Question 11 only
No need for question 11 A​

When all observations on the independent variable are identical in a linear regression model, it leads to a situation known as perfect multicollinearity.

Perfect multicollinearity occurs when there is an exact linear relationship between the independent variables, making it impossible to estimate unique intercept and slope coefficients using ordinary least squares (OLS) regression.

In the presence of perfect multicollinearity, the OLS estimation method fails because it relies on inverting the matrix of the independent variables, which becomes singular or non-invertible when there is a perfect linear relationship. Consequently, it becomes impossible to obtain unique estimates for the intercept and slope coefficients.

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Answer:

102 pounds

Step-by-step explanation:

The solution to the equation x²y' - xy = x² + 4, x > 0, y(1) is y = xln|x| - (2/x) +2

To find the solution, follow these steps:

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The two-column proof that proves that ΔRSV ≅ ΔTSV by the SSS congruence theorem is explained below.

A Two-Column Proof is a method of providing a logical step-by-step demonstration of a mathematical statement or theorem using a column for statements and a column for corresponding justifications or reasons.

Tus, we have the two-column proof as explained below:

Statement                            Reason                                        

1. RS ≅ TS, V is the             1. Given

midpoint of RT.                            

2. RV ≅ TV                          2. Def. of midpoint

3. SV ≅ SV                          3. Reflexive property of congruency.

4. ΔRSV ≅ ΔTSV                 4. SSS

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sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

To find sin(t), cos(t), and tan(t) we need to use the coordinates of the terminal point p(x,y) determined by the real number t.
Given that the terminal point is (1/5, -2/6), we can find the values of sin(t), cos(t), and tan(t) using the following formulas:
sin(t) = y / r
cos(t) = x / r
tan(t) = y / x
where r is the distance from the origin to the point p(x,y), which can be calculated using the Pythagorean theorem:
r = sqrt(x^2 + y^2)
Plugging in the values for the coordinates of p(x,y), we get:
r = sqrt((1/5)^2 + (-2/6)^2) = sqrt(1/25 + 4/36) = sqrt(36/900 + 25/900) = sqrt(61/900)
sin(t) = (-2/6) / (sqrt(61/900)) = -sqrt(61) / 30
cos(t) = (1/5) / (sqrt(61/900)) = sqrt(61) / 15
tan(t) = (-2/6) / (1/5) = -5/3
Therefore, sin(t) = -sqrt(61) / 30, cos(t) = sqrt(61) / 15, and tan(t) = -5/3.

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The solution to the question is 1.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

Squaring both sides of the log

= (2 (√log2(3))²  - (3 (√log3(2))²

= 4log2(3) - 9log3(2)

= 4(3)log2 - 9(2)log3

=  12log2 - 18log3

= 12log2/18log3

= 2log2/3log3

= 1log2² / 1log3³

= 1/1

= 1

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Evaluate:

\( \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy\)

\( {\large\underline{\sf{Solution-}}}\)

\( \: \: \: \: \: \: \displaystyle\int\rm {y}^{2} \sqrt[3]{y} \: dy\)

can be rewritten as

\(\rm \:  =  \: \displaystyle\int\rm {y}^{2} \times {\bigg(y\bigg) }^{\dfrac{1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{2 + \dfrac{1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{6 + 1}{3} } \: dy\)

\(\rm \:  =  \: \displaystyle\int\rm {\bigg(y\bigg) }^{\dfrac{7}{3} } \: dy\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7}{3} + 1} }{\dfrac{7}{3} + 1 } + c\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{7 + 3}{3}} }{\dfrac{7 + 3}{3}} + c\)

\(\rm \:  =  \: \dfrac{ {\bigg(y\bigg) }^{\dfrac{10}{3}} }{\dfrac{10}{3}} + c\)

\(\rm \:  =  \:\dfrac{3}{10} {\bigg(y\bigg) }^{\dfrac{10}{3}} + c\)

Answer:

0.7 or .7

Step-by-step explanation:

7 divided by 10 is 0.7

Answer:

28.5m

Step-by-step explanation:

Find the area of the top triangle first:

a=1/2bh

a=1/2(6)(2)

a=6 m

Next, the second triangle:

a=1/2bh

a=1/2(3)(3)

a=4.5 m

now the rectangle:

a=3(6)

a=18

add your answers: 18+4.5+6 =28.5m

Answer:

1 and 4

5 and 8  

Step-by-step explanation:

bc those are the only two that are exterior angles

Answer:

1 and 4

5 and 8

Step-by-step explanation:

Answer:

sqrt(882) or 29.698

Step-by-step explanation:

AD^2 + DC^2 = AC^2

sqrt(21^2+21^2) = 29.698

Answer:

10

Step-by-step explanation:

(10*2) ÷ (1+1)

Parentheses first

20 ÷2

Then divide

10

Answer:

The answer to the equation is 10.

Step-by-step explanation:

Use PEMDAS/Order of operations.

Parentheses go first.

(10*2) divided by (1+1)

remove the parentheses after working on the equation in them

20 divided by 2

20/2=10

the answer is 10

If you have any questions tell me them in the comments, I will come answer them. Have a good day.

c would be the answer ok

Answer:

it has 5 hopefully this helps you with work

Answer:

Step-by-step explanation:

Given lines:

These have same slopes of 2/3 and therefore are parallel, so no intersection. There is no solution if lines don't intersect.

The graph is attached as well to show lines are parallel.

Answer:

The mean weight of an adult is 66 kilograms with a variance of 144. If 123 adults are randomly selected, the sample mean would follow a normal distribution with a mean of 66 kilograms and a standard deviation of sqrt(144/123) = 3/sqrt(123) kilograms.

We can standardize the sample mean to find the probability that it would be greater than 66.7 kilograms. The standardized value for 66.7 is (66.7 - 66) / (3/sqrt(123)) = 2.3094.

Using a standard normal distribution table, we find that the probability of a standard normal variable being greater than 2.3094 is approximately 0.0104.

Therefore, the probability that the sample mean would be greater than 66.7 kilograms is approximately 0.0104, rounded to four decimal places.

Step-by-step explanation:

The standard form of the equation of the ellipse is (x - 2)² / 4 + (y - 1)² / 9 = 1 with foci (4, 1) and (0, 1) and minor axis of length 6

The midpoint of the segment connecting the foci:

center = ((4+0)/2, (1+1)/2) = (2,1)

The distance between the foci is 2c, where c is the distance from the center to each focus.

Since the foci are (4,1) and (0,1), we have c = 2.

The length of the minor axis is 2b, where b is the distance from the center to each endpoint of the minor axis.

Since the length of the minor axis is 6, we have 2b = 6, so b = 3.

The distance between the center and each endpoint of the minor axis is b, so we have (2,1) ± (3,0).

Thus, the endpoints of the minor axis are (5,1) and (-1,1).

Since the minor axis has length 6, we have b = 3.

To find a, we can use the Pythagorean theorem:

so a²+ 3² = 2², which gives a² = 4.

Therefore, a = 2.

Substituting these values into the equation above, we get:

(x - 2)² / 2²+ (y - 1)² / 3² = 1

Simplifying, we have:

(x - 2)² / 4 + (y - 1)²/ 9 = 1

Hence,  the standard form of the equation of the ellipse is (x - 2)² / 4 + (y - 1)² / 9 = 1.

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Answer:

15

Step-by-step explanation:

The number of words he still need to write in one of his writing sessions would be = 95 minutes.

A graduate is an individual that has completed studies in an institution for a number of years and is being issued a certificate afterwards.

The number of words committed for a day by Nick = 500 words.

He writes 120 words = 30 mins

The total number of words remaining = 500 - 120 = 380 words.

Therefore the time it will take to finish the remaining 380 words in the day = X mins.

If 30 mins= 120 words

X mins = 380 words.

Make X mins the subject of formula;

X mins = 380× 30/120

X mins = 11,400/120

X mins= 95 minutes.

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Answer:

A. -0.97

Step-by-step explanation:

This one's only 0.03 away from -1 and has the strongest correlation out of the four options by far.

Answer:

Step-by-step explanation:

I=prt/100

5000×2×2=20000÷10

I=2000

Answer: To apply the divergence theorem, we need to find the divergence of the vector field F.

∇ · F = ∂/∂x (x − z) + ∂/∂y (y − x) + ∂/∂z (z^2 − y)

= 1 − 0 + 2z

= 2z + 1

Now we need to find the surface integral of F over the closed surface S that bounds the region R.

We can decompose the surface S into two smooth pieces: the top surface S1, given by z = 0, and the curved surface S2, given by z = 16 − x^2 − y^2.

For the top surface S1, the unit normal vector is k, so the surface integral is:

∬S1 F · dS = ∬D F(x, y, 0) · k dA

= ∬D (x − 0)i + (y − x)j + (0^2 − y)k · k dA

= ∬D −y dA

= −∫0^4 ∫0^(2π) r sin θ dθ dr (using polar coordinates)

= 0

For the curved surface S2, we can parameterize it using cylindrical coordinates:

x = r cos θ, y = r sin θ, z = 16 − r^2

The unit normal vector is given by:

n = (∂z/∂r)i + (∂z/∂θ)j − k

= (−2r cos θ)i + (−2r sin θ)j − k

So the surface integral over S2 is:

∬S2 F · dS = ∬D F(x, y, 16 − x^2 − y^2) · ((−2r cos θ)i + (−2r sin θ)j − k) dA

= ∬D [(r cos θ − (16 − r^2))·(−2r cos θ) + (r sin θ − r cos θ)·(−2r sin θ) + (16 − r^2)^2 − (r^2 sin^2 θ − (16 − r^2))] r dr dθ

= ∬D (−16r^3 cos^2 θ − 16r^3 sin^2 θ + 16r^5 − 2r^2 sin^2 θ) r dr dθ

= ∫0^2π ∫0^4 (−16r^3) r dr dθ

= −2048π/3

Therefore, by the divergence theorem:

∬S F · dS = ∭R ∇ · F dV

= ∭R (2z + 1) dV

= ∫0^4 ∫0^(2π) ∫0^(16 − r^2) (2z + 1) r dz dθ dr

= ∫0^4 ∫0^(2π) (16r^2 + 8r) dθ dr

= 512π/3

So the left-hand side and right-hand side of the divergence theorem are equal:

∬S F · dS = ∭R ∇ · F dV

= 512π/3

Therefore, the divergence theorem is verified for the vector field F over the region R.

Answer:

Step-by-step explanation:

\(\sum^{12}_{r=1} r^2 = \frac{12(12+1)(2*12+1)}{6}= A\)

\(\sum_{r=3}^{12}= \sum_{r=1}^{12} - (r_1+r_2)\)

\(r_1= 1^2\)

\(r_2= 2^2\)

you do your math!!

Answer:

257.48 inches

Step-by-step explanation:

pi * radius^2 * Hight

find radius by dividing the diameter in half

pi = 3.14

The theoretical probability of rolling a product greater than 10 can be found by first identifying the total number of possible outcomes. In this case, there are 36 possible outcomes (6 on the first cube multiplied by 6 on the second cube).

Next, we need to determine the number of outcomes where the product is greater than 10. From the table, we can see that there are 11 outcomes where the product is greater than 10: (2,6), (3,5), (3,6), (4,4), (4,5), (4,6), (5,3), (5,4), (5,5), (5,6), and (6,2).

Therefore, the theoretical probability of rolling a product greater than 10 is 11/36.

Explanation: To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes. In this case, there are 11 favorable outcomes and 36 total possible outcomes. So, the probability is 11/36.        

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(a) When performing an ANOVA with the data the alternative hypothesis is at least two of the restaurants have different mean delivery times.

(b)75.8

Analysis of variance. or ANOVA, is a statistical method that separate observed variance data into different components to use for additional tests. A one way ANOVA is used for three or more groups of data, to gain information about the relationship between the dependent and independent variables.

The ANOVA table shows how the sum of squares are distributed according to source of variation, and hence the mean sum of squares.

It is given that a pizza lover wants to compare the average delivery times.

Therefore the null hypothesis and alternate hypothesis implies that,

H₀ =  all restaurants have equal mean delivery time

Hₐ = at least two restaurants have different two deliveries

Hence the alternate hypothesis for performing an ANOVA with the data is at least two of the restaurants have different mean delivery times.

The alternate hypothesis (Hₐ) defines that there is a statistically important relationship between two variables. Whereas null hypothesis states that is no statistical relationship between the two variables.

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Answer:

5 × 5 × 5

Step-by-step explanation:

expanded basically means broken down... since the exponent is three, you have to multiply 5 three times

125

Step-by-step explanation:

5×5×5

25×5

125

this is the correct answet

Answer:

$2.50

Step-by-step explanation:

$3.50 * 5 = $17.50

$17.50 - $15.00 = $2.50

Hope this helps

Answer:

3.50 x 5 = 17.50 - 15.00 = 2.50

Step-by-step explanation:

youll save $2.50

The house's real measurements are 18 feet by 20 feet.

In everyday speech, a dimension is a measurement of an object's length, width, and height, such as a box.

The idea of dimension in mathematics is an expansion of the concepts of one-dimensional lines, two-dimensional planes, and three-dimensional space.

Examples of dimensions include width, depth, and height.

One dimension is that of a line, two dimensions are those of a square, and three dimensions are those of a cube. (3D).

So, scaling is the process of changing a figure's size to produce a picture.

Considering that a scale of 6 cm equals 12 ft.

Hence:

9 cm = 9 cm * (12 ft. per 6 cm) = 18 feet

10 cm = 10 cm * (12 ft. per 6 cm) = 20 feet

Therefore, the house's real measurements are 18 feet by 20 feet.

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Correct question:

A scale drawing of a house shows 9cm x10cm. If 6cm=12 ft, what are the actual dimensions?

We have elaborate below a real-world problem that involves a decimal divided by a decimal.

Since we are given a problem that says that Jake owns a bakery  amd he makes 8.5 boxes of cupcakes in 15.5 hours,  the question is how many cupcakes he makes in 1 hour .So the time taken is 15.5 and the number of cupcakes made in the  15.5 hours is 8.5. So 15 .5hours=8.5 cupcakes, now dividing both sides by 15.5, we get: 1 hour=8.5/15.5 =0.54 = 1 cupcake, therfore, it needs 1 hour  to make 1 cupcake. Here we had two quantities in form of decimals, so there division of expression of decimal dividing a decimal.

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