Which set is infinite?

The trigonometric measures in the context of this problem are given as follows:

We are given the measure of the sine for the angle and we need to find the three measures, sine, cosine and tangent for half the angle.

To find the measure for half the angle, the cosine is needed to apply the identities, and the cosine is calculated by the following identity:

sin²(x) + cos²(x) = 1

[tex]\left(\frac{2}{3}\right)^2 + \cos^2{x} = 1[/tex]

[tex]\cos^2{x} = 1 - \frac{4}{9}[/tex]

[tex]\cos{x} = \pm \sqrt{\frac{5}{9}}[/tex]

The angle is in the first quadrant, in which the cosine is positive, hence:

[tex]\cos{x} = \sqrt{\frac{5}{9}}[/tex]

[tex]\cos{x} = \frac{\sqrt{3}}{3}[/tex]

Then, applying an identity, the sine for half the angle is given as follows:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \cos{x}}{2}}[/tex]

Considering the calculated value for the cosine:

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 - \frac{\sqrt{3}}{3}}{2}}[/tex]

[tex]\sin{\left(\frac{x}{2}\right)} = \sqrt{\frac{3-\sqrt{3}}{6}}[/tex]

The identity for the cosine is:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{1 + \cos{x}}{2}}[/tex]

Hence:

[tex]\cos{\left(\frac{x}{2}\right)} = \sqrt{\frac{3+\sqrt{3}}{6}}[/tex]

The tangent is obtained by the division of the sine and the cosine. The entire division can be placed into a single square root, and the common denominators of six are simplified, hence:

[tex]\tan{\left(\frac{x}{2}\right)} = \sqrt{\frac{3 - \sqrt{3}}{3 + \sqrt{3}}}[/tex]

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Answer:

2/3

Step-by-step explanation:

we use y2-y1/x2-x1 to find slope

5-3/4-1

2/3

The slope is 2/3

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The largest number of boxes that can fit in the crate will be 27.

What is an expression?

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

Given that;

The dimension of the crate is 24cm by 18cm by 15cm.

And, it is to be packed with boxes that are 8cm by 6cm by 5cm.

Now,

By the given data;

Volume of the crate = 24 x 18 x 15

                               = 6480 cm³

And, The volume of the box = 8 x 6 x 5

                                            = 240 cm³

Thus, The largest number of boxes that can fit in the crate = 6480 / 240

                                                                                           = 27

Therefore, The largest number of boxes that can fit in the crate will be 27.

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Tyrannosaurus rex weighs about 0.14 times the weight of Patagotitan mayorum

In solving the proportion of the weights we use multiplication of fractions

Multiplication is a mathematical operator to handle such operation

A Tyrannosaurus rex weighed about 1.4 tons more than one tenth the weight of a Patagotitan mayorum

This is is written mathematically as

Tyrannosaurus rex weight, x = 1.4 * 1/10 * Patagotitan mayorum weight, y

x = 1.4 * 1/10 * y

x = 0.14 *y

x = 0.14y

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The amount that should be deposited in the account to earn a balance of $5, 000 after 19 years and 6 months is $2, 099.43

First, find the periodic rate:

= 4.5% / 2 semi annual periods per year

= 2.25%

Find the number of periods:

= 19 years and 6 months = 19.5 years

= 19.5 years x 2 semi annual periods per year

= 39 periods

The amount to deposit in the account can be found by the future value formula:

Future value = Deposit x ( 1 + rate) ^ number of periods

5, 000 = Deposit x ( 1 + 2.25%)³⁹

Deposit = 5,000 / ( 1 + 2.25%)³⁹

= $2, 099.43

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The value of one-sixth times quantity x plus 24 end quantity equals negative 6 is -180.

The expression simply refers to the mathematical statements which have at least two terms that are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, the expression given will be illustrated as:

1/6x + 24 = -6

Collect like terms

x / 6 = -6 - 24

x/6 = -30

Cross multiply

x = -30 × 6

x = -180

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Answer:

x=1.25 y=1.75

Step-by-step explanation:

8/10=5/5+x

50=8(5+x)

50=40+8x

50-40=8x

10=8x

x=10/8

x=1.25

while Y=8/10=7/7+y

70=8(7+y)

70=56+8y

70-56=8y

14=8y

y=14/8

y=1.75

Answer:

100 seconds

Step-by-step explanation:

200/2 = 100s

The true statement about the function is that (b) the y-intercept of the function is 3

The mathematical statement of the representation of the function is given as

The function f(x) is the absolute value of 3 more than the value of x.

Mathematically, this can be represented as

f(x) = |x + 3|

To determine the y-intercept, we set the x value of the function to 0

This means that we calculate f(x) when x = 0

i.e. f(0)

Substitute the known values in the above equation, so, we have the following representation

f(0) = |0 + 3|

Evaluate the sum

This gives

f(0) = |3|

Remove the absolute bracket

f(0) = 3

Hence, the y-intercept is 3

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Possible question

If the function f(x) is the absolute value of 3 more than the value of x. Select all the true statements.

A. The x-intercept of the function is 3.

B. The y-intercept of the function is 3.

Answer:

D 11%

$30

Step-by-step explanation:

1. A cyclist estimates that he will bike 80 miles this week. He actually bikes 90 miles. What is the percent error of the cyclists estimate rounded to the nearest percent?

A 8%

B 9%

C 10%

D 11%

Actual distance: 90 miles

Estimated distance: 80 miles

percent error = (estimate - real)/real × 100%

percent error = (80 - 90)/90 × 100%

percent error = -11%

His error is 11%. The negative sign just means his estimate is 11% less than the real distance.

Answer: 11%

2. Jack borrows $3,000 at a rate of 4% per year. How much total will he pay if it takes 3 months to repay the loan?

$10

$20

$30

$40

interest = Prt

where P = principal (the amount borrowed or deposited)

r = annual rate of interest

t = time

We have P = $3,000

r = 4% = 0.04

t = 3 months = (3 months)/(12 months) = 0.25 year

interest = $3,000 × 0.04 × 0.25

interest = $30

He pays a total interest of $30.

The answer will be 3 years.

1st 30 pupils at average age of 15.3 yrs. give total age of 15.3 x 30 = 459yrs

2nd group of 30 pupils at average age of 15.2 yrs

give total age of 15.2 x 30 = 456yrs

Difference in age = 459 - 456

= 3 years.

To find the height, envision it as a third side to a right triangle. We have the first side, with a length of 7cm, and the hypotenuse, with a length of 15cm. When we have two sides of a right triangle with given lengths, we can employ the Pythagorean Theorem.

The Pythagorean Theorem states that the square of the hypotenuse, c, is equal to the sum of the squares of the other two sides, or:

[tex]a^2 + b^2 = c^2[/tex]

Well, we have a and c, so we can solve for b.

[tex]7^2 + b^2 = 15^2\\49+b^2 = 225\\49 - 49 + b^2 = 225 - 49\\b^2 = 176\\\sqrt{b^2}=\sqrt{176}\\b = 13.27[/tex]

b ≈ 13.27

Answer:

Step-by-step explanation:

should be both line GJ and JK as well as line HK and JK

The exact value of tan195° is 0.2679.

The given trigonometric ratio is tan195°.

Trigonometric angles are the angles in a right-angled triangle using which different trigonometric functions can be represented. Some standard angles used in trigonometry are 0º, 30º, 45º, 60º, 90º.

Now, the value of  trigonometric ratio is

tan195°=0.2679

Hence, the exact value of tan195° is 0.2679.

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Answer:

  $1377.06

Step-by-step explanation:

You want the monthly payment on a 30 year loan of $162359 at 9.6% interest.

The payment value can be computed by any spreadsheet and most graphing calculators using built-in financial functions. Numerous apps and web sites are available for the same purpose.

The monthly payment is $1377.06 according to the attached calculator output.

The formula used for the purpose is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12·t))

where P is the loan value, r is the annual interest rate, and t is the number of years. For P=162359, r=0.096, and t=30, you have ...

  A = 162359(0.096/12)/(1 -(1 +0.096/12)^-360) ≈ 1377.06

__

Additional comment

The formula assumes the payment is made at the end of the month. Spreadsheet and calculator functions often need to be told that's when the payment is made.

There are 2520 possible ways to arrange the programs

From the question, we have

Total number of jockey records, n = 7

Total number of disc jockey records to select, r = 5

To determine the ways the program can be arranged, we make use of permutation

The number of ways of selection could be drawn is calculated using the following permutation formula

Total = ⁿPᵣ

Where

n = 7 and r = 5

Substitute the known values in the above equation

So, we have the following representation

Total = ⁷P₅

Apply the permutation formula

ⁿPᵣ = n!/(n - r)!

So, we have

Total = 7!/2!

Evaluate

Total = 2520

Hence, the number of ways is 2520

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a) The sample proportion would be of: 0.93.

b) The margin of error would be of: 0.037.

c) The critical value would be of: z = 1.96.

d) The standard error would be of: 0.0189.

e) The critical value for the 90% confidence interval would be of: z = 1.645.

f) The 90% confidence interval would be narrower.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

From the equation, the confidence interval can be described as follows:

The sample proportion plus/minus the margin of error.

For this problem, the interval is given as follows:

(.893, .967).

From the description, the sample proportion is the mean of the two bounds, hence:

Sample proportion = (0.893 + 0.967)/2 = 0.93.

The margin of error is the absolute value of the difference of each bound and the sample proportion, hence:

Margin of error = |0.967 - 0.93| = |0.893 - 0.93| = 0.037.

The critical values are found using the z-table, as follows:

The greater the critical value, the wider the interval, hence a 90% confidence interval would be narrower than the 95% confidence interval;

The standard error is the division of the margin of error by the critical value, hence:

Standard error = 0.037/1.96 = 0.0189 = 1.89%.

The complete problem is given by the image shown at the end of the answer.

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Answer:

See below

Step-by-step explanation:

13 - 5x = 48  Subtract 13 from both sides

-5x = 35

-5x = 35 is the not the same as 5x = 35

-5x = 35  Divide both sides by -5

x = -7

5x  = 35  Divide both sides by 5

x = 7

7 and -7 are not the same solution.  They are two different numbers.

The sentence which supports the idea that people can use the skills they used at their old jobs to make money independently is "If an installer has a place to work, that person can install stereos without a store."

The correct answer option is option C

The essay is about American employees where people who actually needs a job gets a job. Although, this is not always the case especially when the economy slows down.

This slow down in the economy causes businesses to make less profit, thereby, making most people to lose their jobs. The purchasing power of the unemployed (people who lost their job) will reduce causing a decrease in the amount of money made by businesses. This is like a vicious cycle.

However, people who are skilled can still earn a living by doing other available jobs or those who are creative can create new jobs for themselves. For instance, an accountant can become a sales person in a supermarket if he or she lost their job.

In conclusion, a person who lost their job must be determined, hopeful and hard-working and must never give up, most importantly, they should never be idle because an idle mind is the devil's workshop.

Complete question:

Which sentence supports the idea that people can use the skills they used at their old jobs to make money independently?

Answer choices

A"So, car stereo stores have to layoff some of their stereo installers."

B"Often, this person will charge less than the store where he or she used to work."

C. "If an installer has a place to work, that person can install stereos without a store."

D. "At the store where the installer used to work, the store would have made most of the money."

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Answer:

x=48

Step-by-step explanation:

the 2 given angles if added together we know it’ll be 180 degrees

3x-12+x=180

4x-12=180

   +12. +12

4x=192

x=48

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The account balance after20 ​years will be $6900 and the simple interest for 20 years is $1900

The Principal amount = $5,000

Rate of Interest (r) = 1.9 %

Time Period (t) = 20 years

The Simple Interest is given by

[tex]S.I. = \frac{P*r*t}{100}[/tex]

Now, putting the values on the formula, we get:

[tex]S.I. = \frac{5000*1.9*20}{100} = 1900[/tex]

Hence, the interest will be $1900

Now, The Account Balance after 20 years = $ (1900 + 5000) = $6900

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1. The bank discount on the note of $6,000, which will mature in 160 days at 3.5%, is $93.33.

2. The noteholder will receive total proceeds of $5,906.67 after the 3.5% discount.

Bank discount is the difference between the discounted and face (par) values.

For example, if the bank discounts a note, the holder receives a smaller amount than the face value they would have received had they held the note till its maturity.

The bank discount represents the finance charge for cashing the note earlier than its due date.

Amount due at maturity = $6,000

Discount rate = 3.5%

Time (period) = 160 days

Days in the year for ordinary interest = 360 days

Bank discount = $93.33 ($6,000 x 3.5% x 160/360)

The proceeds = $5,906.67 ($6,000 - $93.33)

Thus, the bank discount refers to the difference between the face value and the discounted value resulting from receiving cash from a note before maturity.

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Answer:

x = 36°

Step-by-step explanation:

Hello!

If angles are supplementary, that means that the sum of those angles is 180°.

Set up an equation and solve for x.

The measure of x is 36°.

Answer:

"i agree because.."

Step-by-step explanation:

50 x 20 = 1000

5 x 2 = 10

there are 2 zeros in both factors so placing the 2 zeros at the end of 10 (making 1000) would work since they are the same answer

The distance between point A and point B is 5 units.

According to the question,

We have the following information:

Point A = (-2,2)

Point B = (1,2)

Now, we know that the following formula is used to find the distance between two points:

Distance between two points = [tex]\sqrt{(y2-y1)^{2} +(x2-x1)^{2} )}[/tex]

In this case, we have the values of x1 = -2, y1 = -2, x2 = 1 and y2 = 2.

Distance between two points = [tex]\sqrt{(2+2)^{2} +(1+2)^{2} )}[/tex]

(The sign has been changed from negative to positive because the multiplication of two negative integers is positive.)

Distance = [tex]\sqrt{(4)^{2} +(3)^{2} )}[/tex]

Distance = [tex]\sqrt{16+9}[/tex]

Distance = [tex]\sqrt{25}[/tex]

Distance = 5 units

Hence, the distance between point A and point B is 5 units.

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Proved that Triangle ABD ≅ Triangle CBD

Consider the triangle ABD and the triangle CBD

The length of the side AB = The length of the side BC

The length of the side AD = The length of the side cd

The third side is common

According to the SSS rule congruent . If the three side of the triangle is equal to the three sides of the another triangle then the both triangles are congruent

Then three sides of the triangle ABD is equal to the three sides of the triangle CBD, Therefore the triangle ABD and triangle CBD are congruent

Hence, proved that Triangle ABD ≅ Triangle CBD

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Answer:

=57×2of4+2

=57×8+2

=456+2

=458.

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Answer:

-1

Step-by-step explanation:

you would do -11 + (-5) which will be -16. Then do -16 - (-15) which will get you -1.

The probability of exactly six will fail = 0.0808

What is Probability?

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability. It is crucial to grasp this branch's most fundamental concepts in order to fully comprehend it, including the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc.

In the given question, we have:

We know that Probability in binomial distribution with total components ' n ', probability of success ' p ', and the number "of successes " = [tex]{ }^n c_k p^k(1-p)^{n-k}[/tex]

we know that:

[tex]{ }^n c_k=\frac{n !}{(n-k) ! k !}[/tex]

[tex]\begin{aligned}P(\text { success }) &=P(\text { a part fails })=0.35 \text {. So, } \\P(x=5) &={ }^8 C_5 \times(0.35)^5(0.65)^3 \\&=56 \times(0.005252) \times(0.274625) \\&=0.0808 \\& \text { (Round to } 4 \text {-decimals) }\end{aligned}[/tex]

Hence,

The probability of exactly six will fail = 0.0808

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