Solve (x + 1 < 4) ∩ (x - 8 > -7).

Answer:

daddy wants some more dior

Step-by-step explanation:

Answer:

B. F(x) = 0.4x² - 1

Step-by-step explanation:

→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.

→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.

This means answer choice, "B," is correct.

Answer:

The answer is B

Step-by-step explanation:

→The function F(x) has shifted downwards, meaning there has to be a 1 being subtracted.

→The function F(x) has grown wider, meaning there has to be a number of absolute value less than 1.

This means answer choice, "B," is correct.

Answer:

120 ways

Step-by-step explanation:

There are 3 spots and 6 options

_ _ _

1  2 3

6 ways for 1st chair to be chosen

5 ways for 2nd chair to be chosen (1st chair is chosen already, so there are 5 players left)

4 ways for 3rd chair to be chosen (1st and 2nd are already chosen, only 4 players left)

Multiply 6*5*4 to find the total number of ways (120)

Answer:

4.50 is for two scoops and a normal cone. Upgrades on cone is $0.50 and any additional toppings are also $0.50

Answer:5 × t = 6

Step-by-step explanation:

Step 1: 4.50 + 0.50 = 5

Step 2: We has 5t is 5 × t

Step 3: 5 × t = 6

Answer:

D: 15 and 2

Step-by-step explanation:

Mean

To find the mean, or average, add up all the values in the data set,then divide by the number of values in the data set.

1. Add up all the values

Values: 14, 14, 15, 15, 16, 15, 15, 16

Add them :14+14+15+ 15+16+15+15+16=120

120

2. Divide by the number of values

Count how many numbers are in the data set. In this case there are 8. Divide 120 by 8.

120/8=15

The mean is 15

Range

To find the range, subtract the smallest number in the set from the biggest number in the set.

14, 14, 15, 15, 16, 15, 15, 16

Biggest number: 16

Smallest number: 14

biggest-smallest

16-14=2

The range is 2

Therefore, the answer is D: 15 and 2

observation means number.

mean= sum of all observation ÷ number of observation

= 14+ 14+ 15+ 15+ 16+ 15+ 16

7

= 105

7

= 15

range= the highest observation - lowest observation

= highest number- 16

lowest number- 14

= 16-14

= 2

therefore the answer is

OPTION- D 15;2

A becuase i worked it out and i got that so im really confident

Answer:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

[tex]\bar X= 28.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =4.7[/tex] represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Answer:

P(greater than 1.25 minutes) = 0.8611 (Approx)

Step-by-step explanation:

Given:

Waiting time = 0 - 9 minutes

Find:

Probability that selected passenger has a waiting time greater than 1.25 minutes.

Computation:

⇒ The probability that a randomly selected passenger has a waiting time greater than 1.25 minutes =

⇒  P(greater than 1.25 minutes) = [9-1.25] / 9

⇒ P(greater than 1.25 minutes) = [7.75] / 9

⇒ P(greater than 1.25 minutes) = 0.8611 (Approx)

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

We have,

Given:

Total number of components (n) = 1000

Number of defective components (d) = 350

a.

P(A) is the probability that the first component drawn is defective:

P(A) = d/n = 350/1000 = 0.35

b.

P(B|A) is the probability that the second component drawn is defective given that the first component drawn is defective:

Since one defective component has already been drawn, the total number of components is now 999, and the number of defective components remaining is 349.

P(B|A) = Number of defective components remaining / Total number of components remaining = 349/999 ≈ 0.349

c.

P(A ∩ B) is the probability that both the first and second components drawn are defective:

P(A ∩ B) = P(A) * P(B|A) = 0.35 * 0.349 ≈ 0.122

d.

P([tex]A^c[/tex] ∩ B) is the probability that the first component drawn is not defective (complement of A) and the second component drawn is defective:

[tex]P(A^c)[/tex] is the probability that the first component drawn is not defective:

[tex]P(A^c)[/tex] = 1 - P(A) = 1 - 0.35 = 0.65

Since the first component drawn is not defective, the total number of components remaining is now 999, and the number of defective components remaining is still 350.

P([tex]A^c[/tex] ∩ B) = P([tex]A^c[/tex]) * P(B) = 0.65 * (350/999) ≈ 0.228

e.

P(B) is the probability that the second component drawn is defective:

P(B) = Number of defective components / Total number of components

= 350/1000

= 0.35

f.

P(A|B) is the probability that the first component drawn is defective given that the second component drawn is defective:

P(A|B) = P(A ∩ B) / P(B)

= (0.35 * 0.349) / 0.35

= 0.349

g.

To determine if A and B are independent, we need to compare

P(A) * P(B) with P(A ∩ B).

P(A) * P(B) = 0.35 * 0.35 = 0.1225

P(A ∩ B) = 0.122

Since P(A) * P(B) = P(A ∩ B), A and B are independent events.

It is reasonable to treat A and B as independent because the probability of A and the probability of B are not affected by each other.

The occurrence or non-occurrence of A does not impact the probability of B.

Thus,

The probabilities are:

a. P(A) = 0.35

b. P(B|A) ≈ 0.349

c. P(A ∩ B) ≈ 0.122

d. P(A^c ∩ B) ≈ 0.228

e. P(B) = 0.35

f. P(A|B) = 0.349

g. A and B are independent.

Yes, it is reasonable to treat A and B as though they were independent because P(A) * P(B) = P(A ∩ B).

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ4

Answer:

$350

Step-by-step explanation:

Let d = price of dryer

Then d - 61 is the price of the washer.

The sum of the prices is $639.

d + d - 61 = 639

2d - 61 = 639

2d = 700

d = 350

The price of the dryer is $350

Answer:

63

Step-by-step explanation:

So just find the area of the carpet:

9 * 7 = 63

Answer:

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

Step-by-step explanation:

The question is incomplete:

Three hundred consumers were surveyed about a new brand of snack food, Crunchicles. Their age groups and preferences are given in the table.

                           18–24 25–34 35–55 55 and over Total

Liked Crunchicles   4       9       3 23                  39

Disliked Crunchicles 5        27      28 64              124

No Preference         7        27          10 93                 137

Total                        16        63      41 180            300

One consumer from the survey is selected at random. If the selected consumer is 70 years old, what is the probability that he/she likes crunchicles .

If the consumer is 70 years old is included in the category "55 and over" from this survey. There are 180 subjects in that category.

The number that likes Crunchicles and are 55 and over is 23.

If we calculate the probability as the relative frequency, we have:

[tex]P(\text{L }|\text{ 55+})=\dfrac{P(\text{L \& 55+})}{P(5\text{5+})}=\dfrac{23}{180}=0.1278[/tex]

L: Likes Crunchicles.

The probability that a selected consumer, given that is 70 years old, likes Crunchicles is 12.78%.

Answer:

a = 8

Step-by-step explanation:

Explanation:-

Given P(x) = 2 x+4 a

          Q(x)=4 x - 2

          P( Q(4)) = 60

         P(4 (4) - 2) = 60

        P( 14 ) = 60

       2 (14) + 4 a = 60

        4 a + 28 = 60

Subtracting '28' on both sides , we get

       4 a +28 - 28 = 60 - 28

       4 a = 32

Dividing '4' on both sides , we get

        a = 8

Answer:

x=-77+5√ 231 x=-77-5√231

I got this answer for x and the both equations are equal

Answer:

I think it’s -4

Step-by-step explanation:

-2 plus -2 is -4

since 2 plus 2 is 4

Hope this helps ;)

Answer:

Step-by-step explanation:

It is because 2 plus 2 is 4

so -2 plus -2 is -4

hth!

Answer:

There were 300 students

Step-by-step explanation:

Original * 30 = increase

Add the increase to get the new number

original + increase = 308

original + original*30% = 390

Factor out original number

original ( 1+30%) = 390

Change to decimal form

original ( 1+.30) = 390

original ( 1.30) = 390

Divide by 1.3

original = 390/1.3

             =300

Answer:

A rectangle is a 2 dimensional figure, it is in a plane, so it has two faces, and yes, they are equals.

Answer:  The correct answer is:  " 2x² " .

________________________________

Step-by-step explanation:

________________________________

We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

  →  We are to "add" these 2 (two) expressions together:

     →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

            → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

            →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

             →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

             "(1x² − 2 − 1x)" ;  

         {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

            →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                     →  " +1(1x² − 2 − 1x) " ;

________________________________

Note the distributive property of multiplication:

   →  " a(b+c) = ab + ac " ;

and likewise:

   →  " a(b+c+d) = ab + ac + ad " .

________________________________

So; we have:

→  " +1(1x² − 2 − 1x) " ;

  = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

  =       + 1x²    +    (-2)     +  (-1x) ;

  =       +1x²    −    2   −  1x  ;

  ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

     →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

________________________________

Now, simplify by combining the "like terms" ; as follows:

   +1x² + 1x² = 2x²  ;

   +1x −  1x = 0 ;  

   + 2 −  2  = 0 ;

________________________________

The answer is: " 2x² " .

________________________________

Hope this is helpful to you!

   Best wishes!

________________________________

Answer:

The correct answer is:  " 2x² " .

________________________________

Step-by-step explanation:

________________________________

We are asked:  "What is the sum of:  "x + x² + 2" and "x² − 2 − x" ?

Since we are to find the "sum" ;

 →  We are to "add" these 2 (two) expressions together:

    →     (x + x² + 2) +  (x² − 2 − x) ;

Note:  Let us rewrite the above, by adding the number "1" as a coefficient to:  the values "x" ; and "x² " ;  since there is an "implied coefficient of "1" ;

           → {since:  "any value" ; multiplied by "1"; results in that exact same value.}.

           →     (1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Rewrite as:

            →     1x + 1x² + 2) +  (1x² − 2 − 1x) ;

Now, let us add the "coefficient" , "1" ; just before the expression:

            "(1x² − 2 − 1x)" ;  

        {since "any value", multiplied by "1" , equals that same value.}.

And rewrite the expression; as follows:

           →     (1x + 1x² + 2) +  1(1x² − 2 − 1x) ;

Now, let us consider the following part of the expression:

                    →  " +1(1x² − 2 − 1x) " ;

________________________________

Note the distributive property of multiplication:

  →  " a(b+c) = ab + ac " ;

and likewise:

  →  " a(b+c+d) = ab + ac + ad " .

________________________________

So; we have:

→  " +1(1x² − 2 − 1x) " ;

 = (+1 * 1x²)  +  (+1 *-2) + (+1*-1x) ;

 =       + 1x²    +    (-2)     +  (-1x) ;

 =       +1x²    −    2   −  1x  ;

 ↔    ( + 1x²  −  1x  −  2)

Now, bring down the "left-hand side of the expression:

1x + 1x² + 2 ;

and add the rest of the expression:

    →  1x  +  1x²  +  2  +   1x²  −  1x  −  2 ;

________________________________

Now, simplify by combining the "like terms" ; as follows:

  +1x² + 1x² = 2x²  ;

  +1x −  1x = 0 ;  

  + 2 −  2  = 0 ;

________________________________

The answer is: " 2x² " .

Step-by-step explanation:

Answer:

The number of students reporting readings between 87 g and 89 g is 61

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 88g

Standard deviation = 1g

Percentage of students reporting readings between 87 g and 89 g

87 = 88-1

So 87 is one standard deviation below the mean.

89 = 88+1

So 89 is one standard deviation above the mean.

By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.

Out of 90 students:

0.68*90 = 61.2

Rounding to the nearest whole number:

The number of students reporting readings between 87 g and 89 g is 61

Answer:

x = 2 is the solution of the given equation

Step-by-step explanation:

Step(i):-

Given equation

  [tex]\sqrt{x+6-4} = x[/tex]

squaring on both sides , we get

[tex](\sqrt{x+2})^{2} = x^{2}[/tex]

⇒ x + 2 = x²

⇒x² - x -2 =0

Step(ii):-

  Given x² - x -2 =0

⇒ x² - 2x + x - 2 =0

⇒ x ( x-2) + 1(x - 2) =0

⇒ (x + 1) ( x-2) =0

⇒ x = -1 and x =2

x = 2 is the solution of the given equation

Verification:-

[tex]\sqrt{x+6-4} = x[/tex]

Put x= 2

[tex]\sqrt{2+6-4} = 2[/tex]

[tex]\sqrt{4} = 2[/tex]

 2 = 2

Answer:

6 less than a number is equal to 1 and 4 tenths

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

divide vertical drop by horizontal drop

or vertical increase by horizontal increase

for example, in the graph when y increases by 1 x increases by 1

1/1=1 and thus the gradient is 1

the whole equation is y=x+3

Answer:

The slope = 1.

Step-by-step explanation:

If we count squares down for the top arrow then left to the point where the line cuts the horizontal axis we get 10 and 10.

So the slope = 10/10 = 1.

Answer:

the answer is square root 5 over 2 square root 2

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Measure of arcURN = 270°

In radians:

270° = 270π/180

270° = 3π/2

Now

Area of sector = 1/2r²∅

= 1/2(10)²(3π/2)

= 50(3π/2)

= 75π

Answer:

[tex]x=-10[/tex]

Step-by-step explanation:

[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]

Answer:

A.

Step-by-step explanation:

In the attached file

Answer: Option A.

Step-by-step explanation:

Here we have two equations for the circumference, one for each circle:

C = 2*pi*r

C' = 2*pi*r'

now, if we take the quotient of those two equations, the left side must still be equal to the left side, this means that:

C/C' = 2*pi*r/(2*pi*r') = r/r'

So we have the relation:

C/C' = r/r'

And this is obtained for the division property of equality.

IF A = B, then as both numbers are equal, if we divide both sides by the same thing, then the equality must remain true.

Then the correct option is A.

Answer:

[tex]\$0.26[/tex] has to be paid more if the coupon is applied first

Step-by-step explanation:

Given: A grocery store has a discount of 13% off hand soap. At the same time the hand soap manufacturer has a coupon for $2.00 off.

To find: how much more would be paid if the coupon is applied first

Solution:

Let $ x denotes cost of hand soap

Case 1:

If the discount is given first,

cost of hand soap = [tex]x-\frac{13}{100} x=\$ \frac{87}{100}x[/tex]

If the coupon for $2.00 off is applied,

Final cost of the hand soap = [tex]\$\,(\frac{87}{100}x-2)[/tex]

Case 2:

If the coupon for $2.00 off is applied first,

cost of hand soap = [tex]\$(x-2)[/tex]

If the discount is given then,

final cost of the hand soap = [tex](x-2)-\frac{13}{100}(x-2)=\frac{87}{100}(x-2)[/tex] = [tex]\frac{87}{100}x-\frac{87}{50}[/tex]

Here,

[tex]\frac{87}{100}x-\frac{87}{50}-\frac{87}{100}x+2=\frac{13}{50}=\$0.26[/tex]

So, [tex]\$0.26[/tex] has to be paid more if the coupon is applied first.

Answer:

$0.26

Step-by-step explanation: I took the test

Answer:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]

And replacing:

[tex] \mu_{\bar X}= 5[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]

And the distribution is given:

[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]

Step-by-step explanation:

For this case we have the following info given :

[tex] \mu= 5. \sigma^2 =0.08[/tex]

And the deviation would be [tex] \sigma = \sqrt{0.08}= 0.283[/tex]

For this case we select a sample size of n = 5 and the distirbution for the sample mean would be:

[tex] \bar X \sim N(\mu , \frac{\sigma}{\sqrt{n}})[/tex]

And replacing:

[tex] \mu_{\bar X}= 5[/tex]

And the deviation:

[tex] \sigma_{\bar X}= \frac{0.283}{\sqrt{5}}= 0.126[/tex]

And the distribution is given:

[tex] \bar X \sim N(\mu= 0.08, \sigma= 0.126)[/tex]