A tank contains 1080 L of pure water. Solution that contains 0.07 kg of sugar per liter enters the tank at the rate 7 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate.Required:a. How much sugar is in the tank at the begining?b. Find the amount of sugar after t minutes.c. As t becomes large, what value is y(t) approaching ?

Answers

Answer 1

(a) Let [tex]A(t)[/tex] denote the amount of sugar in the tank at time [tex]t[/tex]. The tank starts with only pure water, so [tex]\boxed{A(0)=0}[/tex].

(b) Sugar flows in at a rate of

(0.07 kg/L) * (7 L/min) = 0.49 kg/min = 49/100 kg/min

and flows out at a rate of

(A(t)/1080 kg/L) * (7 L/min) = 7A(t)/1080 kg/min

so that the net rate of change of [tex]A(t)[/tex] is governed by the ODE,

[tex]\dfrac{\mathrm dA(t)}[\mathrm dt}=\dfrac{49}{100}-\dfrac{7A(t)}{1080}[/tex]

or

[tex]A'(t)+\dfrac7{1080}A(t)=\dfrac{49}{100}[/tex]

Multiply both sides by the integrating factor [tex]e^{7t/1080}[/tex] to condense the left side into the derivative of a product:

[tex]e^{\frac{7t}{1080}}A'(t)+\dfrac7{1080}e^{\frac{7t}{1080}}A(t)=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

[tex]\left(e^{\frac{7t}{1080}}A(t)\right)'=\dfrac{49}{100}e^{\frac{7t}{1080}}[/tex]

Integrate both sides:

[tex]e^{\frac{7t}{1080}}A(t)=\displaystyle\frac{49}{100}\int e^{\frac{7t}{1080}}\,\mathrm dt[/tex]

[tex]e^{\frac{7t}{1080}}A(t)=\dfrac{378}5e^{\frac{7t}{1080}}+C[/tex]

Solve for [tex]A(t)[/tex]:

[tex]A(t)=\dfrac{378}5+Ce^{-\frac{7t}{1080}}[/tex]

Given that [tex]A(0)=0[/tex], we find

[tex]0=\dfrac{378}5+C\implies C=-\dfrac{378}5[/tex]

so that the amount of sugar at any time [tex]t[/tex] is

[tex]\boxed{A(t)=\dfrac{378}5\left(1-e^{-\frac{7t}{1080}}\right)}[/tex]

(c) As [tex]t\to\infty[/tex], the exponential term converges to 0 and we're left with

[tex]\displaystyle\lim_{t\to\infty}A(t)=\frac{378}5[/tex]

or 75.6 kg of sugar.


Related Questions

What is the lateral area of the drawing is it a 200 km.b. 425.c.114d.1021km

Answers

Answer:

114 km

Step-by-step explanation:

Each side is an isosceles trapezoid, so ED=2 since you would need to add 2 to each end of the bottom line to get the top line. Now use Pythagorean Theorem to get ED^2+AD^2=AE^2. Plug in your numbers to solve for AE. This is the height of each trapezoid. Then use your formula for the area of a trapezoid, (B1+B2)h/2, to get the area of each side, then multiply by 4 to get the lateral area since there are 4 sides. Remember lateral area is just the sides, then surface area is when you include the area of the two bases.

Please help! I’ll mark you as brainliest if correct.

Answers

Answer:

160 liters of 25%, 20 liters of 40%, 60 liters of 60%

Step-by-step explanation:

x + y + z = 240

0.25x + 0.4y + 0.6z = 0.35*240 = 84

z = 3y

x = 160

y = 20

z = 60

Fresno County, California is the largest agricultural producing county in the country and almonds are an important crop with more than 99,000 acres harvested. Each acre produces about a ton of almonds and sold at a price of $4300 a ton. The Sagardia Brothers grew 600 acres of almonds . How many tons would the brothers sell if they priced the almonds at $4500 a ton?

Answers

Answer:

0 ton

Step-by-step explanation:

The question states that 99,000 acres are harvested. This suggest that there are plenty sellers of almonds.The Sagardia Brothers grew 600 acres of almonds. this is a small percentage of the total output of almonds. This suggests that the market for almonds is perfectly competitive.

In this type of market, if the price of a seller is above equilibrium price, zero units of the commodity would be bought. This is because the goods sold are homogenous and buyers can easily purchase from other buyers that sell at the market price

The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the:\

Answers

Answer: Expected value

Step-by-step explanation: The expected value of a random variable refers to a predicted variable which is obtained from the summation of the product of all possible values and the probability of occurrence of each value. The expected values gives the mean or average possible value over the cause of a certain experiment or scenario. It is thus the probability weighted average of all possible values or outcomes of an experiment.

The expected value could be represented mathematically as thus;

E(x) = [Σ(x * p(x)]

Where x = all possible values or outcomes of x;

p(x) = corresponding probability of each x value.

In the figure below, angle y and angle x form vertical angles. Angle x forms a straight line with the 50° angle and the 40° angle. A straight line is shown and is marked with three angles. The first angle measures 50 degrees. The second angle measures 60 degrees. The third angle is labeled x. The line between the 40 degree angle and angle x extends below the straight line. The angle formed is labeled angle y. Write and solve an equation to determine the measure of angle y.

Answers

Step-by-step explanation:

sorry but u should provide with a diagram for better understanding of ur question


What is the equation of the line that passes through the point (8,3) and has a slope
of
1/4

Answers

Answer:

y = 1/4x+1

Step-by-step explanation:

Using slope intercept form

y = mx+b

where m is the slope and b is the y intercept

y =1/4 x+b

Substituting in the point

3 = 1/4(8)+b

3 = 2+b

Subtract 2 from each side

3-2 = b

1 =b

y = 1/4x+1

Answer:

y=1/4x+1

Step-by-step explanation:

the equation for a line is y=mx+b

where m is the slope and b is the y-intercept. since we have our slope given and and x,y given we can use that to solve for b. we get:

3=1/4(8)+b

3=2+b

1=b

therefore the y-intercept is b

so the equation is y=1/4x+1

Was it evaluated correctly?
Explain your reasoning
help i need to turn it in a hour ​

Answers

Answer:

no

Step-by-step explanation:

2(4+10)+20

2(14)+20

28+20

48

The volume of a gas in a container varies inversely as the pressure on the gas. If a gas has a volume of 356 cubic inches under a pressure of 6 pounds per square inch, what will be its volume if the pressure is increased to 7 pounds per square inch? Round your answer to the nearest integer if necessary.

Answers

Answer:

[tex]V_2=305.14\ \text{inch}^3[/tex]

Step-by-step explanation:

The volume of a gas in a container varies inversely as the pressure on the gas.

[tex]V\propto \dfrac{1}{P}\\\\V_1P_1=V_2P_2[/tex]

If V₁ = 356 inch³, P₁ = 6 pounds/in², P₂ = 7 pounds/in², V₂ = ?

So, using the above relation.

So,

[tex]V_2=\dfrac{V_1P_1}{P_2}\\\\V_2=\dfrac{356\times 6}{7}\\\\V_2=305.14\ \text{inch}^3[/tex]

So, the new volume is [tex]305.14\ \text{inch}^3[/tex].

Determine the Perimeter of the shape #1.

Answers

Answer:

56.8

Step-by-step explanation:

7.1*8=56.8

The SAT Reasoning Test (formerly called the Scholastic Aptitude Test) is perhaps the most widely used standardized test for college admissions in the United States. Scores are based on a normal distribution with a mean of 1500 and a standard deviation of 300. Clinton College would like to offer an honors scholarship to students who score in the top 10 percent of this test. What is the minimum score that qualifies for the scholarship?

Minimum Score:

Answers

Answer:

The score is  [tex]x = 1884[/tex]

Step-by-step explanation:

From the question we are told that

     The population mean is  [tex]\mu = 1500[/tex]

     The standard deviation is  [tex]\sigma = 300[/tex]

     

From the question we are told that the score follow a normal distribution

i.e     [tex]X \~ \ N( 1500 , 300)[/tex]

The proportion of score in the top 10% is mathematically

           [tex]P(X > x ) = P( \frac{X - \mu}{\sigma } > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

Where x is the minimum score required to be in the top 10%

Now the [tex]\frac{X - \mu}{\sigma } = Z (The \ Standardized \ value \ of \ X)[/tex]

  So

            [tex]P(X > x ) = P( Z > \frac{x - \mu}{\sigma } ) = 0.10[/tex]

So

            [tex]P(X > x ) = P( Z > \frac{x - 1500}{300} ) = 0.10[/tex]

So the critical value of  0.10  from the normal distribution table is  [tex]Z_{0.10} = 1.28[/tex]

So

               [tex]\frac{x - 1500}{300} = 1.28[/tex]

              [tex]x = 1884[/tex]

           

       

A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm

Answers

Answer:

0.0090483

Approximately = 0.00905

Step-by-step explanation:

z = (x - μ)/σ, where

x is the raw score = 3.74

μ is the sample mean = population mean = 4 mm

σ is the sample standard deviation

This is calculated as:

= Population standard deviation/√n

Where n = number of samples = 100

σ = 1.1/√100

σ = 1.1/10 = 0.11

z = (3.74 - 4) / 0.11

z = -2.36364

Using the z score table to determine the probability,

The probability that the average thickness of the 100 sheets is less than 3.74 mm

P(x<3.74) = 0.0090483

Approximately = 0.00905

Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

It measures how many standard deviations the measure is from the mean.  After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means for size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem:

Mean thickness of 4 mm, thus [tex]\mu = 4[/tex].Standard deviation of 1.1 mm, thus [tex]\sigma = 1.1[/tex].Sample of 100, thus [tex]n = 100, s = \frac{1.1}{\sqrt{100}} = 0.11[/tex].

The probability is the p-value of Z when X = 3.74, then:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3.74 - 4}{0.11}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091.

0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

A similar problem is given at https://brainly.com/question/14228383

Name:
Unit 1: Geometry Basics
Date:
Per: Homework 3: Distance & Midpoint Formulas
** This is a 2-page document! **
Directions: Find the distance between each pair of points.
1. 1-4.6) and (3.-7)
2. (-6,-5) and (2.0)
M=(-12,-1)
M=
4. (0.-8) and (3.2)
3. (-1, 4) and (1-1)
5.
.
Directions: Find the coordinates of the midpoint of the segment given its endpoints.
6. /15, 8) and B(-1,-4)
7. M(-5,9) and N[-2.7)
8. P(-3,-7) and Q13.-5)
9. F12.-6) and G(-8,5)
Gina Whion (All Things Algobro. LLC) 2014-2017

Answers

The midpoint is the point that divide a segment into two equal halves, while the distance between points is the number of units between both points.

The distance between

(1,-4.6) and (3,7) is 11.77(-6,-5) and (2,0) is 9.43(-1, 4) and (1-1) is 5.39(0.-8) and (3,2) is 10.44

The coordinate of midpoint of:

(5, 8) and (-1,-4) is (2,2)(-5,9) and (-2,7) is (-.3.5,9)(-3,-7) and (13.-5) is (5,-6)(12,-6) and (-8,5) is (2,-0.5)

The distance in a coordinate geometry is calculated using: [tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex].

The distance between points is calculated as follows:

(1,-4.6) and (3,7)

[tex]d = \sqrt{(1 - 3)^2 + (-4.6 - 7)^2}[/tex]

[tex]d = \sqrt{138.56}[/tex]

[tex]d = 11.77[/tex]

(-6,-5) and (2,0)

[tex]d = \sqrt{(-6 - 2)^2 + (-5 - 0)^2}[/tex]

[tex]d = \sqrt{89}[/tex]

[tex]d = 9.43[/tex]

(-1, 4) and (1-1)

[tex]d = \sqrt{(-1 - 1)^2 + (4 - -1)^2}[/tex]

[tex]d = \sqrt{29}[/tex]

[tex]d = 5.39[/tex]

(0.-8) and (3,2)

[tex]d = \sqrt{(0 - 3)^2 + (-8 -2)^2}[/tex]

[tex]d = \sqrt{109}[/tex]

[tex]d = 10.44[/tex]

The midpoint (M) is calculated using: [tex]M = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]

The coordinate of midpoint is calculated as follows:

(5, 8) and (-1,-4)

[tex]M = (\frac{5-1}{2},\frac{8-4}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{4}{2})[/tex]

[tex]M = (2,2)[/tex]

(-5,9) and (-2,7)

[tex]M = (\frac{-5-2}{2},\frac{9+7}{2})[/tex]

[tex]M = (\frac{-7}{2},\frac{16}{2})[/tex]

[tex]M = (-3.5,9)[/tex]

(-3,-7) and (13.-5)

[tex]M = (\frac{-3+13}{2},\frac{-7-5}{2})[/tex]

[tex]M = (\frac{10}{2},\frac{-12}{2})[/tex]

[tex]M = (5,-6)[/tex]

(12,-6) and (-8,5)

[tex]M = (\frac{12-8}{2},\frac{-6+5}{2})[/tex]

[tex]M = (\frac{4}{2},\frac{-1}{2})[/tex]

[tex]M = (2,-0.5)[/tex]

Read more about distance and midpoints in coordinate geometry at:

https://brainly.com/question/3715220

Find the next three terms in the sequence 4, 16, 36, 64, 100, ...

Answers

Answer:

144 196 256

. .............

Someone help me understand

Answers

Answer:

f¯¹(x) = 23/ (6x + 3)

Step-by-step explanation:

f(x) = (23 – 3x)/6x

The inverse, f¯¹, for the above function can be obtained as follow:

f(x) = (23 – 3x)/6x

Let y be equal to f(x)

Therefore, f(x) = (23 – 3x)/6x will be written as:

y = (23 – 3x)/6x

Next, interchange x and y.

This is illustrated below:

y = (23 – 3x)/6x

x = (23 – 3y)/6y

Next, make y the subject of the above expression. This is illustrated below:

x = (23 – 3y)/6y

Cross multiply

6xy = 23 – 3y

Collect like terms

6xy + 3y = 23

Factorise

y(6x + 3) = 23

Divide both side by (6x + 3)

y = 23/ (6x + 3)

Finally, replace y with f¯¹(x)

y = 23/ (6x + 3)

f¯¹(x) = 23/ (6x + 3)

Therefore, the inverse, f¯¹, for the function f(x) = (23 – 3x)/6x is

f¯¹(x) = 23/ (6x + 3)

Use a definition, postulate, or theorem to find the value of x in the figure described. Point E is between points D and F. If DE = x − 3, EF = 6x + 5, and DF = 8x − 3, find x. Select each definition, postulate, or theorem you will use. A)definition of segment bisector B)definition of midpoint C)Linear Pair Theorem D)Segment Addition Postulate The solution is x =?

Answers

Answer:

Option (D)

x = 5

Step-by-step explanation:

Since point E is in the mid of the segment DF,

Therefore, by the Segment addition postulate,

DF = DE + EF

Since DF = (8x - 3), DE = (x - 3) and EF = (6x + 5)

By substituting these values in the given postulate,

(8x - 3) = (x - 3) + (6x + 5)

8x - 3 = (x + 6x) + (5 - 3)

8x - 3 = 7x + 2

8x - 7x = 3 + 2

x = 5

Therefore, x = 5 will be the answer.

Answer:

x=6 and D

Step-by-step explanation:

1/3 is part of which set of numbers?

Answers

Answer:

[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.

Rational numbers. denoted by [tex] \mathbb Q[/tex]

1/3 is clearly not a natural number or integer.

it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).

Please help asap, will mark Brainliest xoxo

Answers

Answer/Step-by-step explanation:

Given, [tex] b(x) = (\frac{6}{7})^{x} [/tex]

The table for the function are:

When x = -2

[tex] b(-2) = (\frac{6}{7})^{-2} [/tex]

[tex] b(-2) = \frac{1}{(\frac{6}{7})^{2}} [/tex]

[tex] b(-2) = \frac{1}{(\frac{36}{49})} [/tex]

[tex] b(-2) = 1*\frac{49}{36} [/tex]

[tex] b(-2) = \frac{49}{36} [/tex]

When x = -1

[tex] b(-1) = (\frac{6}{7})^{-1} [/tex]

[tex] b(-1) = \frac{1}{(\frac{6}{7})} [/tex]

[tex] b(-1) = 1*\frac{7}{6} [/tex]

[tex] b(-2) = \frac{7}{6} [/tex]

When x = 0

[tex] b(0) = (\frac{6}{7})^{0} [/tex]

[tex] b(0) = \frac{6^0}{7^0} [/tex]

[tex] b(0) = \frac{1}{1} [/tex]

[tex] b(0) = 1 [/tex]

When x = 1

[tex] b(1) = (\frac{6}{7})^{1} [/tex]

[tex] b(1) = \frac{6}{7} [/tex]

When x = 2

[tex] b(2) = (\frac{6}{7})^{2} [/tex]

[tex] b(2) = \frac{6^2}{7^2} [/tex]

[tex] b(2) = \frac{36}{49} [/tex]

4(c+3) =4+c+c+c+c+17

Answers

4c +12 = 4+4c+17
-4c -4c
12 =4+c+17
12=21+c
-21
-9=c
idk if this is what ur looking for?

Please answer this correctly without making mistakes

Answers

Answer:

Put 1/10 in the box.

Step-by-step explanation:

Since, Bluepoint and Milford are at same distance from Weston, the distance further than this to Oakdale is 1/10 miles.

Best Regards!

Answer:

To Oakdale to Milford:

2/5 mi

Step-by-step explanation:

1/10 + 3/20 + 3/20

1/10 = 2/20

then;

2/20 + 3/20 + 3/20 = (2+3+3)/20 = 8/20

8/20 = 2/5

Stephanie is twice as old as her sister Rosa. If Stephanie is 18 years old, how old is Rosa?

Answers

Answer:

rose. is. 18/2=9 years old

Answer:

Stephanie is 18years old and she is twice older than her sister

so rosa is 18÷2(since stephanie is twice older than rosa

so rosa is 9 years old

Which is the zero of the function f(x)=(x+3) (2x-1)(x+2) ?

Answers

Answer:

x= -3     x = 1/2     x=-2

Step-by-step explanation:

f(x)=(x+3) (2x-1)(x+2)

Set equal to zero

0 =(x+3) (2x-1)(x+2)

Using the zero product property

x+3 =0   2x-1 =0    x+2 =0

x= -3    2x =1       x = -2

x= -3     x = 1/2     x=-2

What is the common difference in the arithmetic sequence 1,1.25,1.5,1.75,… ?

Answers

Answer:

0.25.

Step-by-step explanation:

To find the common difference, you need to find the number that each value increases by.

1.75 - 1.5 = 0.25.

1.5 - 1.25 = 0.25.

1.25 - 1 = 0.25.

All values apparently increase by 0.25. So, that is your common difference.

Hope this helps!

Answer:

0.25

Step-by-step explanation:

The common difference is the value added to the first term to get the second term, then added to the second to get the third and so on.

To find the common difference, subtract the first term from the second. Then check by subtracting the second term from the third.

The sequence is:  1,1.25,1.5,1.75

second term - first term

1.25- 1= 0.25

third term- second term

1.5 -1.25= 0.25

The common difference in the arithmetic sequence is 0.25

in the diagram, POS,QOT and ROU are straight lines. find the value of x.​

Answers

Answer: 28

==========================================

Explanation:

Angle UOT is vertical to the angle x. This angle combines with 4x and 40 to get a straight angle of 180 degrees

(angle POU) + (angle UOT) + (angle TOS) = 180

4x + x + 40 = 180

5x + 40 = 180

5x = 180-40

5x = 140

x = 140/5

x = 28

Side note: if x = 28, then 4x = 4*28 = 112.

We see that 112+28+40 = 180, which is the sum of the three angles mentioned earlier. Since we got 180, this confirms the answer.

In the given figure, if POQ is a straight line then find ∠POT. please help !!!!!!

Answers

Answer:

∠POT = 78°

Step-by-step explanation:

If POQ is straight then

x + 18° + 50° + x + 24° = 180° add like terms

2x + 92° = 180°

2x = 180° - 92°

2x = 88° and x = 44 If we say SOT is a straight line then

∠POT + 50° + x + 18° = 180°

∠POT + 102° = 180°

∠POT = 78°

The following sample contains the scores of 6 students selected at random in Mathematics and English. Use the scores in English as the dependent variable Y.

Mathematics score (X) 70 92 80 74 65 83
English score 74 84 63 87 78 90

Σx =464 Σy=476 Σx^2= 36354 Σy^2=38254 Σxy= 36926

Find the sample coefficient of determination and interpret.

a. 0.0575 and prediction accuracy is 5.75%
b. 0.2397 and prediction accuracy is 23.97%
c. 0.0575 and prediction accuracy is 94.25%
d. 0.2397 and prediction accuracy is 76.03%

Answers

Answer:

d the answer is d

Step-by-step explanation:

Sarah knows how important it is to budget her monthly expenses. She earns $3,120 every month and her monthly expenses total to $2,130. Sarah has summarized her monthly expenses using the pie chart below. What percent of Sarah's monthly income is left over after she pays her monthly bills? Round to the dollar​

Answers

Answer: 37.1%

Step-by-step explanation:

2130/3120×100% = 68.3%

100% - 68.3%

=31.7%

37.1%

which makes that $460

May I have brainliest please? :)

Also, the person above me smells like how a diaper tastes

help please I need help :(

Answers

A = 1 and 8

B = 2 and 4

C = 2 and 7

I’m pretty sure this is right? I’m still learning too :p

Answers:Angle 1 and angle 8 are alternate exterior angles (so are angle 5 and angle 4; but you only need to pick one pair)Angle 1 and angle 3 are corresponding angles (there are 3 other possible answers. See the second section below)Angle 2 and angle 7 are alternate interior angles (so are angle 3 and angle 6; but you only need to pick one pair)

=======================================================

Explanations:

For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.

When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are

angle 1, angle 5, angle 4, angle 8

The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.

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

Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.

Angle 1 and angle 3 are corresponding angles because they

a) are to the left of each parallel line (m and n)b) both below the transversal line

So in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs

angle 1 and angle 3angle 2 and angle 4angle 5 and angle 7angle 6 and angle 8

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

As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.

So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.

what number must be added to the sequence of 7,13 and 10 to get an average of 13

Answers

Answer:

22

Step-by-step explanation:

We can write an equation:

(7+13+10+x)/4=13

x represents the number that needs to be added to get an average of

(7+13+10+x)/4=13

(30+x)/4=13

30+x=52

x=22

The number is 22

Hope this helps! Have a wonderful day :)

Which is the best definition of mathematical proof? a/A sequence of statements that demonstrates the truth of an assertion. b/Statements that show the assertion is false using a counterexample. c/A paragraph that always has three parts and shows that an assertion is true. d/Statements in any order that show that an assertion is true.

Answers

Answer:

A. A sequence of statements that demonstrates the truth of an assertion.

Step-by-step explanation:

Mathematical proofs are a series of statements in order that help prove that something is true.

Proofs do not prove that something is false, they are not always 3 parts, and they are not in any order, because they have to be in an organized sequence.

So, A is correct.

Answer:

A sequence of statements that demonstrates the truth of an assertion.

Step-by-step explanation:

What is the difference between a line graph and a scatter plot?

Answers

Step-by-step explanation:

scatter plot s are similar to line graphs in that they start with mapping quantitive data points. The difference is that with a scatter plot, the decision is made the the individual points should not be connected directly together with a line but, instead express a trend

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