The area of a rectangular living room is 450 square feet. The length of the room is 15 feet less than three times the width.

For this type of question the first step is to calculate the slope of the line given by th equation x+2y=7, for this we recall the slope intercept form ( y=mx+b) and put the equation in that form

Then, m=-1/2. Now, since the equation of the line we are looking for is parallel to the previous line the slope must be the same, now we recall the point slope equation

Substituting m=-1/2, and recalling that the line is passing through (-3,4) we get that the point slope equation the line is :

Finally to put it in the slope intercept form, we solve the equation for y:

For part b) we recall that the standard form of the equation of a line is:

Now, we solve for the constant of the equation:

The last equation is the standard form of the equation of the line.

Answer:

I believe the answer is $17.75

Step-by-step explanation:

As if you have a base fee of 13.75 then 0.10 for each additional mile. Then 40 miles x 0.10 is 4. Hope this helps.

If  She then flew to New York where the temperature was 67 degrees. The change in temperature from when Tina left Atlanta and arrived in New York is : D:15°.

Given :

Beginning temperature = 72 degrees

Increase in temperature = 21 degrees

Decrease in temperature = 11 degrees

Temperature outside Atlanta = 67 degrees

First step is to calculate the temperature in Atlanta using this formula

Temperature = (Beginning temperature + Increase in temperature - Decrease in temperature )

Let plug in the formula

Temperature =  72 + 21 -11

Temperature = 82 degrees

Second step is to calculate the change in temperature

Change in temperature = Temperature in Atlanta - Temperature in New York

Change in temperature = 82 degrees - 67 degrees

Change in temperature = 15 degrees

Therefore the correct option is D.

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If the miles Jack has driven, y, varies directly with x, the number of hours driven. If Jack drove 175 miles in 2.5 hours, the number of hours it would take Jack to travel 665 miles is 9.5 hours.

Let x represent the number of hours it would take Jack to travel

Formulate an equation

175 / 2. 5 = 665 / x

The denominator cannot equal 0 because the fraction is defined

so,

x ≠ 0

Hence,

1750 × 25x / 25 = 665 × 25x /x

Reduce the fraction

1750x = 665 × 25

1750x = 16,625

Divide both side by 1750x

x = 16,625 / 1750

x = 9.5

Therefore it will take Jack 9.5 hours.

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In 9.5 hours Jack can travel for 665 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Suppose 2 pens cost 10 dollars, therefore 1 pen costs (10/2) = 5 dollars.

From this unitary value, we can determine the cost of any no. of pens.

Given, Jack drove 175 miles in 2.5 hours.

∴ In one hour Jack can drive (175/2.5) miles.

= 70 miles.

So, to travel 665 miles Jack needs (665/70) hours.

= 9.5 hours or 9 hours and 30 minutes.

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Given that Owen moves half the number of boxes moved by Ariana.

So you can put 2 in the left side upper box, and 1 in the left side lower box.

Now, it is mentioned that Owen mobes 12 boxes. So the corresponding number of boxes moved by Arianna is to be obtained.

So you have to put 12 in the right side lower box. And a variable (say 'x') in the right side upper box.

The vaue of 'x' is to be calculated.

Cross multiply the terms,

Thus, the value of 'x' is 24.

Therefore, Arianna can move 24 boxes in the time when Owen moves 12 boxes.

Question 1Step 1: Problem

Step 2: Concept

Factor the highest common factor out.

Step 3: Method

Step 4: Final answer

4mn(2n + 3)

Question 2

Step 1: Question

Step 2: Concept

Apply laws of exponent

Step 3: Method

Step 4: Final answer

Option D is the correct answer

======================================================

Explanation:

We can use a counter-example.

Pick any positive real number you want to replace x.

I'll pick x = 7

Use the change of base formula to get the following

[tex]\log_{3}(\text{x}) = \frac{\log(\text{x})}{\log(3)}\\\\\log_{3}(7) = \frac{\log(7)}{\log(3)}\\\\\log_{3}(7) \approx \frac{0.8451}{0.4771}\\\\\log_{3}(7) \approx 1.7713\\\\[/tex]

and

[tex]\log_{2}(\text{x}) = \frac{\log(\text{x})}{\log(2)}\\\\\log_{2}(7) = \frac{\log(7)}{\log(2)}\\\\\log_{2}(7) \approx \frac{0.8451}{0.3010}\\\\\log_{2}(7) \approx 2.8076\\\\[/tex]

---------------------------

So if x = 7, then we have,

[tex]\log_{3}(\text{x}) > \log_{2}(\text{x})\\\\\log_{3}(7) > \log_{2}(7)\\\\1.7713 > 2.8076\\\\[/tex]

The last statement is false, so the first statement is false when x = 7.

It turns out that you could pick any positive real number for x and will always get a false statement when saying [tex]\log_{3}(\text{x}) > \log_{2}(\text{x})[/tex]

If the probability of being dealt this type of hand is 7654/133,784,560. the probability of not being dealt this type of hand is:  0.999944..

Probability of complement of the event A =P (Ac) = 1- P(A)

A = event of the particular type of hand

Probability of A :

P(A) = n (A) / n(S)

P(A) = 7480 / 133,784,560​

Ac = event of not being dealt of this type of hand

Probability of Ac:

P (Ac) = 1- P(A)

P (Ac) = 1- 7480 / 133,784,560​

P (Ac) = 133, 777,080 / 133,784,560

P (Ac) = 0.999944

Therefore the probability of not being dealt this type of hand is 0.999944.

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The complete question is :

In 7 card poker,played with a standard 52 card deck 52C7 or 133,784,560 different hands are possible. The probability of being dealt various hands is the number of different ways they can occur divided by 133,784,560. The probability of being dealt this type of hand is 7654/133,784,560. Find the probability of not being dealt this type of hand.

P ( All three are not caused by firmware ) = 8423 %

The probability that the entire batch will be accepted = 0.8423

We are told that out of the 6225 cases of heart pacemaker malfunctions, 346 were found to be caused by firmware.

Thus,

Cases not caused by firmware = 6225 - 346 = 5879

So, the probability of the first case not being affected by the firmware is;

P( first case not caused by firmware ) = 5879/6225

Also,

The probability of the second case not being affected by the firmware is given as;

P(second case not caused by firmware|first case not affected by firmware) = 5878/6224

Similarly,

The probability of the third case not being affected by the firmware is given as;

P(third case not caused by firmware | first and second not caused by firmware) = 5877/6223

Now that we have the three probabilities, it is clear that the occurrences are not independent because the likelihood of one event depends on the likelihood of the others.

Thus, we will make use of the general multiplication rule which is;

P(A & B) = P(B) × P(A|B)

Thus;

P( All three not caused by firmware ) = P(first case not caused by firmware ) × P( second case not caused by firmware | first case not affected by firmware) × P( third case not caused by firmware | first and second not caused by firmware)

Substituting the values,

P(All three not caused by firmware) = ( 5879/6225 ) × ( 5878/6224 ) × ( 5877/6223 )

P(All three are not caused by firmware) = 0.84232558432 = 84.23 %

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Answer: What do you need help with?

Step-by-step explanation:

1: Comment what u need help with

2: We will help you

3: You have been helped :)

Answer:

After doing the math I got 74.44

The equation which represent the prize money given to each person is $1500/w.

For the given condition in question;

Let 'w' be the number of coworkers.

The total money given to buy raffle tickets and won $1500.

This cam be written as;

w worker -------> $1500.

For 1 worker, use unitary method.

Divide both side by w.

1 worker -------> $1500/w.

Thus, the prize money given to each worker is $1500/w.

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The standard error mean if σ = 64 and n = 64 is 8.

The standard error mean is given by the formula σ/√N. In the question provided, we need to note that the standard error mean is designated by σM.

Now applying the formula, we will have this:

σM = 64 ÷√64

The root of 64 = 8.

Therefore, the standard error mean is equal to 64 divided by 8 which is 8.

So, we can arrive at the conclusion that given the standard error mean of σ = 64 and n = 64, the standard error mean will be 8.

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The age of Renu and her brother is 35 and 30 years respectively.

Let the age of Renu be x

Then,

The age of her brother will be x-5

According to the question,

Age of Renu's brother is 35

So,

x-5 = 30

x = 30+5

x= 35

Hence, the age of Renu and her brother is 35 and 30 years respectively.

This question is related to the topic age problem. These problems aim is to find the age of certain people.

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Answer:

m= 0

Step-by-step explanation:

Since the two points have the same y-coordinates, the line passing through them is a horizontal line. Horizontal lines have a slope of zero.

Prove:

[tex]\boxed{slope = \frac{y_1 - y_2}{x_1 - x_2} }[/tex]

Slope between (6, 5) and (-9, 5)

[tex] = \frac{5 - 5}{ - 9 - 6} [/tex]

[tex] = \frac{0}{ - 15} [/tex]

= 0

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We can determine the area of the enlarged picture as follows:

*First, we determine the new dimensions, that is:

*Secondly, we find the area using the formula of area for a rectangle, that is:

From this, we have that the area of the picture after being enlarged equals 250 in^2.

In this simple economy where the market basket for CPI contains two items, the CPI for year 2 is 102.22%.

The CPI means the Consumer Price Index.

The CPI economically indicates the inflationary trend, using a basket of selected consumer goods and services, and computes their total costs for each period.

The base year's total costs set to 100% are used to compare with the current year's.

Price       1 Bottle of     1 Bar of   2 Bars      Total Cost

              Shampoo       Soap     of Soap    Mkt Basket

                    (a)               (b)             (c)          (a) + (c)

Year 1        $6.50           $1.25     $2.50          $9.00

Year 2      $6.60            $1.30     $2.60         $9.20

CPI for Year 1 (base year) = 100% ($9/$9 x 100)

CPI for Year 2 = 102.22% ($9.20/$9 x 100)

Thus, year 2's Consumer Price Index is 102.22%, compared to year 1's.

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Answer:

102.22

Step-by-step explanation:

Edmentum.

The value of x of the Quadratic Equation, (x - 7)² = 36 when the right-hand side is positive is 13 and for the negative right-hand side, it is 1. So the value of x could be 13 and 1 both.

Split into two equations:

(x - 7)² = 36

(x- 7) = √36 or (x- 7) = -√36

For equation (x- 7) = √36 value of x:

x - 7 = √(6)²

x - 7 = 6

x = 13

For equation (x- 7) = -√36 value of x:

x - 7 = -√(6)²

x - 7 = - 6

x = 1

∴ value of x could be 13 and 1 both.

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In the given angle, the value of x is 9°.

As we can see that the two triangles are congruent as 2 pairs of sides are similar to each other.

So, with this the equation will be:

Therefore, in the given angle, the value of x is 9°.

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From the figure, we observe that,

Non-rigid motions are used to map figure 1 onto figure 2.

Here, resizing (stretching horizontally, vertically, or both ways) is a non-rigid transformation.

So, the answer is,

The figures are congruent because non-rigid motions are used to map figure 1 onto figure 2.

The point corresponding to point C is H.

Since we used x and x+2 as consecutive odd integers. "x" to represent Henry's age, Henry's age is 27. Since we used the expression "x+2" to represent Cameron's age, Cameron's age is "27+2" which is just 29.

So the consecutive odd integers, just means they're separated by a value of 2. This can be generally expressed as "a and a+2" where the these two values would be consecutive odd integers assuming "a" is an integer.

So let's express the Henry's age as the variable "x", since it's unknown. Since Cameron is older, and by definition of a consecutive odd integer, Cameron's can be expressed as "x+2"

So the equation we need to set up is 2(Cameron's age) + (Henry's age) = 85

So we can substitute variables we defined to express Cameron and Henry's age:

2(x+2)+x= 85

Distribute the 2:

2x+4+x

Add like terms:

3x+4=85

Subtract 4 from both sides:

[tex]3x= 81[/tex]

Divide both sides by 3:

x=27

Since we used "x" to represent Henry's age, Henry's age is 27. Since we used "x+2" to represent the Cameron's age, Cameron's age is "27+2" which is just 29.

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The single complex number corresponding to each expression:

1. √(-9) = 3i

2. √(-16) = 4i

3. √(-6)√(-24) = 12

4. √(-3)√(-75) = 15

5. (2+√(-12))/2 = 1 + 3i

6. (4 + √(-20))/2 = 2 + 5i

We represent √(-1) as i which is an imaginary number. Complex numbers are numbers of the kind a + ib, where a and b are real numbers.

Hence all real numbers are also complex numbers (i.e., when b = 0).

Also we use some formula for square roots:

√(ab) = (√a )(√b)

Now, to find the single complex number corresponding to each expression:

1. √(-9) = √(9) x √(-1) = 3i

2.  √(-16) = √(16) x √(-1) = 4i

3. √(-6)√(-24) = √(-6 x -24) = √(144) = 12

4. √(-3)√(-75) = √(-3 x -75) = √(225) = 15

5.  (2+√(-12))/2 =  (2+√4√3√(-1))/2 =  (2+2 x (√3)i)/2  = 1+(√3)i

6. (4 + √(-20))/2 = (4 + √4√5√(-1))/2 = (4 + 2 x (√5)i )/2 = 2 + (√5)i

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Given:

Number of appetizers offered = 8

Number of appetizers customer is to select = 6

Number of main courses offered = 9

Number of main courses customer is to select = 6

Number of desserts offered = 3

Number of desserts the customer is to select = 2

Let's determine how many ways this can be done.

This is a combination problem.

To determine the number of ways this can be selected, apply the combination formula below:

Thus, we have:

Solving further, let's apply the formula and combine:

Solving further:

herefore, there are

The product of the numbers are-

For the given number;

Part a: 107 × 11

   1 0 7

 ×   1  1

 ---------

    1 0 7

+ 1 0 7 x

-------------

1  1  7  7

--------------

Thus, 107×11 = 1177

Part b: 72×13

   7  2

 × 1  3

 ---------

  2 1  6

+ 7  2   x

-------------

  9  3   6

--------------

Thus, 72×13 = 936

Part c: 466×27

 4  6  6

 × 2  7

 ---------

 3 2 6 2

+9 3 2  x

-------------

1 2 5 8 2

--------------

Thus, 466×27 = 12582

Therefore, product of the number are found.

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Answer:

C. If I did not go walking, then it is cold.

Step-by-step Explanation:

A conditional statement is a hypothesis followed by a conclusion. The hypothesis in this example being “If it is cold” and then followed by a conclusion “I will not go walking”.

A converse statement swaps the hypothesis and the conclusion of a conditional statement.

When there are 3 women to to 5 men and there is a total of 224 people, the number of men will be 140 men.

From the information, it was stated that there are 3 women to to 5 men and a total of 224 people.

Therefore, it should be noted that the fraction for men that illustrates the information will be:

= 5/(3 + 5) × 224

= 5/8 × 224

= 5 × 28

= 140

Therefore, the number of men is 140 men.

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The total finance charge on the computer purchased on finance by Gary is $58.00

What is finance charge?

The finance charge on the computer purchase is the excess of the total payments over the principal of the loan, where the principal is the purchase price of $1,250 minus the down payment of $150

principal=purchase price-down payment

principal=$1,250-$150

principal=$1,100

total payments=monthly payment*number of months in 2 years

total payments=$48.25

total payments=$48.25*24

total payments=$1,158.00

total finance charge=total payments-principal

total finance charge=$1,158.00-$1,100.00

total finance charge=$58.00

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Answer:

Should the essay be 3-5 paragraphs? Also I can't write the essay here or otherwise your school will find out you plagiarized it.

Step-by-step explanation:

I can send it to you privately.

Here, we want to select the inequality that best represents the situation

Let the number of weeks be x

Total value saved in x weeks at $35 per week will be 35 * x = 35x

Adding this to what she had initially, the total expression becomes 35x + 45

This sum must be the same or greater than what she plans to save

The inequality is thus;