Mathematics High School

## Answers

**Answer 1**

A unit circle table is a table that lists the **coordinates** of points on a unit circle, which is a circle with a radius of 1.

The unit circle is often used in **trigonometry** to represent the relationships between angles and the values of the trigonometric functions sine, cosine, and tangent. The table typically lists the **angle** in radians or degrees in one column, and the corresponding values of sine, cosine, and **tangent** in other columns. The table may also include values for other trigonometric functions such as cosecant, secant, and cotangent, as well as their inverse functions such as arcsine, arccosine, and **arctangent**.

The unit circle table is a useful reference tool for solving trigonometric equations and for understanding the **geometric** properties of the trigonometric functions. Many mathematical and scientific applications use the unit circle, including engineering, physics, and astronomy.

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## Related Questions

The diameter of a circle is 7 ft. Find the circumference to the nearest tenth.

### Answers

**Answer:**

**Step-by-step explanation:**

C=[tex]2\pi R=\pi d[/tex]

if [tex]\pi = 3.14[/tex]

c=3.14*7=21.98

Help! Brainliest! Need help with 10, 12, and 13. I really appreciate it!!

### Answers

The required ST² = TW × RT has been proven for the triangle RST where SW is **perpendicular **from **vertex** S to RT.

What are Similar triangles?

**Similar triangles** are those triangles that have **similar properties**,i.e. angles and **proportionality **of **sides**.

Here,

For the triangle RST where SW is perpendicular from vertex S to RT

Rewrite the equation,

ST² = TW × RT

ST/TW = RT/ST

It implies triangle SWT is similar to triangle RST,

Where,

∠S = ∠W and ∠T = ∠T

So triangle SWT is similar to triangle RST, by AA postulate of similarity.

If triangles are similar,

ST/TW = RT/ST [became valid statement]

ST² = TW × RT

Thus, ST² = TW × RT hence proved.

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Triangle abc was dilated using the rule do,4. Triangle a'b'c' is the result of the dilation. What is ob'? 1. 5 units 3 units 4. 5 units 6 units.

### Answers

If the length of OB was 3/4, then the **length of OB'** after **dilation** is; Option B: 3 units.

Dilation of an object simply means **enlarging or shrinking** the object by a scale factor.

We are told that Triangle ABC was dilated to Triangle A'B'C' using the rule D₀,₄. What this means is that it was enlarged by a scale factor of 4 with point O as the **centre of dilation**.

Now, if the length of OB is 3/4, it means that the new dilated length is gotten from;

Scale factor = new dilated length OB'/(3/4)

New dilated length OB' = (3/4) × 4

New dilated length OB' = 3 units

The question is incomplete. The complete question:

"Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation. Point O is the centre of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths. What is OB'?"

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Which one of the following best defines the notion of the P-value of a hypothesis test? a. The probability of rejecting H_o, whether it's true or not b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true c. The probability of the type I error d. The probability of the type II error

### Answers

P-value of a** hypothesis test **is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about **rejecting **or failing to reject the** null hypothesis.**

A hypothesis test is a statistical method used to test the **validity **of an assumption or a hypothesis about a **population **based on a sample data.

The correct answer is b. The **P-value** of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.

In hypothesis testing, we start with a null **hypothesis**, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.

The P-value is the **probability **of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.

A high P-value indicates that the **sample **data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.

In mathematical terms, the P-value is calculated as the probability of observing a test **statistic **Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.

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. Ed Naiman.

Installment loan of $2,500.00.

Finance charge of $193.25.

Requires 24 monthly payments.

What is the APR?

I

### Answers

**Answer:**

M = (2500 + 193.25) / 24 = $113.03

We can use the monthly payment to calculate the finance charge over the life of the loan, which is equal to 24 times the monthly payment minus the principal amount:

Finance charge = 24 * M - 2500 = 24 * 113.03 - 2500 = 193.25

Now that we have the finance charge, we can calculate the APR:

APR = (Finance charge / Principal amount) * (12 / Number of months) * 100%

APR = (193.25 / 2500) * (12 / 24) * 100%

APR = 7.73%

So, the APR of this loan is 7.73%.

What happens when a distribution is skewed to the right?

### Answers

**Answer:**

**Step-by-step explanation:**

A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.

In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.

Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.

In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.

Spot the Dog gained 4 3/4 ounces each week for the first 6 weeks of his

life. How much weight did Spot the Dog gain during this time?

### Answers

The **weight **gained by the spot dog during his **time** is 57/2 ounces.

What are mathematical operations?

An **operation** is a function in mathematics that converts zero or more input values, also known as "operands" or "arguments," into a clearly defined output value. The operation's complexity is determined by its operand count.

The most frequently studied operations are **unary operations** (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication. The nullary operation, also known as an operation of arity zero, is a constant. A ternary operation, also known as an operation of arity 3, is an example of the mixed product.

Given that, spot the Dog gained 4 3/4 ounces each week for the first 6 weeks of his life.

Convert the mixed fraction into improper fraction:

4 3/4 = 19/4 ounces

The weight gained for 6 weeks is:

19/4 (6) = 114/4 = 57/2

Hence, the weight gained by the spot dog during his time is 57/2 ounces.

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Using the picture below, which trig function can be used to find the length of x?

### Answers

The **length** of the **base** is approximately 8.71 units.

**What is triangle ?**

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always **180 degrees.**

Let's call the two legs of the right triangle a and b, and the hypotenuse c. The hypotenuse is the side opposite the right angle, so in this case, we have **c = 29**. We also know that one of the acute angles is 71 degrees.

Using trigonometry, we can use the **tangent** function to find the length of the base:

**tan(71) = a/b**

We can solve for b by multiplying both sides by b:

b tan(71) = a

Now we can **substitute** c = 29 and solve for b:

**b = c / tan(71)**

b = 29 / tan(71)

**b ≈ 8.71**

Hence, The length of the base is approximately** 8.71 units.**

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Solve for x.

7-3x/2 = 8

x = [?]

### Answers

**Answer: **

**x = -3**

**Step-by-step explanation:**

I did this before

PQRS is parallelogram. If PS = 15, then QR =

### Answers

**Answer:**

QR = 15

**Step-by-step explanation:**

Opposite sides of parallelograms are congruent. This means that their lengths are the same.

Hence,

PS = 15 = QR.

does anyone know how to do this?

### Answers

**Step-by-step explanation:**

Is there more to this question? I feel like the 2021 federal income tax bracket is missing

State the degree of the polynomial.

x²y + x²y² − xy

Enter your answers in the boxes.

### Answers

**Answer:**

Factor:

[tex]xy(xy+x-1)[/tex]

Evaluate:

[tex]xy(xy+x-1)[/tex]

This polynomial is a quadratic polynomial.

**Step-by-step explanation:**

Write and simplify an expression

for the perimeter of the triangle.

8x-4

x+5

6x

Will give Brain liest

### Answers

**Answer:**

= 15x + 1.

**Step-by-step explanation:**

Sum and the length of all three sides

8x - 4 + x + 5 + 6x

8x + x + 6x - 4 + 5

15x + 1.

Are the lines with the equation y = -5x + 1 and y = -5x + 8 parallel? (use a graph, might help)

### Answers

**Answer:**

Yes, the lines y = -5x + 1 and y = -5x + 8 are parallel. This is because they have the same slope (-5) but different y-intercepts (1 and 8). Parallel lines have the same slope, and different y-intercepts.

**Answer:**

For y = -5x + 1

x = [tex]\frac{1-y}{5}[/tex].

And

y = 1 - 5x.

Put on a graph: look at picture 1.

The for y = -5x + 8

x = [tex]\frac{8-y}{5}[/tex]

And

y = 8 - 5x.

Put on a graph: look at picture 2.

**These two lines are parallel.**

what is the distance between the points -3,-8 and 6,-8

### Answers

The **distance **between the **points **-3,-8, and 6,-8 is 3 units.

What is the distance between two points?

The **length** of the **line segment **bridging two points on a plane is known as the **distance **between the points.

Look at the provided points.

Calculate the **distance **between the points using the given **formula**.

Given points are -3,-8 and 6,-8

Given two points lies the **parallel **to X-axis

The **distance **between the two points is

A (-3,-8) and B(6,-8) = X₂ - X₁

6 - 3 = 3 units.

Therefore, the **distance **between two points -3,-8 and 6,-8 is 3 units.

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HELP PLEASE i need the answer for as may as possible o have done the first two!!( A1 and A2) WITH AN EXPLANATION PLEASE IM SO CONFUSED

### Answers

1. The **values** of x in the **equation** are 1 and 10.

2. The values of x are 1 and -4.

How to calculate the values

An **equation** simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

1. y = x²

y = 11x - 10

Combine both **variables**

x² - 11x + 10

x² - x - 10x + 10

x(x - 1) - 10(x - 1)

x - 10 and x - 1 = 0

x = 10 and 1

2. y = x².

y + 3x = 4

x² + 3x - 4

x² +4x - x - 4

x(x + 4) - 1(x + 4)

(x - 1)(x + 4)

x = 1 and -4

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The budget for a project on voting trends includes $3200 for hiring undergraduate students, graduate students, and faculty members to conduct interviews on the day before an election. Each undergraduate student will conduct 30 interviews for $100. Each graduate student will conduct 32 interviews for $150. Each faculty member will conduct 33 interviews for $200. No more than 20 interviewers can be hired.

(a) How many of each type of interviewer should be hired in order to maximize the number of interviews?

(b) What is the maximum number of interviews?

### Answers

To increase the number of interviews, it should be **recommended** that 0 **undergraduate** students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by **statistics**

Simplex Method:

In 1947, George Dantzig invented an algorithm that allows us to take a system of equations and find its **maximum** or **minimum** values that make the equations most efficient. This method is used in linear programming to determine optimization.

If n = the number of **interviews**, then let x = the number of undergraduate students hired, y = the number of graduate students employed, z = the number of faculty members hired.

**Maximization** of n = 30x + 32y + 33z

The **limitations** are: x + y + z 20; 100x + 150y + 200z 3200; and 0;

The answer is 644 because x = 0, y = 16, z = 4.

To increase the number of interviews, it should be **recommended** that 0 **undergraduate** students, 16 graduate students, and 4 faculty members be hired. There can be a maximum of 644 interviews by **statistics** given.

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Solve for x. Round to the nearest tenth.

Thank you!

### Answers

The **value **of the **hypotenuse **x is 19.1

How to determine the value of the hypotenuse x

From the question, we have the following parameters that can be used in our computation:

**Rise **= 17

**Angle **= 63 degrees

The **hypotenuse**, x is then calculated using the following laws of **sines**

sin(63) = 17/x

Make x the subject

So, we have the following representation

x = 17/sin(63)

Evaluate the expression

This gives

x = 19.1

Hence, the value of x is 19.1

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evaluate 9-6 when b =8

### Answers

Answer:

Bx=8

Step-by-step explanation:

U always have to remember to put a “x” or “y” next to your letter it’s important.

Mr. Phil had a boatload of money he decided to leave it to his family but wanted to make sure his goldfish was taken care of today he decided to give 1/2 of his estate to his wife, 30,000 to his daughter half of what was left over to his butler, half of what was left to his goldfish. he realized he had $8000 remaining so he donated to charity. what was the original value of his estate?

### Answers

**Answer:**

208,000

**Step-by-step explanation:**

How do you find the inverse of a modulo?

### Answers

You need to find a number that, when multiplied by a given number modulo a certain value, produces a remainder of 1. This can be done using the extended **Euclidean algorithm**, and the resulting inverse is the residue of the coefficient modulo the **modulus**.

Finding the inverse of a modulo involves finding a number that, when multiplied by a given number modulo a **certain value**, produces a remainder of 1. This process is important in modular arithmetic, where calculations are performed with remainders of a fixed **integer **modulus.

To find the inverse of a modulo, you can use the extended Euclidean algorithm, which is a method for finding the greatest common divisor of two integers.

The steps for finding the **inverse **of a modulo are as follows:

1. Identify the **number **you want to find the inverse of (let's call it "a") and the modulus (let's call it "m").

2. Use the extended Euclidean **algorithm **to find the greatest common divisor of "a" and "m", and the **coefficients **x and y such that ax + my = gcd(a,m).

3. If gcd(a,m) = 1, then "a" has an inverse modulo "m" and the inverse is given by x **mod **m.

4. If gcd(a,m) is not equal to 1, then "a" does not have an inverse modulo "m".

In step 3, x mod m represents the residue of x modulo m, which is the unique **non-negative** **integer **less than m that is congruent to x modulo m. In other words, it is the **remainder **when x is divided by m.

For example, to find the inverse of 5 modulo 7, we can use the extended Euclidean algorithm to find that 2(5) + (-1)(7) = 1. Therefore, the inverse of 5 modulo 7 is 2.

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What is the number of moles in 3.2 x 10^24 atoms of nitrogen?

A. 1.9 moles

B. 5.3 moles

C. 9.5 moles

D. 19.2 moles

### Answers

**Answer:**

b

**Step-by-step explanation:**

Use the Avogadro constant of 6.02 x 10^23

how many seconds in a year riddle

### Answers

Number of **seconds in a year** riddle will be **31,536,000 seconds** in a year ((24 x 60 x 60) x 365).

To calculate number of seconds in year riddle, we need to calculate the no. of seconds in each month.

There are a total 12 months and each month consists of **31, 30 and 28 days** respectively.

Now, calculating the number of seconds in each month **multiplying** the count of months with respect to the number of days in that month.

In January, March, May, July, August, October, December : 31x24x60x60=26,78,400x7=1,87,48,800

In Feb: 28X24x60x60=24,19,200

In April, June, September, November: 30x24x60x60=25,92,000x4=1,03,68,000

Now add all the values: No of Seconds in year riddle =** 1,87,48,800+24,19,200+1,03,68,000**

Totally the value will be equal to **3,15,36,000 seconds**.

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Need help ASAP please!!!!!

### Answers

**Answer:**

122

**Step-by-step explanation:**

the question is asking for the area of the whole shape

however, it's split into a trapezoid and rectangle, so all you have to do is find the area of the respective shapes and then add them

the formula for area of a rectangle is [tex]A = L(W)[/tex]

if you substitue, A = 15(6)

so the area of the rectangle is 90

then, you have the trapezoid

area of a trapezoid = [tex]\frac{1}{2} (h)(b_{1} +b_{2})[/tex]

you might assume that you don't have the second base, but it's in the rectangle - 6

A = 1/2(4)(6+10)

A=32

90+32 = 122

AB= Round your answer to the nearest hundredth.

### Answers

The **length** of the side AB in triangle ABC is 6.58 units.

**What are trigonometric ratios in terms of a right-angle triangle?**

We know a right-angled triangle has three sides they are -: **Hypotenuse**,

**Opposite** and Adjacent.

We can remember SOH CAH TOA which is,

**sin = opposite/hypotenuse**,** cos = adjacent/hypotenuse** and

**tan = opposite/adjacent**.

From the given figure we can conclude that we have length of the adjacent

with an angle of 20° and we have been asked to find the hypotenuse.

We know cos = adjacent/hypotenuse.

∴ cos20° = adjacent/7.

0.937 = adjacent/7.

adjacent = 7*0.937.

**adjacent** = 6.58.

Hence , the **length** of the side AB in triangle ABC is 6.58 units.

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What is the measure of asymmetry?

### Answers

The** measure of asymmetry, **also known as skewness, is a statistical measure that describes the degree of asymmetry in a distribution of data.

It provides information on the shape of the distribution and the deviation of the data from a** normal distribution**. In a symmetrical distribution, the mean, median, and mode are all equal, and the distribution is said to have zero skewness. A distribution that is skewed to the right, or **positively skewed**, has a tail that extends to the right, and the mean is larger than the median. A distribution that is skewed to the left, or negatively skewed, has a tail that extends to the left, and the mean is smaller than the median.

Skewness is calculated by taking the third standardized moment of the distribution, which is the average cubed deviation from the mean, and dividing it by the cube of the **standard deviation. **This gives a measure of the degree of asymmetry of the distribution.

Skewness is an important measure in many fields, including finance, economics, and biology, as it can indicate whether a distribution is likely to produce extreme values, and can help identify outliers in the data. It is also important in hypothesis testing, as many tests assume that the data are normally distributed, and skewed data can affect the validity of the results.

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What is the golden ratio of Fibonacci?

### Answers

The **golden ratio** of Fibonacci, also known as the **divine proportion**, golden mean, or golden section, is a mathematical constant that is approximately equal to **1.618033988749895.**

It is represented by the **Greek letter** phi (φ) and is found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

In mathematical terms, the golden ratio is expressed as:

φ = (1 + √5) / 2

The golden ratio is closely related to the** Fibonacci sequence**, which is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The ratio of consecutive numbers in the Fibonacci sequence converges to the golden ratio as the** sequence progresses.**

For example, the first few numbers in the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

As we divide each number by the one before it, we get closer and closer to the **golden ratio:**

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615...

34/21 = 1.619...

55/34 = 1.617...

89/55 = 1.618...

144/89 = 1.618...

As you can see, the ratio of** consecutive numbers **in the Fibonacci sequence approaches the golden ratio as the sequence progresses. This is why the golden ratio is often referred to as the golden ratio of Fibonacci.

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How much iwater do you add to make each concentration?

1% sugar syrup using 12 g sugar

### Answers

The** amount of water** required to produce 1% sugar syrup from 12g sugar is** 1.2L.**

What is volume of water?

**Volume** is the amount of space occupied by an object, whereas capacity is the ability of an object to hold a substance, such as a solid, **liquid,** or gas.

The **amount of water** that must be added for a given weight of solution is expressed as weight by volume solution (w/v).

w/v (weight by volume percentage):

The **grams of solute **in 100 milliliters of solution are defined as the percent weight per volume.

This method determines the **concentration** of the solution.

The concentration given is **1%.**

The sugar weight is 12g.

**Solvent volume** = weight/concentration

Volume = 12/1 = 12 x 100 mL

**Volume = 1.2 L**

Hence, 1.2l ** of water **is required to produce 1% sugar syrup from 12g of **sugar**

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When data is positively skewed the mean will be?

### Answers

the mean will be greater then the median

A restaurant charges $4. 50 for a slice of pizza that is 1/4 of a pizza and $4. 00 for a slice that is 1/6 of a pizza. One day they cooked 6 pizzas that were all the same size. If they sell all the slices, would they make more money by slicing each pizza into fourths or sixths? How much more? Explain

### Answers

The restaurant would make more money by slicing **each pizza into sixths. **The restaurant would make $36 more than if they sliced **each pizza into fourths**.

To determine if the restaurant would make more money by slicing each pizza into fourths or sixths, we need to calculate the total amount of money they would make for each option.

Option 1: Slicing **each pizza into fourths**

Each pizza would have 4 slices, so 6 pizzas would have a total of 24 slices.Each slice would be sold for $4.50, so the total amount of money made would be 24 slices × $4.50/slice = $108.

Option 2: Slicing **each pizza into sixths**

Each pizza would have 6 slices, so 6 pizzas would have a total of 36 slices.Each slice would be sold for $4.00, so the total amount of money made would be 36 slices × $4.00/slice = $144.

**Comparing** the two options, we can see that the restaurant would make more money by slicing each pizza into sixths. They would make $144 - $108 = $36 more by slicing each pizza into sixths instead of fourths.

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