I need you guys help simplifying these questions!!
1. 6n+5(10n−7)
2. 3−10(4p−1)
3. −4(8k+5)−5(9k+4)

Question 1:

\(\frac{2}{3} n-16=-\frac{5}{6}n+2\), solve for n.

\(\frac{2}{3} n-16=-\frac{5}{6}n+2\)

=> \(\frac{2}{3} n=-\frac{5}{6}n+18\)

=> \(\frac{2}{3} n+\frac{5}{6}n=18\) =>\(\frac{4}{6} n+\frac{5}{6}n=18\)

=> \(\frac{9}{6} n=18\) => \(\frac{3}{2} n=18\)

=> \(n=18(\frac{2}{3})\)

=> \(n=6(2)\)

Sol: n=12

Question 2:

\(5-\frac{1}{3}p=\frac{4}{9}p+12\), solve for p.

\(5-\frac{1}{3}p=\frac{4}{9}p+12\)

=>\(5=\frac{4}{9}p+\frac{1}{3}p+12\)

=> \(5=\frac{4}{9}p+\frac{3}{9}p+12\)

=>\(5=\frac{7}{9}p+12\)

=> \(-7=\frac{7}{9}p\)

=> \(-7(\frac{9}{7}) =p\)

=> \(-(9)=p\)

Sol: p=-9

Question 3:

The relationship between ∠2 and ∠7 is that they are alternate interior angles.

Question 4:

The relationship between ∠1 and ∠3 is that they are corresponding angles.

Question 5:

The relationship between ∠4 and ∠5 is that they are alternate exterior angles.

Using the range to compare the variability of data sets is a rather insensitive measure of data variance is the correct answer.

In this question,

The range tells you the spread of your data from the lowest to the highest value in the distribution. The range is the difference between the smallest and highest numbers in a list or set. To find the range, first put all the numbers in order. Then subtract (take away) the lowest number from the highest.

Data variability also known as spread or dispersion, refers to how spread out a set of data is. Variability gives users a way to describe how much data sets vary and allows users to use statistics to compare their data to other sets of data.

Thus the disadvantage of using range is that it does not measure the spread of the majority of values in a data set, it only measures the spread between highest and lowest values.  

The options are a) It is a rather insensitive measure of data variance, b) It is hard to compute, c) It is a sensitive measure of data variance, d) It does not have any variance.

Hence we can conclude that using the range to compare the variability of data sets is a rather insensitive measure of data variance.

Learn more about range of data variance here

https://brainly.com/question/14617313

#SPJ4

Answer:

-8(3x-8)

Step-by-step explanation:

Factor -8 out of -24x+64

9514 1404 393

Answer:

 5/36

Step-by-step explanation:

5 and 36 have no common factors, so the fraction 5/36 is already in simplest form.

Answer:

Step-by-step explanation:

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

A solution is a process of giving the unknown variables values that make the equation's equality true. A value or group of values (one for each unknown) that, when substituted for the unknowns, cause the equation to produce an equality is known as a solution.

In order to build an equation, the equal sign is placed between two numerical or variable expressions, as in 3x+5=11. The solution to an equation is a number that may be used as the variable to generate a true number statement. 6+5=11 is true, as stated by the formula 3(2)+5=11. The solution is consequently 2,

6+(x/2)=1/4(x-4)-1

(12+x)/2=(x-4-4)/4

24+2x=x-8

x= -32

Therefore, option D is correct.

For the given equation 6+(x/2)=1/4(x-4)-1 the solution is x= -32. So, option D is correct.

To know more about solutions, visit:

https://brainly.com/question/24816340

#SPJ1

Answer:y=5x-3

Step-by-step explanation:

Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.

The amount of water needed to be drank is approximately 2 cups of water are required for every pound of body weight reduced.

Vanessa would need to drink about ten cups of liquid to replace the weight she lost while running.

Refilling fluid: To add fluid to something that has been drained, in particular: to replace any fluids the body has lost from dehydration. assist a patient in hydrating.

Oral rehydration solutions (ORSs), which include Pedialyte, are used to treat dehydration. ORSs, which help replace lost fluids, include the correct ratio of salt, sugar, potassium, and other minerals.

To learn more about rehydrate, visit,

brainly.com/question/4620593

#SPJ4

Complete question - A general rehydration recommendation after exercise is 2.5 cups of fluid for every 1 pound of body weight lost. Using this guideline, how much fluid would Vanessa need to consume to make up for the weight that was lost during her run?

Calculation: 2 cups x lbs of body weight lost = cups of water needed

A. Approximately 4 cups of fluid

B. Approximately 8 cups of fluid

C. Approximately 6 cups of fluid

D. Approximately 10 cups of fluid

7. Vanessa asks if she should start using sports drinks. Which of the following would best answer Vanessa's question?

A. A sports drink is not beneficial for you at this time and may provide unnecessary calories.

B. A sports drink would be beneficial to replace fluid and electrolytes when exercising for less than 30 minutes.

C. A sports drink would be beneficial on days when you are exercising for over an hour at a higher intensity.

8. If Vanessa uses a sports drink in the future, how much glucose, sodium and potassium should be provided per 24 fluid ounces of sports drink?

A. No more than 30 g of glucose, 450 g of sodium and 225 mg of potassium.

B. No more than 75 g glucose, 150 mg sodium, 175 mg potassium.

C. No more than 15 g of glucose, 500 mg sodium, 200 mg potassium.

D. No more than 45 g of glucose, 225 mg of sodium and 275 mg of potassium.

geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately  3.7973 × 10⁹ years old is the sample.

The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.

According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.

t1/2 of U₂₃₈ is 4.5 × 10⁹ years

moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles

moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles

Now, U₂₃₈ → Pb₂₀₆

As Pb₂₀₆ comes from U₂₃₈ hence,

moles of  U₂₃₈ decayed = moles of  Pb₂₀₆

                                        = (0.686 × 10⁻⁶ / 206) moles

Therefore, initial moles of U₂₃₈:

N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles

and N = (1 × 10⁻⁶ / 238) moles

Now, λ (decay constant) = 0.693 / (t1/2)

                                        = 0.693 / ( 4.5 × 10⁹ years)

So,

t = 2.303 / λ × log (N₀ / N)

t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]

t = 14.95 × 10⁹ × 0.254

t = 3.7973 × 10⁹ years.

Thus, the sample is: 3.7973 × 10⁹ years old.

To know more about 238U refer to:

https://brainly.com/question/13993023

#SPJ4

Answer:

Step-by-step explanation:

Let S be the surface area of the prism

     B be the area the base (right-angered triangle)

     L be the lateral surface area

Formula :

S = 2×B + L

……………………

\(B=\frac{12\times 9}{2} = 54\)

\(\text{Length \ of \ the \ third \ side}=\sqrt{12^{2}+9^{2}} =15\)

L = 5×(9 + 12 + 15) = 180

S = 2×B + L

S = 2×54+180 = 288 in²

Answer:

2 hours

Step-by-step explanation:

2 times 35 = 70

70 + 75 = 145

Answer:

He worked 2 hours

Step-by-step explanation:

75 + 35*2 = 145

An equation for the line of best fit for a men's height, y, based on her shoe size, x is; y = 0.25x + 66.6

A line of best fit can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association (correlation) between a data.

In this scenario, the men's shoe size would be plotted on the x-axis of the scatter plot while her height would be plotted on the y-axis.

By critically observing the scatter plot (see attachment) which models the data, we can reasonably deduce that an equation for the line of best fit is given by:

y = 0.25x + 66.6

Interpret the meaning of the residual from part B is given below.

Read more on line of best fit here:

brainly.com/question/12891189

#SPJ1

Answer: You need 27 more dollars.

Step-by-step explanation: This is because for this problem, you need to subtract 65 from 38 to get 27

The solutions for the equation (2x+3)² = 10 is:

Given:

the equation is:

(2x+3)² = 10

we need to solve the following equation.

⇒ (2x+3)² = 10

taking square roots on both sides.

⇒ √(2x+3)² = √10

⇒ 2x+3=±√10

Now solving:

2x+3=√10 and 2x+3=-√10

2x=√10-3 and 2x=-√10-3

x=√10-3/2 and x=-√10-3/2

Hence we get the solutions of the given equation.

Learn more about System of equations here:

brainly.com/question/13729904

#SPJ1

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

Learn more about circumcenter to visit this link

https://brainly.com/question/16276899

#SPJ4

Hey there!

ANSWER: vertex

Fill in the blank:

The endpoint is the vertex of the angle.

This is your answer because an angle is formed by two rays which are the sides of an angle and they have an endpoint called the vertex.

Hope this helps!

\(-TestedHyperr\)

Answer:

Vertex

Step-by-step explanation:

An angle is made the endpoints of two rays meet together, forming the vertex of the angle.

Answer: -34+49i

Step-by-step explanation:

The solution to the system of equations is x = 1 and y = 5. The coordinate of the solution is (1, 5).

The system of equations consists of y = 2x + 3 and -y + 7 = -2. To find the coordinate of the solution, we need to solve the equations simultaneously.

To solve the system of equations, we can start by solving the second equation for y:

-y + 7 = -2

Adding y and subtracting 7 from both sides, we get:

y = 7 - 2

Simplifying, we find:

y = 5

Now that we know the value of y, we can substitute it into the first equation:

y = 2x + 3

5 = 2x + 3

Subtracting 3 from both sides, we have:

2 = 2x

Dividing both sides by 2, we find:

x = 1

Therefore, the solution to the system of equations is x = 1 and y = 5. The coordinate of the solution is (1, 5).

For more information on  equations visit: brainly.com/question/7098873

#SPJ11

The corresponding probabilities are: A. P(R) = 0.72 B. P(R') = 0.28 C. P(A ∩ R) = P(R) * P(A | R) = 0.72 * 0.51 = 0.367 D. P(A | R) = 0.51 E. P(A ∩ R') = P(R') * P(A | R') = 0.28 * 0.10 = 0.028 F. P(A' ∩ R) = P(R) * P(A' | R) = 0.72 * 0.49 = 0.352 G. P(A' ∩ R') = P(R') * P(A' | R') = 0.28 * 0.90 = 0.252

(a) The tree diagram with the corresponding probabilities is:

A (0.51) A' (0.49) A (0.10) A' (0.90)

(b) The proportion of students who earn an A and don't attend class regularly is:

P(A ∩ R') = 0.028

(c) The chance that a randomly chosen student will earn an A in the class is:

P(A) = P(A ∩ R) + P(A ∩ R')

= 0.367 + 0.028

= 0.395

(d) Given that a student earned an A, the chance they attend class regularly is:

P(R | A) = P(A ∩ R) / P(A)

= 0.367 / 0.395

≈ 0.9291 (rounded to four decimal places)

To know more about proportion,

https://brainly.com/question/31010676

#SPJ11

Complete question:

A professor has noticed that students hat attend class regularly, mss no more than two classes per term, generally get better grades. For he class, the overall percent o students who attend regularly s 72% or those who come to class on a regular basis, 51% receive A's. Of those who don't attend regularly, only 10% get A's. (b)Among all students what proportion earn an A and don't attend class regularly?

The exponential equation is y = 2,642(2.5)^x. x represents the number of days.

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given that a video was released to the public, it already had 2,642 views.

One day later, the number of views increased to 3,963.

The number of viewers after one day is ( 3,963 + 2,642 ) = 6,605

Assume that the exponential function y = a(b)^x represents the number of viewers. x represents the number of days.

Putting x = 0 and  y = 2,642 in y = a(b)^x:

2,642 = a(b)⁰

a = 2,642

Putting x = 1 and  y = 6,605 in y = a(b)^x:

6,605 = a(b)¹

Putting a = 2,642:

6,605 = 2,642(b)¹

b = 6,605/2,642

b = 2.5

To learn more about  exponential function, click on the below link:

https://brainly.com/question/27733251

#SPJ1

Answer:

(-4, 2).

Step-by-step explanation:

8x + 5y=-22

-3x - 5y = 2   Adding the 2 equations:

5x = -20

x = -4.

Substitute x = -4 in the first equation:

8(-4) + 5y = -22

5y = -22 + 32

5y = 10

y = 2.

Answer:

\(x=-4,\:\\y=2\)

Step-by-step explanation:

\(\begin{bmatrix}8x+5y=-22\\ -3x-5y=2\end{bmatrix}\\\mathrm{Multiply\:}8x+5y=-22\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:24x+15y=-66\\\mathrm{Multiply\:}-3x-5y=2\mathrm{\:by\:}8\:\mathrm{:}\:\quad \:-24x-40y=16\\\\\begin{bmatrix}24x+15y=-66\\ -24x-40y=16\end{bmatrix}\\\\-24x-40y=16\\+\\\underline{24x+15y=-66}\\-25y=-50\\\begin{bmatrix}24x+15y=-66\\ -25y=-50\end{bmatrix}\\-25y=-50\\\mathrm{Divide\:both\:sides\:by\:}-25\\\frac{-25y}{-25}=\frac{-50}{-25}\\y=2\\\)

\(\mathrm{For\:}24x+15y=-66\mathrm{\:plug\:in\:}y=2\\24x+15\times\:2=-66\\24x+30=-66\\24x+30-30=-66-30\\24x=-96\\\frac{24x}{24}=\frac{-96}{24}\\x=-4\\\\\\x=-4,\:y=2\)

The correct sentence is C, "-3 > -8."

Here's how you can determine which sentence is correct:

In sentence A, -3 is not greater than 2, so sentence A is incorrect.

In sentence B, -3 is not less than -6, so sentence B is incorrect.

In sentence C, -3 is indeed greater than -8, so sentence C is correct.

In sentence D, -3 is not greater than -2, so sentence D is incorrect.

Remember that when comparing two negative numbers, the one with the smaller absolute value is the larger negative number. For example, -8 is a larger negative number than -3 because -8 is closer to 0 (which is the smallest possible number). Similarly, -2 is a larger negative number than -3 because -2 is closer to 0.

Hence, The correct sentence is C, "-3 > -8."

To learn more about Negative Numbers,

visit; brainly.com/question/258076

#SPJ4

Answer:

a) distance traveled is 16 miles.

b) distance traveled is 40 miles.

Step-by-step explanation:

Speed is a scalar quantity which describe the rate of distance moved with time.

i.e speed = \(\frac{distance}{time}\)

Given that: distance = 2 1/3 miles = \(\frac{7}{3}\) miles, time = 3 1/2 minutes = \(\frac{7}{2}\) minutes.

Then;

speed = \(\frac{7}{3}\) ÷ \(\frac{7}{2}\)

          = \(\frac{7}{3}\) x \(\frac{2}{7}\)

          = \(\frac{2}{3}\)

The car's steady speed is 0.67 miles per minute.

a) when the time is 24 minutes, the distance covered can be determine by:

distance = speed x time

              = \(\frac{2}{3}\) x 24

              = 16

distance traveled is 16 miles.

b) When the time is 1 hour (60 minutes), the distance traveled can be determined by:

distance = speed x time

              = \(\frac{2}{3}\) x 60

              = 40

distance traveled is 40 miles.

Answer:x=9

Step-by-step explanation:

-2x+3=-15

Subtract 3 on both sides:

-2x+3-3=-15-3

-2x=-18

Divide -2 on both sides:

-2x/-2=-18/-2

x=9

If the expression (- 2x + 3) is equivalent to (- 15), then [x] is equivalent to 9.

Given is the equation as follows -

- 2x + 3 = - 15

The given equation is -

- 2x + 3 = - 15

Solving, we get -

- 2x = - 15 - 3

- 2x = - 18

 2x = 18

 x = 9

Therefore, if the expression (- 2x + 3) is equivalent to (- 15), then [x] is equivalent to 9.

To solve more questions on functions, expressions and polynomials, visit the link below -

brainly.com/question/17421223

#SPJ2

Answer:

\((x+1)(-3x-6)\)

Step-by-step explanation:

Polynomial Form Steps:

\((1+x)(x*2-5x-6)\\=(x+1)(-3x-6)\)

The price of the turkey based on the percentage given is $15.81.

It was stated that the cost is $15.50 but that there was a 2% increment in price.

Therefore, the new price will be:

= $15.50 + (2% × $15.50)

= $15.50 + $0.31

= $15.81

Learn more about percentages on:

brainly.com/question/24304697

#SPJ1

The population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

All these elements are taken into account when formulating the population growth formula.

r = [(b + i) - (d + e)]/1000

Put the values in the formula.

r =  [(2,000 + 100) - (500 + 200)]/1000

r = 2100 - 700/ 1000

r = 1.4

Thus, the population growth rate (r) for 2009 in the tiny country of fremont is found as 1.4.

To know more about the population growth rate, here

https://brainly.com/question/14174002

#SPJ4

Answer:

19.4

Step-by-step explanation:

7/34 = 4/x, 7x = 136, x = 19.4