LPQR is a right angle. Find m/PQS and mZSQR. Enter deg after any value that
is in degrees.

LPQR Is A Right Angle. Find M/PQS And MZSQR. Enter Deg After Any Value Thatis In Degrees.

Answers

Answer 1

The required measures of the angles ∠PQS and ∠SQR are given as 51 and 49.

What is complementary angles?

Complementary angles are two angles whose measures add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.

Here,
∠PQR is a right angle,
So ∠PQS and ∠SQR are supplementary angles, from the figure.

∠PQR = ∠PQS + ∠SQR
90 = 8x + 131 + 10x + 139
90 = 18x + 270
18x = -180
x = -10

Now,
∠PQS = 8x + 131 = -80 + 131 = 51°
Similarly,
∠SQR = 49°

Thus, the required measure of the angles ∠PQS and ∠SQR are given as 51 and 49.

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Related Questions

Math help needed, within 30 minutes please :)

34.) If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts I’ve. How many ounces of each ingredient do you need to make five gallons? (Note: 1 gal=128 oz.)

Show with steps please! It’s a practice problem and I’m trying to learn. :)

Answers

120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed to make five gallons (640 ounces) of fruit punch

What is an equation?

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

1 gal = 128 oz. Hence:

5 gal = 5 gal * 128 oz. per gal = 640 ounces

If a fruit punch is made using 3 parts strawberries, 2 parts blueberry, 2 parts lime juice, 3 parts simple syrup, and 6 parts sugar. Hence. of 5 gallons:

Amount of strawberry = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces

Amount of blueberry = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces

Amount of lime juice = [2/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (2/16) * 640 = 80 ounces

Amount of simple syrup = [3/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (3/16) * 640 = 120 ounces

Amount of sugar = [6/(3 + 2 + 2 + 3 + 6)] * 640 ounces = (6/16) * 640 = 240 ounces

120 ounce of strawberry, 80 ounce of blueberry, 80 ounce of lime juice, 120 ounce of simple syrup and 240 ounce of sugar is needed

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2. By using a truthtable determine whether the following argument is valid or not If 10,836 is divisible by 12 then 10836 is divisible by 3. If 10,836 is divisible by 3 then the sum of the digits of 10836 is divisible by 3. Therefore, if 10,836 is divisible by 12 then the sum of the digits of 10836 is divisible by 3. (10 marks)​

Answers

Based on the truth table constructed, the premises and conclusions are true, hence, the argument is valid.

What is the validity of the argument?

The validity of the argument is determined as follows:

First statement, S1:

10836/12 = 903

10836/3 = 3612

Second statement, S2:

10836/3 = 3612

1 + 0 + 8 + 3 + 6 = 18

18/3 = 6

Statement 3, S3:

10836/12 = 903

1 + 0 + 8 + 3 + 6 = 18

18/3 = 6

The truth table is given below

   Premise 1     Premise 2    Conclusion

S1.        T                    T                 T

S2.        T                    T                 T

S3.        T                    T                 T

Since all the premises and conclusions are true, the argument is valid.

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Paying into a retirement savings plan will increase taxable income, true or false

Answers

Answer:

true

Step-by-step explanation:

Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?

Answers

The measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.

What is a cone?

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex.

A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

Christmas trees, carrots, party hats, ice cream cones, and traffic cones are five instances of cones in everyday life (used as road dividers).

Let's look at some actual code examples.

Explanation: A cone is a three-dimensional solid shape with a circular base at one end and one pointy edge serving as a vertex.

So, the formula for the volume of the cone is:

Volume = πr² h/3

Now, insert values and calculate as follows:

Volume = πr² h/3

Volume = π12.5² 2.35/3

Volume = 384.51785

Rounding off: 385 miles³


Therefore, the measurement which is closest to the volume of Mount Fuji in cone shape is 385 miles³.

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Mount Fuji in Japan can be modeled as a cone with a diameter of 25 miles and a height of 2.35 miles. Which measurement is closest to the volume of Mount Fuji in cubic miles?

Answer:

385mi

A photograph measuring 4" wide × 6" long must be reduced in size to fit a space four inches long in an advertising brochure. How wide must the space be so that the picture remains in proportion?

Answers

If the photograph is 4" wide and 6" long, then the ratio of the width to the length is 4:6, which can be simplified to 2:3. We need to reduce the photograph so that its length fits into a space of 4 inches.

To keep the proportions the same, we need to reduce the width by the same factor. Let's call the new width x. We can set up a proportion:

2:3 = x:4

To solve for x, we can cross-multiply:

2 × 4 = 3 × x

8 = 3x

Dividing both sides by 3, we get:

x = 8/3

So the space must be 8/3 inches wide, or approximately 2.67 inches wide, in order to keep the photograph in proportion.

Answer:

The proportion of the width to the length of the original photograph is 4:6, which can be simplified to 2:3. To maintain the same proportion, the width of the reduced photograph must also be 2/3 of the length.

Since the length of the space in the brochure is 4 inches, the width of the space must be:

width = (2/3) x length

width = (2/3) x 4

width = 8/3

width ≈ 2.67 inches

Therefore, the width of the space in the brochure should be approximately 2.67 inches to maintain the proportion of the photograph.

Determine the lateral area and the surface area of each triangular prism by determining the area of the shape’s net.
Btw: They are all 1

Answers

The lateral area of the triangular prism is  3 cm².

The surface area of the triangular prism is 4 cm².

How to find the lateral and surface area of a triangular prism?

The diagram above is a triangular prism. The lateral area can be found as follows:

lateral area of the triangular prism = perimeter of the base × height

Therefore,

lateral area of the triangular prism = (1 + 1 + 1) × 1

lateral area of the triangular prism = 3 × 1

lateral area of the triangular prism = 3 cm²

Therefore,

surface area of the triangular prism = perimeter of the base × height + 2(base area)

Therefore,

surface area of the triangular prism =  3 + (1 × 1)

surface area of the triangular prism = 4 cm²

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Use Algorithm, to find the transitive closures of these relations on {1, 2, 3, 4). a) {(1, 2), (2,1), (2,3), (3,4), (4,1)) b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3)} c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)} d) {(1, 1), (1,4), (2,1),(2,3), (3,1), (3, 2), (3,4), (4,2))

Answers

Transitive closures are: a) {(1,2),(2,1),(2,3),(3,4),(4,1)}; b) {(2,1),(2,3),(3,1),(3,4),(4,1),(4,3)}; c) {(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}; d) {(1,1),(1,4),(2,1),(2,3),(3,1),(3,2),(3,4),(4,2)}.

Transitive conclusion is a central idea in chart hypothesis and alludes to the most common way of finding every one of the hubs in a coordinated diagram that are reachable from a given hub. All in all, it is the most common way of deciding every one of the potential ways from a given hub to any remaining hubs in the chart. This can be significant in different settings, like in deciding the connections between objects in a data set, or in dissecting the design of PC programs. Transitive conclusion can be tracked down utilizing different calculations, including the Floyd-Warshall calculation and the Warshall calculation.

To find the transitive conclusion of a connection utilizing the calculation, we follow these means:

Begin with the first connection R.

Process the piece of R with itself (R∘R).

Take the association of R and R∘R.

Assuming the association has changed, rehash stages 2 and 3 until there is no change.

a) {(1, 2), (2,1), (2,3), (3,4), (4,1))

R^2: {(1,1), (1,3), (1,4), (2,2), (2,1), (2,4), (3,1), (3,4), (4,2), (4,1)}

R^3: {(1,1), (1,4), (2,1), (2,4), (3,4), (4,1)}

Transitive conclusion: {(1, 2), (1,4), (2,1), (2,4), (3,4), (4,1)}

b) {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3)}

R^2: {(2,1), (2,4), (3,1), (3,3), (3,4), (4,1)}

Transitive conclusion: {(2, 1), (2,3), (3,1), (3,4), (4,1), (4,3), (3,1), (3,3), (2,4)}

c) {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)}

R^2: {(1,3), (1,4), (2,4), (3,4)}

Transitive conclusion: {(1, 2), (1,3), (1,4), (2,3), (2,4), (3,4)}

d) {(1, 1), (1,4), (2,1),(2,3), (3,1), (3, 2), (3,4), (4,2)}

R^2: {(1,1), (1,3), (1,4), (2,1), (2,2), (2,4), (3,1), (3,2), (3,4), (4,2)}

R^3: {(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2)}

Transitive conclusion: {(1, 1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2)}.

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ANSWER ASAP. 50PTS. BRAINLIEST ANSWER.
What is the area of Triangle PQR on the grid?

A triangle PQR is shown on a grid. The vertex P is on ordered pair 1 and 4, vertex Q is on ordered pair 3 and 1, and the vertex R is on ordered pair 5 and 4.
(1 point)

5 square units
6 square units
10 square units
12 square units

Answers

The Area of given triangle is 8 square units.

Area of Triangle:

Area of triangle is the total area occupied by the triangle or the area enclosed within the three sides of the triangle.

The formula for calculating area of triangle is,

A = 1/2 bh

where b and h represent the base and height of the triangle, respectively.

This formula can be used to calculate triangles of any shape, including scalene, isosceles, and equilateral triangles. Remember that the base and height of a triangle are perpendicular to one another.

Now in the given question,

P(1,4), Q(3,1), R(5,4)

We have PR parallel to the x axis. We'll call that the base,

b = 5 - 1 = 4

The altitude is then the y difference h = 5 - 1 = 4

Then area of given triangle is,

[tex]A=\frac{1}{2}bh\\\\\\A=\frac{1}{2} (4)(4)\\\\A=\frac{1}{2} (16)\\\\A=8[/tex]

Hence, the area of given triangle is 8 square units.

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1
A reforestation drive is conducted in a town. The town had 2,022 trees at the start of the drive. Four months after the start of the
reforestation drive, the town had 4,897 trees.
If n represents the number of months and T represents the number of trees, which of the following equations can be used to model
this situation?
OA. T 718.75 - 2,022
OB. T = 2,022n + 718.75
OC. T 718.75 + 2,022
OD. T = 2875 + 2,022n

Answers

Answer: OD. T = 2875 + 2,022n

Step-by-step explanation: What makes the most sense is

OD. T = 2875 + 2,022n

because they added 2875 to the trees already there and 4,897 was the new total after four months, I also want to point out it has nothing to do with decimals or a 700 number.

What is the physical significance of the slope of a position vs time graph?

Answers

Answer:

The slope of a position vs. time graph has a physical significance as it represents the velocity of an object. If the graph is a straight line, then the velocity is constant. If the graph is curved, then the velocity is changing, which means the object is either accelerating or decelerating. The direction of the slope (positive or negative) indicates the direction of the velocity.

MTH 115 – Principles of Mathematics
Assignment 8.3 – Journal 8

First, complete Technology Assignment 8 before attempting these problems.
You can afford a loan payment of $1200 a month. You have put an offer of $175,000 on a house. You are considering three different loans.

Loan A. P = $175,000 at a rate of 5% with monthly payments for 30 years.

Loan B. P = $175,000 at a rate of 4% with monthly payments for 15 years.

Loan C. P = $175,000 at a rate of 4.5% with monthly payments for 20 years.

Find the payment and total interest for each loan.
Loan A: Payment = Total Interest =
Loan B: Payment = Total Interest =
Loan C: Payment = Total Interest =

Choose the loan you will use and clearly state why you chose that one.

Answers

Using the given information, we can use the PMT function in Excel or a financial calculator to find the monthly payment and total interest for each loan.

Loan A:

P = $175,000

r = 5%/12 = 0.004167 (monthly interest rate)

n = 30 years x 12 months/year = 360 months

Payment = $966.45

Total Interest = $153,522.05

Loan B:

P = $175,000

r = 4%/12 = 0.003333 (monthly interest rate)

n = 15 years x 12 months/year = 180 months

Payment = $1,297.53

Total Interest = $33,555.64

Loan C:

P = $175,000

r = 4.5%/12 = 0.00375 (monthly interest rate)

n = 20 years x 12 months/year = 240 months

Payment = $1,095.09

Total Interest = $66,022.37

Based on the information given, I would choose Loan B because it has the lowest total interest and a reasonable monthly payment that fits within my budget of $1200 per month. While Loan A has a lower interest rate, the longer repayment period results in a significantly higher total interest. Loan C has a lower monthly payment, but the longer repayment period also results in a higher total interest.

What is the meaning of "coefficients"?

Answers

A coefficient is a quantity or number that is related to a variable. The variable is frequently followed by an integer that has been multiplied by the variable.

Define Coefficient.

In mathematics, a coefficient is a quantity that is multiplied by a variable in a single term or in a polynomial's terms. Any sign that represents a constant value can be used, including numbers. It is often a number, however in other situations it could be a letter. In the formula: ax² + bx + c, for instance, x is the variable and a and b are the coefficients.

Therefore, a coefficient can be actual or hypothetical, expressed as a fraction or decimal, positive or negative, and real or imaginary. According to another definition, a coefficient is "Any number we multiply a variable by." For instance, the coefficient of the variable x in the expression 9.3x is 9.3, whereas the coefficient of the expression -5z is -5.

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The following data show the ages of recent award-winning male actors at the time when they won their award. Make a frequency table for the data, using bins of 20-29, 30-39, and so on.
Click the icon to view the ages of male actors.
Complete the table below.
Age
20-29
30-39
40-49
50-59
60-69
70-79
No. of actors

Answers

Here is the frequency table for the data, using bins of 20-29, 30-39, and so on:

Age

20-29: 14 actors30-39: 14 actors40-49: 14 actors50-59: 7 actors60-69: 4 actors70-79: 1 actor

What is a Frequency Table?

A table that is created to display the distribution of a characteristic's frequency of occurrence in accordance with a specific set of class intervals.

With the ages and data sets given, we are able to compute the frequency of occurrence in the data set using the specific class interval given.


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Please help me urgently

Answers

Answer:

Below

Step-by-step explanation:

25 oo pass / hr

# passengers for H hours  would be   2500H

    f (H) = 2500 H

Answer:

a) 2500H

b) 20,000

Step-by-step explanation:

Algebraic equation:

To find the number of passengers carried, multiply the number of passengers carried in an hour by the total hours.

  a)    Passengers carried in an hour = 2500

     Passengers carried in 'H' hours = 2500 * H = 2500H

 

b)  H = 8 hours

  Passengers carried in 8 hours = 2500 * 8

                                                      = 20,000

The base monthly payment for a car lease is $354.12 per month. If a sales tax of 8.25% is added to the base monthly payment, what is the total monthly lease payment? Round to the nearest cent.

Answers

Answer:

the total monthly lease payment is $383.31 rounded to the nearest cent.

Step-by-step explanation:

To calculate the total monthly lease payment, we need to add the sales tax to the base monthly payment.

Sales tax = 8.25% of base monthly payment

Sales tax = 0.0825 x $354.12 = $29.19

Total monthly lease payment = Base monthly payment + Sales tax

Total monthly lease payment = $354.12 + $29.19 = $383.31

Therefore, the total monthly lease payment is $383.31 rounded to the nearest cent.

6-3) the turkalike rug company buys medium grade carpet in 100-foot rolls. the average number of defects per roll is 2.0. assuming that these data follow a poisson distribution, use the poisson spreadsheet template to answer the following questions. a. what is the probability of finding exactly 6 defects in a carpet roll chosen at random? b. what is the probability of finding 3 or fewer defects in carpet roll? using the poisson distribution.

Answers

The probability of finding exactly 6 defects in a carpet roll  is 0.0435 and the probability of finding 2 or fewer defects in a carpet roll is 0.405.

a. To find the probability of finding exactly 6 defects in a carpet roll chosen at random, we can use the Poisson formula:

P(X = 6) = (e^-λ  * λ ^6) / 6!

putting λ = 2.0, we get:

P(X = 6) = (e^-2 * 2^6) / 6! = 0.0435

So the probability of  6 defects in a carpet roll chosen at random is 0.0435.

b. To find the probability of finding 2 or fewer defects in a carpet roll, we can use the cumulative distribution function of the Poisson distribution:

P(X <= 2) = 1 - P(X > 2)

Using the Poisson formula, we can calculate P(X > 2) as follows:

P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

Plugging in λ   = 2.0, we get:

P(X > 2) = 1 - (0.135 + 0.27 + 0.54) = 0.595

So P(X <= 2) = 1 - 0.595 = 0.405

So the probability of finding 2 or fewer defects in a carpet roll is 0.405.

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___The given question is incorrect, the correct question is given below:

The Turkalike Rug Company buys medium grade carpet in 100-foot rolls. The average number of defects per roll is 2.0. Assuming that these data follow a Poisson distribution, use the Poisson spreadsheet template to answer the following questions.

a) What is the probability of finding exactly 6 defects in a carpet roll chosen at random?

b) What is the probability of finding 2 or fewer defects in a carpet roll?

what is the point group for each of the following substituted cyclobutanes? assume that the four-membered ring is flat and that replacing h with x or y changes no other structural parameters.

Answers

The point group of a substituted cyclobutene can be determined by examining its symmetry elements.

In group theory, point groups are used to describe the symmetry of a molecule. The point group of a molecule can be determined by examining its symmetry elements, such as rotation axes, reflection planes, and inversion centers.

In the case of substituted cyclobutene, we can assume that the four-membered ring is flat and that replacing hydrogen atoms with other substituents, such as X or Y, does not affect any other structural parameters.

Now, let's consider the point groups for two substituted cyclobutene: 1,1-dimethylcyclobutane and 1,2-dimethylcyclobutane.

1,1-dimethylcyclobutane has two methyl groups attached to the same carbon atom. The symmetry elements of this molecule include a C2 axis that passes through the two methyl groups and perpendicular to the plane of the ring. There are also two perpendicular mirror planes that bisect the ring and pass through the carbon atom with the two methyl groups.

Using the point group flowchart, we can determine that the point group for 1,1-dimethylcyclobutane is C2v.

On the other hand, 1,2-dimethylcyclobutane has two methyl groups attached to adjacent carbon atoms. This molecule has a C2 axis that passes through the two methyl groups and the ring, as well as two perpendicular mirror planes that bisect the ring and pass through the carbon atoms with the methyl groups.

Using the point group flowchart, we can determine that the point group for 1,2-dimethylcyclobutane is Cs.

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Calculating angle of elevation of sun at different times of the day using your height and the length of shadow cast

Answers

At noon on a clear day, with a height of 6 feet and a length of the shadow of 6 feet, the angle of elevation of the sun is approximately 45 degrees.

What is the angle of elevation?

An angle of elevation is defined as the angle formed between the horizontal plane and the line of sight from the observer's eye to anything above.

Let's assume a height of 6 feet and a length of the shadow of 6 feet.

We'll also assume that we are measuring the angle of elevation at noon on a clear day.

Using the tangent formula, we have:

tan θ = h / s

tan θ = 6/6

θ = tan⁻¹(6 / 6)

θ = tan⁻¹(1)

θ = 45°

Therefore, the angle of elevation of the sun is approximately 45 degrees.

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please answer , im marking brainiest .

Answers

The fraction equivalent to the number A = 0.555... is A = 5/9

What is a Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the value of A is

A = 0.555555..

Here , the value of A is 0.555 and the number 5 is repeating

So , the simplified form of the fraction A is given by

A = 5/9

On simplifying the value of A , we get

A = 0.55555...

Hence , the fraction is A = 5/9

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1853
1854
1850
1851
1852
YEAR
1841
1847
1848
1849
8:59
NUMBER
OF IRISH
IMMIGRANTS
37,772
105,536
112,934
159,398
164,004
221,253
159,548
162,649
101,606
Which of the following statements mos
accurately describes patterns of Irish
immigration in the mid-19th century?
O It remained relatively unchanged.
O
It continually increased between
1847 and 1854.

Answers

The statement that most accurately describes patterns of Irish immigration in the mid-19th century is: its peaked in approximately 1851. The Option D is correct.

What was pattern of Irish immigration to US in mid 19th century?

Irish immigration to the United States in the mid-19th century was characterized by several factors:

Timing: Irish immigration to the United States peaked in the mid-19th century, particularly in the decades following the Great Famine of 1845-1852. During this time, millions of Irish fled to the United States to escape poverty and famine at home.Destination: Irish immigrants tended to settle in cities, particularly in the Northeast, such as Boston, New York, and Philadelphia. These cities offered employment opportunities and a supportive Irish-American community.Employment: Many Irish immigrants in the mid-19th century worked in manual labor jobs, such as construction, manufacturing, and domestic service. They faced significant discrimination and prejudice from the American-born population, who often considered them to be inferior and less capable.

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How do I solve y = 2x + 7
y=-3x+17

Answers

Answer:

Make the expressions equal to each other.

2x + 7 = -3x + 17

Use subtraction, division, and addition to isolate the variable.

2x + 3x + 7 = -3x + 3x + 17

5x + 7 = 17

5x + 7 - 7 = 17 - 7

5x = 10

5x/5 = 10/5

x = 2

y = 11

Step-by-step explanation:

What is 16⅐% of 48? Show work

Answers

To calculate 16⅐% of 48, we first need to convert 16⅐% to a decimal. We can do this by dividing 16 by 100, which gives us 0.16.

Next, we multiply 48 by 0.16 to find the result:

48 * 0.16 = 7.68

So, 16⅐% of 48 is 7.68.
ANSWER- 7 131/175

STEP BY STEP

16 1/7. 113/7.
——— x 48 =. —— x 48 =
100. 100

1356. 131
=113/700 x 48= ——- = 7 —-
175. 175

It is said that 60% of college students have a job outside of school. The college admissions office is investigating on whether this claim is true or not.a) If a test of hypothesis is conducted, describe in in the context of the problem, what would be the type I error:b) If a test of hypothesis is conducted, describe in the context of the problem what would be the type II error:

Answers

The type I error, in the context of the problem, would be the incorrect rejection of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is true, when in fact it is not.

The type II error, in the context of the problem, would be the incorrect acceptance of the null hypothesis. This would mean that the college admissions office would incorrectly conclude that the claim is false, when in fact it is true.

The college admissions office sets up a hypothesis test with the claim being 60% of college students have a job outside of school.

The null hypothesis would be that the claim is false, or that less than 60% of college students have a job outside of school.

The alternative hypothesis would be that the claim is true, or that at least 60% of college students have a job outside of school.

The type I error would be if the college admissions office incorrectly rejected the null hypothesis, that is, if they concluded that the claim is true and at least 60% of college students have a job outside of school when in fact the claim.

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Trig ratios, pls hurry

Answers

The person is 36m away from the boat.

Applying simultaneous equations to solve angle of depression

The given figure is triangular in nature. In order to determine the distance of the person from the boat, we will use the pythagoras theorem.

Given the following parameters

GH = 20m

GK = 30m

The measure of the length HK (The distance of the person from the boat,) is calculated as:

HK^2 = GH^2 + GK^2

HK^2 = 20^2+ 30^2

HK^2 = 400+900
HK^2 = 1300

HK = 36m

Hence the distance of the person from the boat is approximately 36m

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We choose a number from the set {1, 2, 3, . . . , 100} uniformly at random and denote this number by X.
For each of the following choices decide whether the two events in question are independent or not
(a) A = {X is even}, B = {X is divisible by 5}.
(b) C = {X has two digits}, D = {X is divisible by 3}.
(c) E = {X is a prime}, F = {X has a digit 5}. Note that 1 is not a prime number.

Answers

(a) Not independent, as the occurrence of X being even affects the probability of X being divisible by 5 and vice versa.

(b) Not independent, as the occurrence of X having two digits affects the probability of X being divisible by 3 and vice versa.

(c) Independent, as the occurrence of X being a prime does not affect the probability of X having a digit 5, and vice versa.

Two occurrences are often considered independent if their occurrence has no impact on the likelihood of their occurrence. The occurrences in (a) and (b) are not independent since one event's occurrence affects how likely the other is. Because the chance of one event in (c) is unaffected by the likelihood of the other, the occurrences are independent in (c).

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Cuantos frascos de perfume de 12 cl se llenan con un bidón de 15 l?

Answers

Using the method of unit conversion, the number of bottles that can be filled is obtained as 125.

What is unit conversion?

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding.

We can start by unit converting the volume of the drum from liters to centiliters, as the volume of the perfume bottles is given in centiliters -

15 liters = 1500 centiliters

Now we can find the number of 12 cl perfume bottles that can be filled with the drum by dividing the volume of the drum by the volume of each bottle -

Number of bottles = volume of drum / volume of each bottle

Number of bottles = 1500 cl / 12 cl

Number of bottles = 125

Therefore, 125 12 cl perfume bottles can be filled with a 15 l drum.

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How many 12 cl perfume bottles are filled with a 15 l drum?

27. A man is climbing down from 225 feet high descending 25 feet per minute. Write an
equation/function that models this situation.

Answers

Let's define the following variables:

h : the height of the man above the ground at time t in minutes (in feet).
t : time elapsed since the man started descending (in minutes).
At the start of the descent, the man is at a height of 225 feet above the ground, so we can set the initial condition h(0) = 225.

As the man is descending at a rate of 25 feet per minute, the rate of change of h with respect to t is -25.

Therefore, the equation that models this situation is:

h(t) = 225 - 25t

This equation gives the height of the man at any time t during the descent.

Referring to the Fig. in Question #23, find the cosine of angle S. Reduce the answer to the lowest terms.

Answers

The Cosine of angle S in the given triangle is

[tex]\frac{8}{10} =\frac{4}{5}[/tex] .

Trigonometric Identities:

Trigonometric Identities are equality claims that apply the principles of trigonometry and are valid for all possible values of the variables in the equation.

Many particular trigonometric identities can be used to express the relationship between a triangle's side length and angle.Only the right-angle triangle is consistent with the trigonometric identities.

All trigonometric identities are built upon the foundation of the six trigonometric ratios. Some of their names are sine, cosine, tangent, cosecant, secant, and cotangent. Each of these trigonometric ratios is defined using the adjacent side, opposite side, and hypotenuse side of the right triangle. All fundamental trigonometric identities are derived from the six trigonometric ratios.

The Cosine of an angle ∅ in a right triangle is given as ,

Cosine (∅) = [tex]\frac{base}{hypotenuse}[/tex]

Now in the given triangle .

[tex]Cosine (S)=\frac{8}{10} =\frac{4}{5}[/tex]

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Which cross sections is possible in cylinders and cones

Answers

The cross-section of the cylinders and cones is always round.

What is a cross-section area?

The cross-sectional area is the region of a two-dimensional shape produced when a three-dimensional object, such as a cylinder, is cut perpendicular to a preset axis at a point.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions. In elementary geometry, it is regarded as a prism with a circle as its basis.

A three-dimensional geometric shape known as a cone has a flat base and a smooth, tapering vertex. A cone is made up of several line segments, half-lines, or lines that connect to a single point.

As a result, the cross sections of the cones and cylinders are always round.

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The variables x and y are connected by the equation y=(x-3)(x - 5)(x+2).Some corresponding values of x and y are shown in the table below. X -2 0 1 y 0 30 24 (i) Calculate the value of k -1 24 2 12 3 0 4 -6 5 0 (0) 6 k [1] avis​

Answers

The value of k is given as follows:

k = 24.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

From the table, we have that when x = 6, y = k, hence the value of k is found replacing each of the three instances of x by 6, as follows:

k = (6 - 3)(6 - 5)(6 + 2)

k = 3 x 1 x 8

k = 24.

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