10x + 3x - 87 = -10x + 57

The coordinates of the midpoint of the segment connecting points are (4,-1).

To find the coordinates of the midpoint of the segment:

Given points -

Now, add the respective values in the formula:

Therefore, the coordinates of the midpoint of the segment connecting points are (4, -1).

Know more about coordinates here:

https://brainly.com/question/17206319

#SPJ4

Answer:

15, 9, 3n

Step-by-step explanation:

Just multiply the number of red balls by 3 to get total number, and divide the total number by three to get the number of red balls

Answer:

What math game is this?

Oh and this guy is correct.

Step-by-step explanation:

Answer:

Area = 84.1 yd^2

Step-by-step explanation:

Important Note:

For these kinds of problems, it's important to draw the triangle when solving.  I'll attach a picture of a triangle I used to solve for the Area.

In my picture, the angle names S, T, and R are blue and the info we're already given (i.e., r = 10 yd, m∠S = 55°, m∠R = 29°

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

Classifying △ STR:

Thus, we'll have to find the area using a non-right triangle sine area formula.  

Sine formulas for the area of a non-right triangle:

Furthermore, the formulas use a, b, and c for sides and A, B, and C for angles:

Area = 1/2bc * sin (A)

Area = 1/2ac * sin (B)

Area = 1/2ab * sin (C)

Substituting s, t, r, S, T, and R for a, b, c, A, B, and C in the sine area formula:

When we rewrite the sine area formulas by substituting s, t, r, S, T, and R instead of a, b, c, A, B, and C, we have:

Area = 1/2tr * sin (S)

Area = 1/2sr * sin (T)

Area = 1/2st * sin (R)

Layout of the formula:

Thus, we want either angle S to be sandwiched between r and t or angle T to be sandwiched between r and s.

Finding the measure of angle R:

Thus, we can find m∠R by subtracting the sum of m∠S (55°) and m∠T (96°) from 180:

m∠S + m∠T + m∠R = 180

m∠R = 180 - (m∠S + m∠T)

m∠R = 180 - (55 + 96)

m∠R = 180 - 151

m∠R = 29

Thus, m∠R = 29°.

Finding S using the Law of Sines:

To find S, we'll need to use the Law of Sines, which also has three forms:

a / sin (A) = b / sin (B) = c / sin (C)

As the proportion shows, we're able to find either one side or one angle if we have one completed ratio and either one angle in the proportion in which we're trying to find a side or one side in the proportion in which we're trying to find an angle.

Substituting s, t, r, S, T, and R for a, b, c, A, B, and C in the Law of Sines:

When we rewrite the law of sines by substituting s, t, and r, S, T, and R for a, b, c, A, B, and C in the Law of Sines, we have:

s / sin (S) = t / sin (T) = r / sin (R)

Finding s using the Law of Sines:

Since we now know that m∠R = 29°, we can use s / sin (S) = r / sin (R) and plug in 55 for S, 10 for r, and 29 for R to find s:

Step 1:  Multiply both sides by sin (55) to find s:

(s / sin (55) = 10 / sin (29)) * sin (55)

s = 16.8963653

Thus, s = 16.8963653 yd.

It's best not to round until we get to the end so we find an exact value for the area.  Then we'll round it to the nearest tenth.

Finding the Area using Area = 1/2sr * sin (T):

Now, we can plug in 16.8963653 for s, 10 for r, and 96 for T to find the area of △ STR.  Then, we can round to the nearest tenth at the end to find the final answer:

Area △ STR = 1/2sr * sin (T)

Area △ STR = 1/2(16.8963653)(10) * sin (96)

Area △ STR = 84.48182648 * sin (96)

Area △ STR = 84.0190262

Area △ STR = 84.1

Thus, the area of △ STR is about 84.1 yd.

The graph of the parabola for the quadratic function, f(x) = x² -12·x + 27, with the vertex point (6, -9), and the y-intercept, (0, 27), created with MS Excel is attached, please find

The x-coordinates of the vertex of the parabola with an equation of the form; f(x) a·x² + b·x + c are;

-b/(2·a)

The specified quadratic function is f(x) = x² - 12·x + 27

Therefore, a = 1, b = -12, and c = 27

The x-coordinate of the vertex is; x = -(-12)/(2 × 1) = 6

The y-coordinate of the vertex is therefore;

f(6) = 6² - 12 × 6 + 27 = -9

The coordinate of the vertex is therefore; (6, -9)

A point on the graph, such as the y-intercept can be found as follows;

f(0) = 0² - 12 × 0 + 27 = 27

The y-intercept of the graph is (0, 27)

Please find attached the graph of the parabola of the function f(x) = x² - 12·x + 27, created with MS Excel

Learn more on the graph of a quadratic function here: https://brainly.com/question/10441997

#SPJ1

We can establish a "work rate" or velocity for Cody. It will represent the fraction of the job he does in an hour, or the "job per hour". If he does 1 job in 87 hours, it means that he does 1/87 of the job in an hour.

Similarly, when both Cody and Patricia work at the same time, they can do 1/58 of the job in an hour.

The combined job velocity (when they work together) is the sum of their individual velocities. Let's call P the velocity for Patricia:

Now we can solve for P, which will give us the fraction of work Patricia is able to do in 1 hour:

We can simplify the fraction, but for now, let's say Patricia does 29/5046 of the work in an hour. The time she would take to do the hob will be the inverse of that: 5046/29, which simplified gives us:

Then, Patricia will take 174 hours to do the job alone.

If the current interest rate are 4. 25%, You can afford a car of price $36591.75

An interest rate is a fee that a lender assesses to a borrower; it is calculated as a percentage of the principal, or the loaned amount. The annual percentage rate, or APR, is typically used to express the interest rate on a loan (APR).

An interest rate may also apply to earnings from savings accounts or certificates of deposit at a bank or credit union (CD). Annual percentage yields are used to calculate the interest earned on these deposit accounts (APY).

S.I =  P*R*T/100  where:

S.I = Simple interest

R = Rate of interest

P = Principal/Amount

T = Time in years

∴ R = S.I*100/P*T

Given:

P = $325 per month

R = 4.25%

T = 9 years

∵ P is in month we multiply it by 12 = 325×12

                                                   ∴P = $3900

∴ S.I for 9 years = $1491.75

Now,

You can afford a car of expense

3900*9 + S.I = 35,100 + 1491.75

                    = $36591.75

To learn more about simple interest :

brainly.com/question/25845758

#SPJ4

Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

<95141404393>

Therefore, the standard error of the mean, σ= 2.53 (approx).

Random sampling is a part of the sampling technique in which each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

Given: A simple random sample of 10 items resulted in a sample mean of 25.

The population standard deviation is = 8.

We have to find out the standard error of the mean, σ/Sample Size n,

so we will first calculate σ as;

σ = Population standard deviation = 8

Sample Size n = 10

Substituting values in the formula to find the standard error of the mean, we get;σ/√n = 8/√10 = 2.53 (Round off the value to two decimal places)

To know more about   standard error :

https://brainly.com/question/13179711

#SPJ11

The mode of the given data set is 0%.

The mode of a set of data represents the value or values that appear most frequently.

In the given data set:

0%, 0%, 8.1%, 13.6%, 19.4%, 20.7%, 10.0%, 14.2%

We can observe that the value 0% appears twice,

and no other value appears more than once.

Learn more about Mode here:

https://brainly.com/question/30891252

#SPJ11

Answer:

Without knowledge of the specified tolerance or further data, it is not possible to determine the gauge's capability conclusively.

The sample standard deviation of 0.0083 grams from the 15 repeated measurements of one sheet of paper indicates the variability in the weight measurements. A lower standard deviation suggests less variability and, in this case, it indicates that the measurements of the paper weight were relatively consistent.

The study in Technometrics aimed to assess the capability of a gauge by measuring the weight of the paper. With the given summary statistic, it is difficult to draw definitive conclusions about the gauge's capability without additional information.

To evaluate the gauge's capability, it would be helpful to compare the sample standard deviation (0.0083 grams) to a predetermined tolerance or specification limit. This tolerance represents the acceptable range within which the paper weight should fall for it to be considered within the desired capability.

By comparing the standard deviation to the tolerance limit, we can assess if the gauge is capable of providing measurements within the acceptable range. If the standard deviation is significantly smaller than the tolerance, it suggests that the gauge is effective and reliable in measuring the weight of the paper.

However, without knowledge of the specified tolerance or further data, it is not possible to determine the gauge's capability conclusively. Further analysis and context-specific information would be necessary to draw more precise conclusions.

Learn more about gauge's capability from below link

https://brainly.com/question/15734839

#SPJ11

Answer:

Without knowledge of the specified tolerance or further data, it is not possible to determine the gauge's capability conclusively.

The sample standard deviation of 0.0083 grams from the 15 repeated measurements of one sheet of paper indicates the variability in the weight measurements. A lower standard deviation suggests less variability and, in this case, it indicates that the measurements of the paper weight were relatively consistent.

The study in Technometrics aimed to assess the capability of a gauge by measuring the weight of the paper. With the given summary statistic, it is difficult to draw definitive conclusions about the gauge's capability without additional information.

To evaluate the gauge's capability, it would be helpful to compare the sample standard deviation (0.0083 grams) to a predetermined tolerance or specification limit. This tolerance represents the acceptable range within which the paper weight should fall for it to be considered within the desired capability.

By comparing the standard deviation to the tolerance limit, we can assess if the gauge is capable of providing measurements within the acceptable range. If the standard deviation is significantly smaller than the tolerance, it suggests that the gauge is effective and reliable in measuring the weight of the paper.

However, without knowledge of the specified tolerance or further data, it is not possible to determine the gauge's capability conclusively. Further analysis and context-specific information would be necessary to draw more precise conclusions.

Learn more about gauge's capability from below link

brainly.com/question/15734839

#SPJ11

Answer:

2.5 mph

Step-by-step explanation:

70 miles per hour :4 hours

35 miles per hour:8 hours

1 mile per hour:16 hours

60 miler per hour

do 16/6

2.5 hours

Answer:

24s+ 200 ≥ 500

Step-by-step explanation:

Let s be the number of sales

200 + 24s is the amount that they will make

They want to make at least 500 so the  amount they make must be greater than or equal to 500

200 + 24s≥ 500

Changing the order on the left side

24s+ 200 ≥ 500

The solution of this system is (x, y) = (- 6, 2).

The endpoints of line segment AB and its midpoint are described by algebraic expressions. The following relationship between the endpoints and the midpoint is shown by the following formula:

M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)

(- 7 / 2, - 8) = 0.5 · (2 · x, y - 1) + 0.5 · (y + 3, 3 · x + 1)

(- 7 / 2, - 8) = (x, 0.5 · y - 0.5) + (0.5 · y + 1.5, 1.5 · x + 0.5)

(- 7 / 2, - 8) = (x + 0.5 · y + 1.5, 1.5 · x + 0.5 · y)

(x + 0.5 · y , 1.5 · x + 0.5 · y) = (- 5, - 8)

Which is equivalent to the following system of linear equations:

x + 0.5 · y = - 5

1.5 · x + 0.5 · y = - 8

The solution of this system is (x, y) = (- 6, 2).

To learn more on midpoints: https://brainly.com/question/28224145

#SPJ1

Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Answer:

Well if your on chrome book sign out and select add person and make your new email and password and you have a new account.

Step-by-step explanation:

Hope this helps and have a wonderful day!!!

Answer:

Account for what, brain ly

Step-by-step explanation:

step 1: Go to sign up

step 2: create a email

step 3: create password

We are given that R is a random variable with the probability density function (PDF) given

We have, f(r) = 3/4 (1 − (6 − r)² if 5 ≤ r ≤ 7 and f(r) = 0 otherwise.

Area of the circular region: \($A = \pi r^2$\)

For a continuous random variable X with probability density function f(x), the expected value of a function g(X) is given by the following integral:

\($E[g(X)] = \int_{-\infty}^\infty g(x)f(x)dx$\)

Here, our function is the area of the circular region, which is given by A = πR2.

Therefore, we have g(R) = πR².

Substituting this into the formula above, we get:

\($E[\pi R^2] = \int_{-\infty}^\infty \pi R^2f(R)dR$\)

However, f(R) is only non-zero for values of R between 5 and 7. Therefore, we can simplify the above expression as follows:

\($E[\pi R^2] = \int_{5}^7 \pi R^2f(R)dR$\)

Using the given pdf, we can substitute f(R) as follows:

\($f(R) = \begin{cases} \frac{3}{4}(1 - (6 - R)^2) & \text{if } 5 \leq R \leq 7 \\ 0 & \text{otherwise} \end{cases}$\)

Substituting this into the above integral, we get:

\($E[\pi R^2] = \int_{5}^7 \pi R^2\cdot\frac{3}{4}(1 - (6 - R)^2)dR$\)

Expanding the square and simplifying, we get:

\($E[\pi R^2] = \int_{5}^7 \pi R^2\cdot\frac{3}{4}(2R - R^2 - 35)dR$\)

\($E[\pi R^2] = \frac{3\pi }{4}\int_{5}^7 (2R^3 - R^4 - 35R^2)dR$\)

Evaluating the integral, we get:

\($E[\pi R^2] = \frac{3\pi }{4}\left[\frac{1}{2}R^4 - \frac{1}{5}R^5 - \frac{35}{3}R^3\right]_{5}^{7}$\)

\($E[\pi R^2] = \frac{3\pi }{4}\left[\left(\frac{7^4}{2} - \frac{7^5}{5} - \frac{35\cdot7^3}{3}\right) - \left(\frac{5^4}{2} - \frac{5^5}{5} - \frac{35\cdot5^3}{3}\right)\right]$\)

\($E[\pi R^2] = \frac{3\pi }{4}(468.67)$\)

Therefore, the expected area of the resulting circular region is approximately 1101.38 square meters (rounded to four decimal places)

To know more about the "Area of the circular region": https://brainly.com/question/19053586

#SPJ11

We say that there are n-1 degrees of freedom in this case.

The number of values free to vary after certain restrictions have been placed on the data is the definition of degrees of freedom (df). Degrees of freedom are a key concept in inferential statistics and are often used in hypothesis testing and the calculation of confidence intervals. In essence, degrees of freedom represent the number of values in a data set that are free to vary after the mean has been calculated.

For example, if we have a sample of n observations and we know the mean of the sample, then we can calculate the sum of the n observations. However, we cannot set the value of the last observation, as it is determined by the values of the first n-1 observations and the mean. Therefore, we say that there are n-1 degrees of freedom in this case.

Degrees of freedom are also important in the calculation of standard errors, t-tests, and F-tests. In these cases, the degrees of freedom reflect the amount of information in the sample and are used to calculate the probability of observing a particular test statistic under the null hypothesis.

To learn more about probability visit: https://brainly.com/question/30034780

#SPJ11

The approach to probability that assumes that the events are equally likely is d. classical probability.

Classical probability, also known as a priori or theoretical probability, is based on the assumption that all possible outcomes of an experiment or event are equally likely. In this approach, probability is determined by the ratio of favorable outcomes to the total number of equally likely outcomes.

For example, when rolling a fair six-sided die, the classical probability of rolling a specific number, such as a 3, is 1 out of 6 because there is one favorable outcome (rolling a 3) out of six equally likely outcomes (rolling any number from 1 to 6).

Classical probability is often used in situations where the outcomes are known and the sample space is well-defined. However, in practice, events may not always have equally likely outcomes, and other approaches such as empirical or subjective probability may be more appropriate.

Learn more about probability here:

https://brainly.com/question/32004014

#SPJ11

Answer:

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

Given sequence:

Find the common ratio, the ratio of two consecutive terms:

or

Step-by-step explanation:

5(3+6)2-62

(15+30)2-62

30+60-62

90-62=28

Answer:

This is a tough one, I see why you are confused. The answer would be 50

Step-by-step explanation:

I used process of elimination and working backwards

First I took the first option (50) and added 10. Then divided it by 5 to isolate the X value. I plugged the X value into the (11x+3) and got 135. The missing angle is 45. 50+45+85=180

Hope this helped!

5,9,17  cases a triangle Cannot be constructed with the given lengths of sides.

What exactly are triangles?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the three sides' end-to-end connections at a point. The triangle's three angles add up to 180 degrees in total.

What is a triangle and what are its types?

Triangles are three-sided shapes. The various kinds of triangles go by various names. The size of the angles and side lengths determine what kind of triangle it is (corners).

                         Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.

Learn more about Triangles

brainly.com/question/2773823

#SPJ4

Answer:

\(2\sqrt{3}+3\)

Step-by-step explanation:

\($\frac{3}{2 \sqrt 3 - 3}$\)

Rationalize the fraction.

\($\frac{3}{2 \sqrt 3 - 3}\cdot \frac{2 \sqrt 3 + 3}{2 \sqrt 3 + 3} =\frac{6\sqrt{3}+9 }{12-9} =\frac{6\sqrt{3}+9 }{3} =2\sqrt{3}+3 $\)

Note that I used the positive signal because we would have a difference of squares.

Given :

Distance travelled , d = 180 miles.

Time taken , t = 4 hours.

To Find :

Speed in feet per minutes.

Solution :

Distance in feet is , d = 180×5280 = 950400 feet.

Time taken , t = 4×60 = 240 minutes.

Speed is given by , \(s=\dfrac{Distance}{Time \ Taken}\)

\(S=\dfrac{950400}{240}\ ft/min\\\\S=3960\ ft/min\)

Hence, this is the required solution.

The hypothetical constant-benefit payment is $76354.69. Hence, the correct option is b.

To calculate the hypothetical constant-benefit payment for a variable annuity contract, we need to use the present value of an annuity formula. The formula is as follows

Constant-benefit payment = P / [(1 - (1 + r)⁻ⁿ) / r]

Where

P = Accumulated amount in the annuity contract ($750,000)

r = Assumed investment return (9% or 0.09)

n = Life expectancy in years (25)

Using the given values in the formula, we can calculate the constant-benefit payment

Constant-benefit payment

= 750,000 / [(1 - (1 + 0.09)⁻²⁵) / 0.09]

= 750,000 / [(1 - (1.09)⁻²⁵) / 0.09]

= 750,000 / [(1 - 0.115) / 0.09]

= 750,000 / [0.884 / 0.09]

= 750,000 / 9.8

≈ 76354.69

Calculating this value gives us approximately $76354.69.

To know more about constant-benefit payment here

https://brainly.com/question/17233429

#SPJ4

-- The given question is incomplete, the complete question is

"Assume that at retirement you have accumulated $750,000 in a variable annuity contract. The assumed investment return is 9%, and your life expectancy is 25 years. What is the hypothetical constant-benefit payment?

a. $51,481.38  b. $76,354.69  c. $30,000.00   d. $33,333.33  e. The answer cannot be determined"--

Let x be the number of units produced per hour, then:

Answer:

Answer:

6.  x < -5 and x > 2
7.  -5 < x < 2

Step-by-step explanation:

If the circle open, (think O shaped) then the inequality doesn't include that number it is over. If the circle is closed, (think solid black circle) than the number is included in the inequality. Arrows pointing to the right include all numbers greater than the dot, pointing to the left includes all numbers less than where the dot is.

6. We have two open circles. So our inequality symbols will use < and >, not ≤ or ≥. The first of the two arrows starts -5 with an open circle and points to the left, representing all numbers less than -5. So the inequality for that arrow is x < -5. The second arrow shows an open circle at 2 pointing to the right. This represents all numbers greater than 2, excluding 2 itself. So the matching inequality would be x > 2. We put these two inequalities together such that x < -5 and x > 2.

7. We have a single segment that spans -5 to 2 with open circles. This means that the inequality represents values in between -5 and 2, excluding those endpoints. So -4.9999 is included and so is 1.999, but not -5 or 2. The inequality that represents this situtation would be -5 < x < 2.

Any of the mentioned inequalities can be used with a variable of your choosing. (I'm using x as an example)