Nicole has saved $120 toward the purchase of a new bike. She gets a job that pays $12 an hour. She saves 25% of her hourly wage to purchase the new bike. She uses the equation y=(0.25)(12)x+ 120 to determine how much money she has saved toward the purchase of the new bike. What is the slope of the line represented by Nicole's equation?

A. 120
B. 0.25
C. 12
D. 3

P value of the test statistic = 0.0220

NULL and alternative hypothesis

Given that,

p = 0.75

n =200

p^ = 0.68

Testing statistic;

 p = 0.75

q = 1 - p

   = 1 - 0.75

   = 0.25

 [tex]Z = \frac{p^ -p }{\sqrt{\frac{p.q}{n} } }[/tex]

    = 0.68 - 0.75 / √(0.75 × 0.25)/200

    = -2.2861

Z = -2 .29

p value = 2 × (Z ≤ -2.29 )

            = 2 × 0.0110

p value = 0.0220

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The table for  (a) for preferred stock and (b) for common stock based on the average annual dividend per share has been done.

a) Data and Calculations:

Dividends:                              Cumulative               Common Stock

                                        Preferred Stock               Dividends

                                   Dividends   Per share                   Per share

20Y1,     $80,000           $80,000   $0.40                 $0           $0

20Y2,    $90,000             90,000   $0.40                   0           $0

20Y3,   $150,000           150,000   $0.40                   0           $0

20Y4,   $150,000           100,000   $0.40              50,000      $0.10

20Y5,   $160,000           100,000   $0.40             60,000       $0.12

20Y6,   $180,000           100,000   $0.40             80,000       $0.16

b)Average annual percentage return

                           Cost    Market   20Y1   20Y2  20Y3  20Y4  20Y5 20Y6

                                per share

Preferred stock   $20.00 $25.00    2%        2%       2%      2%      2%      2%

Common stock    $15.00  $17.50    0%         0%       0%   0.7%   0.8%   0.11%

Thus, the average annual percentage return is Dividend per share/Initial Cost per share

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Answer:

D = [1,5]

R= [0,4]

.........

The statement that best describes the distribution is C. The data is normally distributed because the majority of the data is in the center.

A histogram is a graphical representation of data points organized into ranges that the user specifies. The histogram, which resembles a bar graph in appearance, condenses a data series into an easily interpreted visual by grouping many data points into logical ranges or bins.

Because the majority of the data is in the center, the data is normally distributed.

Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central region, with values decreasing as one moves away from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are identical.

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We calculated the required interval is 13.341 and 11.46 to estimate true average.

It is a statistical term that express that the value of a specific parameter located within a boundary.

A statistical expression that has upper and lower limit. This value gives assurances to the average or mean value to be within the limit.

Given, number of samples, n =25

sample standard deviation, σ = 2.4%

average tip = sample mean, X = 12.4%

confidence level =95%

We need to construct an interval to estimate the true average tip with 95% confidence level.

We know that confidence level value Zc for 95% = 1.96

Now, confidence interval CI = X±Zc (σ/√n)

                   by putting the given value, CI= 12.4±1.96(2.4/√25)

                                       the interval is 13.341 and 11.46

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The margin of error at 95% confidence is 0.046., the 95% confidence interval of the population proportion of people who would pay off debts with an unexpected tax refund is (0.424, 0.516).

The margin of error is a statistical measure of the variability of a sample statistic from its population value. It is calculated by taking the standard error of the statistic and dividing it by the sample size. It is typically expressed as a percentage and is used to measure the precision of the sample statistic compared to the population statistic. Margin of error is primarily used in confidence intervals to measure the accuracy of survey results. It is also used to measure the impact of random sampling error on the statistical significance of the results.

a. Margin of Error: The margin of error is calculated using the formula Margin of Error = z* (√p*(1-p)/n), where z is the z-score for the 95% confidence interval (1.96), p is the sample proportion (0.47), and n is the sample size (1,026).
Plugging in the values, we get Margin of Error = 1.96 * (√0.47*(1-0.47)/1,026) = 0.046.
Therefore, the margin of error at 95% confidence is 0.046.

b. Confidence Interval: The confidence interval is calculated using the formula Confidence Interval = (p-margin of error, p+margin of error), where p is the sample proportion (0.47) and margin of error is the margin of error (0.046).
Plugging in the values, we get Confidence Interval = (0.47 - 0.046, 0.47 + 0.046) = (0.424, 0.516).

Therefore, the 95% confidence interval of the population proportion of people who would pay off debts with an unexpected tax refund is (0.424, 0.516).

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Answer:

---------------------------

Let the number be x.

Set equation for x and solve:

The operating cost per hour of a plane increases with the number of passengers it carries. More passengers require more fuel, maintenance, and staff, which all increase the overall cost of operating the plane per hour.

Additionally, if the plane is larger and designed to carry more passengers, the operating cost per hour may be higher than for smaller planes.The cost of operating an aircraft per hour is directly related to the number of passengers it carries. As the number of passengers increases, so too does the amount of fuel, maintenance, and personnel needed to safely operate the plane, resulting in a higher operating cost per hour. Additionally, larger planes that can carry more passengers also tend to have higher operating costs per hour than smaller planes.

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Therefore, the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .

The study of numerical estimates of the likelihood that an event will occur or that a proposition is true is known as probability. The probability of an occurrence is a number between 0 and 1, where 0 often indicates that the event is impossible and 1 typically indicates that it will happen.

Here,

Let X1 and X2  represent the weights of the two oranges.

Let  d=X1 - X2 represent the difference in weight.

We're given that

X1 ~ N(12, 1.2^2)

X2 ~ N(12, 1.2^2)

Then,

Then, d N(12-12, 1.22 +1.22) or N (0, 21.22)

So the standard deviation of this √2.1.22 = 1.6971

Let's find

=> P(d>3)

=> 1-(1891)

=> 1-0.9615 = 0.0385

Therefore the probability that the probability that the difference in the weights of the two oranges exceeds 3 ounces is 0.0385 .

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On solving the provided question we can say that, True -When a symmetric matrix's primary determinants are all negative, the symmetric matrix is said to be negative definite.

When integers are arranged in rows and columns, they form a matrix. learns about matrices' dimensions and components for the first time. Numerals are arranged in rows and columns in a rectangular matrix. Consider the two rows and three columns of matrix A.

m rows and n columns make up the m by n matrix. It is common practice to use a variable with two subscripts to represent each member of a matrix. As an illustration, a2,1 denotes the matrix element that is located in row 2, column 1.

When a symmetric matrix's primary determinants are all negative, the symmetric matrix is said to be negative definite.

True

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Answer:

C and D are correct.

Step-by-step explanation:

In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

On solving the provided question we can say that, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

the frequency or reality that something occurs frequently or a great number of times within a specific time frame. The frequency of buses, for instance, has been the subject of more complaints in recent months.

Number of students jumped greater than 8.5 but less than 11.5= frequency of length of jump greater than 8.5 but less than 11.5

AND,

frequency of length of jump greater than 8.5 but less than 11.5 is -

Number of students jumped greater than  8.5 and less than  9.5 + Number of students jumped greater than 9.5 but less than 10.5 + Number of students jumped greater than 10.5 but less than 11.5=

3+3+1=7 ( since, sum of respective frequencies of the three class)

so, Number of students jumped greater than 8.5 but less than 11.5 is 7 students.

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Answer:

3. (x | x > 5)

Step-by-step explanation:

To solve this inequality, we need to isolate the variable on one side and the constant on the other side. To do this, we need to use the properties of inequalities and the order of operations to manipulate the given inequality into a form we can solve.

First, we need to distribute the coefficients in front of the parentheses on the left-hand side of the inequality. This gives us:

4x - 12 - 2x + 2 > 0

Next, we can combine like terms on the left-hand side of the inequality by adding the terms with the variable and subtracting the constant terms. This gives us:

2x - 10 > 0

Now, we have isolated the variable on one side of the inequality and the constant on the other side. To solve the inequality, we need to determine the values of x that make the inequality true.

To do this, we can divide both sides of the inequality by the coefficient of the variable, which gives us:

x - 5 > 0

This inequality is satisfied when x is greater than 5. Therefore, the solution to the original inequality is x > 5.

The differentiation for the given function is f'(x) = -27x⁸- 48x³. The correct option is (A).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = (f(x + h) - f(x)) /(x + h - x).

Geometric meaning of it is the slope of the function at a given point.

The given function is f(x) = (-x⁵ - 4). 3x⁴

It is in the form of u.v, the differentiation is given as below,

uv' + vu'

As per the above expression suppose (-x⁵ - 4) = u and 3x⁴ = v.

Now, the differentiation can be done as follows,

f'(x) = d(-x⁵ - 4)/dx × 3x⁴ + (-x⁵ - 4) × d(3x⁴)/dx

      = -5x⁴ × 3x⁴ + (-x⁵ - 4) × 4 × 3x³

      = -15x⁸ + 12x³(-x⁵ - 4)

      = -15x⁸ - 12x⁸ - 48x³

      = -27x⁸- 48x³  

Hence, the differentiation is obtained as f'(x) = -27x⁸- 48x³.

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The volume of the composite solid is 5770.28ft³

The composite solid is made up of a cylinder and a hemisphere

The volume is the addition of the two solids

Volume=[tex]\pi[/tex]r²h +2/3πr²

The given parameters are

π=22/7

h=22 ft

r=9 ft

Input the values to get

(22/7*9*9*22) + (2/3*22/7*9*9)

Simplifying the terms to get

5600.57+169.71

The volume is = 5770.28c

ft³

In conclusion, the volume of the solid is 5,770.28ft³

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David ought to keep saving money in his simple interest account regardless of his current age.

He will be able to purchase his 30,000 USD boat at that rate each year. David would need to put at least 5 to 10 percent of his income into a savings account with simple interest.

Your initial investment as well as any interest that has already been accrued will earn interest in a compound interest account. The "compounding" factor is the appreciation of interest based on interest that occurs over time. On the other hand, simple interest accounts only pay interest on the initial principal.

Both guaranteed and non-guaranteed substances benefit from compounding. You might lose all of your money or some of it. Stocks, income trusts, real estate, mutual funds, and gold are all examples.

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The percentage of students that have grade point averages that are at least 3.48 is of:

2.5%.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable:

Considering the mean of 2.62 and the standard deviation of 0.43, a grade point average of at least 3.48 is at least two standard deviations above the mean.

100 - 95 = 5% of the measures are at least two standard deviations of the mean. Considering the symmetry of the normal distribution, we have that:

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Answer:

62 degrees

Step-by-step explanation:

(3x-13)+(2x+4)+(180-116)=180

5x-9+64=180

5x+55=180

   -55.  -55

5x=125

/5. /5

x=25

3(25)-13

75-13

62

hopes this helps

The coordinates of A' = (1, 7)

The coordinates of B' = (4, 9)

The coordinates of C' = (3, 6)

There are two ways of translation.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

ΔABC:

Coordinates:

A = (2, 3)

B = (5, 1)

C = (4, 4)

Reflection across y = 5.

So,

A = (2, 5)

There are two units between y = 5 and y = 3.

We add 2 units with the y-coordinate of A = (2, 5)

5 - 3 = 2

So,

A = (2, 5 + 2)

A = (2, 7)

Similarly,

5 - 1 = 4

B = (5, 5 + 4) = (5. 9)

5 - 4 = 1

C = (4, 5 + 1) = (4. 6)

Translation of 1 unit down.

A = (2 - 1, 7) = (1, 7)

B = (5 - 1, 9) = (4, 9)

C = (4 - 1, 6) = (3, 6)

Thus,

The coordinates of ΔA'B'C' are (1, 7), (4, 9), and (3, 6).

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The value of P(A/B) will be = 1/4

As per the question,

As a fair six-sided die is rolled twice

So, the total number of outcomes will be N=6^2=36

A: sum of the two rolls is 5

[tex]$$\begin{aligned}& A=\{(1,4),(2,3),(3,2),(4,1)\} \\& n(A)=4 \\& P(A)=\frac{n(A)}{N}=\frac{4}{36}\end{aligned}$$[/tex]

B: The first roll results in a 2

[tex]B=\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)\}$ \\$n(B)=6$ \\$P(B)=\frac{n(B)}{N}=\frac{6}{36}$ \\$B \cap A=\{(2,3)\}$ \\$\cap(B \cap A)=1$ \\$P(B \cap A)=\frac{n(B \cap A)}{N}=\frac{1}{36}$\\$P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{1 / 36}{4 / 36}=\frac{1}{36} \times \frac{36}{4}$$P(B \mid A)=\frac{1}{4}$[/tex]

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The rate of change of y with respect to x for this line is 4 / 5 .

Given :

The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.

From the graph :

The marked coordinates are ( 5 , 7 ) and ( -5 , -1 ) .

slope m = rate of change of y / rate of change of x

= y2 - y1  / x2 - x1

= -1 -7 / -5 - 5

= -8 / -10

= 8 / 10

= 4 / 5

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1/63.

[tex]\frac{\frac{1}{9} }{7}[/tex]

Check the attached image below.

[tex]\frac{1}{9}*\frac{1}{7}[/tex]

[tex]\frac{1}{9}*\frac{1}{7}=\\\\ \frac{1*1}{9*7} =\\\\ \frac{1}{63}[/tex]

[tex]\frac{\frac{1}{9} }{7}=\frac{1}{63}[/tex]

Option D is the correct answer. The value of 'c' for the given system of linear equations with infinitely many solutions is - 1.

A linear equation is an equation in which the highest power of the variable is always 1 and the equations are the equations of degree 1. It is the equation for the straight line.

The standard form of the linear equation is ax+by+c =0

where a ≠ 0 and b ≠ 0.

Given a system of linear equations are

1. 3x-9y=-6

⇒ x-3y=-2

Therefore,

a1=1, b1=-3, c1=-2

2. [tex]\frac{x}{2} -\frac{3y}{2} =c\\[/tex]

⇒ x-3y=2c

Therefore,    

a2=1, b2=-3, c2=2

For the system of linear equations with infinitely many solutions,

compare c1=c2

2c=-2

⇒ c=-1

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The required age of the bone is approximately 8,200 years.

To estimate the age of a bone that now contains 70% of its original amount of carbon-14, you can use the formula:

age = (half-life / log(2)) x log(original amount / current amount)

In this case, the original amount of carbon-14 is 100% and the current amount is 70%, so the age of the bone can be calculated as:

age = (5730 years / log(2)) x log(100% / 70%)

age = (5730 years / 0.693) x 0.35667

age = 8268 years

Rounded to the nearest 100 years,

age = 8200 years

Therefore, the bone is estimated 8,200 years old.

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For the given circle the value of cotθ is -√30/√19.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The terminal side of an angle θ.

The standard position intersects the unit circle at (√30/7, -√19/7).

We need to find the value of cotθ.

Suppose that θ is an angle in standard position whose terminal side intersects the unit circle at (√30/7, -√19/7)

cotθ=x/y

=-√30/7/√19/7

=-√30/7×7/√19

=-√30/√19

Hence, the value of cotθ is -√30/√19 for the given circle.

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This set {(x, y) | 0 is (a) open, (b) connected, and (c) not simply-connected.

(a) Open: This set is open because all points within the set have a neighborhood that is also within the set.

(b) Connected: This set is connected because there is a path between any two points in the set that does not leave the set.

(c) Not simply-connected: This set is not simply-connected because it contains a hole in the center, which is not a simply-connected space.

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Answer:

[tex]45^{\circ}[/tex]

Step-by-step explanation:

This is a standard result.

infinitely many solutions because these 2 lines are exactly the same line. If you multiply the 2nd equation by 2, you will get the 1st one, or if you divide the 1st equation by 2, you will get the 2nd one.

Answer:

3/10

Step-by-step explanation:

There are 3 blue sectors out of the total 10.