Simplify the expression:
(4k – 4) + ( –9k – 5)

Answer:

C) -3

Step-by-step explanation:

We are given the following equation:

[tex]y-5=-3(x-17)[/tex]

And we want to determine its slope.

Note that this is in point-slope form. Recall that in point-slope form, we have:

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope and (x₁, y₁) is an ordered pair.

From the equation, we can see that the value in front of the parentheses will be the slope of the line.

The value in front of the parentheses of our given equation is -3.

In conclusion, the slope of the line described by the equation is -3.

Hence, our answer is C.  

Answer:

6n=48

Step-by-step explanation:

product means multiplication

6×n=48

6n=48

An equation that shows this relationship is: A. 6n = 48.

In order to solve this word problem, we would assign a variable to the unknown number, and then translate the word problem into an algebraic equation as follows:

Let the variable n represent the unknown number.

Based on the statement "The product of 6 and a number is 48," we can logically deduce the following algebraic equation;

6 × n = 48

6n = 48

n = 48/6

n = 8.

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Answer:

31

Step-by-step explanation:

The computation of eighth graders take only a current events class and not a foreign language class is shown below:-

We will assume the x that shows the number of students which we will take  both languages

So, the equation will be

70 + 54 - x = 93

-x = 93 - 124

x =  31 students

So the number of eighth graders only take a current event class is

= 70 - 39

= 31 students

Answer: 168

Step-by-step explanation:

First, let's count the types of selection:

We can select:

Type of car: a compact car, a midsize, a sport utility vehicle, and a light truck (4 options)

Pack: standard, custom, or sport styling, (3 options)

type of transmission: Manual or automatic (2 options)

Color: (7 options)

The total number of combinations is equal to the product of the number of options in each selection:

C = 4*3*2*7 = 168

Answer:4

Step-by-step explanation:

A zero-coupon bond  doesn’t make any payments. Instead, investors purchase the zero-coupon bond for less than its face value, and when the bond matures, they receive the face value.

To figure the price you should pay for a zero-coupon bond, you'll follow these steps:

Divide your required rate of return by 100 to convert it to a decimal.

Add 1 to the required rate of return as a decimal.

Raise the result to the power of the number of years until the bond matures.

Divide the face value of the bond to calculate the price to pay for the zero-coupon bond to achieve your desired rate of return.

First, divide 4 percent by 100 to get 0.04. Second, add 1 to 0.04 to get 1.04. Third, raise 1.04 to the sixth power to get 1.2653. Lastly, divide the face value of $1,000 by 1.2653 to find that the price to pay for the zero-coupon bond is $790,32.

Answer:

Blue paint=21 ounces

Step-by-step explanation:

3/4 cup=6 ounces

1 cup=8 ounces

3/4 cup of blue paint=6 ounces of blue paint

1 cup of white paint= 8 ounces of white paint

Ava has 28 ounces of white paint

Find the required blue paint

Let the required blue paint=x

Blue paint ratio white paint

6:8=x:28

6/8=x/28

Cross product

6(28)=x(8)

168=8x

x=168/8

x=21 ounces

Answer:

b) no

Step-by-step explanation:

The regression analysis is a statistical technique which is used for forecasting. It determines the relationship between two variables. It determines the relationship of two or more dependent and independent variables. It is widely used in stats to find trend in the data. It helps to predict the values of dependent and independent variables. In the given question, the relationship is determined to identify the relationship between density of seed planted and quality of lawn. The significance level is 1% which means strength of evidence is not strong enough to support the test.

Answer:

Third option

Step-by-step explanation:

We can't factor this so we need to use the quadratic formula which states that when ax² + bx + c = 0, x = (-b ± √(b² - 4ac)) / 2a. However, we notice that b (which is 6) is even, so we can use the special quadratic formula which states that when ax² + bx + c = 0 and b is even, x = (-b' ± √(b'² - ac)) / a where b' = b / 2. In this case, a = 1, b' = 3 and c = 7 so:

x = (-3 ± √(3² - 1 * 7)) / 1 = -3 ± √2

Answer: 4

Step-by-step explanation:

Given functions:

[tex]f(x)=\dfrac{1}{5}|x-15|\\\\ g(x)=(x-2)^2[/tex]

We know that the y--intercept of a function is the value of the function at x=0.

so, put x=0 in both the functions.

The y-coordinate of the y-intercept of f(x) = [tex]f(0)=\dfrac{1}{5}|0-15|=\dfrac{15}{5}=3[/tex]

The y-coordinate of the y-intercept of g(x) = [tex]g(0)=(0-2)^2=2^2=4[/tex]

As 4 > 3, that means he y-coordinate of the greatest y-intercept is 4.

Answer:

[tex]2x^2 + x - 3[/tex]

Step-by-step explanation:

We want to divide [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3[/tex] by [tex]x^2 - 2x + 1[/tex]

To do the long division, divide each term by [tex]x^2[/tex] and then subtract the product of the result and [tex]x^2 - 2x + 1[/tex]  from the remaining part of the equation.

Whatever term/value you obtain from each step of the division is a part of the quotient.

When you reach 0, you have gotten to the end of the division.

Check the steps carefully and follow them below:

Step 1:

Divide [tex]2x^4[/tex] by [tex]x^2[/tex]. You get [tex]2x^2[/tex].

Step 2

Multiply [tex]2x^2[/tex] by  [tex]x^2 - 2x + 1[/tex]  and subtract from [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3[/tex]:

 [tex]2x^4 - 3x^3 - 3x^2 + 7x - 3 - (2x^4 - 4x^3 + 2x^2)[/tex] = [tex]x^3 - 5x^2 + 7x - 3[/tex]

Step 3

Divide [tex]x^3[/tex] by [tex]x^2[/tex]. You get x.

Step 4

Multiply x by  [tex]x^2 - 2x + 1[/tex]  and subtract from  [tex]x^3 - 5x^2 + 7x - 3[/tex]:

[tex]x^3 - 5x^2 + 7x - 3 - (x^3 - 2x^2 + x) = -3x^2 +6x - 3[/tex]

Step 5

Divide [tex]-3x^2[/tex] by [tex]x^2[/tex]. You get -3

Step 6

Multiply -3 by [tex]x^2 - 2x + 1[/tex]  and subtract from [tex]-3x^2 +6x - 3[/tex]:

[tex]-3x^2 +6x - 3 - (-3x^2 + 6x -3) = 0[/tex]

From the three divisions, we got [tex]2x^2[/tex], x and -3.

Therefore, the quotient is [tex]2x^2 + x - 3[/tex].

Question: Find the value of Xº if <ADC = 71°

Answer:

15

Step-by-step explanation:

Given:

<ADC = 71°

<ADB = (x + 7)°

<BDC = (2x + 19)°

Required:

Value of x

Solution:

<ADB + <BDC = <ADC

(x + 7)° + (2x + 19)° = 71°

x + 7 + 2x + 19 = 71

x + 2x + 7 + 19 = 71

3x + 26 = 71

Subtract 26 from both sides

3x + 26 - 26 = 71 - 26

3x = 45

Divide both sides by 3 to make x the subject of formula

[tex] \frac{3x}{3} = \frac{45}{3} [/tex]

[tex] x = 15 [/tex]

The value of x is 15.

536 children = 4 months

536/4 children = 4/4 months ... divide both sides by 4

134 children = 1 month

The clinic treated 134 children in 1 month. This is assuming that every month was the same number of patients.

Step-by-step explanation:

Solution,

Number of children treated in 4 months = 536

Now, let's find the number of children treated in one month:

[tex] = \frac{total \: number \: of \: childrens \: }{total \: month} [/tex]

Plug the values

[tex] = \frac{536}{4} [/tex]

Calculate

[tex] = 134 \: [/tex] childrens

Therefore, A clinic treated 134 childrens in one month.

Hope this helps...

Best regards!!

Answer:

1800 [tex]m^{2}[/tex] is the area of parallelogram.

Step-by-step explanation:

Given that:

Area of a triangle = 900 [tex]m^{2}[/tex]

To find:

Area of a parallelogram which has same height and base as that of the given triangle.

Solution:

First of all, let us have a look at the formula for Area of a parallelogram:

[tex]Area_{Par} = Base \times Height[/tex] ...... (1)

So as to find the area of a parallelogram, we need to have the product of Base and Height of Parallelogram.

Now, let us have a look at the formula for area of a triangle:

[tex]Area_{Tri} = \dfrac{1}{2} \times Base \times Height[/tex]

Given that height and base of triangle and parallelogram are equal to each other.

So,the product of base and height will also be equal to each other.

[tex]900 = \dfrac{1}{2} \times Base \times Height\\\Rightarrow Base \times Height = 2 \times 900\\\Rightarrow Base \times Height = 1800\ m^2[/tex]

By equation (1):

Area of parallelogram = 1800 [tex]m^{2}[/tex]

Answer:

It will take them 2 2/5 days working together

Step-by-step explanation:

To find the time worked

1/a + 1/b = 1/t

Where a and b are the times worked individually and t is the time worked together

1/4 + 1/6 = 1/t

Multiply each side by 12t to clear the fractions

12t( 1/4 + 1/6 = 1/t)

3t + 2t =12

Combine like terms

5t = 12

Divide by 5

t = 12/5

t = 2 2/5

It will take them 2 2/5 days working together

Answer:

after 6 half lives: 210(1/2)^6= 3.28125

Step-by-step explanation:

isotope to be reduced to half its initial mass at first:

210(1/2)=105 half it is original weight

after second life: 210(1/2)^2=105(1/2)=52.5

after third : 210(1/2)^3=52.5/2=26.25

after fourth : 26.25/2=12.125

after fifth : 13.125/2

after 6 half lives: 210(1/2)^6= 3.28125

Answer:

Option d: The data are continuous because the data can take on any value in an interval.

Step-by-step explanation:

The data are continuous if they can take on any value within a range. In this case study, there are different elephants including small/young ones and big ones/old ones.

Thus, their heights will vary and can take on any value within a particular range.

Answer:

11

Step-by-step explanation:

x=-5

-4(-5)-9

=20-9

=11

Hope this helps, and marking me as a brainliest would help me too;)

Answer:

11

Step-by-step explanation:

We just have to plug in -5 for x and when we do so we get f(-5) = -4 * (-5) - 9 = 20 - 9 = 11.

Answer:

(D)R: x+2=7

Step-by-step explanation:

Given the statement P:x=5

An equivalent statement will be a statement whose result is exactly x=5.

From the given options:

R: x+2=7

R: x=7-2

R: x=5

Therefore, R is an equivalent statement.

The correct option is D.

Answer:

The answer is below

Step-by-step explanation:

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation . Assume that the population has a normal distribution. Round the confidence interval limits to the same number of  decimal places as the sample standard deviation.

Answer: Given that:

Sample size (n) = 14, mean ([tex]\mu[/tex]) = 161.3, standard deviation ([tex]\sigma[/tex]) = 12.6

Confidence(C)= 90% = 0.9

α = 1 - C = 1- 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 correspond to a z score of 0.45 (0.5 - 0.05). This gives:

[tex]z_{\frac{\alpha}{2} }=1.645[/tex]

The margin of error (E) is given by the formula:

[tex]E=z_{\frac{\alpha}{2} }\frac{\sigma}{\sqrt{n} } =1.645*\frac{12.6}{\sqrt{14} }=5.5[/tex]

The confidence interval = μ ± E = 161.3 ± 5.5 = (155.8, 166.8)

The confidence interval is between 155.8 lb and 166.8 lb. There is a 90% confidence that the mean is between 155.8 lb and 166.8 lb.

Answer:

[tex]\large \boxed{\sf \ \ 9\text{ years} \ \ }[/tex]

Step-by-step explanation:

Hello,

First of all, a few remarks:

>>> 1 year is 12 months, right?

>>> Monthly compounding means that each month we compute the interest and they will be included in the investment for the next month.

>>> 6% is an interest per year, it means that to compute the interest for 1 month we need to compute by 6% multiplied by [tex]\dfrac{1}{12}[/tex]

Let's do it !

At the beginning, we have:

   $8,000

After 1 month, we will have:

   [tex]8000 + 8000\cdot \dfrac{6\%}{12}=8000\cdot (1+ \dfrac{6}{1200})= 8000\cdot (1+ \dfrac{1}{200})[/tex]

After 2 months, we will have:

   [tex]8000\cdot (1+ \dfrac{1}{200})\cdot (1+ \dfrac{1}{200})=8000\cdot \left(1+ \dfrac{1}{200}\right)^2[/tex]

After n months, we will have

   [tex]8000\cdot \left(1+ \dfrac{1}{200}\right)^n=8000\cdot \left(1.005\right)^n[/tex]

We are looking for n such that

   [tex]8000\cdot \left(1.005\right)^n=13709.60\\\\ln(8000)+ n\cdot ln(1.005)=ln(13709.60)\\\\\\n = \dfrac{ln(13709.60)-ln(8000)}{ln(1.005)}=108[/tex]

So, we need 108 months to reach this amount, which means 108/12=9 years.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Step-by-step explanation:

Can you please include a image?

Thanks!!!

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=4x+3

Answer:

21 cases

Step-by-step explanation:

red cases=2x.    white cases=x

2x+x=81

3x=81

x=21 cases

Answer:

2.01m; 0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

Step-by-step explanation:

0.41m + 2.10m + 3.52m = 6.03 6.03/3= 2.01

The average height of the three trees is 2.01 meters.

Given that,

The heights of the three trees are 0.41m, 2.10m and 3.52m.

To find the average height of the three trees,

Use the formula for calculating the mean

Add up their heights and then divide by the total number of trees.

So, we have:

Average height = (0.41 m + 2.10 m + 3.52 m) ÷ 3

We can simplify this expression:

Average height = 6.03 m ÷ 3

Average height = 2.01 m

Therefore, the average height of the three trees is 2.01 meters.

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Statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Three sides of the triangle ABX are all equal to AX, making ΔABX equilateral. Since this makes central angle AXB measure 60°,

m(arc)AB = 60°

AX = BX = AB

The measure of AXB = 60 degrees

m(arc)AB = 60 degrees

On applying the same argument, the inscribed hexagon is regular.

Statement A is correct.

Thus, statement A " Dylan's reasoning about arc AB is correct, and the hexagon is regular. option (A) is correct.

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Step-by-step explanation:

Given,

a student (Charles) bought a car and sold it in 15 % profit for $4669.

we have the formula,

[tex]cp = \frac{sp \times 100}{100 + p\%} [/tex]

so,

[tex]cp = \frac{4669 \times 100}{100 + 15} [/tex]

by simplifying it we get,

CP is $4060.

Therefore, the cp was $4060.

Hope it helps...

Answer:

366 Minutes

Step-by-step explanation:

Answer:

a

   [tex]R =13[/tex]

b

  [tex]\= x =8.9[/tex]

c

 [tex]var(x) = 16.57[/tex]

d

 [tex]\sigma = 4.1[/tex]

Step-by-step explanation:

From the question we are given a data set  

      2​, 10​, 15​, 4​, 11​, 10​, 15​, 10​, 2​, 10

     The sample size is  n  = 10

 The range is  

         [tex]R = maxNum - MinNum[/tex]

Where maxNum  is the maximum number on the data set  which is 15

 and  MinNum  is the minimum  number on the data set  which is  2

   So

           [tex]R = 15 - 2[/tex]

           [tex]R =13[/tex]

The mean is mathematically represented as

          [tex]\= x = \frac{\sum x_i}{N}[/tex]

substituting values

          [tex]\= x = \frac{2 + 10 + 15 + 4 + 11 + 10 + 15 + 10 + 2 + 10 }{10}[/tex]

         [tex]\= x =8.9[/tex]

The variance is mathematically evaluated as

        [tex]var(x) = \frac{\sum (x - \= x)^2}{N}[/tex]

substituting values

      [tex]var(x) = \frac{(2 - 8.9 )^2 + (10 - 8.9 )^2 + (15 - 8.9 )^2 +(4 - 8.9 )^2 +(11 - 8.9 )^2 +(10 - 8.9 )^2 +(15 - 8.9 )^2 +(10 - 8.9 )^2 +} {10}[/tex]                    [tex]\frac{(2 - 8.9 )^2 +(10 - 8.9 )^2 }{10}[/tex]

[tex]var(x) = 16.57[/tex]

The standard deviation is  [tex]\sigma = \sqrt{var(x)}[/tex]

substituting values

         [tex]\sigma = \sqrt{16.57}[/tex]

        [tex]\sigma = 4.1[/tex]

Answer: 23, 25, 27

Step-by-step explanation:

Let the 3 consecutive odd numbers be x, x+2 and x+4.

So

2x+(x+2)+3(x+4)=152

2x + x + 2 + 3x + 12 = 152

6x+14=152

6x = 152 - 14

x=138/6

x=23

So, the numbers are 23, 25 and 27.