilateral triangle.

in this case the base leg is half of the hypotenuse.

x = 8

in the second triangle we have an angle that is 45 degrees and this means that the triangle has two congruent legs

x = 10

the answer to this equation is 104.25

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y = - 5x + 6

The equation of the line that is parallel to the line y = - 5x + 6 is written as,

y = - 5x + c

The equation passes through (-4, -1), then we have

- 1 = - 5 (-4) + c

- 1 = 20 + c

- 21 = c

The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.

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Answer:

4.19

Step-by-step explanation:

just use the formula 2pir^2

Answer:

4

Step-by-step explanation:

You divide 125 by 40 and that will give you 3 1/8. In the question, it says to use whole numbers and you'd have to go up, giving you 4.

It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.

Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.

here, we have,

The together rate is the sum of the separate rates.

In this question:

Sam's rate is 1/10 for 25 square feet, so 1/20 for 50 square feet.

Your's rate is 1/5 for 25 square feet, so 1/10 for 50 square feet.

Together rate:

1/x = 1/20 + 1/10

or, 1/x = 3/20

or, x = 20/3

or, x = 6.67

so, we get,

It takes you together 6.67 minutes to paint 50 square feet, as you have to consider that the together rate is the sum of the separate rates.

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complete question:

Sam and you are going to paint your room together.

Sam takes 10 minutes to paint 25 square feet.

It takes you 5 minutes to paint 25 square feet.

Sam says, "If we paint together, then it will take 15

minutes for us to cover 50 square feet."

Give an explanation to convince Sam that she is

incorrect

Answer:

To color the hair of one client takes 55 minutes

To give a client a haircut takes 72-55 which is 17

Step-by-step explanation:

i hope this helps ;)

Answer:

Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.

Step-by-step explanation:

Toll Brothers is a luxury home builder that would like to test the hypothesis that the average size of new homes exceeds 2,400 square feet. Test to see if the average size of new homes exceeds 2,400 square feet.

At the null hypothesis, we test if the average is of 2400 square feet, that is:

[tex]H_o: \mu = 2400[/tex]

At the alternate hypothesis, we test if the average is greater than 2400 square feet, that is:

[tex]H_a: \mu > 2400[/tex]

The test statistic is:

Since we have the standard deviation for the sample, we use the t-distribution.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

2400 is tested at the null hypothesis:

This means that [tex]\mu = 2400[/tex]

A random sample of 36 newly constructed homes had an average of 2,510 square feet with a sample standard deviation of 480 square feet.

This means that [tex]n = 36, X = 2510, s = 480[/tex]

Test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{2510 - 2400}{\frac{480}{\sqrt{36}}}[/tex]

[tex]t = 1.375[/tex]

Pvalue of the test and decision:

The pvalue of the test is the probability of finding a sample mean of at least 2510, which is the pvalue of t = 1.375 with 36 - 1 = 35 degrees of freedom, using a one-tailed test.

With the help of a calculator, this pvalue is of 0.09

Since the pvalue of the test is 0.09 > 0.01, we do not reject the null hypothesis that the average size of new homes is of 2400 square feet.

Answer:

  Line D

Step-by-step explanation:

You want to know which line is not parallel or perpendicular to the other given lines:

 A: 2y -x = 2

  B: 4y = -8x -4

  C: y = -2x +4

  D: 5y = 10x +15

We can write each of these equations in standard form to make it easier to compare them. That form is ...

  ax +by = c

where a > 0 and a, b, c are mutually prime.

The equations are ...

  A: x -2y = -2

  B: 2x +y = -1

  C: 2x +y = 4

  D: 2x -y = -3

Equations with the same coefficients of x and y will be parallel:

  2x +y = -1  and  2x +y = 4 . . . . lines B and C

Equations with coefficients that have been swapped, with one negated, will be perpendicular:

  x -2y = -2  and  2x +y = -1 . . . . lines A and B

Line A is perpendicular to parallel lines B and C, so line D is the odd one out.

  Line D doesn't fit.

Answer:

3 packs

Step-by-step explanation:

1 pack = $3

To see how many she could buy divide the money she has by how much each pack costs

9/3 = 3

$3 for each pack is the same as

3+3+3 = 6+3 = 9

So on solving the provided question, we can say that the value of k is 4, in this linear equation question.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

1/2k +6= 4k-8

Multiplying both sides by 2,

k+12= 8k-16

7k=28

Therefore,

       k=4

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Step-by-step explanation:

that is a college level question ? and you don't know the answer ?

that is basic, basic, basic ...

you go on the x-axis to -2.

from there you go either up or down and look at what y-value are you crossing the functional curve.

it is -1.

so, the "output" for x = -2 is y = -1. or simply -1.

Answer: She will need 3 extension cords.

Step-by-step explanation:

If the farthest hedge is 40 yards away, that means it is 120 feet away because 1 yard equals 3 feet. If the cord on her trimmer is 10 feet and her extension cords are 50 feet long, 10+50+50+50= 160 feet. This means she would need 3 extension cords. 2 extension cords would not be long enough.

Answer:

12.6

Step-by-step explanation:

you basically subtract 32.4 and 45 to get your final answer because if a question has the words " how much more " you will most likely have to subtract or include subtraction

The annual cost if she chooses to make monthly payment is $1920 and money saved is $170

The given parameters that will help us to determine the incomes are

a)  Annual cost if she chooses to make one annual monthly installment is $1920

b) Money saved is she makes one annual payment is $(1920-1750)= $170

3) Volume of gas = 60 L

Efficiency rating = 10.2km/L

Average drive = Volume / Efficiency = 60/10.2 = 5.9km/L

b) Cost of gas = 149.9⊄⊄/L

Number of liters =60

= 60*149.9

=$8994

c) Constant gas price = $149.9⊄/L

Number of weeks /year = 52

=52*149.9

= $7795

4) Morgan pay $15/hr

Number of hours per week = 40

Gross monthly income = 40*15*4

=$2400

b)   Monthly income $2400

Amount left after deduction = 85%

=0.85*2400

Net income = $2040

In conclusion Mindley receives $1920 monthly and saves $170

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Answer:

SA = 2520 ft^2

Step-by-step explanation:

a = 21ft

b = 29ft

c = 20ft

h = 30ft

SA = 2[tex]A_{B}[/tex] + (a+b+c)h

[tex]A_{B}[/tex] = s(s﹣a)(s﹣b)(s﹣c)

s = [tex]\frac{a + b + c}{2}[/tex]

SA= ah + bh + ch + [tex]\frac{1}{2}[/tex] [tex]\sqrt{-a^4 + 2(ab)^2 + 2(ac)^2 - b^4 + 2(bc)^2 - c4}[/tex]

SA= (21 * 30) + (29 * 30) + (20 * 30) +

       [tex]\frac{1}{2}[/tex] [tex]\sqrt{-(21)^4 + 2(21 * 29)^2 + 2(21 * 20)^2 - (29)^4 + 2(29 * 20)^2 - (20)^4}[/tex]

SA = 2520 ft^2

Answer:

27

Step-by-step explanation:

(1/3) * x = 9

x = 9 * (3/1)

x = 27

Hope this helps!

Answer:

let the number be x

1/3*x=9

x/3=9

x=9*3

x=27

Step-by-step explanation:

therefore the number is 27

Observing the given figure , It is a balanced balance which signifies both side should be equal, The answer is 2=-8-x and x=-10.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics. A set of two or more linear equations with two or more variables each constitutes a system of linear equations, all of which are taken into account simultaneously. Finding a numerical value for each variable in the system that will simultaneously satisfy all of the system's equations is necessary to identify the one and only solution to a system of linear equations.

There are three ways to solve systems of linear equations :

2=-8-x is the required balanced equation.

-x = 2 + 8

x= -10

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Answer:

Lateral surface area is 847.8 centimeters^2

Step-by-step explanation:

The formula for determining the lateral surface area of a cylinder is expressed as

Lateral surface area = 2πrh

Where

r = radius of the cylinder

h = the height of the cylinder

From the information given,

r = 9 centimeters

h = 15 centimeters

π = 3.14

Lateral surface area = 2 × 3.14 × 9 × 15 = 847.8 centimeters^2

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