Chapter6 Lesson 6 the distributive property part 2

Answer:

AB = 10.398

Step-by-step explanation:

By cosine rule, we have:

AB² = AC² + BC² - 2(AC)(BC)cos(ACB)

⇒ AB² = 7² + 10² - 2(7)(10)cos(73)

⇒ AB² = 49 + 100 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140cos(73)

⇒ AB² = 149 - 140(0.292)

⇒ AB² = 149 - 40.88

⇒ AB² = 108.12

⇒ AB = √(108.12)

⇒ AB = 10.398

The inequality that represent the solution set of the situation is x ≥ 72.

a ) Average = (total number) divided by (number of items)

The final exam counts as two test.

Let the final exam be x.

The weight of the final exams on the average is 2.

Thus the final exam can be written as 2x.

Hence our inequality will be as follows:

(71 + 79 + 67 + 83 + 2 x) / 6 ≥ 74

(300 + 2 x) / 6 ≥ 74

Solving the above, we get:

300 + 2 x ≥ 444

2x ≥ 444 - 300

2x ≥ 144

x ≥ 72

b) The above answer is x ≥ 72, it means that if Shureka is aiming at getting an average of 74 or above, then she should be able to get a minimum score of 72 or above.

Therefore, we get that, the inequality that represent the solution set of the situation is x ≥ 72.

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The unit cost of an apple in a crate of 250 apples is $2.63.

Given the following data:

To determine the unit cost of an apple:

In this exercise, you're required to calculate the cost of one apple in a crate, knowing that there are 250 apples in total at a cost of $95.

Thus, we would divide the total number of apples by the total cost of all the apples as follows:

\(Unit\;cost = \frac{Total\;apples}{Total\;cost}\)

Substituting the given parameters into the formula, we have;

\(Unit\;cost = \frac{250}{95}\)

Unit cost = $2.63

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(a). The Tanakas paid a total of $523,906.40 for the townhome.

(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.

Simple interest is the type of interest that is calculated on the principal amount only.

It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.

(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.

Down payment = $41,000

Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40

Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40

(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.

Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000

Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40

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we have the given points

(-5,4)

(2,4)

(-5,-2)

plot the given points

see the attached figure

therefore

The mean absolute deviation (MAD) of this data set is 3

The statement is given as

"all of the values are either 3 beats per minute above the mean or 3 beats per minute below the mean"

As a general rule, the mean absolute deviation of a dataset measures the average difference between each data element and the mean value of the dataset

From the statement, we have

Above/Below = 3 beats per minute

This means that

Mean absolute deviation = 3

Hence. the mean absolute deviation (MAD) of this data set is 3

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The reconciliation for Bane can be summarized as,

Adjusted bank balance = $1380.

A bank reconciliation is defined as a method which is used to match the balances for a cash account in an organization's records of accounting with the bank statement.

Given that,

Beginning checkbook balance is $1400.

Service charge = $20

Adjusted balance = $1400 - $20 = $1380

Also, given that,

Ending balance on the statement = $1480

Deposit in transit = $200

Checks outstanding = $300

Adjusted balance = $1480 + 200 - 300

                              = $1380

Hence the adjusted balance is $1380.

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The width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

What is width in rectangle ?

In a rectangle, the width refers to the measurement of the shorter side of the rectangle, which is perpendicular to its length.

Let x be the width of the blanket in inches. Then the length of the blanket is x + 18 inches.

The area of the blanket is given by:

Area = Length x Width

5760 sq inches = (x + 18) inches * x inches

Expanding the right-hand side and solving for x, we get:

\(x^2 + 18x - 5760 = 0\)

We can solve this quadratic equation using the quadratic formula:

\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 18, and c = -5760. Plugging in these values, we get:

\(x = (-18 \pm \sqrt{(18^2 - 4(1)(-5760))}) / 2(1)\)

\(x = (-18 \pm \sqrt{(18^2 + 23040)}) / 2\)

x ≈ 67.42 or x ≈ -85.42

Since the width cannot be negative, the width of the blanket to the nearest tenth of an inch is approximately 67.4 inches.

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Answer:  57 1/3

Step-by-step explanation:

Area = (height * base) divided by 2

A = (b*h)/2

10 3/4 times 10 2/3 = 114 2/3

114 2/3 divided by 2 is 57 1/3

Answer: 57 1/3

Area of a triangle= 1/2*base*height

A=1/2* 10 3/4* 10 2/3

1/2* 10 3/4= 5 3/8

5 3/8 * 10 2/3 =57 1/3

Step-by-step explanation: Hope this helps!! :)) Mark me brainliest ! :))

Answer:

b = 4

r = 3

Step-by-step explanation:

r + b = 7

solve for 'r' to get r = 7-b

now substitute '7-b' for r in the second equation:

3.75(7-b) + 2.75b = 22.25

26.25 - 3.75b + 2.75b = 22.25

-b = -4

b = 4

r = 3

Jared bought 3 cans of red paint (r = 3) and 4 cans of black paint (b = 4).

To solve this problem, using algebraic equations. Jared recently bought cans of red and black paint, and we want to find out how many cans of each color he purchased. We know that the cost of a red can is $3.75, the cost of a black can is $2.75, and Jared spent a total of $22.25 on the paint. We will set up two equations based on the given information and solve them simultaneously to find the values of "r" (number of red cans) and "b" (number of black cans).

Let's use the following variables:  

r  : Number of red cans purchased  

b : Number of black cans purchased

Now, we can set up two equations based on the information given in the problem:

1. The total number of cans purchased:  

  Since Jared bought 7 cans in total, we can write this as:

   r + b = 7  ... (Equation 1)

2. The total cost of the cans:  

  The cost of each red can is $3.75, so the total cost of all red cans is 3.75r. The cost of each black can is $2.75, so the total cost of all black cans is 2.75b. Jared spent a total of $22.25, so we can write this as:

    3.75r + 2.75b = 22.25  ... (Equation 2)

Now, we have a system of two equations with two variables. We will use the method of substitution or elimination to solve for r and b.

Using substitution, we can rearrange Equation 1 to solve for r:  

r = 7 - b

Now, we can substitute this value of r into Equation 2:

3.75(7 - b) + 2.75b = 22.25

Next, distribute and simplify the equation:

26.25 - 3.75b + 2.75b = 22.25

Combine the b terms:

-1b = 22.25 - 26.25

Simplify further:

-1b = -4

Finally, divide both sides by -1 to find the value of b:

b = 4

Now that we have the value of b, we can find r by substituting the value of b into Equation 1:

r + 4 = 7

Subtract 4 from both sides:

r = 7 - 4

r = 3

Therefore, Jared bought 3 cans of red paint (r = 3) and 4 cans of black paint (b = 4).

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Answer:

Area of triangle is 1 inches²

Step-by-step explanation:

We are given:

Base of triangle = 16 inches

Height of triangle = \(\frac{1}{8} \:\) inches

We need to find:

Area of triangle

The formula used to find Area of triangle is:

\(Area \:of\: triangle=\frac{1}{2}\times b \times h\)

where b is base and h is height.

Putting values and finding area:

\(Area \:of\: triangle=\frac{1}{2}\times 16 \times \frac{1}{8}\\ Area \:of\: triangle=\frac{16}{16}\\ Area \:of\: triangle=1\:inches^2\)

So,  Area of triangle is 1 inches²

Answer:

Explanation:

Here, we want to get the cost per pound of the soup

What we have to do here is, to sum up the costs and divide by the total pounds of ingredients

To get the cost of each ingredient, we have to multiply the number in pounds by each cost per pound

Mathematically, we have the cost per pound as follows:

Answer:

C. Seasonal variation

Step-by-step explanation:

Distinct pattern around a trend line can be caused by seasonal variation.

Seasonal variation refers to a component of a time series which can be defined as the repetitive and predictable movement around the trend line in a year or less. It is caused by temperature, rainfall, public holiday and cycles of season

Seasonal variation can be detected by measuring the quantity of interest for small time intervals, such as days, weeks, months or quarters.

Firms affected by seasonal variation are usually interested in knowing their performance relative to the normal seasonal variation. They need to identify and measure this seasonality so as to help with planning.

If an equilateral triangle has a perimeter of 24 feet. the area of the circle is approximately 50.27 square feet.

Since the perimeter of the equilateral triangle is 24 feet, each side has a length of 8 feet (since all three sides are equal).

The diameter of the circle is equal to the length of one side of the equilateral triangle, which is 8 feet. Therefore, the radius of the circle is half the diameter, which is 4 feet.

The area of a circle is given by the formula:

A = πr^2

where A is the area and r is the radius.

Plugging in the value of the radius, we get:

A = π(4 feet)^2

A = 16π square feet

A ≈ 50.27 square feet (rounded to two decimal places)

Therefore, the area of the circle is approximately 50.27 square feet.

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Answer:

The sum of angles is 180°.

:. 90° + 50° + x° = 180°

140° + x° = 180°

x = 140° - 180°

:. x = 40°

:. The missing angle = 40°

Step-by-step explanation:

:. = therefore

Answer:

-4 and -2

Step-by-step explanation:

First find all the factors of 8, that would be 1 and 8, -1 and -8, 2 and 4, and -2 and -4.

Then, adding the groups of numbers you have should show you what would equal -6. So 1 + 8 = 9, -1 + (-8) = -9, same vice versa, 2 + 4 = 6, -2 + (-4) = -6. So -2 and -4 would be your two numbers.

Answer:

C The probability values do not add to 1

Step-by-step explanation:

Given

The above table

Required

Why is it not a probability distribution

In probability, the sum of all probabilities must equal 0.

But in this case:

\(\sum P(x) \ne 0\)

Because:

\(0.08 + 0.23 + 0.44 + 0.12 + 0.24 \ne 0\)

\(1.11 \ne 0\)

Hence:

Option (c) answers this question

It's important to control for these confounding variables to ensure that the results of the experiment accurately reflect the impact of the independent variables (irrigation and fertilizers) on the dependent variable (growth of Colorado blue spruce trees).

Confounding variables are extraneous variables that can influence the relationship between the independent variable (irrigation and fertilizer) and the dependent variable (growth of Colorado blue spruce trees).

In this experiment, some confounding variables that might be present include:

Soil quality: Soil quality can affect the growth of the Colorado blue spruce trees and may differ between the moist and dry regions.

Climate: Climate, including temperature, humidity, and precipitation, can affect the growth of the trees and may differ between the two regions.

Sun exposure: The amount of sunlight the trees receive can affect their growth and may differ between the two regions.

Pest and disease pressure: The presence of pests and diseases can affect the growth of the trees and may differ between the two regions.

Genetic variability: There may be genetic variability between the Colorado blue spruce trees in the moist and dry regions, which could affect their growth.

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Step-by-step explanation:

A≈3.14mi²

Answer:

  red : blue = 2 : 1

Step-by-step explanation:

It is convenient to write the ratios so that the number representing green marbles is the same in both cases.

  red : green = 3 : 1 = 6 : 2

Then we have ...

  red : green : total = 6 : 2 : 11

The number of ratio units for blue marbles is then 11 -6 -2 = 3, so we have ...

  red : green : blue : total = 6 : 2 : 3 : 11

Then red : blue = 6 : 3 = 2 : 1

No. The reported return rate appears lower than expected.

To determine whether the reported rate of return is reasonable or not, we can calculate the expected rate of return based on the investment amount and the ending value of the account.

First, we need to calculate the total number of quarters that have elapsed between the initial investment and the current quarter. Let's assume that the investment has been held for n quarters.

Then, we can use the following formula to calculate the expected rate of return:

Expected rate of return = (Ending value / Initial investment) ^ (1/n) - 1

Plugging in the given values, we get:

n = 1 (since we are only given information for a single quarter)

Initial investment = 26,245

Ending value = 26,292

Expected rate of return = (26,292 / 26,245) ^ (1/1) - 1 = 0.18%

Comparing the expected rate of return of 0.18% with the reported rate of return of -0.02%, we can see that they are quite different. However, it's important to note that a single quarter's rate of return may not be indicative of the overall performance of the investment.

Therefore, while the reported rate of return seems lower than expected, we would need to consider the performance over a longer period of time to make a more informed assessment of the investment's performance.

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Answer:

\(log_{100}20 = 0.6505\)

Step-by-step explanation:

log20 = 1.301 (when you see only "log" with no base, it is taken as a base 10)

This basically means:

\(10^{1.301} = 20\)  (This is the log in exponential form)

Since we don't know what  \(log_{100}20\)  is equal to, we will say  \(log_{100}20\) = x

So to solve for \(log_{100}20\) = x, you do the same thing. (convert to exponential form)

\(100^{x} =20\)

Now you will notice that both of these equations are equal to 20.

Since 20 = 20,

we can say \(100^{x}\) = \(10^{1.301}\)

Another way of saying 100, is \(10^{2}\) (make the bases the same)

Now we get \(10^{2x} = 10^{1.301}\)      

(we get 2x because an exponent to the power of an exponent (\(2^{x}\)) is the same as 2 * x)

Because you have the same base, you can just ignore the 10s and focus on the exponents. So you get:

2x = 1.301

x = 0.6505

The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

Given that:

y = total cost

x = miles

We are also given the system of linear equations that models the scenario given as:

y = 0.27x + 27 --> equation 1

y = 0.21x + 45 --> equation 2

To find the value of x, make both equations equal to each other and solve:

0.27x + 27 = 0.21x + 45

Combine like terms

0.27x - 0.21x = -27 + 45

0.06x = 18

Divide both sides by 0.06

0.06x/0.06 = 18/0.06

x = 300

To find the value of y, plug in the value of x into equation 1, and find y:

y = 0.27(300) + 27

y = 81 + 27

y = 108

Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).

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Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

Answer:

3:7

Step-by-step explanation:

Let x = pounds of the $10 rice in the mixture

Let y = pounds of the $30 rice in the mixture

Total cost of the $10 rice = 10x

Total cost of the $30 rice = 30y

(10x + 30y) / (x + y) = 24

Solve this equation for y/x:

10x + 30y = 24(x + y)

10x + 30y = 24x + 24y

30y - 24y = 24x - 10x

6y = 14x

y/x = 6/14  simplify the fraction

y/x = 3/7

So, the ratio of the two different types of rice (y:x) is 3:7, meaning a pound of the rice mixture has 3 parts of the $30 rice to 7 parts of the $10 rice.

x = -6.

\(\sf \dfrac{3x+4}{3} -\dfrac{2x}{x-3} =x\)

Applying the distributive property of multiplication on the left hand side:

\(\sf (3)(\dfrac{3x+4}{3} -\dfrac{2x}{x-3}) =x(3)\\ \\ \\{3x+4} -\dfrac{(3)2x}{x-3}=3x\\ \\ \\{3x+4} -\dfrac{6x}{x-3}=3x\)

Applying the distributive property of multiplication:

\(\sf (x-3)({3x+4} -\dfrac{6x}{x-3})=3x(x-3)\\ \\ \\(x-3)({3x+4}) -6x=3x(x-3)\\ \\ \\(x)(3x)+(x)(4)+(-3)(3x)+(-3)(4) -[6x]=3x(x-3)\\ \\ \\\)

Check the image below to see an illustration of this process.

\(\sf 3x^{2} +4x-9x-12 -[6x]=3x(x-3)\\ \\ \\3x^{2} +4x-9x-12 -6x=3x(x-3)\\ \\ \\3x^{2} -11x-12 =3x(x-3)\)

Now simplifying on the right hand side (applying the same logic as last step).

\(\sf 3x^{2} -11x-12 =3x(x-3)\\ \\ \\3x^{2} -11x-12 =(3x)(x)+(3x)(-3)\\ \\ \\3x^{2} -11x-12 =3x^{2}-9x\)

\(\sf 3x^{2} -11x-12+9x =3x^{2}-9x+9x\\ \\ \\3x^{2} -2x-12 =3x^{2}\)

\(\sf 3x^{2} -2x-12-3x^{2} =3x^{2}-3x^{2}\\ \\ \\-2x-12 =0\)

\(\sf -2x-12+12=0+12\\ \\ \\-2x=12\)

\(\sf \dfrac{-2x}{-2} =\dfrac{12}{-2} \\ \\ \\x =-6\)

If "x= -6" is the correct answer, substituting "x" by "-6" on the original equation should return the same value on both sides of the equal (=) symbol. Let's test!

\(\sf \dfrac{3(-6)+4}{3} -\dfrac{2(-6)}{(-6)-3} =(-6)\\ \\-6=-6\)

That's correct!

x = -6 is the corect answer.