What is the scale of a map if 1 cm on a map represents 20 km in real life?

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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These work out to 60,466,176 case insensitive combinations of letters.

There are 10 digits 0–9.

The are 26 letters in the modern alphabets.

However, you didn’t specify whether capital and lowercase letters count as the same letter or separate. In the former case, there are 26 letters, in the latter, there are 52.

There is also such a thing as lowercase numbers, but since they aren’t in common standard usage, I won’t count those.

You also didn’t specify that characters couldn’t be repeated, so I am going to assume that the same character can appear multiple times in a 5 character combination.

Also, since the combinations are an alphanumeric string of characters rather than a number, I will assume that leading zeroes are allowed.

So, there are either 36 (10 digits and 26 letters).

To find the number of combinations you multiply the number of possibilities for each character;

36 x 36 x 36 x 36 x 36

These work out to 60,466,176 case insensitive combinations of letters.

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The weighted mean cost of a haircut for Malachi is $15.67, divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

We must compute the total cost of all haircuts and divide it by the total number of haircuts in order to determine the weighted mean price of a haircut for Malachi. The expense of each haircut must be weighed according to the frequency with which it occurred, though, because they varied in price.

To begin, let's figure out how much each haircut will cost overall:

2 haircuts at $12.00 each = $24.00

3 haircuts at $15.00 each = $45.00

1 haircut at $25.00 = $25.00

Total cost = $24.00 + $45.00 + $25.00 = $94.00

Next, We must determine the total number of cuts:

2 haircuts + 3 haircuts + 1 haircut = 6 haircuts

Finally, The weighted mean cost of a haircut can be determined by dividing the total cost by the total number of haircuts:

The weighted mean cost of a haircut = Total cost / Total number of haircuts

= $94.00 / 6 haircuts

= $15.67 per haircut (rounded to the nearest cent)

Therefore, Malachi's weighted mean haircut expense is $ 15.67 , divided by the total number of haircuts, which comes to 6, to yield a total cost of $94.00.

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Answer:

(4/3, 7/3)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

7x - y = 7

x + 2y = 6

Step 2: Rewrite Systems

Equation: x + 2y = 6

Step 3: Redefine Systems

7x - y = 7

x = 6 - 2y

Step 4: Solve for y

Substitution

Step 5: Solve for x

Answer:

Step-by-step explanation:

70+5x+15=180

5x+85=180

5x=95

x=19

Answer:

2 triangles and 3 rectangles

Step-by-step explanation:

Because all triangular prisms have 2 triangle faces and 3 rectangle faces

The volume of the right prism include the following: 8,640 in³.

In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:

Volume of a rectangular prism = L × W × H

Where:

Next, we would determine the area of the triangle at the base of the right prism as follows:

Base area = 1/2 × ( 36 × 12)

Base area = 1/2 × 432

Base area = 216 in².

Now, we can calculate the the volume of this right prism:

Volume = base area × height

Volume = 216 × 40

Volume = 8,640 in³.

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Answer:

4(3x-y)

Step-by-step explanation:

Given:

\(\displaystyle \large{3(3x-y)-(y-3x)}\)

To factor this kind of expression, first, find the common factor.

\(\displaystyle \large{3(3x-y)-(-3x+y)}\\\displaystyle \large{3(3x-y)+(3x-y)}\)

Notice that in the expression, we have both same (3x-y). Therefore, (3x-y) is our factor.

Let u = 3x-y

\(\displaystyle \large{3u+u}\\\displaystyle \large{4u}\)

Change u back to 3x-y:

\(\displaystyle \large{4(3x-y)}\)

Therefore, the factored expression is 4(3x-y).

Answer:

Gretchen will earn $48 from mowing in 4 hours

Data

Amount earned on each lawn = $12

Number of hours mowing = 4 hours

Step-by-step explanation:

This is the measure of one unit against another unit. An example of this is speed which is the rate of distance covered to time.

In this case, she mows 1 lawn in each hour and earns $12 on each.

To calculate for 4 hours

She earns $48 from mowing 4 lawns

Answer:

12 lawns - $144

Step-by-step explanation:

Well 3 lawns(L) = 1 hour(H)

So then 3(L)*4(H)

Now we have a total of 12 lawns.

12(L)*$12 = $144

The correct option is: A) The winning time increased by an average of 0.4 second per year from year 2 to year 4.

To find the average rate of change from year 2 to year 4, we need to calculate the difference in winning time divided by the difference in years.

The winning time in year 2 is 28.4 seconds, and the winning time in year 4 is 29.2 seconds. The difference in winning time is 29.2 - 28.4 = 0.8 seconds.

The difference in years is 4 - 2 = 2 years.

Now, we can calculate the average rate of change:

Average rate of change = (difference in winning time) / (difference in years)

= 0.8 seconds / 2 years

= 0.4 seconds per year

Therefore, the average rate of change from year 2 to year 4 is 0.4 seconds per year.

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Answer:

96 liters

Step-by-step explanation:

Two liters are in each bottle, so that means they sold 12 bottles of oil each day. Multiply that with 8 days to get the answer:

12 × 8 = 96

Ninety-six liters.

Based on the given probabilities:

Events A and B are independent.

Events B and C are mutually exclusive.

Events C and A are independent.

To determine whether pairs of events are independent or mutually exclusive, we need to analyze their conditional probabilities.

Pair A and B:

P(A) = 0.26, P(B) = 0.5, and P(A|B) = 0.26. The fact that P(A|B) is equal to P(A) suggests that events A and B are independent. This means that knowing the occurrence of event B does not affect the probability of event A.

Pair B and C:

P(B) = 0.5, P(C) = 0.45, and P(B|C) = 0. The fact that P(B|C) is equal to 0 implies that events B and C are mutually exclusive. This means that if event C occurs, event B cannot occur, and vice versa.

Pair C and A:

P(C) = 0.45, P(A) = 0.26, and P(C|A) = 0.26. The fact that P(C|A) is equal to P(C) suggests that events C and A are independent.

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Complete question is:

Given the following information about events A, B, and C, determine which pairs of events, if any, are independent and which pairs are mutually exclusive.

P(A)= 0.26

P(B)= 0.5

P(C)= 0.45

P(A|B)= 0.26

P(B|C)=0

P(C|A)=0.26

The computer equipment was acquired at a cost of $73,700 with an estimated residual value of $34,600 and a useful life of 5 years. The depreciable cost of the equipment is $39,100. The straight-line rate is 20%, and therefore, the annual straight-line depreciation for the computer equipment is $7,820.

a. To determine the depreciable cost, we subtract the estimated residual value from the initial cost: $73,700 - $34,600 = $39,100.

b. The straight-line rate is calculated by dividing 100% by the estimated useful life of the equipment. In this case, the straight-line rate is 100% / 5 = 20% per year.

c. The annual straight-line depreciation is found by multiplying the depreciable cost by the straight-line rate. Thus, the annual depreciation is $39,100 * 20% = $7,820 per year.

By following these calculations, we can determine that the depreciable cost of the computer equipment is $39,100, the straight-line rate is 20%, and the annual straight-line depreciation amounts to $7,820.

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Answer:

See the Answer Below:) I am certain this is the answer

Step-by-step explanation:

Answer:

23.2

Step-by-step explanation:

Answer:

$75

Step-by-step explanation:

25÷4= 6.25

6.25×12= 75

The total of 12 movies would be $75.

\(4 * 3 = 12\)

\(25*3=75\)

Thus, you're answer is $75.

The 15 and 9 units side lengths of the parallelogram ABCD, and the 36° measure of the acute interior angle, A indicates the values of the ratios are;

1. AB:BC = 5:3

2. AB:CD = 1:1

3. m∠A : m∠C= 1 : 4

4. m∠B:m∠C = 4:1

5. AD: Perimeter ABCD = 3:16

A ratio is a representation of the number of times one quantity is contained in another quantity.

The shape of the quadrilateral ABCD in the question = A parallelogram

Length of AB = 15

Length of BC = 9

Measure of angle m∠A = 36°

Therefore;

1. AB:BC = 15:9 = 5:3

2. AB ≅ CD (Opposite sides of a parallelogram are congruent)

AB = CD (Definition of congruency)

AB = 15, therefore, CD = 15 transitive property

AB:CD = 15:15 = 1:1

3. ∠A ≅ ∠C (Opposite interior angles of a parallelogram are congruent)

Therefore; m∠A = m∠C = 36°

∠A and ∠D are supplementary angles (Same side interior angles formed between parallel lines)

Therefore; ∠A + ∠D = 180°

36° + ∠D = 180°

∠D = 180° - 36° = 144°

∠D = 144°

m∠A : m∠C = 36°:144° =1:4

m∠A : m∠C = 1:4

4. ∠B = ∠D = 144° (properties of a parallelogram)

m∠B : m∠C = 144° : 36° = 4:1

5. AD ≅ BC (opposite sides of a parallelogram)

AD = BC = 9 (definition of congruency)

The perimeter of the parallelogram ABCD = AB + BC + CD + DA

Therefore;

Perimeter of parallelogram ABCD = 15 + 9 + 15 + 9 = 48

AD:Perimeter of the ABCD  = 9 : 48  = 3 : 16

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The area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

Given that, the dimensions of a rectangle (x-1) and (x+3).

The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.

Here, the area of a rectangle

= (x+3)×(x-1)

= x²+3x-x-3

= x²+2x-3

Hence, the area of a rectangle with the dimensions (x-1) and (x+3) is x²+2x-3 square units.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the area of a rectangle with the dimensions (x-1) and (x+3).

Answer:

4n

Step-by-step explanation:

1. -7n-5n= -2n

2. -2n + 6= 4n

Answer:

-2 + 6

Step-by-step explanation:

Hopefully I helped :) Sorry if i didn't atleast i tried !

Answer: y = -2/3x + 6

Step-by-step explanation:

Answer:

The first choice

Step-by-step explanation:

It is word for word what is in the question

Answer:

The total population = 9514.2857143 people.

Step-by-step explanation:

Let the total population be represented by X

In the question, we are told that,1332 people are under the age of 20 and this value = 14% of the total population.

Therefore, the total population is calculated as

14% of X = 1332

14/100 × X = 1332

14X/100 = 1332

Cross Multiply

14X = 1332 × 100

X = 1332 × 100/14

X = 9514.2857143

Therefore, the total population = 9514.2857143 people.

Answer:

45

Step-by-step explanation:

Answer:

8x + 12y + 15z

Step-by-step explanation:

Given the sales rate of three items: 8$ for t-shirts, 12$ for sweaters, and 15$ for jeans. It also states that these rates are represented by the corresponding variables being x for t-shirts, y for sweaters, and z for jeans.

To complete the expression, just combine the rate with the corresponding variables. i.e 8$ for t-shirts, and x for shirts = 8x, 12$ for sweaters and y for sweaters = 12y, 15$ for jeans, and z for jeans = 15z. Finally, sum them together.

8x + 12y + 15z

Answer:

2x + 17 = 81 is the equation

x=32

Step-by-step explanation:

2x + 17 = 81

subtract 17 from 81, which is 64

64 divided by 2 is 32

to check the answer, 2 times 32 = 64 + 17 = 81

hope this helped :)

Answer:

1. 5/12

2. 3/8

3. 1/4

Step-by-step explanation:

There is a 0.022 percent chance that a student may receive a quiz grade of 95 or above.

The z-score formula is as follows:

z = (95-85)/8.0

= 1.25

Using the z-score table, calculate the probability:

P(z >= 1.25)

= 0.022

The z-score formula can be used to determine the likelihood that a student would receive a quiz grade of 95 or higher. The data set's mean and standard deviation are considered in the formula. The mean score on the quiz in this instance is 85, and the standard deviation is 8.0. By deducting the mean from the desired score (95), the z-score can be computed by dividing the result by the standard deviation (8.0). The z-score in this instance is 1.25.  The likelihood that a student will receive a quiz grade of 95 or higher can be determined using the z-score table. The likelihood of a z-score of 1.25 or higher is 0.022, according to the table. This indicates that there is a 0.022 percent chance that a student will receive a quiz grade of 95 or above.

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Answer:

Either  

8.2  x 10^5

is already in standard notation

or you want  

820,000

Step-by-step explanation: To convert from scientific notation to common form move the decimal point in the mantissa (in this case  8.2 ) to the right the number of places indicated by  10 's exponent (in this case 5). [If the exponent is negative the decimal point will be moved to the left].

Answer:

bottom left: -6 + (-1/3)

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

P = 2l + 2w

= 2(12) + 2(18)

= 24 + 36 = 60