Which size would you see on the box for a new television whose screen measures 36 inches wide by 27 inches high? A. 9" B. 45" C. 50" D. 63"

Answer:

Hypotenuse = 13.798 cm, Angle1 = 27.4° and Angle2 = 62.59°

Step-by-step explanation:

The first step to help us understand the question would be to draw it out.

A right angled triangle, with the two sides that make the right angle being x and y (it does not matter which way you put x and y).

I have attached the quick sketch I will refer to.

To find the length of the hypotenuse (lets call it H) we can use Pythagoras theorem as shown below

[tex]{x^{2}+y^{2}} = H^{2}[/tex]

Substitute in our values for x and y, and solve for H

[tex]{6.35^{2}+12.25^{2}} = H^{2}[/tex]

[tex]190.385 = H^{2}[/tex]

[tex]\sqrt{190.385} = H[/tex]

H = 13.79 cm

To find the other two angles of the triangle we will use trigonometry

I will first look for angle ∅. Since we have all three sides of the triangle we can use any of the three trig functions, I chose to use Tan

Tan ∅ [tex]= \frac{opposite}{adjacent}[/tex]

Substitute in our values for x and y, and solve for ∅

Tan ∅ = [tex]\frac{6.35}{12.25}[/tex]

∅ = [tex]tan^{-1} \frac{6.35}{12.25}[/tex]

∅ = 27.4°

Now do the same for angle β. I chose to use Tan again

Tan β [tex]= \frac{opposite}{adjacent}[/tex]

Substitute in our values for x and y, and solve for β

Tan β = [tex]\frac{12.25}{6.35}[/tex]

β = [tex]tan^{-1} \frac{12.25}{6.35}[/tex]

β = 62.59°

Answer:

Step-by-step explanation:

Let s, b, a represent the numbers of servings of steak, baked eggs, and acorn squash, respectively. Then the equations we want to solve are ...

  40s +20b +4a = 64 . . . . grams of protein

  10s +2b +20a = 29 . . . . grams of carbohydrate

  1s +20b +32a = 72.5 . . . milligrams of vitamin A

There are any number of calculators or web sites that will solve this system of equations for you. The solution is ...

  s = 0.5

  b = 2

  a = 1

The dietitian should provide 1/2 serving of steak, 2 servings of baked eggs, and 1 serving of acorn squash.

Answer:

D. F(x) = 2(x-3)^2 + 3

Step-by-step explanation:

We are told that the graph of G(x) = x^2, which is a parabola centered at (0, 0)

We are also told that the graph of the function F(x) resembles the graph of the function G(x) but has been shifted and stretched.

The graph of F(x) shown is facing up, so we know that it is multiplied by a positive number. This means we can eliminate A and C because they are both multiplied by -2.

Our two equations left are:

 B. F(x) = 2(x+3)^2 + 3

 D. F(x) = 2(x-3)^2 + 3

Well, we can see that the base of our parabola is (3, 3), so let's plug in the x value, 3, and see which equation gives us a y-value of 3.

y = 2(3+3)^2 + 3 =

2(6)^2 + 3 =

2·36 + 3 =

72 + 3 =

75

That one didn't give us a y value of 3.

y = 2(3-3)^2 + 3 =

2(0)^2 + 3 =

2·0 + 3 =

0 + 3 =

3

This equation gives us an x-value of 3 and a y-value of 3, which is what we wanted, so our answer is:

D. F(x) = 2(x-3)^2 + 3

Hopefully this helps you to understand parabolas better.

Answer:

Step-by-step explanation:

Answer:

972^1/4 = 4 ⁴√3

448^1/3 = 4 ³√7

3528^1/2 = 42√2

4050^1/4 = 3 ⁴√50

Hope this helps.

Answer:

  4.  the set of all natural numbers, the set of all whole numbers, the set of all integers, the set of all rational numbers, and the set of all real numbers

Step-by-step explanation:

√9 = 3

3 is every kind of number except irrational. It belongs to the sets of ...

Answer:

A. or every 1 ton increase in precompression stress, the shear strength of the joint is estimated to increase by 0.987 tons.

Step-by-step explanation:

Hello!

The engineers created a regression model to estimate the relationship between the "shear strength of masonry joints" (Y), measured in tons, and the "precompression stress" (X), measured in tons.

^Y= a + bXi

Using the regression output:

Estimate of the y-intercept: a= 1.192

Estimate of the slope: b= 0.987

In general terms you can interpret the slope as:

"Is the modification of the estimated mean of Y when X increases one unit"

In this case it means that every time the precompression stress increases one ton, the shear strength of the joint is estimated to increase 0.987 tons.

I hope this helps!

Answer:

a) The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

b) $0.57

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96*\frac{1.86}{\sqrt{41}} = 0.57[/tex]

So the answer for b) is $0.57.

The lower end of the interval is the sample mean subtracted by M. So it is 12.22 - 0.57 = $11.65

The upper end of the interval is the sample mean added to M. So it is 12.22 + 0.57 = $12.79

The 95% confidence interval to estimate the average fee for the population is between $11.65 and $12.79

Answer:

A whole number that can be made by multiplying other whole numbers.

Example: 18 can be made by 3 × 6 so is a composite number.

16 can be made by 4 x 4 so it is a square root and a composite number

14 can be made by 2 x 7 so is is a composite number.

It is not a prime number as all Composite Number have factors other than 1 and itself). The first few composite numbers (sometimes called "composites" for short) are 4, 6, 8, 9, 10, 12, 14, 15, 16,

Answer:

We need to examine the natural numbers.

The natural numbers are the counting numbers,

1, 2, 3, 4, 5, 6, ...

The number 1 is neither prime nor composite.

All natural numbers greater than 1 are either prime or composite.

A prime number is a number that has exactly two factors, itself and 1.

A composite number has more than 2 factors.

A composite number is a natural number greater than 2 that is not a prime number.

Examples:

Prime: 2, 3, 5, 7, 11, ...

Composite: 4, 6, 8, 9, 10, 12, ...

Answer:

The test statistic for the hypothesis test is -1.202.

Step-by-step explanation:

We are given that a report on the nightly news broadcast stated that 10 out of 129 households with pet dogs were burglarized and 23 out of 197 without pet dogs were burglarized.

Let [tex]p_1[/tex] = population proportion of households with pet dogs who were burglarized.

[tex]p_2[/tex] = population proportion of households without pet dogs who were burglarized.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1=p_2[/tex]     {means that both population proportions are equal}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1\neq p_2[/tex]     {means that both population proportions are not equal}

The test statistics that would be used here Two-sample z-test for proportions;

                           T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of households with pet dogs who were burglarized = [tex]\frac{10}{129}[/tex] = 0.08

[tex]\hat p_2[/tex] = sample proportion of households without pet dogs who were burglarized = [tex]\frac{23}{197}[/tex] = 0.12

[tex]n_1[/tex] = sample of households with pet dogs = 129

[tex]n_2[/tex] = sample of households without pet dogs = 197

So, the test statistics  =  [tex]\frac{(0.08-0.12)-(0)}{\sqrt{\frac{0.08(1-0.08)}{129}+\frac{0.12(1-0.12)}{197} } }[/tex] 

                                     =  -1.202

The value of z test statistics is -1.202.

Answer: [tex]\frac{21}{4}[/tex]

Step-by-step explanation:

Multiply each side by 2 to get rid of the fraction on the right side. That basically gets rid of the 1/2 and the 2.

Youre now stuck with 2x + y = 21. They gave us y which is 2x. 2x + 2x = 4x

You now have 4x = 21

Divide each side by 4 to get x = 21/4

Answer:

It can produce 1590 loaves of bread per day.

Step-by-step explanation:

Given that the bread machine operates only 10 hours per day. So in order to calculate how many loaves can be produce a day, you have to multiply it by 10 :

[tex]1hour = 159loaves[/tex]

[tex]10hours = 159 \times 10[/tex]

[tex]10hours = 1590loaves[/tex]

Answer:

[tex]P(selecting a red t-shirt)=1/2[/tex]

Step-by-step explanation:

CHECK THE COMPLETE QUESTION BELOW;

A laundry basket has 24 t-shirts in it. Four are Navy, 12 are red, and the rest is white. What is the probability of randomly selecting a red t-shirt

EXPLANATION

Total number of the t-shirt in the laundry basket = 24

Number of Navy t-shirt = 4

Number of red t- shirt = 12

The number of white t- shirt in the laundry basket can be calculated as follow;

Total number of t- shirt - (Number of Navy t-shirt + Number of red t- shirt)

Number of white t- shirt = 24 -(4+12)

Number of white t- shirt = 8

The probability of randomly selecting a red t-shirt = [tex]Number of red t- shirt/Total number of the t-shirt[/tex]

[tex]P(selecting a red t-shirt)=12/24[/tex]

[tex]P(selecting a red t-shirt)=1/2[/tex]

Answer:

A

Step-by-step explanation:

Integers are negative and positive whole numbers

Answer: A. 0.8

Step-by-step explanation:

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14

Answer:

3u-2v = [tex]\sqrt{505\\}[/tex]

5u-v = [tex]\sqrt{1,157}[/tex]

2u-3v = [tex]\sqrt{1,300}[/tex]

u+4v = [tex]\sqrt{4,505}[/tex]

Step-by-step explanation:

I just started by doing the results for each of the operations given.

3u-2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u-2v and you get a resultant vector of (19, 12).

You calculate this by doing the square root of 19^2 + 12^2, which is the square root of 505.

5u-v:

5u = (-15, 40)       v = (-14, 6)

Do the operation of 5u-v and you get a resultant vector of (-1, 34).

You calculate this by doing the square root of (-1)^2 + 34^2, which is the square root of 1,157.

2u-3v:

2u = (-6, 16)   3v = (-42, 18)

Do the operation of 2u-3v and you get a resultant vector of (36, -2).

You calculate this by doing the square root of 36^2 + (-2)^2, which is the square root of 1,300.

3u+2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u+2v and you get a resultant vector of (-37, 36).

You calculate this by doing the square root of (-37)^2 + 36^2, which is the square root of 2,665. This is not a given tile, so we can just ignore this one.

u+4v:

u = (-3, 8)       4v = (-56, 24)

Do the operation of u+4v and you get a resultant vector of (-59, 32).

You calculate this by doing the square root of (-59)^2 + 32^2, which is the square root of 4,505.

Since this is a given tile, I didn't do 7u-2v, but you would use the same methodology.

Answer:

[tex]cos=\frac{4}{5}[/tex]

Step-by-step explanation:

Cosine is the adjacent side over the hypotenuse (You can remember sin, cos, and tan by using sohcahtoa or sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite over adjacent). I think a picture would help, too.

I attached a picture of what I think the triangle would look like.

If the picture is right (we're assuming it is) and going with what we're given (the triangle was addressed as triangle XYZ, meaning that angle Y is in the middle and that's the one we'll use).

Looking at my picture then:

[tex]cos=\frac{64}{80} \\cos=\frac{8}{10} \\cos=\frac{4}{5}[/tex] .

Answer:

  x = -1/5, x = 1

Step-by-step explanation:

Maybe you want to find x.

Subtract the right side and collect terms.

  6x^2 +4x^2 -6x -4 -(2x -2) = 0

  10x^2 -8x -2 = 0

  5x^2 -4x -1 = 0 . . . . . . divide by 2

  (5x +1)(x -1) = 0 . . . . . . factor

Solutions are the values of x that make these factors zero:

  5x +1 = 0   ⇒   x = -1/5

  x -1 = 0   ⇒   x = 1

Solutions are x = -1/5, x = 1.

Answer:

  D.  x is all real numbers

Step-by-step explanation:

The graph only goes from -11 to +11 in the horizontal direction, but that domain is not a choice. Apparently, we're to assume the graph extends to infinity both to the left and the right.

The domain is the horizontal extent of the function, so is ...

  x is all real numbers

[tex]answer = 17.85 {inches} \\ solution \\ radius = 5 \: inches \\ perimeter \: of \: quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 5}{4} + 2 \times 5\\ = \frac{31.4}{4} + 10 \\ = \frac{31.4 + 10 \times 4}{4} \\ = \frac{31.4 + 40}{4} \\ = \frac{71.4}{4} \\ = 17.85 \: {inches} \\ hope \: it \: helps[/tex]

Answer:

17.85 in

Step-by-step explanation:

2πr is formula for the circumference but [tex]\frac{1}{2}[/tex]×π×r is the circumference for the quarter circle.

0.5×π×5=

2.5π≈

7.85

7.85+5+5=17.85 in

Answer:

1. Option c

2. Option d

Step-by-step explanation:

This type of survey is includes a sample made up of voluntary responses. People only choose to or do not choose to respond.

This type of sampling method is most of the time unbelievable because generally only people with strong opinions about this particular questions will respond and it is usually towards the same direction as the question and this might not reflect the opinion of the whole population making the survey biased.

Part A: The respondents are a voluntary response sample (Option C)

Part B: Responses may not reflect the opinions of the general population (Option D)

The total number of internet users = 1072

Percentage of the total number of people that chose to respond = 38%

Note that this survey does not compel all the population to respond to the survey. Responses are gotten from voluntary respondents.

Also note that a voluntary response sample is a sample that consists of participants who chose to participate in a sample group voluntarily.

In this type of survey, the people who decided to provide voluntary responses to the survey are called voluntary response samples

The percentage of those that chose to respond to this survey (38%) is less than half of the total population. This obviously shows that the responses may not reflect the opinions of the general population

Learn more on sampling methods here: https://brainly.com/question/16587013

Answer:

  1/12

Step-by-step explanation:

  blue = (3/8)collection

  blue&pocket = (2/9)blue = (2/9)(3/8)collection

  blue&pocket = (6/72)collection = (1/12)collection

1/12 of Noah's collection is blue and has a pocket.

Answer:

< DKC = [tex]60^{0}[/tex]

Step-by-step explanation:

A square is a quadrilateral that has equal length of side. While an equilateral triangle is one with equal length of sides and equal values of angles.

Given square ABCD and that equilateral triangle ABK is outside the square, both figures share side AB. This shows that the length of the sides of the triangle is the same as the length of the side of the square.

i.e /AD/ = /CD/ = /BC/ = /AB/ = /AK/ = /KB/

Thus, < DKC = [tex]60^{0}[/tex] (property of angles in an equilateral triangle)

Answer: 1/4

Step-by-step explanation:

The cheesiest recipe would be 1 cup and the least cheesy recipe would be 3/4 cups

1 - 3/4 = 1/4

Answer:

[tex]\frac{1}{4}[/tex] cup of cheese

Step-by-step explanation:

The least cheesiest recipe uses [tex]\frac{3}{4}[/tex] cup of cheese while the most cheesiest uses 1 cup of cheese.

[tex]1-\frac{3}{4} =\\\\\frac{1}{4}[/tex]

The most cheesiest uses [tex]\frac{1}{4}[/tex] cup more cheese than the least cheesiest.

Answer:

The price p could be any of $8 or $15 .

Step-by-step explanation:

The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.

x = 2300 - 100p

xp = 12000

therefore,

x = 12000/p

insert the value of x in the equation

x = 2300 - 100p

12000/p = 2300 - 100p

12000/p + 100p - 2300 = 0

multiply through by p

12000 + 100p² - 2300p = 0

100p² - 2300p + 12000 = 0

divide through by 100

p² - 23 + 120 = 0

Find the number that we can multiply to give 120 and add to give - 23. The number are -15 and - 8.

p² - 8p - 15p + 120 = 0

p(p - 8) - 15(p - 8) = 0

(p - 8)(p - 15)

p = 8 or 15

x = 2300 - 100p

x = 2300 - 100(8)

x = 2300 - 800

x = 1500  pencil sharpener sold

or

x = 2300 - 100(15)

x = 2300 - 1500

x = 800 pencil sharpener sold

The price could be any of $8 or $15 .

Answer:

a)  "K" is proportional Constant   K= 0.0833

b)     The value of b = 99.639

Step-by-step explanation:

Explanation :-

Given   'a' is directly proportional to 'b'

                     a ∝ b

                 a  =  k b ....(i)

where "K" is proportional Constant

Case(i):-

when a =6  and b=72

              a  =  k b    

         ⇒ 6 = k (72)

       ⇒  [tex]K = \frac{6}{72} = \frac{1}{12} = 0.0833[/tex]      

Case(ii):-      

Given  a = 8.3  

          a  =  k b    

⇒   8.3 = 0.0833 ×b

⇒  [tex]b = \frac{8.3}{0.0833} = 99.639[/tex]

Final answer:-

a)"K" is proportional Constant   K= 0.0833

b)     The value of b = 99.639

Answer:

a. The mean would be 0.067

The standard deviation would be 0.285

b. Would be of 1-e∧-375

c. The probability that both of them will be gone for more than 25 minutes is 1-e∧-187.5

d. The likelihood of at least of one of the taxis returning within 25 is 1-e∧-375

Step-by-step explanation:

a. According to the given data the mean and the standard deviation would be as follows:

mean=1/β=1/15=0.0666=0.067

standard deviation=√1/15=√0.067=0.285

b. To calculate How likely is it for a particular trip to take more than 25 minutes we would calculate the following:

p(x>25)=1-p(x≤25)

since f(x)=p(x≤x)=1-e∧-βx

p(x>25)=1-p(x≤25)=1-e∧-15x25=1-e∧-375

c. p(x>25/2)=1-p(x≤25/2)=1-e∧-15x25/2=1-e∧-187.5

d. p(x≥25)=1-e∧-15x25=1-e∧-375

Answer:

a) [tex]\sigma_{\bar x} = 1.414[/tex]

b) [tex]\sigma_{\bar x} = 1.414[/tex]

c) [tex]\sigma_{\bar x} = 1.414[/tex]

d) [tex]\sigma _{\bar x} = 1.343[/tex]

Step-by-step explanation:

Given that:

The random sample is of size 50 i.e the population standard deviation  =10

Size of the sample n = 50

a) The population size is infinite;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

b) When the population size N= 50000

n/N = 50/50000 = 0.001 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

c)  When the population size N= 5000

n/N = 50/5000 = 0.01 < 0.05

Thus ; the finite population of the standard error is not applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma_{\bar x} = \dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]\sigma_{\bar x} = \dfrac{10}{\sqrt{50}}[/tex]

[tex]\sigma_{\bar x} = 1.414[/tex]

d) When the population size N= 500

n/N = 50/500 = 0.1 > 0.05

So; the finite population of the standard error is applicable in this scenario;

Therefore;

The standard error is determined as:

[tex]\sigma _{\bar x} = \sqrt{\dfrac{N-n}{N-1} }\dfrac{\sigma}{\sqrt{n} } }[/tex]

[tex]\sigma _{\bar x} = \sqrt{\dfrac{500-50}{500-1} }\dfrac{10}{\sqrt{50} } }[/tex]

[tex]\sigma _{\bar x} = 1.343[/tex]

Answer:

No roots

Step-by-step explanation:

the discriminant Δ = 12²-4×(-10)×(-9) = -216

since ∆ is negative then the equation -10x^2 + 12x − 9 = 0 has no solution .

Answer:

y + 6 = -3(x - 1) - Point Slope

y=-x+8 - Slope Intercept

2x - 5y = 9 - Standard

Step-by-step explanation:

Point Slope Form is: [tex]y-y_1=m(x-x_1)[/tex]

y + 6 = -3(x - 1) would be in point slope form, where the point is (1,-6) and the slope is '-3'.

Slope-intercept form is: [tex]y=mx+b[/tex]

y=-x+8 is in slope intercept form, where '-1' is the slope and '8' is the y-intercept.

This only leaves 2x - 5y = 9, which is in standard form.

All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

All the expressions are,

1) y = -x + 8  

2) 2x - 5y = 9  

3) y + 6 = -3(x - 1)

Now, All the correct linear equation with the name of its form are,

1) y = -x + 8   =   Slope-intercept form

2) 2x - 5y = 9  =  Standard form

3) y + 6 = -3(x - 1)  =  Point-slope form

Learn more about the mathematical expression visit:

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Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.

The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 2.35

μ2 = 2.58

s1 = 0.46

s2 = 0.47

n1 = 30

n2 = 25

t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)

t = - 1.8246

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862

df = 51

We would determine the probability value from the t test calculator. It becomes

p value = 0.0746

Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.