A researcher is interested in finding a 95% confidence interval for the mean number of times per day that college students text. The study included 210 students who averaged 28 texts per day. The standard deviation was 21 texts.A. The sampling distribution follows a_______.1. "F"2. "normal"3. "T"4. "Chi-square" B. With 95% confidence the population mean number of texts per day of is between_______and______texts. A. 1. "24.92"2. "25.79"3. "27.37"4. "25.14"B. 1. "31.19"2. "31.20"3. "29.28"4. "30.86" C. If many groups of 210 randomly selected students are studied, then a different confidence interval would be produced from each group. About_______% of these confidence intervals will contain the true population mean number of texts per day and about______% will not contain the true population mean number of texts per day.A. 1. "5"2. "95"3. "1"4. "99"B. 1. "95"2. "99"3. "5"4. "1"

Answers

Answer 1

Answer: A. The sampling follows a normal distribution.

              B. Between 25.14 and 30.86

              C. About 95% will contain the true mean and about 5% won't

Step-by-step explanation: A. The sampling is normally distributed because:

it has a symmetric bell shape, mean and median are both the same and located at the center of graphic, approximately 68% of the data falls within one standard deviation;95% falls within two standard deviations;99.7% within 3 standard deviations;

B. For a 95% confidence interval: α/2 = 0.025

Since n = 210, use z-score = 1.96

To calculate the interval:

mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]

Replacing for the values given:

28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]

28 ± [tex]1.96*1.45[/tex]

28 ± 2.84

lower limit: 28 - 2.84 = 25.14

upper limit: 28 + 2.84 = 30.86

Confidence Interval is between 25.14 and 30.86.

C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.


Related Questions

One number is 4 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 370, find the numbers.
The three numbers are
(Use a comma to separate answers as needed.)

Answers

Answer:

  45, 180, 145

Step-by-step explanation:

Let n represent the first number. Then "one number" is 4n, and the third number is n+100. The sum of the three numbers is ...

  n + 4n + (n+100) = 370

  6n = 270

  n = 45

  4n = 180

  n+100 = 145

The three numbers are 45, 180, 145.

The report "Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel" summarizes data from a survey of a representative sample of 800 teens between the ages of 12 and 17. The following statements were made on the basis of the resulting data.

- 75% of all American teens own a cellphone
- 66% of all American teens use a cellphone to send a receive text messages
- 26% of American teens age 16-17 have used a cellphone to text while driving

Required:
a. Is the inference made one that involves estimation or one that involved hypothesis testing?
b. What is the population of interest? American teenagers? American teenagers between ages 12-17? Americans? Teenagers?

Answers

Answer:

"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"

a. The inference made involves estimation.  The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.

This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements.  The statements were not an attempt to establish the statistical significance of some claims.

b. The population of interest is American teenagers between 12-17.

Step-by-step explanation:

An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17.  The statistics serve as an approximation to the population parameter.

Inference based on hypothesis testing establishes if a claim has statistical significance by providing  statistical evidence in favor of the claim or against it.

John receives a perpetuity paying 2 at the end of year 4, 4 at the end of year 6, 6 at the end of year 8, etc. The present value of this perpetuity at an annual effective rate of 10% equals X. Calculate X

Answers

Answer:

45.35

Step-by-step explanation:

From the above question, we are told that the annual effective rate = 10% = 0.10

Note also that payment is been made every 2 years

Hence , we apply the formula of effective interest rate for a period of 2 years.

Effective Interest rate(j) = (1 + r)² - 1

= (1 + 0.10)² - 1

= 1.10² - 1

= 1.21

= 0.21

Present value of perpetuality = t/[j × j/(1 + r)²]

Where t = time in years = 2

r = 0.10

= 2/ [0.21 × 0.21/(1 + 0.10)²

= 54.87528

Present value at time t = 0

= 54.87528(1 + r)^-2

= 54.87528(1 + 0.10) ^-2

= 54.87528(1.10)^-2

= 45.35

Therefore, the present value at time (t) is 0 = 45.35

Find the doubling time of an investment earning 8% interest if interest is compounded continuously. The doubling time of an investment earning 8% interest if interest is compounded continuously is ____ years.

Answers

Answer:

Step-by-step explanation:

Using FV = PV(1 + r)^n where FV = future value, PV = present value, r = interest rate per period, and n = # of periods

1/PV (FV) = (PV(1 + r^n)1/PV divide by PV

ln(FV/PV) = ln(1 + r^n) convert to natural log function

ln(FV/PV) = n[ln(1 + r)] by simplifying

n = ln(FV/PV) / ln(1 + r) solve for n

n = ln(2/1) / ln(1 + .08) solve for n, letting FV + 2, PV = 1 and rate = 8% or .08 compound annually

n = 9

n = ln(2/1) / ln(1 + .08/12) solve for n, letting FV + 2, PV = 1 and rate = .08/12 compound monthly

n = 104 months or 8.69 years

n = ln(2/1) / ln(1 + .08/365) solve for n, letting FV + 2, PV = 1 & rate = .08/365 compound daily

n = 3163 days or 8.67 years

Alternatively

A = P e ^(rt)

Given that r = 8%

= 8/100

= 0.08

2 = e^(0.08t)

ln(2)/0.08 = t

0.6931/0.08 = t

t= 8.664yrs

t = 8.67yrs

Which ever approach you choose to use,you will still arrive at the same answer.

How hot does it get in Death Valley? The following data are taken from a study conducted by the National Park System, of which Death Valley is a unit. The ground temperatures (°F) were taken from May to November in the vicinity of Furnace Creek. Compute the mean, median, and mode for these ground temperatures. (Enter your answers to one decimal place.) 147 153 170 172 185 181 182 185 181 170 181 167 153 145

Answers

Answer:

Mean: 169.4

Median: 171

Mode: 181

Step-by-step explanation:

I first sorted the numbers by value, least to greatest.

145 147 153 153 167 170 170 172 181 181 181 182 185 185

We can see that 181 occurs the most, 3 times, so it's the mode.

The median of this set will be the middle number(s).

When we take away 6 numbers from both sides we are left with 170 and 172, and the mean of these two numbers is 171. So the median is 171.

We can add all the numbers and divide by 14 to get the mean.

[tex]147+153+170+172+185+181+182+185+181+170+181+167+153+145=2372\\\\2372\div14\approx169.4[/tex]

Hope this helped!

11
12
13
14
15
16
Write the appropriate pronoun that can replace the subject in this sentence.
Tomás va a comer galletas.
ella
O él
Ο Ο Ο Ο
O nosotros
O usted

Answers

Answer:

The answer is usted

Step-by-step explanation:

And if you want to learn more download duolingo

The P​-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that​ ________.

Answers

Answer:

The P​-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

Step-by-step explanation:

The P​-value is the probability of getting a test statistic at least as extreme as the one representing the sample​ data, assuming that the null hypothesis is true.

The p-value is the probability that, if the null hypothesis were true,sampling variation would yield and estimate that is further away from the hypothesised value than our data estimate. The p-value shows us how possible it is to get a result like this if the null hypothesis is true.

Assuming we have a null hypothesis and an alternative hypothesis computed as follows.

[tex]H_o : \mu = 5 \\ \\ H_1 : \mu \neq 0.5[/tex]

If P-value is less than or equal to [tex]\mu[/tex] , we will reject the null hypothesis.

What's the solution of the following linear system? 5x + 2y = 9 –5x – 2y = 3

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

(-39/35, 9/7)

▹ Step-by-Step Explanation

5y + 2y = 9

-5x - 2y = 3

Solve the equation:

y = 9/7

-5x - 2y = 3

Substitute the value of y:

-5x - 2 * 9/7 = 3

x = -39/35

(x, y) = (-39/35, 9/7)

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

5x + 2y = 9-5x - 2y = 3

To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.

This leaves us with 0 on the left side and on the right side,

9 + 13 = 12 so we are left with the equation 0 = 12.

Since 0 = 12 is a false statement, this means that

there is no solution to our system of equations.

How would the margin of error change if the sample size increased from 200 to 400 students? Assume that the proportion of students who say yes does not change significantly.

Answers

Answer:

(MOE) the Margin of Error will decrease by the square root of 2

Step-by-step explanation:

The Margin of Error (MOE) is an inverse function of sample size n ( more precisely of the square root of sample size ). That relation means changes in sample size ( keeping constant other variables of the distribution) will imply opposite changes in the Margin of Error. If we double the sample size increasing it from 200 up to 400,  the Margin of Error will decrease by the square root of 2

70% of what number is 56​

Answers

Answer:80
Because we do the inverse so 56*10=560 then we do 560/7=80 then we work from 80 and do 70% to see if our answer is right
Hope this helped

Answer:

the number is 80

Step-by-step explanation:

let x be an unknown number so from the above question we deduce that

(70/100)*x=56

70x/100=56

70x=56*100

70x=5600

70x/70=5600/70

x=80

If A = { 10, 30,} B = { 10, 20, 30, 40, 50, 60, 70, 80,90} find A ∩ B There are options. Choose one option only: A- { 30 ,10} B- { 90 ,30 ,10} C- { 90 } D- { 80, 70, 60, 50, 40, 20 }

Answers

[tex]A \cap B=\{10,30\}[/tex]

Answer:

[tex] \boxed{ \purple{10 \: , 30}}[/tex]

Option A is the correct option

Step-by-step explanation:

[tex] \mathrm{Given}[/tex]

A = { 10 , 30 }

B = { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }

Now, let's find A ∩ B

A ∩ B = { 10 , 30 } ∩ { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }

The intersection of sets A and B is the set of all elements which belong to both A and B

A B = { 10 , 30 }

The intersection of sets A and B is denoted by ( A ∩ B ) and read as A intersection B.

Hope I helped!

Best regards!

A restaurant hands out a scratch-off game ticket with prizes being worth purchases at the restaurant. The back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100. What are the odds that the ticket is worth at least $25?

Answers

Answer: 0.05412

Step-by-step explanation:

Formula : Odds of having an event is given by  [tex]o=\dfrac{p}{1-p}[/tex], where p = probability that event happens.

In terms to find p , we use [tex]p=\dfrac{o}{1+o}[/tex]

Given, he back of the ticket lists the odds of winning each dollar value: 0.05 for $10, 0.04 for $25, 0.01 for $50, and 0.003 for $100.

Let X be the worth of ticket.

Then, the probability that the ticket is worth at least $25 =

[tex]P(X\geq 25)=P(X=25)+P(X=50)+P(X=100)[/tex]

[tex]=\dfrac{0.04}{1+0.04}+\dfrac{0.01}{1+0.01}+\dfrac{0.003}{1+0.003}\\\\=0.05135[/tex]

The odds that the ticket is worth at least $25 = [tex]\dfrac{0.05135}{1-0.05135}[/tex]

=0.05412

hence, the odds that the ticket is worth at least $25 is 0.05412 .

given the vector with a manitude of 9m at an angle a of -80 degrees, decompose this vector into two vector components oarallel to the x axis with a slope of

Answers

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.

I NEED FULL EXPLANATION

(4 - 3i) ^2

Answers

Answer:

Rewrite  

( 4 − 3 i ) 2  as  ( 4 − 3 i )( 4 − 3 i ) . ( 4 − 3 i) ( 4 − 3 i ) Expand  ( 4 − 3 i ) ( 4 − 3 i )

using the FOIL Method.

4 ⋅ 4 + 4 ( -3 i ) − 3 i ⋅ 4 − 3 i ( − 3 i )

Simplify and combine like terms.

7 − 24 i

Step-by-step explanation:

Answer:

7 -24i

Step-by-step explanation:

(4 - 3i) ^2

(4-3i) * (4-3i)

FOIL

first 4*4 = 16

outer 4 * -3i = -12i

inner -3i *4 = -12i

last -3i*-3i = 9i^2 = 9 (-1) = -9

Add together

16 -12i-12i -9

Combine like terms

7 -24i

Select the correct answer from each drop-down menu.
Nirja has 24 marbles. The number of marbles Nirja has is 6 more than the number of marbles Tim has.
If Tim has x marbles, the equation that represents the situation is
The value of x that makes the equation true is
Reset
Next

Answers

Answer:

24 = x+6

x = 18

Step-by-step explanation:

N = 24

T = x

N = x+6  

24 = x+6

Subtract 6 from each side

24-6 = x+6-6

18 = x

Time has 6 marbles

Nirja has 6 more than Tim,

So you can subtract 6 from 24 to find x:

24-6 = x

Or you can add 6 to x to equal 24:

x + 6 = 24

You don't list the choices but it should be one of these.

Solve:

24 - 6 = x

x = 18

CALC 1: Spud's mom is going to make him a round birthday cake, and has asked for your help. Spud is a bit weird, and has already
announced that when he slices the cake, your slice will have a perimeter of 16 inches, because you're his favorite friend, and
that's his favorite number. Since you're helping his mom with the baking, what diameter cake will you recommend she makes
so that you end up with the most possible cake at weird Spud's party? (Hint: you can ignore the thickness df the cake, since
this will be the same, regardless of its diameter.)
10.1
in

Answers

Answer:

15.7 in  

Step-by-step explanation:

A slice of a round pie is a sector of a circle.

The perimeter of a slice is the arc length s plus twice the radius r.

P = s + 2r

s = rθ = r(16/360) = r/22.5. So,

16 = (r/22.5) + 2r = (r + 45r)/22.5 = 46r/22.5

16 × 22.5 = 46r

360 = 46r

r = 7.826  

D = 2r = 2 × 7.826 = 15.7 in

The diameter of the cake should be 15.7 in.

Check:

[tex]\begin{array}{rcl}P & = & s + 2r\\& = & \dfrac{r}{22.5} + 2r\\\\16 & = & \dfrac{7.826}{22.5} + 2 \times 7.826\\\\16 & = & 0.35 + 15.65\\16 & = & 16.00\\\end{array}[/tex]

It checks.

 

A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 10 H1: μ > 10 Is this a one- or two-tailed test?

Answers

Answer:

The  test is a two -tailed test

Step-by-step explanation:

From the question we are told that

    The  sample size is n  =  31

     The  sample mean is  [tex]\= x =11[/tex]

      The sample standard deviation is  [tex]\sigma = 3[/tex]

       The null hypothesis is  [tex]H_o: \mu \le 10[/tex]

         The  alternative hypothesis is  [tex]H_1 : \mu > 10[/tex]  

         The level of significance is [tex]\alpha = 0.05[/tex]

 

The test  statistics is mathematically represented as

       [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

      [tex]t = \frac{ 11 - 10 }{ \frac{3}{\sqrt{ 31} } }[/tex]

     [tex]t = 1.85[/tex]

The  p- value is mathematically represented as

       [tex]p-value = p( t > 1.856) = 0.0317[/tex]

Looking at the value of  [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value < \alpha[/tex] hence we reject the null hypothesis

Given the that the p value is less than 0.05 it mean the this is a two-tailed test

help please precalc will give brainliest

Answers

In part (D), we found

[tex]2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)[/tex]

so the phase [tex]\phi[/tex] is [tex]\tan^{-1}\left(\frac52\right)\approx1.19\,\rm rad[/tex], which falls between 0 and [tex]\frac\pi2[/tex]. This means the weight is somewhere between the maximum positive position (where [tex]\phi[/tex] would be 0) and the equilibrium position (where [tex]\phi[/tex] would be [tex]\frac\pi2[/tex]), and would be traveling in the negative direction.

Evaluate the expression you got in part f for d = 5.

Answers

Answer:

2(8-d)

2(8-5)   (substituting d=5)

2(3)

=6

Step-by-step explanation:

The required expression is f = 6 for d =5 in the for the expression f = 2 (8 -d).

What is an algebraic expression?

An algebraic expression is consists of variables, numbers with various mathematical operations,

The expression,

f = 2 (8 - d)              (1)

To evaluate the expression for d = 5

Substitute the value of d = 5 in equation (1),

f = 2 (8 - 5)

f = 2 x 3

f = 6

The required expression is f=6.

To know more about Algebraic expression on:

https://brainly.com/question/19245500

#SPJ2

Subtract 5p + 8q from the sum of 5p + 4q and – 9p + 69.

Answers

Answer:

-9p -4q + 69

Step-by-step explanation:

5p +4q + (-9p +69)

=> 5p + 4q -9p +69

=> -4p +4q +69

Now, we need to subtract 5p +8q from -4p + 4q +69

=> -4p +4q +69 - (5p +8q)

=> -4p + 4q +69 - 5p -8q

=> -9p -4q + 69

Answer: -9p - 4q + 69

Explanation:

(5p + 4q + (-9)p + 69) - (5p + 8q)
= 5p + 4q - 9p + 69 - 5p - 8q
= -9p - 4q + 69

i need help thank u so much in advance !

Answers

Answer:

Questions .(1) 2/m. (2). m-1 . (3) 2 . (4) m

Answer:

(2m²-4m)/2(m-2)=

2m(m-2)/2(m-2)= m

the answer is mm²-2m+1/m-1   ⇒  (factorize the nominator)

(m-1)(m-1)/m-1   ⇒ ( m-1/m-1)=1

then answer is m-1(m²-3m+2)/(m²-m)=the answer is (m-2)/mm²-m-2/m²-1=(m-2)(m+1)/(m-1)(m+1)=the answer is m-2/m-1

A research center is interested in investigating the height and age of children who are between 5 to 9 years old. In order to do this, a sample of 15 children is selected and the data are given below.


Age (in years) Height (inches)

7 47.3

8 48.8

5 41.3

8 50.4

8 51

7 47.1

7 46.9

7 48

9 51.2

8 51.2

5 40.3

8 48.9

6 45.2

5 41.9

8 49.6


Requried:

a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children?

b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model?

c. How much of the variation in the sample values of height does the model estimated in part (b) explain?

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Age(x)

7

8

5

8

8

7

7

7

9

8

5

8

6

5

8

Height (Y)

47.3

48.8

41.3

50.4

51

47.1

46.9

48

51.2

51.2

40.3

48.9

45.2

41.9

49.6

The estimated regression equation:

ŷ = 2.73953X + 27.91395

Where ;

X = independent variable

ŷ = predicted or dependent variable

27.91395 = intercept

C.) To obtain the variation in sample values of height estimated by the model, we obtain the Coefficient of correlation:

Using the online pearson correlation Coefficient calculator :

The correlation Coefficient is 0.9696.

which means that the regression model estimated in part (b) explains approximately (0.9696 * 100) = 96.96% = 97% of the variation in the height in the sample.


sin 3/5
4/5
3/4
5/4

Answers

Answer:

[tex]\boxed{\frac{3}{5}}[/tex]

Step-by-step explanation:

The trigonometric functions are described as follows:

[tex]sin = \frac{opposite}{hypotenuse}\\\\cos = \frac{adjacent}{hypotenuse}\\\\tan = \frac{opposite}{adjacent}[/tex]

Using reference angle ∠A, use the sin trigonometric function. This will be the side opposite (cannot be the hypotenuse) of ∠A over the side adjacent (cannot be the hypotenuse).

The side opposite of ∠A is 3. The hypotenuse of the triangle is 5.

[tex]\boxed{\frac{3}{5}}[/tex]  is the final answer!

Which is the exponential form of log9 5 = y

Answers

Answer:

Step-by-step explanation:

[tex]\log _9\left(5\right)=y\\y=\log _9\left(5\right)[/tex]

Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!

Answers

Answer:

ok as we know 15 is a whole number by itself and 3/8 is the decimal part

so we know it is 15. something

that something is 3/8 to find decimal you do 3/8

3/8 is = .375

so 15.375 is the answer

hope it helps

brainliest give me pls

Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }

Answers

Answer:

A, E

Step-by-step explanation:

There should be 2^8-1 proper subsets of A. Its every one besides { }

A refrigeration system at your company uses temperature sensors fixed to read Celsius (0C) values, but the system operators in your control room understand only the Fahrenheit scale. You have been asked to make a Fahrenheit (°F) label for the high temperature alarm, which is set to ring whenever the system temperature rises above -10°C. What Fahrenheit value should you write on the label?

Answers

Answer:

14 °F

Step-by-step explanation:

To answer this problem, we will use the known celsius to fahrenheit conversion formula.

[Celsius * (9/5)] + 32 = Fahrenheit

Now we just plug in the value of celsius:

[-10 * (9/5)] + 32 = Fahrenheit

[ -2 * 9 ] + 32 = Fahrenheit

[ -18 ] + 32 = Fahrenheit

14 = Fahrenheit

So you should right 14(°F) on the label.

Cheers.

In this triangle, which of the following is true?​

Answers

We know that this is a right triangle, so one of the sides has to be 90 (indicated by the square on the corner)  The angles of all triangles must add to exactly 180.  Subtract 90 and 35 from 180

If we do that, we get 55.  We know that the unknown angle is 55 now.  Now, it asks us for b.  We can pythagoras theorem which states that (a^2 + b^2 = c^2)  We already know c (c is 20)  It does not tell us 2 of the sides but we do know that the answer is either B or D.  

The side opposite of 90* should be the largest.  The size opposite of 55 would be the second largest one.  The side opposite of 35 would be the smallest one.  Using pythagoras theorem again, I can try plugging in both 11.47 and 16.38 with c^2 - b^2 = a^2  

11.47:

400 - 132 =268  (sq root now = 16.37) this would mean that A is larger than B.  B should be larger than A.  Try the other one

16.37:

400 -268 = 132 (sq root = 16.37) this would mean that B is larger than A which is what we want.

Thus, 16.37  = B and the last option would be correct (D)

Hope this helps, give an honest rating for me please

Let T (x, y) = (x + 1, y + 1) and S (x, y) = (x + 5, y + 4). In what
quadrant is S (T (P)) when P(-7, 1)?

Answers

Answer:

quadrant 2

Step-by-step explanation:

What is the area of the region bounded by the three lines with equations $2x+y = 8$, $2x-5y = 20$ and $x+y = 10$?

Answers

Answer:

  42

Step-by-step explanation:

A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...

  equations 1, 2: A(5, -2)

  equations 2, 3: B(10, 0)

  equations (3, 1): C(-2, 12)

Then the area can be found from the coordinates using the formula ...

  A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|

  = (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|

  A = 42

The area of the triangular region is 42 square units.

Other Questions
A. 19B. 20C. 15D. 25 Help please !! Is 3+(-4) the same as -4+3 ? Explain What do you think a persuasive angle is? Difference between matter and energy Bismah is building 5 raised garden beds in a community garden. Each raised garden bed will need 1 7 8 bags of soil. How many bags of soil will Bismah need for all 5 raised garden beds? How has the games changed over the years? Which best states the central idea of this excerpt? It is always necessary to work with a partner when dealing with unidentified substances. Extreme precautions must be taken when dealing with potentially hazardous materials. Scientists are well known for being overly cautious and for taking unnecessary safety measures. It is standard procedure to wear both space suits and hearing protectors in laboratories. The distance between two points on a number line can be found by taking the blank of the blank of the coordinates. absolute value sum quotient difference product A market research firm supplies manufacturers with estimates of the retail sales of their products from samples of retail stores. Marketing managers are prone to look at the estimate and ignore sampling error. A random sample of 36 stores this year shows mean sales of 83 units of a small appliance with a standard deviation of 5 units. During the same point in time last year, a random sample of 49 stores had mean sales of 78 units with standard deviation 3 units.Required:Construct a 95 percent confidence interval for the difference in population means. How are pH and pOH ?A. pH = 14 + pOH B. pOH = 14 - pH C. pOH = 14 + pH D. pH = 14 - pOH A fruit tray was served at a meeting. During the meeting, 4 out of 10 strawberries were eaten. Which model has a shaded region that represents the amount of strawberries eaten during the meeting? Very few countries in the world _________ as like Bangladesh. now developing is now developing are now developing now developed HELP!!!!!!!!!!!!!!!!!!!!!!!!!!! In 5 hours a small plane can travel downwind for 4000 kilometersor upward 3000 kilometers. Find the speed of this plane with no wind and the speed of the wind current.write as an equation Use the discriminant to determine the number of real solutions to the equation. 8n^27n=7 what is the sum of 1.3 and 5.07 2. Skip and Peggy are brother and sister and they fight about everything. Skip says that perfectly competitive firms maximize profit where marginal revenue equals marginal cost. Peggy says perfectly competitive firms maximize profit where price equals marginal cost. Settle this sibling rivalry once and for all. Liam tried to define a translation. - Point A maps to point A' - Every point P maps to point P' such that PP' is parallel to AA' and points in the same direction as AA' Which counterexample shows that Liam's definition does not fully define a translation? what is the value of -19- (-18)? Select the equivalent expression. (8^-5/2^-2)^-4 = ? Choose 1 answer: A. 1/8*2^2 B. 2^6/8^9 C. 8^20/2^8