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Calculate the volume of the following three-dimensional object

By using the multiple regression equation, the predicted y-values for the values of the given independent variables include the following:

(a) ý = 207.02.

(b) ý = 194.18.

(c) ý = 270.02.

(d) ý = 305.42.

In Statistics and Mathematics, a regression line simply refers to a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line refers to a line which best fits a set of data.

Next, we would determine the predicted y-values for the values of the given independent variables as follows;

ý = -51.7+03x₁ + 4.8x₂

(a) x₁ = 72 and x₂ = 8.9

ý = -51.7+03(72) + 4.8(8.9)

ý = 207.02.

(b) x₁ = 65 and x₂ = 10.6

ý = -51.7+03(65) + 4.8(8.9)

ý = 194.18.

(c) x₁ = 81 and x₂ = 16.4

ý = -51.7+03(81) + 4.8(16.4)

ý = 270.02.

(d) x₁ = 88 and x₂ = 19.4

ý = -51.7+03(88) + 4.8(19.4)

ý = 305.42.

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Answer:

42 square units

Step-by-step explanation:

Each square on the grid is 2 units by 2 units.

Bases: OC = 10; SK = 4

Height: OS = 6

area = (b1 + b2)h/2

area = (10 + 4)(6)/2

area = 42

Answer: 42 square units

Answer:

The area of trapezoid is 42 square unit.

Step-by-step explanation:

According to the question

A trapezoid which is consist of many square shapes and each grid square equals 2 units . We need to find the area of trapezoid.

To calculate the area of trapezoid we have given :-

Finding the area of trapezoid :-

Area of trapezoid = ½ × ( 4 + 10 ) × 6

Area of trapezoid = ½ × 14 × 6

Area of trapezoid = ½ × 84

Area of trapezoid = 42

Hence,

The area of trapezoid is 42 square unit.

Answer : The required sample size is approximately 26 for each type of thread so that the power of the test is 0.95 when the true difference between thread types A and B is 8 kilograms.

Explanation :

Let's assume µ₁ to be the average tensile strength of thread A and µ₂ to be the average tensile strength of thread B. To test the claim that the average tensile strength of thread A exceeds the average tensile strength of thread B by at least 12 kilograms. That is,µ₁ - µ₂ ≥ 12                                                                                                                                               The null hypothesis H₀ is: µ₁ - µ₂ ≤ 12 and, the alternative hypothesis H₁ is: µ₁ - µ₂ > 12. The sample sizes for the two types of thread are n₁ = n₂ = 50. Given that thread A has an average tensile strength of 56.7 kilograms with a standard deviation of 6.28 kilograms, while thread B has an average tensile strength of 77.8 kilograms with a standard deviation of 5.61 kilograms.                                                                                                                                                                         To determine the sample size required to achieve a power of 0.95 when the true difference between thread types A and B is 8 kilograms, we use the formula for the power of the test as follows:                                                               Power = P (Z > z₁-α - (zβ/√n))P (Z > z₁-α - (zβ/√n)) = 0.95.                                                                                                                      When the true difference between thread types A and B is 8 kilograms, that is,µ₁ - µ₂ = 8.                                                            The population variance of the two groups areσ₁² = 6.28² = 39.54σ₂² = 5.61² = 31.63                                                                      The pooled variance is given by:S² = [(n₁ - 1)S₁² + (n₂ - 1)S₂²] / (n₁ + n₂ - 2) = [(49)(39.54) + (49)(31.63)] / (50 + 50 - 2) = 70.585 n = (z₁-α + zβ)² * S² / δ²  Where z₁-α = critical value at α level of significance = 1.65 for a one-tailed test at α = 0.05.zβ = critical value at β level of significance = 1.65 + 0.84 = 2.49 for 0.95 power of the test.δ = µ₁ - µ₂ = 8  Substituting the values, we get n = (1.65 + 2.49)² * 70.585 / 8²≈ 25.8

Hence, the required sample size is approximately 26 for each type of thread so that the power of the test is 0.95 when the true difference between thread types A and B is 8 kilograms.

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Answer:

8

Step-by-step explanation:

We can see here that option A. Reliability; valid; reliable completes the sentence.

A researcher is an individual who engages in the systematic investigation and study of a particular subject or topic to expand knowledge, gain insights, and contribute to the existing body of information in that field. Researchers can be found in various disciplines, such as science, social sciences, humanities, technology, and more.

Thus, it will be:

They decided to use "Depression Index of Diagnosis" because it has a higher reliability than the other and only when it is valid it can be reliable.

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Answer:

303.2 cubic inches

Step-by-step explanation:

20.6in × 3.8in ×2.9in + 3.7in × 7.1in × 2.9in

= answer

Answer:

62.8319 mi²

Step-by-step explanation:

The volume formula here is V = (area of base)(height),

If we fill in the given measurements, we get:

V = π(2 mi)²(5 mi) = 62.8319 mi²

(a) Point-Normal Form: -11x - 8y - 9z + 45 = 0

(b) General Form: -11x - 8y - 9z + 45 = 0

(c) Vector Form: r = (0, -1, 3) + s(11, 8, 9) + t(0, 0, 1)

(d) Parametric Form: x = 11s, y = -1 + 8s, z = 3 + 9s + t

(a) Point-Normal Form:

To find the equation of a plane in point-normal form, we need a point on the plane and the normal vector to the plane. Let's choose the point (0, -1, 3) from the given points. To find the normal vector, we can take the cross product of two vectors formed by the points.

Vector 1: (2, 2, 1) - (0, -1, 3) = (2, 3, -2)

Vector 2: (-3, 2, 5) - (0, -1, 3) = (-3, 3, 2)

Normal Vector: N = (2, 3, -2) x (-3, 3, 2) = (-11, -8, -9)

Using the point (0, -1, 3) and the normal vector (-11, -8, -9), the equation of the plane in point-normal form is:

-11(x - 0) - 8(y + 1) - 9(z - 3) = 0

(b) General Form:

To write the equation of the plane in general form, we can rearrange the point-normal form equation:

-11x - 8y - 9z + 45 = 0

(c) Vector Form:

The vector form of the equation can be written as:

r = (0, -1, 3) + s(11, 8, 9) + t(0, 0, 1)

(d) Parametric Form:

The parametric form of the equation can be written as:

x = 0 + 11s + 0t

y = -1 + 8s + 0t

z = 3 + 9s + t

Note: In all forms, s and t represent scalar parameters.

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b= 2.7 yd

The answer is: 2.7yd

The statement which is not true about logistic regression is that logistic regression assumes a symmetric probability distribution of Y. Option C is the correct answer.

Logistic regression assumes a binary or binomial distribution for the response variable Y, representing two possible outcomes (e.g., 0 or 1). It models the relationship between predictor variables and the probability of a specific outcome using a logistic function. Logistic regression can handle predictor variables that are continuous, categorical, or a combination of both.

It is commonly used for classification tasks, where the goal is to predict the probability or class membership of an observation. The coefficients in logistic regression can have any value, including negative values, and they contribute to the log-odds ratio, which is then transformed into probabilities using the logistic function.

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Answer:

The age of paintings is - 26,601 years .

Step-by-step explanation:

Lets calculate-

A= [tex]0.25 A[/tex]o

Therefore ,

[tex]A= A[/tex]o [tex]e^-^0^.^0^0^0^1^2^1^t[/tex]

[tex]ln0.25=-0.000121t[/tex]

[tex]-3.2188=-0.000121t[/tex]

[tex]t=\frac{-3.2188}{-0.000121}[/tex]

  t= 26,601.65

Therefore , the age of paintings is 26,601 years old.

Answer: I do not know

Answer:

A decrease by 14 percent

Step-by-step explanation:

50 - 43 is 7

14 percent of 50 is 7

Interval of increase: (-∞, -1) ∪ (3, +∞)

Interval of decrease: (-1, 3)

Given function is f(x) = x³ - 3x² - 9x + 4

Differentiating with respect to x,

f'(x) = 3x² - 6x - 9

f'(x) = 3 (x² - 2x - 3)

f'(x) = 3 (x² - 3x + x - 3)

f'(x) = 3 (x(x - 3) + (x - 3))

f'(x) = 3 (x - 3) (x + 1)

For increasing or decreasing,

f'(x) = 0

3 (x - 3) (x + 1) = 0

x = - 1, 3

In interval (-∞, -1 ), f'(x) = positive,

⇒ f(x) is increasing on (-∞, -1 ),

In interval (-1, 3), f'(x) = negative,

⇒ f(x) is decreasing on (-1, 3),

In interval (3, ∞), f'(x) = positive,

⇒ f(x) is increasing on (3, ∞),

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Given question is incomplete, the complete question is below

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x³ - 3x² - 9x + 4 (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.)

The area of a parallelogram is base x height, or A = bh.

a) A = 6 x 10, so A = 60 cm²

b) A = 15 x 8, so A = 120 cm²

1) the null and alterative hypotheses are  - H_o: p=0.20 H_1:p<0.26 (option C)

2)

1) The null hypothesis is that the population proportion of yellow peas is equal to 20%. The alternative hypothesis is that the population proportion of yellow peas is less than 20%.

hence,  H_o: p=0.20 H_1:p<0.26

2) The test statistic is calculated as follows  -

z = (pa   - p₀) / √(p₀(1-p₀)/ n)

Where  -

pa is the sample proportion of yellow peas (0.25)

p₀ is the hypothesized proportion of yellow peas (0.20)

n is the sample size (537)

The test statistic is -2.17

p- value =P(Z < -2.17)

The p -value is   0.0306.

Since the p-value is less than the significance level of 0.05,we reject the null hypothesis and    conclude that there is sufficient evidence to suggest that the population proportion of yellow peas is less than 20%.

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Answer:

A=2(wl+hl+hw)

Step-by-step explanation:

Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the surface area.

Answer:

Option (C) 198 cm² will be the answer.

Step-by-step explanation:

Surface area of rectangular prism=2(lb+bh+lh)

where l=length, b=breadth and h=height.

Here, the length is 9cm, breadth is 6cm and height is 3cm.

By applying the formula,

2{(9*6)+(6*3)+(9*3)}

2{54+18+27}

2*99

198cm²

d.0.003 choice correctly shows 0.3% as a decimal.

Here, we have,

given that,

the percent is: 0.3%

now, we know that,

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.

now, we get,

0.3%

=0.3 ÷ 100

=0.003

now, we know, 0.003 is a decimal.

so, we get,

d.0.003 choice correctly shows 0.3% as a decimal.

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Answer:  i am not sure but thanks for the points have a good day

Step-by-step explanation:

Answer: 1/4

Step-by-step explanation: Probability is favorable outcomes/ all outcomes, to first choose a science book, the probability is 10/20, or one-half, and then to pick one again, is also 1/2, so you multiply them together to find the probability of both happening and you get 1/4!

A random variable is normally distributed with a mean of 40 and a standard deviation of 2.5. P(XS 43.75) is  0.9332

Given: A random variable is normally distributed with a mean of 40 and a standard deviation of 2.5.

We have to find P(X<43.75).

We have to find the probability of getting a random variable below 43.75 using the normal distribution formula.

Z = (X - μ) / σ

Z = (43.75 - 40) / 2.5

Z = 1.5

The probability of a random variable being less than 43.75 is the same as the probability of a standard normal random variable being less than 1.5.

P(Z < 1.5) = 0.9332 (using the standard normal distribution table)

Thus, the P(X < 43.75) is approximately 0.9332 (to four decimal places).

Hence, the required probability is 0.9332.

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Answer:2.8333

Step-by-step explanation:

Answer: 9.70$

Step-by-step explanation: The equation is 53.89 * 0.18 = 9.7002 but, If you round to the nearest hundred it is 9.70$. Hope this helped!!!

The amount of tip waitress get from the Lawrence family is $63.5902.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

The total amount of dinner was $53.89.

Tip= 18%

So, the tip amount will be

= 53.89 x 18/100

= 53.89 x 0.18

= 9.7002

And, the total amount to pay

= 53.89+ 9.7002

= $63.5902

Hence, the amount of tip waitress get is $63.5902.

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Answer:

A

Step-by-step explanation:

option A has two linear equations that intersect at one point

option B has two linear equations that are parallel and do not intersect

option C has one linear equation and an absolute value equation that intersect at two points

option D has one linear equation and a quadratic equation that intersect at two points

The amount paid on September 19 that is equivalent to $1,900 paid on December 1, with an interest rate of 5.9% compounded daily, is approximately $1,930.53.

To determine the amount paid on September 19 that is equivalent to $1,900 paid on December 1, we can use the concept of compound interest.

The formula to calculate compound interest is:

A = P(1 + r/n)^(nt)

Where:

A = final amount

P = principal amount (initial payment)

r = annual interest rate (in decimal form)

n = number of times interest is compounded per year

t = time in years

In this case, we need to find the equivalent amount on September 19. The time between September 19 and December 1 is approximately 74 days.

Using the formula, we can calculate the equivalent amount as follows:

A = 1900(1 + 0.059/365)^(365/74)

Calculating this expression will give us the equivalent amount on September 19. Let me calculate that for you.

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Answer:

60π cm2

Step-by-step explanation:

Given:

Leading coefficient of a trinomial = 3

Constant term = [tex]-5[/tex]

To find:

The equation of trinomial.

Solution:

If an expression contains three terms, then it is known as trinomial.

The general form of a trinomial which contains leading term and a constant is:

[tex]ax^2+bx+c[/tex]

Where, a,b,c are real non-zero numbers. Here, a is the leading coefficient and c is the constant.

Putting a=3 and c=-5, we get

[tex]3x^2+bx+(-5)[/tex]

[tex]3x^2+bx-5[/tex]

Therefore, the required trinomial is  [tex]3x^2+bx-5[/tex], where b is a non zero real number.

Answer:  

area = pi*24^2/4 = 452 yd^2

so that means you will need 452/59 = 7.6 (or 8) gallons