Consider the following multiple regression model. What are the correct null and alternative hypotheses to test whether the variable x2 is significant? Select one.

Answer:

The bases are not the same.

Step-by-step explanation:

12/3 is not equal to 11/3

Therefore we cannot add the exponents together.

Hope I helped :)

Answer:

(see below)

Step-by-step explanation:

12³ × 11³ is NOT equivalent to (12 × 11)\(^{3(3)}\) because:

1) 12³ and 11³ don't have the same bases. They have to both have a base of 11 or of 12.

2) 12³ × 11³ and (12 × 11)\(^{3(3)}\) are different because (12 × 11)\(^{3(3)}\) is a whole different number altogether. Here's why:

12³ × 11³ = 1728 × 1331

              = 2,299,968

(12 × 11)\(^{3(3)}\) = \((132)^{9}\)

                  = 1.216649217 × \(10^{19}\)

However, (12 × 11)³ would be equivalent to 12³ × 11³.

(12 × 11)³ = (132)³

               = 2,299,968

Answer: 5 \(\frac{7}{12}\) cups

Step-by-step explanation:

   Subtract whole number values:

8 - 3 = 5 cups

   Subtract fractions:

* Get common denominators

5/6 ➜ 10/12

1/4 ➜ 3/12

* Subtract

10/12 - 3/12 = 7/12

   Answer:

5 7/12 cups

Answer:

67/12 cups of rice

Step-by-step explanation:

We Know

Jayden has 8 5/6 cups of rice.

8 5/6 = 53/6

He uses 3 1/4 cups to make dinner.

3 1/4 = 13/4

How many cups of rice does Jayden have left?

We Take

53/6 - 13/4 = 212/24 - 78/24 = 134/24 = 67/12

So, Jayden has  67/12 cups of rice left.

Answer: 21

Step-by-step explanation: The amount the gold bar weighs is extra information and is meant to throw you off, 526/24 is 21.9 but because you can’t have a decimal amount of gold bars it’s just 21 in each pot.

The area of the sector in terms of π is 35.6π inches squared.

The area of the sector is approximately  111.6 inches square

The area of sector of a circle is the amount of space enclosed within the boundary of the sector.

Therefore,

area of a sector = ∅ / 360 × πr²

where

Therefore,

∅ = 200 degrees

r = 8 inches

area of the sector = 200 / 360 × 8²π

area of the sector = 200 / 360 × 64π

area of the sector =12800π/  360

area of a sector = 35.6π inches squared

Let's find the area of the sector with π = 3.14

area of a sector = 35.6 × 3.14 = 111.6 inches square

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Answer:

(a). 5√6

Step-by-step explanation:

\( \sqrt{10} \times \sqrt{15} \\ = \sqrt{150} \\ = \sqrt{25 \times 6} \\ = 5 \sqrt{6} \)

The finance charge on $500 at 49.9% APR will be $20.79 for one month.

Finance charge = principal × rate

Now monthly charge= P×R×(1/12)

charge = 500 ×0.499 ÷12 = $ 20.79166.. ≈ $20.79

APR is the short hand representation of annual percentage rate which is the rate of interest issued by a bank on a credit card or a loan.

An interest rate is the amount of interest that is payable each period stated as a percentage of the total that was lent, deposited, or borrowed.

The principal amount of the loan , interest rate of the loan , frequency of compounding the interest on the rate, and duration or time of the loan, deposit amount, or borrowing determine the total amount of the interest on the sum that was lent or borrowed.

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Answer:

7/10 or 0.7

The probability of Sara NOT picking an orange is 7/10

Step-by-step explanation:

Given that the basket of fruit contains;

10 lemons,

1 pear,

6 oranges, and

3 apples

Total number of fruits N = 20

The probability of not picking orange P(O');

P(O') = 1 - P(O) ........1

P(O) = probability of picking orange

P(O) = number of orange/total number of fruits

P(O) = 6/20

Applying equation 1;

P(O') = 1 - 6/20

P(O') = 14/20 = 7/10

P(O') = 7/10 or 0.7

Answer:

7.4 < h

Step-by-step explanation:

89 < 12h

Divided both sides by 12

7.4 < h

The answer is:

Work/explanation:

The objective of this problem is to isolate the variable. So in the inequality \(\bf{89 < 12h}\), we should isolate h.

So I divide each side by 12

\(\bf{7.417 < h}\)

Answer:

144 sq inches

Step-by-step explanation:

3ft= 36 inches

36 * 4= 144

Answer:

$0.41

Step-by-step explanation:

1 ice cream cone: $2.75

2 ice cream cones: 2 * $2.75 = $5.50

7.5% of $5.50 =

= 0.075 * $5.50

= $0.4125

Answer: $0.41

The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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The variance of Billy's grades obtained from his test scores is 15.76

The variance is a measure of variability or spread a dataset. The variance can be calculated from the sum of the square of the differences of the data points from the mean divided by the number or count of the data points.

The variance of Billy's test scores can be calculated by finding the mean or the average of the scores, then finding the sum of the squares of the differences of each score from the mean as follows;

The mean score = (89 + 88 + 93 + 90 + 81)/5 = 88.2

The square of the differences of the values from the mean can be calculated as follows;

(89 - 88.2)² = 0.64, (88 - 88.2)² = 0.04, (93 - 88.2)² = 23.04, (90 - 88.2)² = 3.24, and (81 - 88.2)² = 51.84

The sum of the square of the differences is therefore;

0.64 + 0.04 + 23.04 + 3.24 + 51.84 = 78.8

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Answer:

5.63 Happy to Help :)

Step-by-step explanation:

Elijah was travelling before his stop than afterwards with speed of 0.5 km/h.

To solve for distance use the formula for distance d = vt, or distance equals speed times time. Rate and speed are similar since they both represent some distance per unit time like miles per hour or kilometers per hour.

Before his stop, the velocity =\(\frac{0.4km}{0.1 h}\)

                                              = 4 km/h

After his stop, the velocity =\(\frac{2.7km}{2.2 h}\)

                                               = 3.5 km/h

So, 4-3.5 km/h= 0.5 km/h

Elijah was travelling before his stop than afterwards with speed of 0.5 km/h

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The difference between the distance travelled by any point on the record and it's label is; 27.57cm.

According to the task content, it follows from observation that the quantity required is the difference between the circumference in each case and can be evaluated as follows;

Difference = π(17.78 - 9)

Difference = (22/7) × 8.78

Difference = 27.57cm.

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The value of x is x= π/8

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

2tan x/1-tan² x= 1

We know that tan π/4= 1

So, 2tan x/1-tan² x= tan π/4

Also, we know that tan 2x=  2tan x/1-tan² x

Again, 2tan x/1-tan² x= tan π/4

tan 2x= tan π/4

Now comparing we get

2x= π/4

x= π/8

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y=x+3

hope this helps!

Answer:

28. B

29. D

30. A

Step-by-step explanation:

28.

2 5/8 yd × 5/6 yd =

= 21/8 × 5/6 yd²

= 105/48 yd²

= 35/16 yd²

= 2 3/16 yd²

Answer: B

29.

2641 becomes 6241.

In 6241, the 6 is in the thousands place.

6 × 1000 = 6000

Answer: D

30.

90 + 7 × (7 - 1) =

Use the correct order of operations.

= 90 + 7 × 6

= 90 + 42

= 132

Answer: A

The expected value of the winnings from the game is $3.24.

To find the expected value of the winnings, we multiply each possible payout by its corresponding probability and sum them up.

Expected Value = (2 x 0.64) + (4 x 0.18) + (6 x 0.12) + (8 x 0.04) + (10 x 0.02)

Expected Value = 1.28 + 0.72 + 0.72 + 0.32 + 0.20

Expected Value = 3.24

Therefore, the expected value of the winnings from the game is $3.24.

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Answer:

The area is \(80\)

Step-by-step explanation:

rectangle in the middle; 24

both triangles on the side; 56

In total; 80

According to the information we can infer that the volume of the cube is 343cm³ and the rectangular prism is 105cm³.

To calculate the volume of the figures we must take into account the information of the measurements of each of its sides. Once we identify this information we can apply the following procedure. To find the volume of a figure we must multiply its sides, in the case of a cube it would be:

7*7*7=343cm³

On the other hand, to calculate the volume of the rectangular prism we must do the following multiplication:

7*5*3=105cm³

According to the above, the volume of these figures would be: 343cm³ the cube, and the rectangular prism 105cm³.

Note: Here is the question in English:

Calculate the volume of each figure

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Answer:

The probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Step-by-step explanation:

We use the Exponential distribution,

Since we are given that on average, 5 pregnant women with high blood pressure come per week,

So, average = m = 5

Now, on average, 5 people come every week, so,

5 women per week,

so, we get 1 woman per (1/5)th week,

Hence, the mean is m = 1/5 for a woman arriving

and λ = 1/m = 5 = λ

we have to find the probability that it takes higher than a week for a high BP pregnant woman to arrive, i.e,

P(X>1) i.e. the probability that it takes more than a week for a high BP pregnant woman to show up,

Now,

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

Now, the probability density function is,

\(f(x) = \lambda e^{-\lambda x}\)

And the cumulative distribution function (CDF) is,

\(CDF = 1 - e^{-\lambda x}\)

Now, CDF gives the probability of an event occuring within a given time,

so, for 1 week, we have x = 1, and λ = 5, which gives,

P(X<1) = CDF,

so,

\(P(X < 1)=CDF = 1 - e^{-\lambda x}\\P(X < 1)=1-e^{-5(1)}\\P(X < 1)=1-e^{-5}\\P(X < 1) = 1 - 6.738*10^{-3}\\P(X < 1) = 0.9932\\And,\\P(X > 1) = 1 - 0.9932\\P(X > 1) = 6.8*10^{-3}\\P(X > 1) = 0.0068\)

So, the probability that on a particular week, the hospital will receive on high BP pregnant woman is 0.0068

Answer:

Step-by-step explanation:

Direct proportional relationship formula

Given values

Find the value of k using the formula

The equation for this case is

Find the value of y when x = 5

Answer:

A.  y = 9.8x

B.  49 newtons

Step-by-step explanation:

Part A

Definition of the given variables:

If the gravitational force is directly proportional to the mass, then:

   \(y \propto x \implies y=kx \quad \textsf{(for some constant k)}\)

Given:

Substitute the given values into the equation and solve for k:

\(\implies 19.6=2k\)

\(\implies k = 9.8\)

Therefore, the direct variation equation is:  \(y=9.8x\)

Part B

To find the gravitational force of an object with mass of 5 kg, substitute x = 5 into the found equation from part A and solve for y:

\(\implies y=9.8(5)\)

\(\implies y=49\:\: \sf newtons\)

Working backward, the number that Lara started with in performing the mathematical operations was 15.

We can use mathematical operations to determine the initial number that Lara started with.

Mathematical operations include addition, subtraction, division, multiplication, etc.

Let the number that Lara started with = x

x < 20

x ÷ 2 + 6 = y

y ÷ 3 = 4.5

y = 13.5 (4.5 x 3)

x ÷ 2 + 6 = 13.5

x ÷ 2 = 7.5

x = 15 (7.5 x 2)

Thus, Lara started performing the mathematical operations with 15 and got a final result of 4.5.

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Answer:

I think its D, Correct me if I'm wrong!

Step-by-step explanation:

Answer:

$6.84

Step-by-step explanation:

This is quite a simple question, simply add the new deposited amount into the original balance to get your answer.

Answer:

Step-by-step explanation:

18 cubic units.

:::::

Length = 90÷(6×3) = 10 units

:::::

10 cubes × (4 cm³)/cube = 40 cm³

:::::

2×5×6

and

5×3×4