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Using the z-distribution, with a critical z-score of z = 1.645, the 90% confidence interval is (-16.4%, -9.66%).

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, they are given as follows:

The interval is:

[tex]p \pm zs[/tex]

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Then the bounds of the interval are:

As a percentage, the 90% confidence interval is (-16.4%, -9.66%).

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The values of a and b are 1/4 and 1/5 respectively

The function is given as:

16x^2 - 25y^2 = 1

The above function is a horizontal hyperbola.

A horizontal hyperbola that passes through the origin is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Rewrite 16x^2 - 25y^2 = 1 as

[tex]\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1[/tex]

By comparison, we have:

[tex]a^2 = \frac{1}{16}[/tex]

[tex]b^2 = \frac{1}{25}[/tex]

Solve for  a and b

[tex]a = \frac{1}{4}[/tex]

[tex]b = \frac{1}{5}[/tex]

Hence, the values of a and b are 1/4 and 1/5 respectively

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Answer:

81m + 27t

Step-by-step explanation:

Using distributive property, this expression can be solved.

So 9(9m + 3t) has operations in it.

9 would be multiplied by whatever is in the parenthesis followed by the variable.

So 9 * 9 = 81.

9 * 3 = 27.

So putting it together with the variables.

It would be:

⇒ 81m + 27t  

The probability of winning the lottery with one ticket is mathematically given as

P(W)=2.99484408*10^{−8}

Generally, the equation for the probability is  mathematically given as

P(1st ball)=1/34

one ball drawn remain

34-1=33

P(2nd ball)=1/33

In conclusion, the probability of winning the lottery with one ticket is

P(W)=1/34*1/33*1/32*1/31*1/30

P(W)=2.99484408*10^{−8}

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The total time spent on his/her cell phone in a year’s time is less than the total time spent waiting in line when shopping in a lifetime.

x= 1825 hrs

z=4929.4 hrs.

This is further explained below.

let's say on average a person spends 5 hours on a mobile phone.

Individual annual mobile phone use time.

x=  5x365

x= 1825 hrs

let's consider an average every day a person, spent 5 minutes in the queue when shopping.

Take the average person. 70-year life for a person.

Hence in a year, he spent

y=365x5 mints

y=1825 min

y=30.42 hrs

Hence lifetime time spent on line

z = 70 x 30.42

z=4929.4 hrs.

In conclusion, we estimate that the typical individual will spend z=4929.4 hours waiting in line for merchandise throughout the course of their lifetime.

z=4929.4 hrs.

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The student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct.

The phrase "at least" means the minimum that is true or possible.

Mathematically, by "at least," we mean 'equal to or greater than.'

Since each bag of nuts contain 16 ounces,

The 1st bag contains x/2 ounces (50%) of plain nuts and x/2 ounces (50%) of chocolate-covered nuts.

The 2nd bag contains x/5 ounces (20%)of plain nuts and 4x/5 ounces (80%) of chocolate-covered nuts.

If half of the 1st bag is mixed with half of the 2nd bag, each bag will contain only 65% (that is, 25% (50%/2) from the 1st bag and 40% (80%/2) from the 2nd bag).

Thus, the student, who suggests that if we do half and half of each bag, we will be giving them at least 60%, is correct since they will not be given less than 60% of chocolate-covered nuts inside.

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When x = 64 and y = 3, we will have:

z = 3,313.21

First, we know that z varies directly with x and inversely with y², then we can write:

z = k*x/y^2

Where k is a constant.

We know that z = 182 when x = 25 and y = 8, replacing that we can find the value of k.

182 = k*25/(8²)

k = 182*8²/25 = 465.92

Now, we just need to evaluate the function in x = 64 and y = 3.

z = (465.92)*64/3² = 3,313.21

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Using complementary angles, it is found that a solution to the given equation is:

D. x = 16, sin 38° = cos 52°.

Two angles are called complementary if the sum of their measures is of 90º. If two angles A and B are complementary, we have that:

cos(A) = sin(B) and sin(A) = cos(B).

In this problem, the expression is:

cos(3x + 4) = sin(2x + 6).

Hence:

3x + 4 + 2x + 6 = 90

5x = 80

x = 16.

Then:

Which means that option D is correct.

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On a number line 1.77 would be located between 1 and 2 but it would be closer to 2 than 1.

A number line is used to show the positioning of numbers. 1.77 is between 1 and 2. So, it would be located between 1 and 2 on the number line. Because 1.77 can be rounded off to 2, it would be closer to 2.

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The solution to the given linear equation are -4 and 2

Quadratic equations are equations that has a leading degree of 2. Given the expression below

(x-3)(x+1)=5

Expand

x^2+x - 3x - 3 = 5

x^2 - 2x - 8 =0

Factorize

x^2 + 4x - 2x - 8= 0

x(x+4)-2(x+4) = 0

x = -4 and 2

Hence the solution to the given linear equation are -4 and 2

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The events are not mutually exclusive.

Two events that cannot occur at the same time are called Mutually exclusive event.

It is given that

A sample of 75 books is selected from a library.

Event A:  At least 10 of the authors are female

Event B : At least 10 of the books are fiction.

Both can happen simultaneously

Therefore the events are not mutually exclusive.

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Answer:

x = - 1

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] (8x + 12) = 3 ( multiply both sides by 4 to clear the fraction )

3(8x + 12) = 12 ( divide both sides by 3 )

8x + 12 = 4 ( subtract 12 from both sides )

8x = - 8 ( divide both sides by 8 )

x = - 1

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1. Then the correct option is A.

A mathematical indicator of the degree of the association seen between fluctuation of 2 factors is the correlation coefficient.

A correlation coefficient between number of miles driven and number of gallons of gas remaining is most likely to be 0 to -1.

Then the correct option is A.

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Answer:

(x-2)/(x-1)

Step-by-step explanation:

(x-2)/(x-1)

Answer: b.) 40

Given that:

f(x) = 5 × 2ˣ

To find f(3), simplify insert [x = 3] in the given equation:

f(3) = 5 × 2³

f(3) = 5 × 2 × 2 × 2

f(3) = 40

Hello !

    3y + 12 =2(y + 30)

⇔ 3y + 12 = 2y + 60

⇔ y + 12 = 60

⇔ y = 60 - 12

⇔ y = 48

Answer:

y = 48

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

3y + 12 is an exterior angle of the triangle , so

3y + 12 = y + 30 + y + 30 ( base angles of an isosceles Δ are congruent )

3y + 12 = 2y + 60 ( subtract 2y from both sides )

y + 12 = 60 ( subtract 12 from both sides )

y = 48

Answer: 84°

Step-by-step explanation:

On a unit circle, coterminal angles are angles that are in the opposite position of the asked angle. 1524° revolves around 127/15π times across the entire unit circle.

84° is the only positive coterminal angle between 0 and 360 that is in the opposite position of 1524°.

Keep in mind, that there are more coterminal angles, namely 444°, 804°, 1164°, and 1524° itself, but they are outside of the range of 0 and 360 degrees.

The equation of the parabola is y = 0.015x^2 + 0.06x + 1

A parabola is represented as:

y = ax^2 + bx + c

The points are given as:

(-4,1), (-2,0.94) and (0,1)

When these points are substituted in y = ax^2 + bx + c, we have the following linear equations

16a - 4b + c = 1

4a - 2b + c = 0.94

c = 1

In (a), we have:

16a - 4b + c = 1

4a - 2b + c = 0.94

c = 1

Remove the variables (leaving the coefficients)

a      b       c

16    -4      1        1

4      -2     1        0.94

0      0     1          1

So, the matrix representation of the system of equations is:

[tex]\left[\begin{array}{ccc}16&-4&1\\4&-2&1\\0&0&1\end{array}\right] \left[\begin{array}{c}1&0.94&1\end{array}\right][/tex]

Using a graphing calculator, we have the inverse of the coefficient matrix to be

[tex]\left[\begin{array}{ccc}0.125&-0.25&0.125\\0.25&-1&0.75\\0&0&1\end{array}\right][/tex]

Using a graphing calculator, we have the solution to the system of equations to be

a = 0.015

b = 0.06

c = 1

Recall that:

y = ax^2 + bx + c

So, we have:

y = 0.015x^2 + 0.06x + 1

Hence, the equation of the parabola is y = 0.015x^2 + 0.06x + 1

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Answer: [tex]\frac{25\pi}{4}[/tex]

Step-by-step explanation:

The area of the entire circle is [tex]\pi(5^2)=25\pi[/tex].

The area of a quarter of the circle is thus [tex]\frac{25\pi}{4}[/tex]

Answer: [tex]p=7, q=3[/tex]

Step-by-step explanation:

The midline of the function is

[tex]\frac{10-4}{2}=3 \implies q=3[/tex]

This means that to obtain a maximum of 10, when [tex]\sin x[/tex] reaches it's maximum, 1, [tex]g(x)=p+q=10 \implies p=7[/tex]

Answer:

x = 3

Explanation:

[tex]\sf Given \ equation: \ log_{10} (1000) = x[/tex]

Solving steps:

[tex]\rightarrow \sf log_{10} (1000) = x[/tex]

apply rule: logₐ(b) = c  then  b = aᶜ

[tex]\rightarrow \sf 1000 = 10^x[/tex]

rewrite following

[tex]\rightarrow \sf 10^3= 10^x[/tex]

cancel out bases

[tex]\rightarrow \sf x = 3[/tex]

Answer:

d.) x = 3

Step-by-step explanation:

you simply need to know 10 to power of how many makes 1000 , In case didn't know you can replace the value of x with the given options and see if it can be solved or not .

Answer:

y = (-2/3)x + 5/6

Step-by-step explanation:

The general structure of a line in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. You have been given the value of "m". To find the value of "b", you can plug the slope and the values from the point (2, -1/2) into the general equation.

m = -2/3

Point (2, -1/2):

x = 2 and y = -1/2

y = mx + b                                  <----- Slope-intercept form

y = (-2/3)x + b                            <----- Insert -2/3 in "m"

-1/2 = (-2/3)(2) + b                      <----- Insert "x" and "y" values from point

-1/2 = -4/3 + b                            <----- Multiply -2/3 and 2

-3/6 = -8/6 + b                           <----- Give the fractions common denominators

5/6 = b                                      <----- Add 8/6 to both sides

Thus, the equation of the line is:

y = (-2/3)x + 5/6

The average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces

The range is given as:

Sport                   Weight range of ball used

Volleyball            260-280 grams

Basketball           600-650 grams

Water Polo         400-450 grams

Lacrosse            142-149 grams

Football       14-15 ounces

The average of each weight is calculated as:

Average = (Max + Min)/2

So, we have:

Volleyball = (260+280)/2 = 270 grams

Basketball = (600+ 650)/2 = 625 grams

Water Polo = (400+450)/2 = 425 grams

Lacrosse = (142+149)/2 = 145.5 grams

Football = (14+15)/2 = 14.5 ounces

Hence, the average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces

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Missing information in the question

Sport                   Weight range of ball used

Volleyball            260-280 grams

Basketball           600-650 grams

Water Polo         400-450 grams

Lacrosse            142-149 grams

Football       14-15 ounces

The net present value of machine is $5982

An investment is an asset or item acquired with the goal of generating income or appreciation.

As, 4th Year Cash Flow

= Salvage Value + Expected End Year Net Cash Flow

= $1,200 + $12,500

= $13,700

Year     Cash flow ($)             PVF at 8%             Present value ($)

0               37,500                         1.000                     -36,300

1                  12,500                      0.9259                 11573.75

2                 12,500                      0.8573                 10716.25

3                  12,500                      0.7938                 9922.5

4                  13,700                      0.7350                  10069.5

Net value                   5982

Hence, net present value of machine is $5982

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Probability helps us to know the chances of an event occurring. The correct option is D, not picking a circle.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

For the theoretical probability to be 3/4, the number of desired outcomes must be 6. Therefore, let's check the number of desired outcomes,

Not picking a triangle = 4

Picking a square = 3

Picking a shape with only straight edges = 0

Not picking a circle = 6

Not picking a square = 5

Hence, the correct option is D, not picking a circle.

The group of the shape is given in the below image.

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The value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

The expression is given as:

[tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

Divide 90 by 2

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

As a general rule, we have:

[tex]\frac{\cos(\frac{\pi}{A}) i\sin(\frac{\pi}{A})}{\cos(\frac{\pi}{B}) i\sin(\frac{\pi}{B})} = \cos(\frac{\pi}{2B/A}) + i\sin(\frac{\pi}{2B/A})[/tex]

The above means that:

A = 4 and B = 12

So, we have:

2B/A = 2 * 12/4

Evaluate

2B/A = 6

So, the equation becomes

[tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex]

Substitute [tex]\frac{\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = \cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6})[/tex] in [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

[tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

Hence, the value of the quotient is  [tex]\frac{45\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})} = 45(\cos(\frac{\pi}{6}) + i\sin(\frac{\pi}{6}))[/tex]

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Complete question

What is the quotient of [tex]\frac{90\cos(\frac{\pi}{4}) i\sin(\frac{\pi}{4})}{2\cos(\frac{\pi}{12}) i\sin(\frac{\pi}{12})}[/tex]

Answer: B. x^2 + 3

Step-by-step explanation:

2x^2 + 2 -(x^2 - 1)

2x^2 + 2 - x^2 + 1

x^2 + 3

The value of line AL is 21. 51cm

To find line AL,

Using

Sin α = opposite/ hypotenuse to find line AB

Sin 90 = x/ 24

1 = x/24

Cross multiply

x = 24cm

Now, let's find line AC

Sin angle B = line AC/24

Note that to find angle B

angle A + angle B + angle C = 180

But angle B = 2 Angle A

x + 2x + 90 = 180

3x + 90 = 180

3x = 180-90

x = 30°

Angle B = 2 × 30 = 60°

Sin 60 = x/ 24

0. 8660 = x/24

Cross multiply

x = 24 × 0. 8660

x = 20. 78cm

We have the angle of A  in the given triangle to be divide into two by the bisector, angle A = 15°

To find line AL, we use

Cos = adjacent/ line AL

Cos 15 = 20. 78/ line AL

Line AL = 20. 78/ cos 15

Line AL = 20. 78 / 0. 9659

Line AL = 21. 51 cm

Thus, the value of line AL is 21. 51cm

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