Write the equation of the line with a slope of 3/2 that contains the point (-4,-2).

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ Q(\stackrel{x_1}{0.3}~,~\stackrel{y_1}{1.8})\qquad R(\stackrel{x_2}{2.7}~,~\stackrel{y_2}{3.9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{2.7+0.3}{2}~~,~~\cfrac{3.9+1.8}{2} \right)\implies \left(\cfrac{3}{2}~,~\cfrac{5.7}{2} \right)\implies (1.5~,~2.85)[/tex]

Final answer:

The coordinates of the midpoint are (1.35, 2.85).

Explanation:

The coordinates of the midpoint of a segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. In this case, the x-coordinate of the midpoint is (0 + 2.7) / 2 = 1.35, and the y-coordinate of the midpoint is (1.8 + 3.9) / 2 = 2.85. Therefore, the midpoint of the segment with endpoints Q(0.3, 1.8) and R(2.7, 3.9) is (1.35, 2.85).

Answer:

69.09 yd^2

Step-by-step explanation:

14.1*9.8=138.18

138.18*0.5=69.09

Answer:

69.09 square yd.

Step-by-step explanation:

Area of a triangle is

[tex]A=\dfrac{1}{2}\times base\times height[/tex]

From the given figure it is clear that height of the triangle is 9.8 yd and base of the triangle is 14.1 yd.

Substitute the given values in he above formula, to find the area of triangle.

[tex]A=\dfrac{1}{2}\times 14.1\times 9.8[/tex]

[tex]A=69.09[/tex]

Hence, the area of triangle is 69.09 square yd.

Answer:

  B.  {(4,6), (8,8), (–3,6)}

Step-by-step explanation:

You can graph the equation and plot the points, or you can try the points algebraically. For the latter, it is convenient to rearrange the inequality a bit.

  y ≥ 1/4x + 5 . . . . . given

  4y ≥ x + 20 . . . . . multiply by 4

You can use this form, or you can subtract x to get ...

  4y -x ≥ 20

Trying the offered points, we want 4y-x to be at least 20. We get ...

  A: 4(-17) -(-3) = -65 . . . . less than 20

  B: 4(6)-4 = 20 . . . a solution

     4(8) -8 = 24 . . . a solution

     4(6)-(-3) = 27 . . . a solution . . . . set B contains solutions to the inequality

  C: 4(4)+3 = 19 . . . . less than 20

  D: 4(-1)-(-2) = -2 . . . . less than 20

Answer:

[tex]f^{-1}(x)=6(x+7)^{3}[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\sqrt[3]{\frac{x}{6}}-7[/tex]

Let

[tex]y=f(x)\\ y=\sqrt[3]{\frac{x}{6}}-7[/tex]

Exchanges the variable x for y and y for x

[tex]x=\sqrt[3]{\frac{y}{6}}-7[/tex]

Isolate the variable y

[tex]x+7=\sqrt[3]{\frac{y}{6}}[/tex]

elevates to the cube both members

[tex](x+7)^{3}=\frac{y}{6} \\ \\y=6(x+7)^{3}[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=6(x+7)^{3}[/tex] ------> inverse function

ANSWER

[tex]3 \: radians[/tex]

EXPLANATION

The formula for the calculating the length of an arc is

[tex]l = r \theta[/tex]

where theta is in radians.

From the diagram

[tex]l = 12cm[/tex]

[tex]r = 4cm[/tex]

We substitute the values to obtain;

[tex]4\theta = 12[/tex]

Divide both sides by 4 to get;

[tex]\theta = \frac{12}{4} [/tex]

[tex]\theta = 3 \: radians[/tex]

[tex]4x^2 - 25=(2x-5)(2x+5)[/tex]

Answer:

x^9

Step-by-step explanation:

The rule of exponents that applies is ...

(a^b)^c = a^(b·c)

For your problem, you have a=x, b=(3/2), c=6, so ...

(x^(3/2))^6 = x^(3/2·6) = x^9

Answer:

[tex]x^9[/tex]

Step-by-step explanation:

We are given that an expression

[tex]\left\{(x)^{\frac{3}{2}\right\}^6[/tex]

We have to simplify the given expression

In order to simplify the expression we will use given below rule

We know that [tex](a^b)^c= a^{b\cdot c}[/tex]

Using this rule

[tex](x)^{\frac{3}{2}\cdot 6}[/tex]

[tex](x)^{3\cdot 3}[/tex]

[tex]x^9[/tex]

[tex]\left\{(x)^{\frac{3}{2}\right\}^6=x^9[/tex]

Answer: The answer is D

Step-by-step explanation:

Factor and set each set equal to zero to get x=0,2,-1,1

Answer:

D

Step-by-step explanation:

x¹³ - 2x¹² - x¹¹ + 2x¹⁰ = 0

x¹⁰(x³ - 2x² - x + 2) = 0

x¹⁰ [x²(x - 2) - (x - 2)] = 0

x¹⁰(x² - 1)(x - 2) = 0

x = 0 (multiplicity 10)

x = 1

x = -1

x = 2

Answer:

-6s-c+1

Step-by-step explanation:

(-3s-4c+1)+(-3s+3c)

We have been given the above expression. To find the sum, we simply collect the like terms and combine them;

(-3s-4c+1)+(-3s+3c) = -3s + -3s -4c + 3c + 1

-3s + -3s -4c + 3c + 1 = -3s - 3s + 3c - 4c + 1

-3s - 3s + 3c - 4c + 1 = -6s - c + 1

Therefore;

(-3s-4c+1)+(-3s+3c) = -6s-c+1

Answer:

Step-by-step explanation:

Club B's savings of $17 - 13 = $4 in fee is eaten up at the rate of $24 -22 = $2 per month in monthly fees. It will take $4/($2/mo) = 2 mo for the total costs to be equal.

After 2 months, the amount at each club will be ...

_____

If you want to write equations, the club costs (a and b) in terms of months (m) of membership are ...

  a = 17 +22m

  b = 13 +24m

The difference is zero when ...

  a - b = 0

  (17 +22m) -(13 +24m) = 0

  4 -2m = 0 . . . . . . . simplify

  4 = 2m . . . . . . . . . add 2m . . . Note that 4 is 17-13; 2 is 24-22, as above.

  4/2 = m = 2 . . . . . . divide by the coefficient of m

The difference in total cost will be zero after 2 months.

The mean retirement age is 59.7

The sample mean is a statistic obtained by calculating the arithmetic average of the values of a variable in a sample.

To calculate the arithmetic mean of a set of data we must first add up (sum) all of the data values (x) and then divide the result by the number of values (n). Since ∑ is the symbol used to indicate that values are to be summed (see Sigma Notation) we obtain the following formula for the mean (M):

M=∑ x/n

Given, the sample data of ages of 9 employees respectively are

52, 63, 67, 50, 59, 58, 65, 51, 56.

Mean of sample data

M=∑ x/n

M=(52+63+67+50+59+58+65+51+56)/9

M=537/9

M=59.667

Hence, the mean for the given sample data round to one more decimal place than is present in the original data values is 59.7

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Note- The complete question is mentioned below

Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than is present in the original data values. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.

52, 63, 67, 50, 59, 58, 65, 51, 56.

Final answer:

To find the mean retirement age for the 9 employees, add up all ages, divide by the number of employees, yielding a mean retirement age of 71.6 years.

Explanation:

Mean Retirement Age Calculation:

Add up all the ages: 65 + 67 + 68 + 70 + 72 + 74 + 75 + 76 + 77 = 644

Count the number of ages, which is 9

Divide the total sum of ages by the number of employees to find the mean: 644 / 9 = 71.6 years

Answer:

complementary angles

Step-by-step explanation:

∠1 and ∠2 form a right angle and are complementary, that is they sum to 90°

17 pieces. She had two and she had to have 15 to give to the children. If each child got 3 and there is 5. This turns into 3*5=15. Then you would add 15+2 to get 17

Sara initially had 17 candies. This computation is based on the 2 pieces she kept for herself and the three pieces of candy each of her five children received.

The subject of this question is mathematics, specifically it deals with basic arithmetic and problem solving. According to the problem, Sara kept 2 pieces of candy for herself and then gave each of her 5 children 3 pieces. In mathematical terms, this can be represented as an equation: 2 (pieces Sara kept) + 5 (children) * 3 (pieces each child received) = Total pieces of candy Sara had initially.

To solve this equation, first multiply the number of children by the pieces each received: 5 * 3 = 15. Then add the pieces Sara kept: 2 + 15 = 17. Therefore, Sara initially had 17 pieces of candy.

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5. Next time include the entire page in the photo.  I'm guessing it's U at the top right and O at the bottom right.

First box.  

SE ≅ SU

Given

Second box

angle 1 ≅ angle 2

Those are vertical angles, which are always congruent

Third box

angle E = angle U

Given

Next box, three arrows in.

triangle MES ≅  triangle OUS

Angle - Side - Angle

Last box:

MS ≅  SO

Corresponding parts of congruent triangles.

-----------

6.

First box:

angle E ≅ angle U

Given

Second box:

NS ≅ NS

reflexivity (aka it's the same segment)

Third box:

angle 1 = angle 2

Definition of angle bisector

Next box:

triangle WNS ≅  triangle ENS

Angle - Side - Angle

Next:

WN ≅  EN

Corresponding parts of congruent triangles.

Answer:

5. Next time include the entire page in the photo.  I'm guessing it's U at the top right and O at the bottom right.First box.  SE ≅ SUGivenSecond boxangle 1 ≅ angle 2Those are vertical angles, which are always congruentThird boxangle E = angle UGivenNext box, three arrows in.triangle MES ≅  triangle OUSAngle - Side - AngleLast box:MS ≅  SOCorresponding parts of congruent triangles.-----------6.First box:angle E ≅ angle UGivenSecond box:NS ≅ NSreflexivity (aka it's the same segment)Third box:angle 1 = angle 2 Definition of angle bisectorNext box:triangle WNS ≅  triangle ENSAngle - Side - AngleNext: WN ≅  ENCorresponding parts of congruent triangles

The cans of paints and areas are illustrations of equivalent ratios.

5.5 cans are needed to paint an area of 2200 units square

The given parameter is:

[tex]\mathbf{Cans : Area = 1 : 400}[/tex]

Express as fraction

[tex]\mathbf{\frac{Cans }{ Area }= \frac{1 }{ 400}}[/tex]

Multiply both sides by Area

[tex]\mathbf{Cans= \frac{1 }{ 400} \times Area}[/tex]

When the area is 2200, we have:

[tex]\mathbf{Cans= \frac{1 }{ 400} \times 2200}[/tex]

[tex]\mathbf{Cans= 5.5}[/tex]

Hence, 5.5 cans are needed to paint an area of 2200 units square

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5.5 cans of paint are required to cover an area of 2200 square units, but since you can't have half a can, you would actually need 6 cans of paint.

This problem can be solved using simple division, which is a common concept in Mathematics. Given that one can of paint covers 400 square units, to find out how many cans of paint are needed to cover an area of 2200 square units, we need to divide the total area by the area that one can covers. So, 2200 ÷ 400 = 5.5.

However, you cannot have half a paint can, so you would need 6 cans of paint to fully cover the area. Here, we apply the mathematical principle of rounding up because you can't use half a can of paint.

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Answer:

Step-by-step explanation:

Look at the picture.

Answer:

Unusual

Step-by-step explanation:

we know that

The z-score is a measure of how close the given data point is to the mean of the values given with the standard deviation

so

if its z-score is greater than or equal to -2, or less than or equal to 2., then the data value is considered ordinary

if its z-score is less than -2 or greater than 2, then the data value is considered unusual

A data value is considered an outlier if its z-score is less than -2 or greater than 2.

Z-scores are a statistical measure that standardizes data, enabling comparisons across different datasets.

A z-score tells us how many standard deviations a data point is from the mean.

When a z-score is below -2 or above 2, it suggests that the data point is significantly distant from the mean of the dataset.

This indicates that the data point is an extreme observation, differing substantially from the rest of the data.

Outliers can be caused by various factors, such as measurement errors, data entry mistakes, or genuine anomalies in the underlying data. Identifying and handling outliers is crucial for robust statistical analysis and modeling.

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Answer:

[tex]W=839.464\ ft*lbf[/tex]

Step-by-step explanation:

The work done is the product of the magnitude of the force applied to the object by the magnitude of the displacement of the object by the cosine of the angle between the force and direction of the displacement. This is:

[tex]W=|F|*|r|cos(\theta)[/tex]

In this case

[tex]\theta=30\°[/tex]

|F|=180 pound force

The magnitude of vector AB is:

[tex]|r|= \sqrt{5^2 + 2^2}\\\\|r|= \sqrt{29}\ fr[/tex]

Finally the work is:

[tex]W=180*\sqrt{29}*cos(30\°)[/tex]

[tex]W=839.464\ ft*lbf[/tex]

Answer:

the answer is option 1, A

Step-by-step explanation:

Final answer:

Julian needs to practice at least 8 and 1/6 hours on each of the last two days of the week.

Explanation:

To determine the minimum number of hours Julian needs to practice on each of the last two days of the week, we can use an inequality. Julian needs to spend at least seven hours each week practicing the drums, and he has already practiced five and one-third hours this week. Let's represent the minimum number of hours he needs to practice on each of the remaining two days as 'x'. The inequality can be written as:

5 1/3 + 2x ≥ 7

Now let's solve the inequality:

So, the minimum number of hours Julian needs to practice on each of the last two days of the week is 8 and 1/6 hours (or approximately 8.17 hours).

Answer:

The correct answer to this problem is the second option: YZ is the longest side.

Step-by-step explanation:

In order to solve this problem, we need to understand the relationship between angle measure and side lengths in a triangle.  

In a triangle, the longest side is located across from the largest angle measure, the smallest side is located across from the smallest angle, and the middle length side is located across from the medium sized angle.

Using this knowledge, we can conclude that since XYZ is the smallest angle, XZ must be the smallest side.  We can also state that since YXZ is the largest angle, YZ is the longest side.  

Looking at the answer options, the only choice that aligns with this information is the second option: YZ is the longest side, and thus we can conclude that this is the correct answer.

Hope this helps!

YZ is the longest side

Step-by-step explanation:

Answer: 15 lines of symmetry.

Step-by-step explanation:

There are 15 lines of symmetry does a 15 sided polygon have.

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

Number of lines of symmetry does a 15 sided polygon have

Since, We know that;

Number or line of symmetry is equal to number of sides of polygon.

Here, Number of side = 15

Hence, There are 15 lines of symmetry does a 15 sided polygon have.

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Answer:

Ans1.

Outlier

A value that "lies outside" (is much smaller or larger than) most of the other values in a set of data.

Cluster

When data seems to be "gathered" around a particular value.

For example: for the values 2, 6, 7, 8, 8.5, 10, 15, there is a cluster around the value 8.

Ans.2

A line of best fit  (or "trend" line) is a straight line that best represents the data on a scatter plot.  

This line may pass through some of the points, none of the points, or all of the points.

i will explain through an example

1.  Prepare a scatter plot of the data on graph paper.

2.  Using a strand of spaghetti, position the spaghetti so that the plotted points are as close to the strand as possible.

3.  Find two points that you think will be on the "best-fit" line.  

4.  We are choosing the points (9, 260) and (30, 530).  

You may choose different points.  

5.  Calculate the slope of the line through your two points (rounded to three decimal places).

6.  Write the equation of the line.  

7.  This equation can now be used to predict information that was not plotted in the scatter plot.

Question: Predict the total calories based upon 22 grams of fat. ANS: 427.141 calories

Ans.3

1.Frequency is the number of times a result occurs, while “relative frequency” is the number of times the result occurs divided by the number of times the experiment is repeated.

2.Frequency can easily be determined by conducting a simple experiment and noting how many times the event in question occurs; no calculations are needed. On the other hand, relative frequency is determined by using simple division.

Answer:

1.40

Step-by-step explanation:

Last week, the price of oranges at the farmers market was 1.75

This week, the price has reduced by 20%

20% of 1.75 = 0.2 × 1.75 = 0.35

The price of the oranges this week is 1.75 - 0.35 = 1.40

Answer:

hey mate.

Step-by-step explanation:

Select the correct answer

What is the 10th term of the geometric sequence 3,6, 12, 24,48 ...?

A. 512

B. 3,072

C. 768

D. 1,536

is ... 768

Answer:

D

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r is the common ratio

r = 6 ÷ 3 = 12 ÷ 6 = 24 ÷ 12 = 48 ÷ 24 = 2

Using a₁ = 3 and r = 2, then

[tex]a_{10}[/tex] = 3 × [tex]2^{9}[/tex] = 3 × 512 = 1536 → D

Answer:

The answer to this question is p-125, because P is the cost of the bike, and reduce = subtract. YW :)

If p is the mountain bike's initial price in dollars, the (P- $ 125 is an algebraic equation indicates the lowered price.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation.

If p is the initial price of the mountain bike in dollars, the algebraic equation (P- $ 125) reflects the reduced price.

Hence, (P- $ 125) is the correct expression.

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Answer:

  D. x to the power of nine

Step-by-step explanation:

The applicable rule of exponents is ...

  (x^a)^b = x^(ab)

You have a=3/2, b=6, so ab = 3/2·6 = 9.

  (x^(3/2))^6 = x^(3/2·6) = x^9

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{64}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{0\qquad \textit{from the ground}}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf h(t)=-16t^2+64t+0\implies h(t)=-16t^2+64t\implies \stackrel{\textit{hits the ground}~\hfill }{0=-16t^2+64t} \\\\\\ 0=-16t(t-4)\implies t= \begin{cases} 0\\ \boxed{4} \end{cases}[/tex]

Check the picture below, it hits the ground at 0 feet, where it came from, the ground, and when it came back down.

Answer:

  $48.97

Step-by-step explanation:

Let p represent the marked price of the mower. Then the price with tax is ...

  with tax = p + 7.3%×p = 1.073p

The amount Flicka paid is the amount tendered less the change she received, so is ...

  3×$20 - 7.45 = with tax = 1.073p

To find p, we can divide by its coefficient:

  (3 × $20 - 7.45)/1.073 = p ≈ $48.97

The selling price before taxes was $48.97.

_____

Comment on the problem

If you check the answer, you find the amount with tax is ...

  $48.97 × 1.073 ≈ $52.54481 ≈ $52.54

so the change Flicka would have received would have been $7.46, not $7.45. If the price were $48.98, then the change would have been $7.44. There is no price at which the mower can be marked that will make the total with tax come to $52.55. There is no solution to this problem.

Answer:

$48.97

Step-by-step explanation:

She paid three $20 bills

3 × 20 = $60

She received $7.45 change

60 - 7.45 = $52.55

The mower was for $52.55 with sales tax.

The sales tax is 7.3%.

Before the sales tax (reduce tax).

52.55 × (1-7.3%)

= $48.97

Answer:

  D.  543.46

Step-by-step explanation:

The formula for the remaining balance on the loan is ...

  A = P(1 +r)^n +p((1 -(1 +r)^n)/r)

where P is the principal, p is the monthly payment, r is the monthly interest rate, and n is the number of months.

We have P=135,000, p = TBD, r = 3.6%/12 = .003, n = 20×12 = 240.

___

The monthly payment is given by the same formula by setting A=0. In this case, n is 25 years, or 300 payments. Solving for p, we get, ...

  p = Pr(1 +r)^n/((1 +r)^n -1) = Pr/(1 -(1 +r)^-n)

So, the monthly payment is ...

  p = 135,000×0.003/(1 -1.003^-300) = 683.10

Using this value in the formula for remaining balance, we get ...

  A = 135000(1.003^240) +683.10((1 -1.003^240)/0.003) = 37,459.20

___

80% of this balance is 29,967.36. The answer choices only make sense if we assume the interest penalty is equivalent to the interest being compounded monthly:

  $29,967.36 × (1.003^6 -1) = $543.47

The closest match among answer choices is ...

  D.  543.46