A random sample of 11 students produced the following data, where x is the hours spent per month playing games, and y is the final exam score (out of a maximum of 50 points). The data are presented below in the table of values.
x y
14 46
15 49
16 37
17 42
18 37
19 31
20 25
21 23
22 20
23 15
24 12
What is the value of the intercept of the regression line, b, rounded to one decimal place?

Answer:

  28) -1

  29) 9

  30) x^2+4x+7

  31) x-2

Step-by-step explanation:

Given:

  f(x) = x + 2

  g(x) = x^2 +3

Find:

  28) f(-3)

  29) f(g(2))

  30) g(f(x))

  31) f-1(x)

Solution:

Put the function argument values into the expression and do the arithmetic.

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

__

29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9

__

30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7

__

31) The meaning of y = f^-1(x) is x = f(y).

  x = f(y) = y+2

  y = x -2

  f^-1(x) = x -2

Answer:

  x^2 +y^2 = 4y

Step-by-step explanation:

Using the usual translation relations, we have ...

  r^2 = x^2+y^2

  x = r·cos(θ)

  y = r·sin(θ)

Substituting for sin(θ) the equation becomes ...

  r = 4sin(θ)

  r = 4(y/r)

  r^2 = 4y

Then, substituting for r^2 we get ...

  x^2 +y^2 = 4y . . . . . matches the first choice

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:

[tex]\huge\boxed{a=9 ; b = -8}[/tex]

Step-by-step explanation:

[tex]f(x) = \frac{ax+b}{x}[/tex]

Putting x = 1

=> [tex]f(1) = \frac{a(1)+b}{1}[/tex]

Given that f(1) = 1

=> [tex]1 = a + b[/tex]

=> [tex]a+b = 1[/tex]  -------------------(1)

Now,

Putting x = 2

=> [tex]f(2) = \frac{a(2)+b}{2}[/tex]

Given that f(2) = 5

=> [tex]5 = \frac{2a+b}{2}[/tex]

=> [tex]2a+b = 5*2[/tex]

=> [tex]2a+b = 10[/tex]  ----------------(2)

Subtracting (2) from (1)

[tex]a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9[/tex]

For b , Put a = 9 in equation (1)

[tex]9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8[/tex]

Answer:

The  90% confidence interval is  [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample size is  n =  64

     The sample  mean is  [tex]\= x = \$ 32, 000[/tex]

     The  standard deviation is  [tex]\sigma= \$ 8, 200[/tex]

Given that the confidence interval is  90% then the level of significance is mathematically evaluated as

             [tex]\alpha = 100 - 90[/tex]

             [tex]\alpha = 10 \%[/tex]

            [tex]\alpha = 0.10[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table , the value is  

       [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

  Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{ \sqrt{n} }[/tex]

  =>   [tex]E = 1.645 * \frac{ 8200 }{ \sqrt{64} }[/tex]

  =>   [tex]E = 1686.13[/tex]

The 90% confidence interval is mathematically represented as

      [tex]\= x - E < \mu < \= x + E[/tex]

 =>    [tex]32000 - 1689.13 < \mu < 32000 + 1689.13[/tex]

=>    [tex]\$ \ 30313.9< \mu < \$ \ 33686.13[/tex]

Answer:

(5x³+3x²-5x+4) + (8x³-5x²+8x+9)

= 5x³+3x²-5x+4 +8x³-5x²+8x+9

= 5x³+8x³+3x²-5x²-5x+8x+4+9

= 13x³-2x²+3x+13

Hope this helps

if u have question let me know in comments ^_^

Answer:

x

Step-by-step explanation:

probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true

Answer:

Within the factors hindering expression in music, tempo is the most important number of factors such as your mood.

Step-by-step explanation:

If one wants to convey a message, they should try these:

a) Use real life

b) introduce symbolism

c) convey sensory disruption, e.t.c.

Hope these helps.

Answer:

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = 3.5

Step-by-step explanation:

Given that:

Consider the following ordered data. 6 9 9 10 11 11 12 13 14

From the above dataset, the highest value = 14  and the lowest value = 6

The median is the middle number = 11

For Q1, i.e the median  of the lower half

we have the ordered data = 6, 9, 9, 10

here , we have to values as the middle number , n order to determine the median, the mean will be the mean average of the two middle numbers.

i.e

median = [tex]\dfrac{9+9}{2}[/tex]

median = [tex]\dfrac{18}{2}[/tex]

median = 9

Q3, i.e median of the upper half

we have the ordered data = 11 12 13 14

The same use case is applicable here.

Median = [tex]\dfrac{12+13}{2}[/tex]

Median = [tex]\dfrac{25}{2}[/tex]

Median = 12.5

Low             Q1                Median              Q3                 High

6                  9                     11                      12.5                14

The interquartile range = Q3 - Q1

The interquartile range =  12.5 - 9

The interquartile range = 3.5

Answer:

150,000

Step-by-step explanation:

1 m = 100 cm

260 m = 260 * 100 cm = 26000 cm

15 m = 15 * 100 cm = 1500 cm

area of floor = LW = 26000 cm * 1500 cm = 39,000,000 cm^2

area of 1 tile = 26 cm + 10 cm = 260 cm^2

number of tiles needed = 39,000,000/260 = 150,000

Answer: 150,000 tiles

Answer:

so to get a third you divide it by 3

first convert it to fraction

so it is 26/3

so do 26/3 divided by 3

so we do keep switch flip

26/3*1/3

so answer is 26/9 or 2 8/9

Step-by-step explanation:

Answer:

[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]

Step-by-step explanation:

8 2/3 tablespoons of red chilies is required for a recipe.

One-third of the original recipe would mean that the quantity of red chilies will be also one-third.

8 2/3 × 1/3

Convert to an improper fraction.

26/3 × 1/3

Multiply the fractions.

26/(3 × 3) = 26/9

Convert to a mixed fraction.

26/9 = 2 8/9

Step-by-step explanation:

Hello, there!!!

It's so simple here,

Here,

we have is 1 angle is 120°and other is 3x°.

now,

3x°=120° {because when two st.line intersects eachother then the opposite angle formed are equal}

so, 3x°=120

or, x=120°/3

=40°

Therefore, the value of x is 40°.

Hope it helps....

Answer:

C(x)=1.2x+8,000.

Step-by-step explanation:

C(x)=cost per unit⋅x+fixed costs.

The manufacturer has fixed costs of $8000 no matter how many drinks it produces. In addition to the fixed costs, the manufacturer also spends $1.20 to produce each drink. If we substitute these values into the general cost function, we find that the cost function when x drinks are manufactured is given by

In order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

Given is that the manufacturer of a granola bar spends $1.20 to make each bar and sells them for $2.

Suppose that you have to sell [x] number of bars to make profits. So, we can write -

{2x} - {1.20x} > {8000}

0.8x > 8000

8x > 80000

x > 10000

Therefore, in order to make the profits, the manufacturer must make the quantity of greater than 10000 bars.

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

brainly.com/question/17421223

#SPJ2

Answer:

D

Step-by-step explanation:

To determine the range we must solve this inequality;

● 1200000<1800000-250x<1300000

Substract 1800000 from both sides.

● 1200000-1800000<1800000-250x<1300000-1800000

● -600000< -250x < -500000

Divide both sides by 250

● -600000/250 < -250x/250 < -500000/250

● -2400 < -x < -2000

Multiply both sides by -1 and switch the signs

● 2000 < x < 2400

The correct option is D. 2000<= x <= 2400

Given, the value of an airplane depends on the flight hours,

[tex]V= 1800000-250x[/tex], here x is the flight hours.

We have to calculate the range of x After one year.

Since, [tex]V= 1800000-250x[/tex]

[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]

Since the value of the plane is between $1,200,000 and $1,300,000. So,

[tex]x=\dfrac{1800000-1200000}{250}[/tex]

[tex]x=\dfrac{600000}{250}[/tex]

[tex]x=2400\\[/tex]

When V is 1300000 then x will be,

[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]

[tex]x=\dfrac{500000}{250}[/tex]

[tex]x=2000[/tex]

Hence the range of x will be from 2000 to 2400.

The correct option is D. 2000<= x <= 2400.

For more details on range follow the link:

https://brainly.com/question/10185991

Step-by-step explanation:

(AUB)' means they are all outside the set A and B so thats 0. Hope it helps

Answer:

Step-by-step explanation:

from the question,

the mean 14

the standard deviation is 3

and sample size is 10.

since the n which is the sample size is 10, then the distribution is mound shaped.

why?

this is due to the fact that the random variable from which we took the sample is mound shaped.

The sampling distribution of the mean is normally distributed although the question says the random variable is not normally distributed. so the shape is bell shaped and normally distributed.

the standard deviation of the mean is

3/√10

= 0.948

Answer: 2(x + 8) is the expression.

Use distributive property to simplify,

2x+16

I didn't know which answer you wanted so....

Answer:

2(x + 8)

Step-by-step explanation:

Hello!

Twice the sum means we multiply by 2

2

the sum of a number and eight is x + 8

2 * x + 8

Since we have to twice the sum we put x + 8 in parenthesis to show to do that first

2(x + 8)

Hope this Helps!

Answer:

60

Step-by-step explanation:

5 is 60 inch

Answer:

A. they are parallel because their slopes are equal.

Step-by-step explanation:

edge 2020

Answer:

its A in egde

Step-by-step explanation:

The question is not clear, but it is possible to obtain distance, s, from the given function. This, I would show.

Answer:

s = 17 units

Step-by-step explanation:

Given f(t) = t³ - 8t² + 27t

Differentiating f(t), we have

f'(t) = 3t² - 16 t + 27

At t = 0

f'(t) = 27

This is the required obtainaible distance, s.

Answer:

Option b. None is the correct option.

The Answer is 63%

Step-by-step explanation:

To solve for this question, we would be using the z score formula

The formula for calculating a z-score is given as:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We have boxes X and Y. So we will be combining both boxes

Mean of X = 100 lb

Mean of Y = 5 lb

Total mean = 100 + 5 = 105lb

Standard deviation for X = 1 lb

Standard deviation for Y = 0.5 lb

Remember Variance = Standard deviation ²

Variance for X = 1lb² = 1

Variance for Y = 0.5² = 0.25

Total variance = 1 + 0.25 = 1.25

Total standard deviation = √Total variance

= √1.25

Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,

For 104lb

z = (x-μ)/σ,

z = 104 - 105 / √25

z = -0.89443

Using z score table ,

P( x = z)

P ( x = 104) = P( z = -0.89443) = 0.18555

For 1061b

z = (x-μ)/σ,

z = 106 - 105 / √25

z = 0.89443

Using z score table ,

P( x = z)

P ( x = 106) = P( z = 0.89443) = 0.81445

P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555

= 0.6289

Converting to percentage, we have :

0.6289 × 100 = 62.89%

Approximately = 63 %

Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%

Since there is no 63% in the option, the correct answer is Option b. None.

The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be 63%.

It is also called the Gaussian Distribution. It is the most important continuous probability distribution. The curve looks like a bell, so it is also called a bell curve.

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with a mean of 100 lb and 5 lb and standard deviation of 1 lb and 0.5 lb, respectively.

The percent of filled boxes weighing between 104 lb and 106 lb is to be expected will be

Then the Variance will be

[tex]Var = \sigma ^2[/tex]

Then for X, we have

[tex]Var (X) = 1^2 = 1[/tex]

Then for Y, we have

[tex]Var (Y) = 0.5^2 = 0.25[/tex]

Then the total variance will be

[tex]Total \ Var (X+Y) = 1 + 0.25 = 1.25[/tex]

The total standard deviation will be

[tex]\sigma _T = \sqrt{Var(X+Y)}\\\\\sigma _T = \sqrt{1.25}[/tex]

For 104 lb, then

[tex]z = \dfrac{104-105}{\sqrt{25}} = -0.89443\\\\P(x = 104) = 0.18555[/tex]

For 106 lb, then

[tex]z = \dfrac{106-105}{\sqrt{25}} = 0.89443\\\\P(x = 106) = 0.81445[/tex]

Then

[tex]P(104 \leq Z \leq 106) = 0.81445 - 0.18555 = 0.6289 \ or \ 62.89\%[/tex]

Approximately, 63%.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

Answer:

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Step-by-step explanation:

([tex]a^{8}[/tex]) * [tex]\frac{3}{2}[/tex]

Remove the parenthesis by multiplying

[tex]\frac{3}{2}[/tex][tex]a^{8}[/tex]

This expression cannot be simplified further

[tex]\large\boxed{\frac{3}{2}a^{8}}[/tex]

Hope this helps :)

Answer: $ 36,840.

Step-by-step explanation:

contribution margin=62% =0.62

fixed monthly expenses = $45,000

Sales =  $132,000

We assume that the fixed monthly expenses do not change.

Then, company's net operating income = (contribution margin×Sales )-fixed monthly expenses

=$( (0.62×132000)-45000 )

= $ (81840-45000)

= $ 36,840

Hence, the best estimate of the company's net operating income in a month when sales are $132,000 is $ 36,840.

Answer: 7 mi

Step-by-step explanation: since the distance from bluepoint to Manchester is 12 9/10 mi and you know that bluepoint to Silverstone is 5 9/10 subtract that and you get 7 mi as your answer

Answer:

7 miles

Step-by-step explanation:

Hey there!

Well given BM and BS, we need to subtract them.

12 9 /10 - 5 9/10

9/10 - 9/10 = 0

12 - 5 = 7

Silvergrove to Manchester is 7 miles.

Hope this helps :)

Answer:

see below

Step-by-step explanation:

the observed ph is 6.32

the mean pH of Tap water is shown below

                       sum of observations

Mean (Tap) = -----------------------------------

                       number of observations

 (7.24 +7.05 +7.07 +6.6 +7.28 +7.29 +7.05 +6.7 +7.16 +7.07 +7.12 +6.56

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

                                                      12

= 7.016

then mean pH of bottle water is shown below

                            sum of observations

Mean (Bottles) = -----------------------------------

                             number of observations

 (5.35 + 5.29 + 5.46 + 5.4 + 5.95 + 6.22 + 5.43 +5.48 +6.06 +5.33 +5.46 +5.41)

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

                                                      12

= 5.57

theoretically.. the higher the pH values should be between 0 to 14.

based from the above results, the mean tap water has an average of 7.016 and by looking at the pH chart... its a neutral or pure water.

while the average pH Bottles has 5.57, this means its more acidic water, or by looking at the pH chart its an acid rain water.

a 6.32pH is below pure water, based on the chart looks like a urine/saliva.

Answer:

5x^3-2

[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]

Explanation:

The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.

We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.

Answer:

  146/45

Step-by-step explanation:

Let x represent the value of the number of interest. Then we can do the following math to find its representation as a fraction.

  [tex]x=3.2\overline{4}\\10x=32.4\overline{4}\\10x-x=9x=32.4\overline{4}-3.2\overline{4}=29.2\\\\x=\dfrac{29.2}{9}=\boxed{\dfrac{146}{45}}[/tex]

__

Comment on procedure

The power of 10 that we multiply by (10x) is the number of repeated digits. Here, there is a 1-digit repeat, so we multiply by 10^1. If there were a 2-digit repeat, we would compute 10^2x -x = 99x to rationalize the number.

Answer:

36

Step-by-step explanation:

formula of area for square:

A=s^2

s=6

A=6^2

A=36

Answer:

36

Step-by-step explanation:

I got it right

Answer:

y=4/7x

Step-by-step explanation:

perpendicular lines have opposite slopes. that means reciprocal and opposite sign.