7. Which type of interest can be described as
interest that is earned on the principal amount
only?
A Compound interest
B Simple interest
C Both simple and compound interest
D Neither simple nor compound interest

Answers

Answer 1

The type of interest that is earned on the principal amount only is called Simple Interest.

Identifying the type of interest

Simple interest is calculated based on the principal amount of the loan or investment and does not take into account any interest that may have accumulated in previous periods.

The formula for calculating simple interest is:

I = PRT

where I is the interest earned, P is the principal amount, R is the annual interest rate, and T is the time period in years.

In contrast, compound interest takes into account both the principal and any accumulated interest from previous periods, resulting in a larger interest payment over time.

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Related Questions

Graph the equation include aleast 3 ordered pairs
y=0.5x + 2

Answers

Answer:

(2, 3)

(0, 2)

(-2, 1)

Step-by-step explanation:

This equation is in slope-intercept form:

[tex]y=mx+b[/tex],

where [tex]m[/tex] is the line's slope, and [tex]b[/tex] is the y-coordinate of its y-intercept.

Using this knowledge, we can identify the following:

[tex]m = 0.5 = \frac{1}{2}[/tex]

[tex]b = 2[/tex]

Now, we can graph the line with a slope of 1/2 and a y-intercept at y = 2 (see the attached image).

But, even if we were not to graph it, we could still find integer points to the left and right of the y-intercept using the fact that:

[tex]\text{slope} = \dfrac{\text{rise}}{\text{run}} = \dfrac{\Delta y}{\Delta x} = \dfrac{1}{2}[/tex]

So, we can say that the following points are on the line:

(0, 2) ← y-intercept

(0 + 2, 2 + 1) = (2, 3) ← point to the right

(0 - 2, 2 - 1) = (-2, 1) ← point to the left

Identify the expression that is not equivalent to 6x + 3.

Answers

The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

What are expressions?

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.

For instance, "4 added to 2" will have the mathematical formula 2+4.

So, we have the expression:

= x² + 10x + 24

Now, solve when x = 3 as follows:

= x² + 10x + 24

= 3² + 10(3) + 24

= 9 + 30 + 24

= 63

Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

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Correct question:

Evaluate the expression when x = 3.

x² + 10x + 24

a. 81

b. 86

c. 63

d. 60

How do you solve this equation in Derive Linear Equations - Quiz - Level H: What is the slope of the line?

Answers

The slope of the given line is 1/3 for the line passes through (0, 2) and (3, 3).

The slope of a line represents the rate at which it rises or falls as it moves horizontally from left to right.

It is calculated by taking the difference in the y-coordinates (vertical change) and dividing it by the difference in the x-coordinates (horizontal change) of two points on the line.

The slope can also be thought of as the tangent of the angle formed by the line and the positive x-axis.

In this problem, we are given that the slope of the line is 1/3.

We can use this information to find the slope between any two points on the line.

Let's consider the points (0, 2) and (3, 3) that lie on the line.

The change in y-coordinates is 3 - 2 = 1, and the change in x-coordinates is 3 - 0 = 3.

Therefore, the slope between these two points is 1/3.

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The question is -

What is the slope of the line?

Derive Linear Equations-Quiz-Level H

A random sample of 100 adults are asked if they pay for monthly subscriptions that they do not use, like a magazine, app, or online program simply. Many do, because they have never taken the time to cancel the subscription. A 95% confidence interval for the proportion of adults who to pay for subscriptions they do not use is 0. 352 to 0. 548.

a. Interpret the confidence interval.

b. Calculate the point estimate and the margin of error.

c. Based upon this survey, a reporter claims that a majority of adults continue to pay for monthly subscriptions they do not use. Use the confidence interval to evaluate this claim

Answers

a) The 95% confidence interval indicates that we are 95% confident that the true proportion of adults who pay for monthly subscriptions they do not use is between 0.352 and 0.548.

b) The point estimate is 0.5 or 50%. The margin of error is 0.024 or 2.4%.

The 95% confidence interval indicates that if we were to repeat this survey many times, about 95% of the intervals we calculate would contain the true proportion of adults who pay for monthly subscriptions they do not use in the population.

Specifically, based on the sample data, we are 95% confident that the true proportion of adults who pay for monthly subscriptions they do not use is between 0.352 and 0.548.

b. The point estimate is the sample proportion, which is calculated by taking the number of adults in the sample who pay for subscriptions they do not use and dividing by the total sample size

point estimate = number of adults in sample who pay for subscriptions they do not use / total sample size

= (number of "yes" responses) / 100

= (0.5 x 100) / 100

= 0.5

So the point estimate is 0.5 or 50%.

The margin of error is calculated by taking half of the width of the confidence interval

margin of error = (upper limit of confidence interval - point estimate) / 2

= (0.548 - 0.5) / 2

= 0.024

So the margin of error is 0.024 or 2.4%.

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The given question is incomplete, the complete question is:

A random sample of 100 adults are asked if they pay for monthly subscriptions that they do not use, like a magazine, app, or online program simply. Many do, because they have never taken the time to cancel the subscription. A 95% confidence interval for the proportion of adults who to pay for subscriptions they do not use is 0. 352 to 0. 548.

a. Interpret the confidence interval.

b. Calculate the point estimate and the margin of error.

1. The largest of 2 integers is one more than three times the smaller. If the sum of the two integers is 37, find the larger integer.

2. For two consecutive integers, the sum of the smaller and twice the larger is 29. Find the smaller integer.

Answers

1.  we can use the first equation to find y = 3x + 1 = 3(9) + 1 = 28 So, the larger integer is 28, (2).  The smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

What is an integer ?

An integer is a whole number ,neither a fraction or a decimal, in mathematics. Integers can be zero, positive, or negative.

Integer examples include -3, -2, -1, 0, 1, 2, 3, and so forth.

The letter "Z" stands for the set of integers.

In mathematics and allied disciplines such as computer science, physics, and finance, integers are utilized extensively.

What is a whole number ?

A whole number is a non-negative integer in mathematics, which indicates that it is either a positive integer or zero.

Negative and fractional numbers are not included in whole numbers. The full integers 0, 1, 2, 3, 4, and so on are examples.

In many different branches of mathematics as well as in other disciplines, such as arithmetic, algebra, and geometry, whole numbers are used. They are also employed in daily tasks like quantity calculations and object counts.

According to question :-

Let's call the smaller integer x and the larger integer y. We know that:

y = 3x + 1 (the largest of the two integers is one more than three times the smaller)

x + y = 37 (the sum of the two integers is 37)

We can use substitution to solve for y in terms of x:

x + (3x + 1) = 37

4x + 1 = 37

4x = 36

x = 9

Now we can use the first equation to find y:

y = 3x + 1 = 3(9) + 1 = 28

So the larger integer is 28.

Let's call the smaller integer x and the larger integer y. We know that:

y = x + 1 (the integers are consecutive)

x + 2y = 29 (the sum of the smaller and twice the larger is 29)

We can substitute y = x + 1 in the second equation:

x + 2(x + 1) = 29

Simplifying and solving for x:

3x + 2 = 29

3x = 27

x = 9

So the smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

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can someone give me the answers to these 5?? pleaseee!!

Answers

The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00

How to find the number summaries ?

Calculate the MAD:

First, find the mean of the data set:

mean = (sum of all values) / (number of values)

mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10

mean = 88.00 / 10 = 8.80

Then, find the mean of these absolute deviations:

MAD = (sum of absolute deviations) / (number of values)

MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10

MAD = 4.10 / 10 = 0.41

Calculate the range:

range = maximum value - minimum value

range = 10.00 - 8.00 = 2.00

Find Q1 and Q3:

{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}

Q1 is the median of the lower half, and Q3 is the median of the upper half.

Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}

Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}

Q1 = median of lower half = 8.25

Q3 = median of upper half = 9.25

Calculate the IQR:

IQR = Q3 - Q1

IQR = 9.25 - 8.25 = 1.00

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4.834 * 10 ^ 9 as an ordinary number

Answers

Answer:

4834000000

That is your answer.

Spinning a spinner that has 5 equal sections marked 1 through 5 and anding on an even number. Find the probability and write answer in simplest form.

Answers

The probability of spinning an even number is 2/5, which can be written in simplest form.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

The spinner has 5 equal sections marked 1 through 5. Two of the five numbers are even (2 and 4). Therefore, the probability of spinning an even number is:

Probability of spinning an even number = (number of even numbers) / (total number of possible outcomes)

Probability of spinning an even number = 2/5

Hence, The probability of spinning an even number is 2/5, which can be written in simplest form.

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Find The Values Of X and Y

Answers

The characteristics of the sum of the angles, (supplementary and complementary) and the indicated angles in the question indicates;

x = 6

y = 24

What are supplementary angles?

Supplementary angles are two angles that have a sum of 180° and together form a linear pair.

The angles ∠PTQ and ∠QTR are linear pair angles, therefore;

m∠PTQ + m∠QTR = 180°

m∠PTQ = (5·y)°

m∠QTR = (2·y + 12)°

Therefore; m∠PTQ + m∠QTR = (5·y)° + (2·y + 12)° = (7·y + 12)°

(7·y + 12)° = 180° (Substitution property)

7·y + 12 = 180

7·y = 180 - 12 = 168

y = 168/7 = 24

y = 24

The angles ∠QTR and ∠RTS are complementary angles, therefore;

m∠QTR + m∠RTS = 90°

m∠QTR = (2·y + 12)°

m∠RTS = (5·x)°

Therefore; (2·y + 12)° + (5·x)° = 90°

(5·x)° = 90° - (2·y + 12)°

x = (90° - (2·y + 12)°)/5

x = (90° - (2 × 24 + 12)°)/5 = 6

x = 6

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I don’t see answer
Pleas tell answer thanks

Answers

you have to tell the question first

Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as , and they will reduce the.

first blank having: Tax credits
or
tax reductions

second having: amount of taxable income
or
amount of tax owned

Answers

Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income.

The first blank should be filled with "tax reductions" and the second blank should be filled with "amount of taxable income."

The first blank should be filled with "tax reductions". Tax reductions reduce the amount of income that is subject to tax, whereas tax credits directly reduce the amount of tax owed.The second blank should be filled with "amount of taxable income." Business expenses and charitable donations are deductible from taxable income, meaning they reduce the amount of income that is subject to tax. By reducing the taxable income, the amount of tax owed will also be reduced.

Hence, the correct statement would be: "Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income."

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consider the following computer output. source df ss ms f p-value factor ? 117.4 39.1 ? ? error 16 396.8 ? total 19 514.2 a. how many levels of the factor were used in this experiment? b. how many replicates did the experimenter use? c. fill in the missing information in the anova table. d. what conclusions can you draw about differences in the factor-level means?

Answers

The computer output provided.

It seems that the experimenter used one factor in the experiment.

It is unclear how many levels of the factor were used, as this information is missing from the output.


The total number of observations in the experiment, which is not given. Estimate the number of replicates based on the degrees of freedom for error, which is 16.

Assuming that each replicate had equal sample size, we can calculate the total number of observations as follows:
[tex]Total observations = (df for error + df for factor) + 1[/tex]
[tex]Total observations = (16 + df for factor) + 1[/tex]
[tex]Total observations = 17 + df for factor[/tex]
Since we do not know the value of df for factor, we cannot determine the exact number of replicates.

We can say that the experimenter used at least 17 observations in total.
To fill in the missing information in the ANOVA table, we need to know the number of levels of the factor and the number of replicates. Assuming that there were k levels of the factor and n replicates, we can calculate the following:
[tex]SS factor = MS factor \times (n - 1) \times k[/tex]

[tex]MS factor = SS factor / (k - 1)[/tex]
[tex]F = MS factor / MS error[/tex]

P-value = probability of obtaining an F-statistic as extreme as the observed value, assuming the null hypothesis is true
Without knowing the values for k and n, we cannot fill in the missing information in the ANOVA table.
Finally, based on the information given, we cannot draw any conclusions about differences in the factor-level means. We need more information about the experiment, such as the hypothesis being tested, the nature of the factor, and the specific levels being compared, in order to make any meaningful conclusions.

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1. Julia wants to buy a parcel of land in Montana so that she can raise bison. If the minimum down
payment on the land is $25,000, find the amount she must invest now at 8%, compounded quarterly,
to have her down payment in 4 years. Use the table of values below.

$16,542.98
$17,230.91
$19.235.12
O$18.211.25

Answers

Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

How did we get this value?

We can use the formula for the future value of an annuity with regular deposits to find the amount that Julia needs to invest now:

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

where:

P = quarterly deposit

r = annual interest rate = 8%

n = number of compounding periods per year = 4 (quarterly)

t = number of years = 4

FV = future value of the annuity (i.e. the down payment)

We want to solve for P, which is the amount Julia needs to invest each quarter. Rearranging the formula, we get:

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

Substituting the given values, we get:

P = 25,000 * (0.08/4) / ((1 + 0.08/4)^(4*4) - 1)

P ≈ $4,901.43

So Julia needs to invest $4,901.43 every quarter for 4 years to have a down payment of $25,000. Checking the table of values, we see that the closest answer is $4,542.98, so that is the amount she needs to invest.

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When the angle of elevation of the sun is 65°, a building casts a shadow that is 6m long. What is the height of the building to the nearest tenth of a meter?

Answers

The height of the building is approximately 18.6 meters to the nearest tenth of a meter.

What is trigonometry?

Trigonometry is one of the most significant branches of mathematics, with numerous applications in a wide range of fields. The study of the relationship between the sides and angles of a right-angle triangle is the focus of the "Trigonometry" branch.

We can use trigonometry to solve this problem. Let's draw a diagram:

In the diagram, h is the height of the building, d is the distance from the building to the tip of the shadow, and the angle of elevation of the sun is 65°.

We can see that the height of the building and the distance to the tip of the shadow form a right triangle, and the angle of elevation is the angle opposite the height of the building. Therefore, we can use the tangent function to find the height of the building:

tan(65°) = h/d

Multiplying both sides by d, we get:

h = d tan(65°)

We know that the length of the shadow is 6 m, so d = 6. Substituting this into the formula, we get:

h = 6 tan(65°)

Using a calculator, we get:

h ≈ 18.6

Therefore, the height of the building is approximately 18.6 meters to the nearest tenth of a meter.

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In how many ways can two variables be chosen from X1, X2, S1, S2, S3 and assigned the value 0? ways (Type a whole number.)

Answers

There are 10 ways to choose two variables from X1, X2, S1, S2, S3 and assign the value 0.

To choose two variables from X1, X2, S1, S2, and S3, and assign the value 0, you can use the combination formula. In this case, there are 5 variables (n=5) and you want to choose 2 (r=2). The combination formula is C(n, r) = n! / (r!(n-r)!).

Applying the formula:
C(5, 2) = 5! / (2!(5-2)!)
C(5, 2) = 120 / (2! * 3!)
C(5, 2) = 120 / (2 * 6)
C(5, 2) = 120 / 12
C(5, 2) = 10

So, there are 10 ways to choose two variables from X1, X2, S1, S2, and S3, and assign the value 0.

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jordan drove 378 miles in 7 hours. if he can keep the same pace, how long will it take him to drive 1,188 miles?

Answers

Jordan would take 22 hours to drive 1,188 miles at the same speed he drove 378 miles in 7 hours.

How to find the time that Jordan take to drive 1,188 miles?

We can use the formula:

time = distance / speed

where speed is constant, to find the time it would take Jordan to drive 1,188 miles.

The speed at which Jordan drove can be calculated as:

speed = distance / time

where distance is 378 miles and time is 7 hours.

speed = 378 / 7 = 54 miles per hour

Now, we can use the speed to find the time it would take to drive 1,188 miles:

time = distance / speed = 1,188 / 54 = 22 hours

Therefore, if Jordan can maintain the same pace, it would take him 22 hours to drive 1,188 miles.

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Write the number in numerical form:
Six hundred six and four thousand, three hundred fifteen ten-thousandths

Answers

The number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

Writing the number in numerical form:

Given that

Six hundred six and four thousand, three hundred fifteen ten-thousandths

To write this number in numerical form, we need to add the values of each of its digits:

6 × 100 + 0 × 10 + 6 × 1 + 4 × 0.1 + 3 × 0.01 + 1 × 0.005 = 606.4315

Therefore, the number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

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If the area of an equilatral is 81 to the root of 3 cm squarefind the perimeter of the triangle

Answers

The perimeter of the equilateral triangle with an area of 81√3 cm² is 54 cm.

An equilateral triangle is a type of triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.

Let's denote the side length of the equilateral triangle by "a".

The formula for the area of an equilateral triangle is

Area = (√3/4) × a^2

We are given that the area is 81√3 cm², so we can set up the equation

81√3 = (√3/4) × a^2

Solving for "a", we get:

a = 18 cm

Now that we know the side length, we can find the perimeter by multiplying it by 3 (since it's an equilateral triangle):

Perimeter = 3a = 3 × 18 cm = 54 cm

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In ΔTUV, u = 380 inches, � m∠V=151° and � m∠T=25°. Find the length of t, to the nearest 10th of an inch

Answers

The length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

To determine the length of t in triangle TUV, we can use the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.

In this case, we have:

- u = 380 inches (the length of side u)

- m∠V = 151° (the measure of angle V)

- m∠T = 25° (the measure of angle T)

We need to find the length of side t.

Using the law of sines, we can set up the equation;

sin(25°) / t = sin(151°) / 380

To solve for t, we can cross multiply and then divide by sin(25°):

t = (380 x sin(25°)) / sin(151°)

t ≈ 85.6 inches

Therefore, the length of t, to the nearest tenth of an inch, is approximately 85.6 inches.

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an assumption of the linear model of communication is the belief that _____.

Answers

The communication is a one-way process in which a message is conveyed from a sender to a receiver is one of the assumptions made by the linear model of communication.

The straightforward linear model of communication presents communication as a process with distinct beginnings and endings.

But this model ignores the fact that communication is frequently a more complex and involved process that needs context, feedback, and a variety of channels.

The linear model presumes that the message is clearly understood by the recipient and that it is received by the recipient free from distortion or interference.

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An assumption of the linear model of communication is the belief that communication is a one-way process where a sender transmits a message to a receiver through a channel. This model assumes that communication is a linear process where the sender encodes a message, which is then sent through a channel to the receiver who decodes the message.

In the linear model, the sender encodes a message, sends it through a channel, and the receiver decodes the message. This model does not account for feedback or interaction between the sender and receiver, assuming that communication is a straightforward and direct transmission of information without any complexities or interruptions.

This model assumes that there is little to no feedback or interaction between the sender and receiver, and that the message is transmitted and received accurately without any distortion. However, this assumption is often criticized for oversimplifying the complex nature of communication and ignoring the role of context and feedback in the communication process.

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Please someone help me with this

Answers

Answer:

9(x+y) and 9x+9y are correct

Step-by-step explanation:

Ex: 9(3+5) = 27 and 9(3)+9(5)=27

they both would give you the same answers if you used the same numbers how i did in the example

not good at explaining it i tried my best ;)

when solving an oblique triangle given three sides, use the ---select--- form of the law of cosines to solve for an angle.

Answers

When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.

When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.

The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.

The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.

The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:

⇒ c² = a² + b² - 2ab × cos(C),

To solve for an angle, we would rearrange the equation to find the cosine of the angle,

⇒ Cos(C) = (a² + b² - c²)/(2ab),

Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,

⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),

This helps us to find the measure of angle C, depending on the units used in the original triangle sides.

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The given question is incomplete, the complete question is

When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.

we want to estimate a population mean using a 99% confidence interval and a random sample of 35 individuals. what is the critical t-score?

Answers

The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

How to estimate a population mean using a 99% confidence interval?

To estimate a population mean using a 99% confidence interval and a random sample of 35 individuals, you need to find the critical t-score.

Step 1: Determine the degrees of freedom. For a sample of 35 individuals, the degrees of freedom (df) = sample size - 1 = 35 - 1 = 34.

Step 2: Find the critical t-score using a t-table or an online calculator. For a 99% confidence interval and 34 degrees of freedom, the critical t-score is approximately 2.733.

Your answer: The critical t-score for estimating the population mean using a 99% confidence interval and a random sample of 35 individuals is approximately 2.733.

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in a shipment of 15 room air conditioners, there are 5 with defective thermostats. two air conditioners will be randomly selected (without replacement) and inspected. what is the probability that the selected two are both defective? round your answer to four decimal places.

Answers

The probability of both selected room air conditioners are defective is equal to 0.0952 rounded to four decimal places.

Total number of room air conditioners in shipment = 15

Number of defective room air conditioners = 5

The probability of the first air conditioner being defective is 5/15.

Since there are 5 defective air conditioners out of a total of 15.

After one air conditioner has been inspected,

There will be 4 defective air conditioners left out of a total of 14.

The probability of the second air conditioner also being defective, given that the first one was defective, is 4/14.

Probability of both air conditioners being defective.

Multiply probability of first air conditioner being defective by probability of second air conditioner being defective.

Given by first one was defective,

P(both defective) = (5/15) x (4/14)

Simplifying this expression ,

P(both defective) = 2/21

Therefore, the probability that the selected two air conditioners are both defective is 0.0952 rounded to four decimal places.

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you are thinking of combining designer whey and muscle milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates. how many servings of each supplement should you combine in order to meet your requirements?

Answers

We need approximately 12 servings of Designer Whey and 2 servings of Muscle Milk to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

Let x be the number of servings of Designer Whey and y be the number of servings of Muscle Milk needed to obtain a 7-day supply that provides exactly 262 grams of protein and 54 grams of carbohydrates.

From the information given, we know that each serving of Designer Whey provides 20 grams of protein and 3 grams of carbohydrates, and each serving of Muscle Milk provides 16 grams of protein and 9 grams of carbohydrates.

Therefore, we can set up the following system of equations:

20x + 16y = 262

3x + 9y = 54

To solve for x and y, we can use any method of solving a system of equations. For example, we can use substitution:

From the second equation, we can solve for x in terms of y:

x = (54 - 9y)/3 = 18 - 3y

Substituting this into the first equation, we get:

20(18 - 3y) + 16y = 262

Simplifying, we get:

80y = 182

Solving for y, we get:

y = 2.275

Substituting this into the equation x = 18 - 3y, we get:

x = 12.175

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One rectangle is "framed" within another. Find the area of the shaded region if the "frame" is 2 units wide.

Answers

The area of the shaded region with dimensions length=5 units and width=2 units is 10 units².

What is area?

It is the extent to which a flat (2-D) figure, surface, or shape of an object occupies all available space.The area of a flat, two-dimensional figure is the area that is enclosed or covered by the boundary of the figure. Additionally, it is the quantity of unit squares that completely cover a closed figure's surface. Square measurements of area include sq. mm, cm2, and m2. Additionally, it describes the area located inside a closed shape's border or limit.

Area of rectangle = length x width

Given dimensions of outer rectangle:length=9 units & width=6 units

Also given that there is a width of frame is 2 units between outer & inner rectangle on all its boundaries.

To find the area of shaded inner rectangle, we need its dimensions.

Length=length of outer rectangle- 2 times width of frame

           =9 - 2(2)

           =9-4

           =5 units

Widthth=width of outer rectangle- 2 times width of frame

           =6 - 2(2)

           =6-4

           =2 units

Area of shaded portion= area of rectangle

                                      = L x W

                                      = 5 x 2

                                      =10 units²

Area of shaded portion=10 units²

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an open box will be made by cutting a square from each corner of a 16-inches by 10-inches piece of cardboard and then folding up the sides. what size square should be cut from each corner in order to produce a box of maximum volume? what is that maximum volume?

Answers

The size of the square to cut is 5/3 inches and the maximum volume of the box is 266.67 cubic inches.

To find the size of the square to cut and the maximum volume, we can follow these steps:

Let's call the length of each side of the square to be cut x inches. So the dimensions of the base of the box would be (16-2x) inches by (10-2x) inches.

The height of the box would be x inches since we are folding up the sides.

The volume of the box can be found by multiplying the length, width, and height: V = (16-2x)(10-2x)x.

To find the maximum volume, we can take the derivative of V with respect to x and set it equal to zero, since the maximum volume occurs at a critical point.

After taking the derivative and simplifying it, we get the equation 24x^2 - 520x + 1600 = 0.

Solving this quadratic equation, we get x = 5/3 or x = 20/3. Since x must be less than 5 (the length of the shorter side), the only feasible solution is x = 5/3 inches.

Plugging this value of x back into the equation for the volume, we get V = (16-2(5/3))(10-2(5/3))(5/3) = 266.67 cubic inches.

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Find the Length of the Arc ^PQ and round your answer to the nearest Hundredth place.

Please help

Answers

The length of an arc is PQ is 9.42 units.

How to find the length of an arc?

The length of an arc is PQ can be found as follows:

length of an arc = ∅ / 360 ×2πr

where

∅ = central angler = radius of the circle

Therefore,

∅ = 60 degrees

r = 9 units

length of the arc  = 60 / 360 × 2 × 3.14 × 9

length of the arc =  1 / 6 × 56.52

length of the arc =  56.52 / 6

length of the arc  = 9.42 units

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Imma give h Brainliest!!!

Answers

Answer:

Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.

Triangle on the left

180 - 90 - 42 = 48

Triangle on the right:

180 - 90 - 48 = 42

Since the angles measurements are the same, the triangles are similar.

Helping in the name of Jesus.

Answer: Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The two triangles have the same angles, so they are similar by the Angle-Angle Theorem.

the weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. refer to exhibit 6-3. what percent of players weigh between 180 and 220 pounds?

Answers

The approximately 57.62% of football players weigh between 180 and 220 pounds.

How to find percent of players weigh between 180 and 220 pounds using standard normal distribution?

Since the weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds, we can use the standard normal distribution to find the proportion of players who weigh between 180 and 220 pounds.

We first need to convert the weights to standard units by using the formula:

z = (x - mu) / [tex]\Sigma[/tex]

where:

x = the weight we want to convert to standard units

mu = the mean weight of the players (200 pounds)

sigma = the standard deviation of the players' weights (25 pounds)

For the lower end of the range, we have:

z1 = (180 - 200) / 25 = -0.8

For the upper end of the range, we have:

z2 = (220 - 200) / 25 = 0.8

Now, using a standard normal distribution table or calculator, we can find the proportion of players between z1 and z2:

P(-0.8 < z < 0.8) = 0.7881 - 0.2119 = 0.5762

Therefore, approximately 57.62% of football players weigh between 180 and 220 pounds.

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