Please please help :((((

Answer:

Average rate of change of the function will be = (-1.5)

Step-by-step explanation:

Average rate of change of a function f(x) is determined by the formula,

Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex] If a < x < b

We have to find the average rate of change of a function g(t) between the interval [-3, 1]

From the given table,

For t = -3,

g(-3) = 6

For t = 1,

g(1) = 0

Therefore, average rate of change of the function in the given interval

= [tex]\frac{g(1)-g(-3)}{1-(-3)}[/tex]

= [tex]\frac{0-6}{1+3}[/tex]

= [tex]-\frac{3}{2}[/tex]

= - 1.5

Answer:

1/2

Step-by-step explanation:

The possible outcomes are

1,2,3,4,5,6,7,8,9,10

Factors of 6 are 1,2,3,6

or a 4

1,2,3,4,6 are the outcomes we want

There are 5 "good" outcomes

P( 4 or a factor of 6) = "good" outcomes/ total

                                  = 5/10

                                   =1/2

Answer:

[tex]\boxed{\frac{1}{2} }[/tex]

Step-by-step explanation:

There are total 10 outcomes.

[tex]1,2,3,4,5,6,7,8,9,10[/tex]

The probability of selecting 4 is 1 outcome out of total 10 outcomes.

Factors of 6 are [tex]1,2,3,6[/tex].

These are 4 outcomes out of total 10 outcomes.

The probability of selecting 4 or a factor of 6 is:

[tex]\displaystyle \frac{1}{10} +\frac{4}{10} =\frac{5}{10} =\frac{1}{2}[/tex]

Hi there! :)

Answer:

[tex]P(heads) = \frac{1}{8}[/tex]

Step-by-step explanation:

Probability of a coin landing on heads:

[tex]P(heads) = \frac{1}{2}[/tex]

Find the probability of getting heads 3 times:

[tex]\frac{1}{2} * \frac{1}{2} * \frac{1}{2} = \frac{1}{8}[/tex]

Therefore, the probability of the coin showing heads for 3 tosses is:

[tex]P(heads) = \frac{1}{8}[/tex]

Answer:

Step-by-step explanation:

2 3x2y3

*a clearer picture containing the graph is shown in the attachment

Answer:

20% of the class earned a D

Step-by-step Explanation:

Step 1: Determine the total number of students represented on the graph:

9 students => D

5 students => C

14 students => B

17 students => A

Total number of students = 45

Step 2: Express each category of students who scored a particular grade as a fraction and as percentage.

9 students => D => [tex] \frac{9}{45} = \frac{1}{5} [/tex] => as percentage, we have [tex] \frac{1}{5} * 100 = 20 percent [/tex]

5 students => C => [tex] \frac{5}{45} = \frac{1}{9} [/tex] => as percentage, we have [tex] \frac{1}{9} * 100 = 11.1 percent [/tex]

14 students => B => [tex] \frac{14}{45} [/tex] => as percentage, we have [tex] \frac{14}{45} * 100 = 31.1 percent [/tex]

17 students => A => [tex] \frac{17}{45} [/tex] => as percentage, we have [tex] \frac{17}{45} * 100 = 37.8 percent [/tex]

Step 3: Check each statement to see if they are true or not based on the calculations above.

Statement 1: "⅕ of the students earned a C."

This is NOT TRUE From our calculation, ⅑ of the students earned a C.

Statement 2: "3% more students earned an A than a B." This is also NOT TRUE.

37.8% earned A, while 31.1% earned a B. Thus, about 6.7% more students earned an A than a B.

Statement 3: "20% of the class earned a D".  This is TRUE.

Check calculation in step 2.

Statement 4: "¼ of the class earned a B". This is NOT TRUE.

¼ is 25% of the class. Those who earned a B account for 31.1% not 25% (¼ of the class).

The correct statement is: "20% of the class earned a D"

Answer:

We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.

Step-by-step explanation:

We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.

Let p = population proportion of smokers among those with four years of college

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 27%      {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}

Alternate Hypothesis, [tex]H_A[/tex] : p < 27%      {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}

The test statistics that will be used here is One-sample z-test for proportions;

                             T.S.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]  ~   N(0,1)

where, [tex]\hat p[/tex] = sample proportion of smokers = [tex]\frac{144}{785}[/tex] = 0.18

           n = sample of subjects = 785

So, the test statistics =  [tex]\frac{0.18-0.27}{\sqrt{\frac{0.27(1-0.27)}{785} } }[/tex]

                                     =  -5.68

The value of z-test statistics is -5.68.

             P-value = P(Z < -5.68) = Less than 0.0001

Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.

Since the value of our test statistics is less than the critical value of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.

Answer:

45

------

75

Step-by-step explanation:

Let x be the value of the numerator and x+30 be the value of the denominator

This is equal to 3/5

x             3

-------- = -------

x+30      5

Using cross products

5x = 3(x+30)

Distribute

5x = 3x+90

Subtract 3x from each side

2x = 90

Divide by 2

x = 45

The fraction is

45

-----

30+45

45

------

75

[tex]\dfrac{x}{x+30}=\dfrac{3}{5}\\\\5x=3(x+30)\\5x=3x+90\\2x=90\\x=45\\\\\dfrac{x}{x+30}=\dfrac{45}{45+30}=\dfrac{45}{75}[/tex]

Answer:

One - way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Step-by-step explanation:

ANOVA is a statistical technique designed to test mean of one or more quantitative populations.  In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA. It is a statistical technique designed to test mean of one or more quantitative populations. In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA.

One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

It should be the statistical technique that are made for testing the mean for one or more than one quantitative population. In two-way ANOVA it should be equivalent to the block mean. Here the column block represent the square be the three-way ANOVA.

Therefore, One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Learn more about evidence here: https://brainly.com/question/6764645?referrer=searchResults

Answer:

Those two are 0.25

4/16 = 1/4

5/20 = 1/4

Answer: Please Give Me Brainliest, Thank You!

4/16 = 5/20 = 1/4

Step-by-step explanation:

Because If you divide 4 and 16 by 4 you get 1/4 and if you divide 5 and 20 with 5 you get 1/4

Answer:

-52

Step-by-step explanation:

Think of it this way.  Opposite means to take the negation.  So we are taking the negation of the negation of negative 52.  This means mathematically:

- ( - ( -52 ) ) == -52

Cheers.

Answer:

x=18

Step-by-step explanation:

x/6 - 7 = -4

x/6 = 3

(x/ 6) * 6 = 3*6

x = 18

Answer:

Step-by-step explanation:

To find the common ratio between the terms of the sequence divide the previous term by the next term.

That's

Or

Therefore the common ratio of the sequence is - 3

Hope this helps you

Answer:

-3

Step-by-step explanation:

Answer:

no it is not 1/3

Step-by-step explanation:

(x-2) / (x-6)

This does not simplify

Rewriting x-2 as (x-6 +4)

(x-6 +4)/ ( x-6)

Replacing x-6 as m

( m+4) /m

Simplifying

m/m + 4/m

1 + 4/m

Replacing m with x-6

1 + 4/ ( x-6)

This is not 1/3

Answer:

The mean, variance, and standard deviation of the binomial distribution are 10, 8, and 2.83 respectively.

Step-by-step explanation:

We have to find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p, i.e; n = 50 p = 0.2.

Let X = binomial random variable

So, X ~ Binom(n = 50, p = 0.2)

Now, the mean of the binomial distribution is given by;

         Mean of X, E(X) = n [tex]\times[/tex] p

                                    = 50 [tex]\times[/tex] 0.2 = 10

Now, the variance of the binomial distribution is given by;

        Variance of X, V(X) = n [tex]\times[/tex] p [tex]\times[/tex] (1 - p)

                                         = 50 [tex]\times[/tex] 0.2 [tex]\times[/tex] (1 - 0.2)

                                         = 10 [tex]\times[/tex] 0.8 = 8

Also, the standard deviation of the binomial distribution is given by;

        Standard deviation of X, S.D.(X) = [tex]\sqrt{\text{n} \times \text{p} \times (1 - \text{p})}[/tex]

                                                              = [tex]\sqrt{\text{50} \times \text{0.2} \times (1 - \text{0.2})}[/tex]

                                                              = [tex]\sqrt{8}[/tex] = 2.83

Answer:

The value of x is 30°

Step-by-step explanation:

We are given that the outer angle of the parallelogram is 60 degrees. Therefore it's respective inner angle will be 180 - 60 = 120 degrees. And, by properties of a parallelogram, the angle opposite to this angle will be 120 degrees as well.

If we draw extend the line creating angle 2x, then we will make ( 1 ) a vertical angle to 2x, ( 2 ) a 90 degree angle, and ( 3 ) and angle that we can let be y. Therefore, 2x + y = 90, and 3x + y = 120.

[tex]\begin{bmatrix}2x+y=90\\ 3x+y=120\end{bmatrix}[/tex] ,

[tex]\begin{bmatrix}6x+3y=270\\ 6x+2y=240\end{bmatrix}[/tex] ,

[tex]6x+2y=240\\-\\\underline{6x+3y=270}\\y=30[/tex],  

[tex]2x + (30) = 90,\\2x = 60,\\x = 30[/tex]

Solution : x = 30°

Answer:

x = 30

Step-by-step explanation:

a+ 60 = 180

a = 120

3x+b = 120  because opposite angles in a parallelogram are equal

2x+90+b = 180 since it forms a line

2x+b = 90

We have 2 equations and 2 unknowns

3x+b = 120

2x+b = 90

Subtracting

3x+b = 120

-2x-b = -90

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

x = 30

Answer:

Stocks = $15,500

Bonds = $107,250

CD's = $47,250

Step-by-step explanation:

S + B + C = 170000

.0325S + .038B .067C = 7745

60,000 + C = b

S = $15,500

B = $107,250

C = $47,250

Answer:

Simple Interest : $ 4400

Step-by-step explanation:

We want to calculate the interest on $ 10,000, at 5.5% interest rate per year, over a course of 8 years.

We can use the simple interest formula here, or :

I = P × r × t,

Where P is the principle amount, $ 10,000, r is the interest rate, 5.5% each year, or in decimal form 5.5 / 100 = 0.055. t is the time, 8 years.

Simple Interest : 10000 × 0.055 × 8 =  $4400.00

Then again the interest can be added to the principal amount ( $10,000 ) to receive some new amount after 8 years, which is $ 14,000. However the simple interest earned in 8 years at a rate of 5.5% should be $4400.

The simple interest earned on the amount is $4,400

Interest is the total amount that would be paid or earned from making an investment or taking a loan over a period of time.

Simple Interest  = principal x time x interest rate

principal = amount borrowed = $10,000

time = 8 years

Interest rate = 5.5%

10,000 x 0.055 x 8 = $4,400

To learn more about simple interest, please check: https://brainly.com/question/9352088?referrer=searchResults

Answer:

51

Step-by-step explanation:

Without resorting to L'Hopitâl's rule,

[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}[/tex]

With the rule, we get the same result:

[tex]\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}[/tex]

Answer: The point estimate of the population proportion is . 485.​

The margin of error is 0.273.​

Step-by-step explanation:

Confidence interval for population proportion(p):

sample proportion ± Margin of error

Given:  Lower bound of confidence interval  = 0.212

Upper bound = 0.758

⇒sample proportion - Margin of error=0.212  (i)

sample proportion + Margin of error= 0.758  (ii)

Adding (i) and (ii) , we get

2(sample proportion) =0.970

⇒ sample proportion = 0.970÷2= 0.485

Since sample proportion is the point estimate of the population proportion.

So, the point estimate of the population proportion=  0.485

Now put sample proportion =0.485 in (ii), we get

0.485+ Margin of error= 0.758

⇒  Margin of error= 0.758 - 0.485 =0.273

i.e. The margin of error is 0.273.​

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

Explanation:

Count out the spaces, or use subtraction, to find the horizontal side BC is 2 units long. Similarly, you'll find the vertical side AC is 4 units long.

Use the pythagorean theorem to find the length of segment AB.

a^2 + b^2 = c^2

2^2 + 4^2 = c^2

4 + 16 = c^2

20 = c^2

c^2 = 20

c = sqrt(20)

We stop here since it matches with choice B.

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

Optionally, we can simplify like so

sqrt(20) = sqrt(4*5)

sqrt(20) = sqrt(4)*sqrt(5)

sqrt(20) = 2*sqrt(5)

Answer:

The answer is [tex]\sqrt{20}[/tex].

Step-by-step explanation:

Use the Pythagorean Theorem.  

[tex]2^{2} + 4^{2} = c^{2} \\4+16 = c^{2} \\\sqrt{20} = c[/tex]

if they're in a bundle of 10 then theres 10 pencils

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

Temp. 174 176 177 178 178 179 180 181

Ratio 0.86 1.31 1.42 1.01 1.15 1.02 1.00 1.74

Temp. 184 184 184 184 184 185 185 186

Ratio 1.43 1.70 1.57 2.13 2.25 0.76 1.37 0.94

Temp. 186 186 186 188 188 189 190 192

Ratio 1.85 2.02 2.64 1.53 2.48 2.90 1.79 3.16

A)

Using the online linear regression calculator, the lie of best fit which models the data above is :

ŷ = 0.09386X - 15.55523

Where ;

X = independent variable

ŷ = predicted or dependent variable

- 15.55523 = intercept

0.09386 = gradient / slope

B)

Point estimate when tank temperature is 186

ŷ = 0.09386(186) - 15.55523

ŷ = 17.45796 - 15.55523

ŷ = 1.90273

C)

Residual error (y - ŷ), ŷ = 1.90273 when x = 186

(0.94 - 1.90273) = −0.96273

(1.85 - 1.90273) = −0.05273

(2.02 - 1.90273) = 0.11727

(2.64 - 1.90273) = 0.73727

D)

To determine the proportion of observed variation in efficiency ratio, we find the Coefficient of determination R^2, which can be found using the online Coefficient of determination calculator : the r^2 value obtained is 0.4433.

Answer:

2hrs 24mins

Step-by-step explanation:

Very simple the time they will meet again at the point will be the LCM of their various time taken to complete a cycle.

Ans LCM(24, 36, 48) = 144 mins

= 2hrs 24mins

Answer:

The answer is 2 hours and 24 minutes

Step-by-step explanation:

Hope you get this right:)

Answer:  $9,000

Step-by-step explanation:

Step 1

Calculate the amount of dividends the company will pay to all its shareholders.

= 15% of profits

= 15% * 6,000,000

= $900,000

Step 2

Calculate how much dividends each share will get;

$900,000 to 2 million shares of Company Y.

= 900,000/2,000,000

= $0.45

Step 3

Calculate how much the Mutual fund will get for its 20,000 shares

= 20,000 * 0.45

= $9,000

Answer:

(4,4)⋅(4,4)

Step-by-step explanation:

Answer:

[tex]x = -\frac{3}{2}[/tex] or [tex]x = 1[/tex]

Step-by-step explanation:

Using the zero product property, first step is to set the given equation, [tex] 2x^2 + x - 1 = 2 [/tex] , to zero. Then factorise the left side.

Thus,

[tex] 2x^2 + x - 1 = 2 [/tex]

Subtract 2 from both sides

[tex] 2x^2 + x - 1 - 2 = 2 - 2 [/tex]

[tex] 2x^2 + x - 3 = 0 [/tex]

Factorise the left side

[tex] 2x^2 + 3x - 2x - 3 = 0 [/tex]

[tex] x(2x + 3) - 1(2x + 3) = 0 [/tex]

[tex] (x - 1)(2x + 3) = 0 [/tex]

Find the solution

[tex] x - 1 = 0 [/tex]

Or

[tex]2x + 3 = 0[/tex]

[tex] x = 1 [/tex]

Or

[tex]2x + 3 = 0[/tex]

[tex]2x = -3[/tex]

[tex]x = -\frac{3}{2}[/tex]

The answer is: [tex] x = 1 [/tex] or [tex]x = -\frac{3}{2}[/tex]

Answer:

The probability is  [tex]P(X < 12) = 0.99286[/tex]

Step-by-step explanation:

From the question we are told that

        The population mean is [tex]\mu = 12 \ oz[/tex]

         The  standard deviation is  [tex]\sigma = 0.1 \ oz[/tex]

          The sample mean is  [tex]\= x = 12.1 \ oz[/tex]

          The sample size is  n = 6 packs

The standard error of the mean is mathematically represented as

              [tex]\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }[/tex]

substituting values

            [tex]\sigma_{\= x } = \frac{0.1}{\sqrt{6} }[/tex]

            [tex]\sigma_{\= x } = 0.0408[/tex]

Given that the can’s contents follow a Normal distribution then then  the probability that the mean contents of a six-pack are less than 12 oz is mathematically represented as

         [tex]P(X < 12) = P ( \frac{X - \mu }{ \sigma_{\= x }} < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]

Generally  [tex]\frac{X - \mu }{ \sigma_{ \= x }} = Z (The \ standardized \ value \ of \ X )[/tex]

So

         [tex]P(X < 12) = P ( Z < \frac{\= x - \mu }{ \sigma_{\= x }} )[/tex]

substituting values

       [tex]P(X < 12) = P ( Z < \frac{12.2 -12 }{0.0408} )[/tex]

      [tex]P(X < 12) = P ( Z < 2.45 )[/tex]

From the normal distribution table the value of [tex]P ( Z < 2.45 )[/tex] is  

           [tex]P (Z < 2.45)0.99286[/tex]

=>   [tex]P(X < 12) = 0.99286[/tex]

Answer:

The angle of elevation is not properly represented

Step-by-step explanation:

Given

The question in the attachment;

Required

Determine the error

See attachment for proper representation of the angle of elevation;

Solving further (From the Attachment)

[tex]Tan22 = \frac{x}{3000}[/tex]

Multiply both sides by 3000

[tex]x = 3000 * tan22[/tex]

[tex]x = 3000 * 0.4040[/tex]

[tex]x = 1212[/tex]

The cliff is about 1212 feet high

Answer:

length times width

Step-by-step explanation: