Pls help question in photo

Pls Help Question In Photo

Answers

Answer 1

Therefore , the solution of the given problem of expressions comes out to be 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

Expression : What is it?

With shifting variables, estimates that mix joining, deactivating, and random division should be made. They could accomplish the following if they united: A math problem, some facts, and software. Formulas, parts, and arithmetic operations like additions, subtractions, omissions, and groupings can all be found in a declaration of truth. Both words and sentences can be evaluated and analysed.

Here,

The distributive property of multiplication must be used to multiply the two factors jointly in order to simplify the expression:

=> (x-1)(3x²-5x-3) = x(3x²) - x(5x) - x(3) - 1(3x²) + 1(5x) + 1 (3)

Condensing each term:

=> 3x³ - 5x²- 3x - 3x² + 5x + 3

=> 3x³ - 8x²+ 2x + 3

Therefore, 3x³ - 8x²+ 2x + 3 is the abbreviated expression in standard form.

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Related Questions

-5 x blank equals 35

Answers

Answer:

-7

Step-by-step explanation:

A negative number times a negative number is positive. Because -5 is negative and 35 is positive the other factor must be negative as well.

5 x 7 = 35

So, -5 x -7 also equals 35

Question 2) Suppose you work for the Cheapo Coffee company and are tasked with studying their coffee shops around the country. You are interested in studying the number of cups of coffees sold per day at different cheapo coffee shops. To study this you randomly select 4 major cities from across the US. You visit each oh the cheapo coffee stores in these cities for a day and record the value is the number of customers they serve. You ultimately visit 17 shops and get the following data.
35, 43, 48, 52, 58, 67, 73, 85, 106, 125, 136, 174, 199, 213, 274, 351
a. What is the population in this question?
b. What is the sample in this question

Answers

a. The population in this question is all the Cheapo Coffee stores around the country.

b. The sample in this question is the 17 coffee shops that were visited and their daily sales data was recorded.

In statistics, a population is the entire group of individuals, items, or events that we are interested in studying. In this case, the population is all the Cheapo Coffee stores across the country, and we are interested in studying the number of cups of coffee sold per day at these stores.

However, it is often impractical or impossible to study the entire population, so we select a subset of the population, which is called a sample.

The sample is a representative subset of the population that we study to draw conclusions about the population as a whole. In this case, the sample consists of 17 Cheapo Coffee stores that were randomly selected from four major cities in the US, and the number of cups of coffee sold per day was recorded for each store.

We can use the data from the sample to estimate the average number of cups of coffee sold per day at all Cheapo Coffee stores across the country, which is the parameter of interest in this study.

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Twelve students are going to listen to a talk. The group consists of 3 chemistry majors, 2 business majors, 3 political science majors and 4 journalism majors. In how many ways can these students sit in their twelve seats if they must be grouped by major?

Answers

There are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

How to find  how many ways can these students sit in their twelve seats if they must be grouped by major

There are four groups based on major: chemistry, business, political science, and journalism. We need to find the number of ways the 12 students can sit in their assigned seats while maintaining the grouping by major.

We can approach this problem by first considering the number of ways each group can be seated separately, and then multiply the results together to get the total number of arrangements.

For the chemistry group, there are 3 students who can be seated in any order.

For the business group, there are 2 students who can be seated in any order.

For the political science group, there are 3 students who can be seated in any order.

Finally, for the journalism group, there are 4 students who can be seated in any order.

Therefore, the total number of arrangements for the 12 students is:

3! * 2! * 3! * 4! = 6 * 2 * 6 * 24 = 1,728

Therefore, there are 1,728 ways for the 12 students to sit in their assigned seats while maintaining the grouping by major.

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simplify the expression if m = -7 and n = 4: 5m + 9n

Answers

Answer:

If m = -7 and n = 4, then we can substitute these values into the expression:

5m + 9n = 5(-7) + 9(4)

= -35 + 36

= 1

Therefore, 5m + 9n simplifies to 1 when m = -7 and n = 4.

Step-by-step explanation:

19. What is the length of side JN? (Round your answer to the nearest tenth.) 65 39 53

Answers

We οbtain JN  44.3 by rοunding tο the nearest tenth, Length οf side JN is rοughly  44.3 units lοng as a result. Therefοre 44.3 is the right respοnse.

What is the measurement οf a triangle's side?  

The sides οf a triangle are straight lines that are jοined by the three vertices οf the triangle. In οther wοrds, we can say that the sides οf a triangle are line segments that meet each οther at the vertices οf the triangle.

The sides οf a right-angled triangle can be fοund οut by using variοus methοds like the Pythagοras theοrem οr by using the perimeter οf the triangle. In case sοme οf the angles and οther side lengths are given, we can use the law οf cοsines οr the law οf sines tο find the lengths οf the sides οf a triangle.

Law of sines

sin(∠A)/a = sin(∠B)/b = sin(∠C)/c

Therefore,

39/sin(53°) = JN/sin(65°)

JN = (39×sin(65°))/sin(53°)

JN = 44.3

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4.02 Lesson Check Arithmetic Sequences (9)

Answers

Answer:

a₉ = - 24

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁ = 8 and d = - 4 , then

a₉ = 8 + (8 × - 4) = 8 + (- 32) = 8 - 32 = - 24

Answer:

Tn = a + (n - 1)d

T9 = 8 + (9 - 1) × -4

T9 = (8 + 8) × -4

T9 = 16 × -4

T9 = -64

It is an arrangement of things in a definite order

Answers

A sequence is an ordered list of elements or objects that follows a specific pattern or rule, where the order of the terms is important.

A sequence is an ordered list of numbers, symbols, or other mathematical objects. The order in which the elements appear is important and determines the identity of the sequence. For example, consider the following two sequences:

1, 3, 5, 7, 9

3, 5, 1, 7, 9

The first sequence consists of odd numbers in ascending order, while the second sequence consists of the same numbers but in a different order. These two sequences are different because the order of the terms is different.

Sequences can have different patterns or rules that determine the order of the terms. For example, the sequence of Fibonacci numbers, which is a famous sequence in mathematics, has the following pattern:

1, 1, 2, 3, 5, 8, 13, 21, 34, ...

Each term in the sequence (starting with the third term) is the sum of the two preceding terms.

This pattern continues indefinitely, creating a sequence that has a distinct pattern and order.

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What is the arrangement of objects in a definite order called?

town A is 60 km from town B and 61km from town C a road connects town B and C directly find the length of the road for class 7 ncert

Answers

Answer:Using the triangle inequality, we can conclude that the distance between towns B and C must be less than 121 km (the sum of the distances between towns A and B, and between towns A and C).

To find the exact length of the road connecting towns B and C, let's use the Pythagorean theorem.

Let x be the length of the road connecting towns B and C. Then we have:

x^2 = 61^2 + 60^2

x^2 = 3721 + 3600

x^2 = 7321

x ≈ 85.6 km

Therefore, the length of the road connecting town B and C is approximately 85.6 km.

Step-by-step explanation:

There is a 50% chance that a newborn baby will be a boy. For families with four children, what is the probability that all the children are boys?
Select one:
A. 0.2512 B. 0.0625 C. 0.3754 D. 0.1587

Answers

The option B, 0.0625, is the correct answer.


The probability that all children are boys is 1/2 × 1/2 × 1/2 × 1/2 = 1/16. The probability of the event is 0.0625. The probability that all the children are boys is 0.0625.Therefore, option B, 0.0625, is the correct answer.

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The number of bacteria in a culture is given by the function

0. 3t

n(t) = 920e

where t is measured in hours.

(a) What is the relative rate of growth of this bacterium population?

Your answer is

percent

(b) What is the initial population of the culture (at t=0)?

Your answer is

(c) How many bacteria will the culture contain at time t=5?

Your answer is

Answers

a) The continuous rate of growth of this bacterium population is 45%

b) Initial population of culture at t = 0 is 950 bacteria

c) number of bacterial cultures contain at t = 5 is 9013 bacteria

The number of bacteria in a culture is given by the function n(t) =950[tex]e^{0.450t}[/tex] Where t is measured in hours

what is the continuous rate of growth of this bacterium population

The number of bacteria in a culture is given by

n(t) = 950[tex]e^{0.45t}[/tex]

a) rate of growth is

Bacteria growth model N(t) = no[tex]e^{rt[/tex]

Where r is the growth rate

hence r = 0.45

             = 45%

b) Initial population of culture at t = 0

n(0) = 950[tex]e^0[/tex]

      = 950

      = 950 bacteria

c) number of bacterial culture contain at t = 5  

n(5)      = 950[tex]e^{0.45*5}[/tex]

     = 9013.35

     = 9013 bacteria

the complete question is-

The number of bacteria in a culture is given by the function n(t) =950e^0.45t Where t is measured in hours A) what is the continuous rate of growth of this bacterium population? Your answer is __ percent B) what is the initial population of the culture (at t=0) your answer is __ C) how many bacteria will the culture contain at time t=5 ? Your answer is __ Round to the nearest bacteria

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I seriously cannot figure this out please help me :( IT'S SO LATE PLEASE

Answers

Tia's statement that the graph is a x^5 function is correct

How to determine who is correct

The statements from the question are:

Tia = x^5 functionMarcus = x^4 function

The zeros and the multiplicities in the format (zero, multiplicity) from the question are (-3, 1), (-1, 2), (2, 1) and (3, 1)

The equation of the polynomial can be expressed as

P(x) = (x - zero)^multiplicity

When the zeros and the multiplicities are substituted, we have

P(x) = (x + 3)(x - 3)(x - 2)(x + 1)^2

Expand

P(x) = (x^2 - 9)(x - 2)(x + 1)^2

When evaluated, we have

P(x) = x^5 - 12x^3 - 2x^2 + 27x + 18

The above is a x^5 function

Hence, Tia is correct

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Which equation represents a line which is parallel to the line y = − 2/3x − 3

Answers

Answer:

Any line with a slope of -2/3 that doesnt have an intercept of -3

Step-by-step explanation:

y = − 2/3x − 3 is written in slope-intercept form y = mx + b, where m is the slope, and b is the y intercept

What your looking for is a line with the same -2/3 slope

Important! If a line has the same slope AND intercept, then they are identical, not parallel

please help if you can

Answers

Using variation, the model for F = 42(m/p)

What do you mean by variation?

There is a direct variation between the two variables whenever one quantity directly influences the other, such as when one quantity increases relative to the other and vice versa. There is a connection between two variables when one of them is a constant multiple of the other. Because of their immediate connection, the two variables are referred to as directly proportional.

Inverse variation establishes a proportionality between two quantities that are inversely related. There are two separate proportionalities. They are the direct variation and inverse variation. The two quantities are said to be directly proportional if an increase or decrease in one generates an equal increase or decrease in the other. In an inverse variation, on the other hand, one quantity increases while the other falls.

Now as F is directly proportional to m and inversely to p, so we can form a model as:

F = 42(m/p)

So that F=36 when m =6 and p =7.

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A bag contains red, blue, and green tokens. Don randomly
chooses one token from the bag, records the color, and
replaces the token before choosing another token. He
performs the experiment 100 times. The final tally of the
results is shown in the table below.

Answers

Answer:

The correct probability is 16/100, or 4/25.

Unit 8 Right Triangles & Trigonometry Homework 3: similar Right triangles & geometric mean

Answers

In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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How to do?
‍♀️‍♀️‍♀️‍♀️‍♀️
Can anyone give me the answer?!

Answers

x + 3x + 2x = 180°

Being straight angle...

6x = 180°

[tex]x = \frac{180}{6} \\ [/tex]

x = 30°

you deposit 4,000 in an account earning 5% interest compounded
continuously. Write an equation that model this situation.
A(t)=

Answers

The interest compounded equation to model the given situation is A(t) = 4000[tex]e^{0.05t}[/tex].

To model the given situation, the interest compounded can be written as the given equation of:

A(t) = A0e^(rt)

Where:

A(t) is the amount of money after t years

A0 is the initial amount of money, in this case,

r is the interest rate expressed as a decimal

t is the time in years that the money is invested.

From the case, we know that:

Initial deposit = $4,000

Interest rate = 5%

Time period = t (undetermined)

So, substituting the values given in the problem, the equation to model the given situation is:

A(t) = A0e^(rt)

A(t) = 4000e^(0.05t)

Therefore, A(t) = 4000e^(0.05t) is the required equation that models the given situation.

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i sell a car for £6502 making a 22% profit. how much did i buy it for originally

Answers

Answer:

£5329.51

Step-by-step explanation:

Knowing that £6502 is the price with 22% profit, we can understand that £6502 is 122% of the original price meaning that the individual would have had to multiply their original value by 1.22 to get £6502!

To find our answer we, therefore, have to do the inverse...

6502 ÷ 1.22 = 5329.5082

Turning the value into money we round to 2d.p leaving our answer as...

£5329.51

Hope this helps, have a lovely day! :)


A gardener will use up to 250 square feet for planting flowers and vegetables. She wants the area used for vegetables to be at least four times the area used for
flowers. Let x denote the area (in square feet) used for flowers. Let y denote the area (in square feet) used for vegetables. Shade the region corresponding to all
values of x and y that satisfy these requirements.

Answers

The inequality equation that can be used to solve this problem is x + y ≤ 250 and y ≥ 4x

What is an equation?

An equation is an expression that shows the relationship between numbers and variables using mathematical operators such as addition, subtraction, exponent, multiplication and division.

Let x denote the area (in square feet) used for flowers and y denote the area (in square feet) used for vegetables.

A gardener will use up to 250 square feet for planting flowers and vegetables, hence:

x + y ≤ 250    (1)

She wants the area used for vegetables to be at least four times the area used for flowers. Hence:

y ≥ 4x     (2)

Plotting both equations using geogebra, the solution is the darker region.

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Find d. Round to the nearest tenth.

Answers

Answer:

d=50.3

Step-by-step explanation:

cos(29)/1=44/d

cos29d/cos29=44/cos29

d=50.31

d=50.3

I dont know how to do this

pls answer if u know with simple working

Answers

Answer:

17,20,23...

Step-by-step explanation:

you just have to add 3 that's how the pattern works.

Diego has 90 songs on his playlist. How many songs are there for each genre?

Answers

Answer: Diego's playlist has 36 songs in rock genre, 9 songs in Country genre, 27 songs in hip hop genre and 24 songs in electronica genre.

Based on the number of songs Diego has and the proportion of the genres, Diego's song classification is:

Rock = 36 songsCountry = 9 songsHip Hop = 27 songsElectronica = 18 songs

The number of songs from a particular genre is:

[tex]= \text{Total number of songs}\times\text{Percentage of genre}[/tex]

Rock:

[tex]= 40\% \times 90[/tex]

[tex]\bold{= 36 \ songs}[/tex]

Country:

[tex]= 10\% \times 90[/tex]

[tex]\bold{= 9 \ songs}[/tex]

Hip hop:

[tex]= 30\% \times 90[/tex]

[tex]\bold{= 27 \ songs}[/tex]

Electronica:

[tex]= (100\% - 40\% - 10\% - 30\%) \times 90[/tex]

[tex]\bold{= 18 \ songs}[/tex]

In conclusion, there are various genres on Diego's phone.

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Complete Question:

Diego has 90 songs on his playlist. How many songs are there for hip-hop?

40% rock

10% country

30% hip-hop

The rest is electronica

(10 POiNTS!!!)Find the value of x that makes this a true statement.
−3(x − 100) = −5(x − 100) + 6

Answers

Answer: x = 100

Step-by-step explanation:

Can you answer all of these please

Answers

The area of the composite figures are:

1: 106.28 sq. yd.

2: 79.27 sq. in.

3: 64.28 sq. m.

4: 44.82 sq. ft.

5: 406 sq. cm.

6: 629.46 sq. km.

How to find the area of a composite figure?

To find the area of a composite figure, you can break it down into simpler shapes such as triangles, rectangles, circles, etc. and then find the area of each individual shape and add them together.

No. 1

Area = area of semicircle + area of rectangle + area of semicircle

Area = (1/2 * πr²) + (L*W) + (1/2 * πr²)

r = 6/2 = 3 yd, L = 13 yd and W = 6 yd

Area = (1/2 * π*3²) + (13*6) + (1/2 * π*3²)

Area = 14.14 + 78 + 14.14

Area = 106.28 sq. yd.

No. 2

Area = area of semicircle + area of triangle

Area = (1/2 * πr²)  + (1/2 *base* height)

r = 10/2 = 5 in, base = 10 in and height = 8 in

Area = (1/2 * π * 5²)  + (1/2 * 10 * 8)

Area = 39.27 + 40

Area = 79.27 sq. in.

No. 3

Area = area of square + area of semicircle + area of semicircle

Area =  L² + (1/2 * πr²) +  (1/2 * πr²)

L = 6 m,  r = 6/2 = 3 m

Area =  6² + (1/2 * π * 3²) +  1/2 * π * 3²)

Area =  36 + 14.14 + 14.14

Area = 64.28 sq. m.

No. 4

Area = area of semicircle + area of rectangle

Area =  (1/2 * πr²) + (L * W)

r = 5/2 = 2.5 ft, L = 7 ft and W = 5 ft

Area =  (1/2 * π * 2.5²) + (7 * 5)

Area =  9.82 + 35

Area = 44.82 sq. ft.

No. 5

Area = area of triangle + area of rectangle

Area =  (1/2 * base * height) + (L * W)

base = 10cm, height = 14 cm, L = 24 cm and W = 14 cm

Area =   (1/2 * 10 * 14) + (24 * 14)

Area =  70 + 336

Area = 406 sq. cm.

No. 6

Area = area of semicircle + area of triangle

Area =   (1/2 * πr²) + (1/2 * base * height)

r = 26/2 = 13 km, base = 28 km and height = 26 km

Area =   (1/2 * π * 13²) + (1/2 * 28 * 26)

Area =  265.46 + 364

Area = 629.46 sq. km.

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The bar graph shows the results of rolling a number cube 300 ​ times. How does the experimental probability of rolling a number greater than 1 compare with the theoretical probability?


The experimental probability of rolling a number greater than 1 is __%, which is close to the theoretical probability of __%

Answers

The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

What is probability?

Calculating the likelihood that an event will occur or a statement will be true is the subject of probability theory, a branch of mathematics. A risk is a number between 0 and 1, where 1 denotes certainty and a probability of about 0 denotes the likelihood that an event will occur. The likelihood that an event will take place is mathematically expressed as probability. Probabilities can also be expressed as percentages ranging from 0% to 100% or as integers between 0 and 1. the proportion of equally plausible possibilities that actually happen in relation to all other outcomes when a specific event occurs.

The bar graph displays how many times a number cube was rolled along with the outcome. The graph shows that the number cube was rolled 300 times in total, yielding the number larger than 1 200 times.

Experimental probability is calculated as follows: 200/300 = 0.6667, or 66.67%, where experimental probability = (number of times greater than 1)/(total number of rolls)

Theoretical probability is calculated as follows: 5/6 = 0.8333 or 83.33% (number of possibilities greater than 1) / (total number of possible outcomes).

The experimental likelihood of rolling a number greater than 1 is 66.67%, which, according to the calculations above, is close to the theoretical probability of 83.33%.

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Sooo my friend sent me this and I’ve been puzzled, I think there are no correct options but need someone’s opinion. Any nerds like me out there?

Answers

Answer: first off i am not a nerd ur just a dummyboi second  this is simple math grade 4 really the answer is 24

Step-by-step explanation:

In a cube that is 3x3, 19 cubes can be seen. 8 are hidden.

In a cube that is 4x4, 37 cubes can be seen. 27 are hidden.

In a cube that is 5x5, 61 cubes can be seen. 64 are hidden.

In a cube that is 6x6, 91 cubes can be seen. 125 are hidden.

19+8=27 if ur making a 3x3 cube answer is 24

A diet plan claims that women have a mean weight of 145 lbs. Assume that the weights of women have a standard deviation of 30. 86 lb. A sample of 40 weights of women has a mean weight of 153. 2 lb. Find the P-value and, using a 0. 05 significance level, state the conclusion about the null hypothesis

Answers

The null hypothesis is that the mean weight of women is 145 lbs.The P-value is 0.0145. At a 0.05 significance level, the null hypothesis can be rejected. This suggests that the mean weight of women is not 145 lbs.

The null hypothesis is that the mean weight of women is 145 lbs. To test the hypothesis, we need to calculate the P-value. The mean of the sample of 40 weights is 153.2 lbs, with a standard deviation of 30.86 lb. The P-value is calculated using a z-score formula which is (153.2-145)/(30.86/sqrt(40)) = 0.0145. Since the P-value is less than 0.05, this suggests that the mean weight of women is not 145 lbs. Therefore, at a 0.05 significance level, the null hypothesis can be rejected.

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Matthew has an investment that is now worth $21 537.82. Find the original amount
he invested if he has had the money invested at 2.5% per month for 3 years.

Answers

The answer would be $179.48183

Find the length of AC in this right-angled triangular
prism.
Give your answer in centimetres (cm) to 1 d.p.
44 cm
A
E
42 cm
B
F
57 cm
с

Answers

The length of AC in this right-angled triangular prism is approximately 60.66 cm.

What is Pythagoras theorem?

For right angle triangle,

Hypotenuse² = Height²+Base²

However, we can use the Pythagorean theorem to find the length of AC if we know the lengths of AE and EC and ED.

If we assume that face AEC is the base of the prism and the right angle is at vertex E, then we can use the Pythagorean theorem to find the length of AC:

AC² = AE²+ EC²

We are given that AE = 43 cm, but we don't know the length of EC. However, we can use the fact that the base of the prism is a rectangle to find EC. Since opposite sides of a rectangle are equal, we have:

EC = 51 cm and ED = 45 cm

Substituting this into the equation above, we get:

AC² = 43² + 51²

AC² = 3680

AC ≈ 60.66 cm (to 1 decimal place)

Therefore, the length of AC in this right-angled triangular prism is approximately 60.66 cm.

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Correct question is "Find the length of AC in this right-angled triangular prism. Give your answer in centimetres (cm) to 1 d.p.

Base is ED 51 cm and height is AE 43 cm of the prism."

Consider the t distribution with 5 degrees of freedom.

(a) What proportion of the area under the curve lies to the right of t = 2. 015?

(b) What proportion of the area lies to the left of t = −3. 365?

(c) What proportion of the area lies between t = –4. 032 and t = 4. 032?

(d) What value of t cuts off the upper 2. 5% of the distribution?

Answers

The cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

(a) 0.974

(b) 0.998

(c) 0.996

(d) 2.571

(a) To find the proportion of the area under the curve to the right of t = 2.015, we first calculate the cumulative probability of t = 2.015 from the t-distribution table. The cumulative probability of t = 2.015 is 0.974, which means that 0.974 or 97.4% of the area under the curve lies to the right of t = 2.015.

(b) To find the proportion of the area under the curve to the left of t = −3.365, we calculate the cumulative probability of t = −3.365 from the t-distribution table. The cumulative probability of t = −3.365 is 0.998, which means that 0.998 or 99.8% of the area under the curve lies to the left of t = −3.365.

(c) To find the proportion of the area under the curve between t = –4.032 and t = 4.032, we calculate the cumulative probability of t = 4.032 and subtract the cumulative probability of t = −4.032. The cumulative probability of t = 4.032 is 0.995 and the cumulative probability of t = −4.032 is 0.003. Subtracting the two gives us 0.996, which means that 0.996 or 99.6% of the area under the curve lies between t = –4.032 and t = 4.032.

(d) To find the value of t that cuts off the upper 2.5% of the distribution, we calculate the cumulative probability of t from the t-distribution table. The cumulative probability of t for the upper 2.5% of the distribution is 0.975, which corresponds to a value of t = 2.571. Therefore, the value of t that cuts off the upper 2.5% of the distribution is 2.571.

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