Guenther drove 260 miles in 5 hours. He has 494 more miles to drive on his trip. If he continues at this same average speed, what will his driving time in hours be for the remainder of his trip?

the parameters we are estimating using the OLS method must be themselves linear

What are the Gauss Markov assumptions?

Gauss Markov Assumptions

Linearity: the parameters we are estimating using the OLS method must be themselves linear. Random: our data must have been randomly sampled from the population. Non-Collinearity: the regressors being calculated aren't perfectly correlated with each other.

What are the properties of Gauss Markov Theorem?

The Gauss-Markov theorem states that if your linear regression model satisfies the first six classical assumptions, then ordinary least squares (OLS) regression produces unbiased estimates that have the smallest variance of all possible linear estimators.

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Answer:

c

Step-by-step explanation:

c

The teacher requires 1.5 gallons of paint for the whole class

Quantity of paint available with the teacher = 1 gallon

Fractions: In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain amount, or an object.

Portion of the class covered by 1 gallon of paint = 2/3 class

Let x represent the whole class

Formulating the equation:

The portion of the class covered out of the whole class*Total class = Paint required for the portion of the class

So, for 2/3x = 1

x = 3/2

x = 1.5 gallon

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Answer

8:28 Hope this helps.

Answer:

y = 15/4 mm

x = 36/5 mm

Step-by-step explanation:

In similarity triangles, the corresponding sides are in same ratio.

          [tex]\sf \dfrac{3}{y}=\dfrac{4}{5}\\\\\bf Cross \ multiply,\\\\ y*4 = 3*5\\\\ y =\dfrac{15}{4}\\\\\boxed{y = \dfrac{15}{4}}[/tex]

                               [tex]\sf \dfrac{x}{9}=\dfrac{4}{5}\\\\x = \dfrac{4}{5}*9\\\\x = \dfrac{36}{5}\\\\\boxed{x = \dfrac{36}{5} \ mm}[/tex]

Hello!

Let's solve:

   [tex]\text{Write down the equation}\\\dfrac{6\dfrac{2}{3} }{\dfrac{1}{5} } \\\\\\\text{Convert the nominator, a mixed partial fraction to an improper fraction}\\\dfrac{\dfrac{20}{3} }{\dfrac{1}{5} } \\\\\\\text{When dividing by a fraction, flip the fraction over and multiply its reciprocal}\\\dfrac{20}{3} *\dfrac{5}{1} = \dfrac{100}{3} \\\\\\\text{Convert the improper fraction back mixed partial fraction}\\\dfrac{100}{3} =33\dfrac{1}{3}[/tex]

Answer: [tex]\dfrac{100}{3} \text{ or }33\dfrac{1}{3}[/tex]

Hope that helps!

Answer:

Here is your Answer and I'm from South Africa

If a trader is given a 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, then

(I) The discount amount will be ¢6750000

(II) The final amount that the trader will have to pay to buy the goods will be ¢38250000.  

As per the question statement, a trader is given 15 Percent discount on goods bought from a factory and the original price of the item bought from the factory is ¢45000000.

We are required to calculate the discount amount, and the final amount that the trader will have to pay to buy the goods.

To solve this question, we simply need to calculate 15 percent of 45000000, and then subtract the calculated discount amount from ¢45000000.

Therefore, 15 percent of ¢45000000 = ¢[(15/100) * 45000000]

                                                   = ¢(15 * 450000)

                                                   = ¢6750000

That is, on 15 percent discount on the factory price of certain goods, the factory price being ¢45000000, the discount amount is ¢6750000.

And, considering the discount of ¢6750000 on the factory price of ¢45000000, the final amount that the trader will have to pay to buy the goods = ¢(45000000 - 6750000)

           = ¢38250000.

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-4, -1/2, 3, 13/2, 10,… represents an arithmetic sequence.

An arithmetic sequence progresses with a common difference which is the difference of consecutive terms.

So for each of the number sequences, we will try to check if the consecutive terms has a common difference.

A) 32, 16, 8, 4, 2,...

16-32 = -16

8-16 = -8

4-8 = -4

2-4 = -2

As the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

B)5, 10, 20, 40, 80,...

10-5 = 5

20-10 = 10

40-20 = 20

80-40 = 40

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

C) -4, -1/2, 3, 13/2, 10,…

-1/2- -4 = 7/2

3- -1/2 = 7/2

13/2-3 = 7/2

10-13/2 = 7/2

This sequence has a common difference and hence is an arithmetic sequence.

D) 4, 8/3, 16/9, 32/27, 64/81,…

8/3-4 = -4/3

16/9-8/3 = -8/9

32/27-16/9 = -16/27

64/81-32/27 = -32/81

Here also the differences of consecutive terms are not same, this sequence is not an arithmetic sequence.

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Answer:

$4,000 in the 10% per year account

$11,000 in the 12% per year account

Answer:

m/4 = 3x - 30

Step-by-step explanation:

Hello!

Let's subtract the second equation from the first equation:

Now, solve for m.

Multiply both sides by 12 to get rid of the denominators

Plug in 12x - 120 for m in m/4

The value of m/4 is 3x - 30.

Answer:

you can ask questions for clarification

The fraction is 47/200. The decimal is 0.235.

A percentage can be written in a fraction form by putting 100 on the denominator. For example, the fraction corresponding to x % is x/100.

For converting a percentage into a decimal first it should be converted into fractions as fractions can only be converted into decimal.

For example, the decimal for the fraction 50% is 0.5, which is given by writing 50% as 50/100 = 0.5 after putting decimal on 2 places left to 50.

So here the given percentage is 23.5%.

The corresponding fraction is 23.5/100 = 235/1000 = 47/200 after eliminating the decimal on the numerator and simplifying.

Now the corresponding decimal is, 0.235. Since 1000 is in the denominator for 235/1000, we can simply find the decimal by putting decimal point on 3 places left to 235.

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Reason:

The equation is in y = mx+b form where

m = 20 = slope

b = 0 = y intercept

The slope is the rate of change. It tells us how fast y increases.

slope = rise/run = 20 = 20/1

rise = 20 = increase the earnings by 20 dollars

run = 1 = each time the number of hours go up by 1

The value of b for the given line is 1

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. We may determine whether a given point lies on a line using the equation of any line.

Given that : y = 3x + b; (2, 7)

y =3x + b

7 = 6 + b

1 = b

The value of b for the given line is 1

The line's equation is a linear equation of degree one.

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The tree is approximately 27 ft tall if the answer is rounded off to the nearest foot when the similar triangle formula is applied.

Two triangles can be said to be similar if their corresponding angles are seen as congruent and thereafter their corresponding sides are in proportion.

Similar Triangles Definition

Angle - Angle (AA)

Side - Angle - Side (SAS)

Side - Side - Side (SSS)Similar triangles are triangles that have the same shape, but their sizes may vary.

If Diane, mirror, and the exact bottom of the tree are placed as points on the ground all lying on one line, then the two right triangles can be stated as:

LEFT: y and 35 as the legs and unknown hypotenuse.

RIGHT: 6 and 7.9 as the legs and unknown hypotenuse.

The two angles pointed at the mirror are seen as of same measure that means that 35 and the hypotenuse of LEFT triangle makes same angle measure as the 7.9 and the hypotenuse of that of the RIGHT triangle.

Since these two are seen as similar triangles,

y/35 = 6/7.9

⇒y = 26.58

⇒ y ≈ 27 ft

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If the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

What is dividend, divisor and quotient?

The dividend in this case refers to the number that is being divided. The divisor is the integer that divides a given number. The quotient is the sum that we arrive at as a result. The residual is the number that the divisor leaves after partially dividing the original integer.

Let x be the quotient after dividing 782 by 1523.

[tex]\frac{782}{1523} = x\\0.5134 = x\\x = 0.51[/tex]

Therefore, if the dividend is 782 and the divisor is 1523, then the quotient is, 0.51.

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Answer:

a -7

b 18

c -13

d -5

e 0

f -7

g 0

h -6

Step-by-step explanation:

too lazyy

At hour 9, the temperature recorded was = 75 degrees

At hour 13, the temperature recorded was = 95 degrees

The rate of change = Change in the temperature / Change in the time

⇒ The rate of change = 95 - 75 degrees / 13 - 9 hour

⇒ The rate of change = 20 degrees / 4 hours

⇒ The rate of change = 5 degrees per hour

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If we look at the series, one third of the current term gives the numerical value of the next term.

If we need to express it algebraically, we can write the following equation.

Therefore, our common multiplier can be found as follows. Because this sequence is a geometric sequence.

In geometric sequences, any term can be written in terms of the first term. Below is an example.

Since we know the numerical values of the first term and the common factor of the series, we can easily find the seventh term.

The value illustrated shows that x is -55 units to the left of 0.

From the given statement we have the value of x is negative. Therefore, we need the complete statement about x being positive.

Therefore we have to put an alternate sign to the given statement we get -x is 55 units to the right of 0.

Negation to the given statement about x is -(-x) is -(55) units to the left of 0. The statement will be that x is -55 units to the left of 0.

By using  the drop-down menus to complete the given statement about x is -55 units to the left of 0.

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Answer:13x9x6=702

Step-by-step explanation:

The sum of two hundred even numbers in the sequence from 0 to 398 is 39800

To find the sum of two hundred even numbers from 0 to 398, we can use the formula of sum of an arithmetic progression.

[tex]S_n = \frac{n}{2}[2a(n-1)]d[/tex]

The number of terms given here is 200, the first term is 0 and the common difference is 2

Substituting the values into the equation

[tex]S_n = \frac{n}{2}[2a+(n-1)]d\\S_n = \frac{200}{2}[2*0+(200-1)*2\\S_n = 100(0+199)*2\\S_n = 39800[/tex]

The sum of two hundred even numbers from 0 to 398 is 39800

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The answer to this question represents the possible choices that we have when solving a division.

When solving this division operation, and we use technology, we get the following result:

Then, we can conclude that:

We can conclude that the answer to this division is, approximately, 20. This could be an answer to this operation.

In this case, we can see the integer part of the answer, 20, and a fraction:

And we know that:

Answer:

-6

Step-by-step explanation:

-3x = 18

divide both sides by -3

18 ÷ -3 = -6

The probability that a randomly selected student in the class test scored marks which is less than 82 is 0.9192

It is given that in a test, the scores for an exam normally distributed has a mean of 75 and a standard deviation of 5. We have been asked to find the probability that a randomly selected student scored less than 82.

From the question we have,

Mean = 75

Standard deviation (SD)  = 5

Therefore, the probability that a randomly chosen student has a score of less than 82 is represented as:

(P) Probability ( X < 82) = P { Z < [tex]\frac{82-75}{5}[/tex] }

                = P {Z < 7/5}

                = P {Z <1.4}

                = Area from - ∞ to  1.4

                = 0.9192

From the z table the area under the normal curve that corresponds to  1.4 is  0.9192

Hence the required probability of that a randomly selected student scored less than 82 is 0.9192

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Answer:

g(8)=17

Step-by-step explanation:

Given :
g(a)=a²+2a-63

Substitute a = 8 :

g(8)=8^2+2(8)-63

= 64+16-63

=17

To calculate the total number of miles the delivery truck drove, we add the lengths of the three routes together.

-> It drove 123 + 10 + 15 = 148 (miles).

The least common multiple for 12 and 15 is 60, the least common multiple for 6 and 15 is 30, and the least common multiple for 9 and 15 is 45.

In mathematics, the term "least common multiple" is used to refer to a multiple of two or more numbers share and that is the smallest number possible.

Mulitiply the numbers given by 1, 2, 3, 4, etc. until your find the first common number.

Lets use the numbers given

12 x 1 = 12        15 x 1 = 15

12 x 2 = 24       15 x 2 = 30

12 x 3 = 36       15 x 3 = 45

12 x 4 = 48       15 x 4 = 60

12 x 5 = 60

Based on this, the least common multiple is 60

6 x 1 = 6          15 x 1 = 15

6 x 2 = 12       15 x 2 = 30

6 x 3= 18

6 x 4 =24

6 x 5 =30

Based on this, the least common multiple is 30

9 x 1 = 9           15 x 1 = 15

9 x 2 = 18         15 x 2 = 30

9 x 3= 27         15 x 3 = 45

9 x 4 =36

9 x 5 =45

Based on this, the least common multiple is 45

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Answer:

p=2+1.1m

Step-by-step explanation:

p=price, m=miles