Use the information given below to find sin(α+ β)

Answer:

b. R-square must be greater than 1.0

Step-by-step explanation:

For a least square regression fit, Assumptions include : Absence of heteroscedasticity, which is the variation must not occur in the variance of the error term. That is the variance between error term and each observation is consistent.

Also, Lack of correlation between observations of the error term and also between independent variables and the error term. It is highly recommended that error term be randomized and normally distributed variable.

The value of R - squared being greater Than 1 is. not an assumption of the least square principle for fitting a regression line.

9514 1404 393

Answer:

  17

Step-by-step explanation:

The number of handshakes among n people is n(n -1)/2. Then ...

  n(n -1)/2 = 136

  n(n -1) = 272 = 17×16*

  n = 17

There were 17 people at the party.

_____

* This factoring can be facilitated by recognition that √272 ≈ 16.5, the number midway between the consecutive factors.

Answer: 56.3%

Step-by-step explanation:

1. Kennedy should go to Mapel Avenue park for (coordinate 1) because the distance is 2 units away from her house

2. Kennedy should go to Mapel Avenue park for (coordinate 2) because it is 2.25 unites away.

To calculate distance for the parks, we use the formula

Distance = √((x2 - x1)² + (y2 - y1)²)

For example, if we input the coordinate for coordinate 2, it would be

1: √(2 - 2)² + √(1.5 - (-3/4))² = 2.25

2: √(-1/2 - 2)² + √(-3/4 - (-3/4))² = 2.5

2.25 is a shorter distance than 2.5

The answers above are in response to the full question below;

Location                          Coordinates 1           Coordinates 2

Mapel Avenue park          (2, 1)                        (2, 1.5)

Oak wood park                 (-2, 3)                       (- 1/2,  - 3/4)

Kennedy's House              (2, 3)                       (2, -3/4)

There are two parks near Kennedy's house. She wants to go to the park closer to her house. To which park should kennedy go?

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Answer:

No

She needs 3/80 cup more

Step-by-step explanation:

She needs 3/8 cup plus 3/5 cup.

3/8 + 3/5 = 15/40 + 24/40 = 39/40

She has 15/16 cup

15/16

39/40 = 78/80

15/16 = 75/80

She has 75/80 cup and needs 78/80 cup.

She does not have enough sugar.

78/80 - 75/80 = 3/80

She needs 3/80 cup more.

Answer:

75%

Step-by-step explanation:

3/12 = 25% are cracked.

9/12 = 75% are still intact.

Mark me brainliest plls.

========================================================

Explanation:

Focus on the bottom most triangle. The upper angle of this triangle is 360/5 = 72 degrees. This is because the regular pentagon is split into five congruent (aka identical) triangles.

Each of the triangles are isosceles. Let x be the measure of the base angles.

Use the rule that adding the three angles of a triangle gets us 180

angle1+angle2+angle3 = 180

x+x+72 = 180

2x+72 = 180

2x = 180-72

2x = 108

x = 108/2

x = 54 is the answer

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

Another way to get the answer:

i = interior angle of a regular polygon with n sides

i = 180(n-2)/n

i = 180(5-2)/5

i = 180(3)/5

i = 540/5

i = 108

Each interior angle of a regular pentagon is 108 degrees.

Angle x marked in blue is half that, so it is 108/2 = 54 degrees

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

A third method:

E = exterior angle of a regular polygon with n sides

E = 360/n

E = 360/5

E = 72 degrees is the measure of each exterior angle

i = 180 - E

i = 180-72

i = 108 is the measure of each interior angle.

To wrap things up, we follow the same exact steps at the end of the 2nd section to get 108/2 = 54 as our answer.

The value of the operation is 3.

The first step is to solve for the terms in the brackets. The decimals would be added first

8.7 + 3.3 = 12

The second step is to determine the square of one-half

\(\frac{1}{2}\)² = \(\frac{1}{2}\) x \(\frac{1}{2}\) = 1/4

The third step is to multiply, 1/4 by 12

1/4 x 12 = 3

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Answer:

Step-by-step explanation:

Step 1:First Make 3/4 and 5/6 into like fractions.Find the L.C.M of 4 and  

            6,which is 12.

            3*3/4*3=9/12

             5*2/6*2=10/12

Step 2:Subtract 9/12 from 10/12,which is 1/12.

Answer:

x is the variable

Step-by-step explanation:

Answer:

Binomial

Step-by-step explanation:

There is two expression

The total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

To calculate the total value of the annuity in 16 years, we can use the formula for the future value of an annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV is the future value of the annuity,

P is the yearly payment,

r is the interest rate per compounding period, and

n is the number of compounding periods.

In this case, the yearly payment (P) is $693, the interest rate (r) is 5.3% or 0.053, and the number of compounding periods (n) is 16.

Let's substitute these values into the formula and calculate the total value of the annuity:

FV = 693 * ((1 + 0.053)^16 - 1) / 0.053

FV = 693 * (1.053^16 - 1) / 0.053

Using a calculator, we can evaluate the expression inside the parentheses:

1.053^16 ≈ 1.9738

Substituting this value back into the formula:

FV = 693 * (1.9738 - 1) / 0.053

FV = 693 * 0.9738 / 0.053

FV ≈ 12739.62

Therefore, the total value of the annuity in 16 years, with yearly payments of $693 and an interest rate of 5.3% compounded annually, is approximately $12,739.62.

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Answer:

isosceles triangle

Step-by-step explanation:

first by using corresponding angle theorem:

<A=<C

<A=50°

then by using exterior angle theorem:

<A+<C=<B(the outer angle)

50°+<C=<B,<B=180°-80°(angle B lies in a staight line)

<B=100°

50°+<C=100°

<C=50°

The line plot, histogram, and box plot provide different visual representations of the reading time data. By analyzing these plots, we can observe the distribution and characteristics of the data, such as central tendency, spread, and outliers.

Line Plot:

A line plot displays data points on a number line, representing the frequency or count of each value.

In this case, the line plot will show the minutes spent reading on the x-axis and the count of students on the y-axis.

For the given data, the line plot will show 10, 20, 30, 40, and 60 on the x-axis, with the corresponding counts displayed above each value.

Histogram:

A histogram displays data distribution by dividing the range of values into intervals or bins and representing the frequency of values falling into each bin.

The histogram will have the minutes spent reading on the x-axis and the count or frequency of students on the y-axis.

The intervals will be 10-19, 20-29, 30-39, 40-49, and 50-59, with the last interval being 60+.

The height of each bar in the histogram will represent the number of students falling into each interval.

Box Plot:

A box plot (also known as a box-and-whisker plot) provides a visual representation of the distribution of data, including measures of central tendency and variability.

The box plot will show a horizontal line inside a box, with whiskers extending from the box, and possibly individual data points beyond the whiskers.

The box will represent the interquartile range (IQR), showing the middle 50% of the data.

The line within the box will represent the median value.

The whiskers will indicate the minimum and maximum values, excluding outliers.

By analyzing these plots, you can observe the central tendency, spread, and distribution of the reading time data. For example, you can identify any outliers, notice the most common reading durations, and observe any patterns or trends within the dataset.

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Answer:

Well a parallelogram has congruent opposite sides.
We need to find the value of a here.

A shape’s angle must add up to following this equation
180(n-2) = ?

Now solve for this equation right here with “n” as “sides.

THis shape has 4 sides so 180(4-2) = 360

You have each interior angle of the parrlelogram which is 360.
Let’s solve 112 and 4b +8 first.

We know they have to be equal since opposite angles of a parrlelogram has to be equal.

112 = 4b + 8

104 = 4b
26 = b

You have b as 26.

Now solving it we know that two angles “G” and “I” are both 112.

112 *2 = 224

Thats one side done.
Now the opposite…

With 224 already being taken away subtract 360 by 224 since we figured out 360 was the amount of all the interior angles in the shape add upo to. 360 - 224 = 136

136 is the other two angles ADDED UP.

Divide it by 2 since both has to be equal and be the same.

68

Now solve for a.

2a = 68.

= 34

Answer:

34

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary

2a + 112 = 180

2a = 68

a = 34

Receiving $4.88 dividend out of the closing stock price of $59.95, means that the stock yield is 8.1%

Dividend is defined as a distribution of payment by a company to its shareholders that is originated from the company's profit and is payable to the shareholders every quarter in a given year, while stock yield is defined as an income generated by the stock being held by the shareholders.

To determine the percentage of stock yield, we will need to divide the closing price of the stock which is $59.95 with the amount of dividend distributed for each stock held which is $4.88, and the calculation is as follows:

59.95/4.88×100%=8.1%

Therefore the stock yield is 8.1%

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Answer

1,1/2,3/2,1.25,1.25

Step-by-step explanation:

Answer:

2000 is the answers.............

Answer:

Step-by-step explanation:7.5x10^1

The population of the United States is 7.5 times greater than the population of California.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation. It might also be called standard index form or scientific form.

Given that California has approximately 4 x 10⁷ people living in it. The population of the entire United States is approximately 3 x 10⁸ people.

The United States how many times greater than California will be calculated as:-

Number of times = 3 x 10⁸ /  4 x 10⁷

Number of times = 0.75 x 10 = 7.5

Therefore,  the population of the United States is 7.5 times greater than the population of California.

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The range of the absolute value function y = |x| is all non-negative numbers, which can be expressed as [0, ∞).

The absolute value function is a type of mathematical function that measures the distance between a given number and zero. It is denoted by two vertical bars surrounding the number or expression.

The range of the absolute value function is the set of all non-negative numbers. This is because the absolute value of any number is always a positive number or zero.

For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3.This means that the output of the function can never be negative and can range from zero to infinity.

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The range of the absolute value function below is C. f(x) < 1.

The domain and range of a function are the components of a function. The domain is the set of all the input values of a function and range is the possible output given by the function. Domain→ Function →Range.

The range of a function is the set of all its outputs. Example: Let us consider the function f: A→ B, where f(x) = 2x and each of A and B = {set of natural numbers}.

The function y=|ax+b| is defined for all real numbers. So, the domain of the absolute value function is the set of all real numbers. The absolute value of a number always results in a non-negative value.

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What is the range of the absolute value function below?

f(x) > -4

f(x) > -1

f(x) < 1

f(x) < 4

Answer:

The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.

Step-by-step explanation:

We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\(\alpha = \frac{1 - 0.95}{2} = 0.025\)

Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).

That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.

Now, find the margin of error M as such

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which \(\sigma\) is the standard deviation of the population and n is the size of the sample.

\(M = 1.96\frac{2}{\sqrt{100}} = 0.392\)

The lower end of the interval is the sample mean subtracted by M. So it is 1972 - 0.392 = 1971.608 milligrams

The upper end of the interval is the sample mean added to M. So it is 1972 + 0.392 = 1972.392 milligrams

The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.

1. 76.56.

2. 96

3. The largest solution to the equation x²+16x+28=138 is 6.71.

4. The smallest solution to the equation x²+14x+14=145 is 5.96.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result (19/2)² = 76.56.

2. This is calculated by taking the coefficient of x (30) and dividing it by two (30/2) and then squaring the result (30/2)² = 96.

3. This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (16) plus or minus the square root of the coefficient of x squared (16²) minus 4 times the coefficient of the x term (4x16) minus the constant (28) divided by 2 times the coefficient of the x term (2x16).

4.  This is calculated by using the quadratic formula, by taking the opposite of the coefficient of x (14) plus or minus the square root of the coefficient of x squared (14²) minus 4 times the coefficient of the x term (4x14) minus the constant (14) divided by 2 times the coefficient of the x term (2x14).

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1.  For the given equation, c need to be 90.25 to complete the square.

2. 225

3. The largest solution to the equation x²+16x+28=138 is 6.

4. The smallest solution to the equation x²+14x+14=145 is -14.

Equations are used to express relationships between variables and solve mathematical problems.

1. This is calculated by taking the coefficient of x (19) and dividing it by two (19/2) and then squaring the result

(19/2)² = 90.25.

2. This is calculated by taking the coefficient of x (30) and dividing it by two which is (30/2) and then squaring the result

(30/2)² = 225.

3. The largest solution to the equation x²+16x+28=138 is 6.

This can be calculated by using the quadratic formula to solve the equation.

(a=1, b=16, c=28)

x = -8 ± √((16)² - 4(1)(28))/2(1).

x = -8 ± √(240)/2

x = 6 or -14.

Since 6 is the larger solution, it is the largest solution to the equation.

4.  The smallest solution for x2+14x+14=145 can be determined by using the Quadratic Formula.

a=1, b=14, and c=14

x = [-14 ± √(142-4(1)(14))]/(2(1))

x = [-14 ± √(196)]/2

x = [-28/2] or [14/2]

x = -14 or 7

Therefore, the smallest solution for x2+14x+14=145 is x=-14.

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The equation of a quadratic function P with rational coefficients that have a zero of 3 + 7i is; P(x) = x² - 6x + 58

We are given one of the zero of the quadratic function as 3 + 7i.

The given zero of the function is a complex number and we know that when dealing with complex numbers, if the zero of the function is of the form a + bi then we can deduce that the other zero of the function will be a - bi.

This means that the other zero of our function is 3 - 7i.

Thus, the factors of the quadratic function are;

(x - (3 + 7i)) and (x - (3 - 7i))

Thus, the equation of the quadratic function is;

P(x) = (x - (3 + 7i)) × (x - (3 - 7i))

We know that i² = -1

Thus, our equation is;

P(x) = x² - 6x + 58

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Answer:you need to show the diagram in order for me to

Step-by-step explanation:

The appropriate hypotheses for this test are: H0: There is no difference in the distribution of responses. Ha: There is a difference in the distribution of responses.

The chosen hypotheses are based on the objective of the investigation, which is to determine if there is convincing evidence that the distribution of responses about eating the potato salad differs between employees who are sick and those who are not sick.

The null hypothesis (H0) assumes that there is no difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This means that the proportion of employees who ate the potato salad would be the same in both groups, and any observed difference in the distribution of responses is due to random chance or factors unrelated to being sick or not sick.

On the other hand, the alternative hypothesis (Ha) proposes that there is a difference in the distribution of responses about eating the potato salad between the sick and non-sick employees. This suggests that the proportion of employees who ate the potato salad would be significantly different in the two groups, indicating a possible association between consuming the potato salad and getting sick.

By formulating these hypotheses, the investigation aims to evaluate whether the data provides convincing evidence to reject the null hypothesis in favor of the alternative hypothesis, indicating a meaningful relationship between eating the potato salad and falling sick.

Therefore, the correct answer is:

H0: There is no difference in the distribution of responses about eating the potato salad among those who are and are not sick.

Ha: There is a difference in the distribution of responses about eating the potato salad among those who are and are not sick.

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Amanda family cannot travel more than 244 miles without needing to refill the gas tank.

Inequality is the non equal comparison of numbers or variables.

Let x represent the number of miles that they can travel before filling their gas tank.

Their car can travel no more than 352 miles without filling their tank. Also, they have traveled 108 miles since they last filled the gas tank. Hence:

x + 108 < 352

x < 244

This means that Amanda family cannot travel more than 244 miles without needing to refill the gas tank.

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The ounces of shaving cream will be 230 ounces.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, Mrs. Liu is mixing glue and shaving cream to make snowman puff paint for her art class. The ounces of glue to ounces of shaving cream must have a ratio of 7:15. If she is mixing 56 ounces of glue ,the shaving cream will be:

= 56 ÷ 7/15

= 56 × 15/7

= 120

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Answer:

x=7/8

Step-by-step explanation:

x/8+3=10

x/8=7

x=7/8

Answer:

Step by step explanation:

The rule for reflecting on the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

That means: