Which graph shows the solution to the system of linear inequalities?

y > Two-thirdsx + 3

y ≤ Negative one-thirdx + 2





Mark this and return

Answer:

x = 80

y = 130

Step-by-step explanation:

The 2 angles are supplementary. so, x-30 + x+50 = 180.

We solve and get 2x = 180-20

x = 80

y = x+50, because of parallel rules.

y = 130

Answer:

x = 80

y = 130

Step-by-step explanation:edge 2020

Answer:

[tex]B= 3.14 * 4^4 = 50.24cm^2\\h = 16cm\\V=B*h=50.24*16=803.84cm^3[/tex]

Step-by-step explanation:

The area of the base is the area of a circle with a radius equal to 4 cm. It means that the area can be calculated as:

[tex]B = 3.14 * r^2\\B= 3.14 * 4^4 = 50.24cm^2[/tex]

The height of the cylinder is shown in the picture, it is equal to 16 cm.

Finally, the volume of the cylinder can be calculated as:

[tex]V = B*h=50.24*16 = 803.84cm^3[/tex]

Where B is the base and h is the height of the cylinder.

Answer:

a

  The null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

The Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

b

     [tex]\sigma_{\= x} = 0.8944[/tex]

c

   [tex]t = -2.236[/tex]

d

  Yes the  mean population is  significantly less than 21.

Step-by-step explanation:

From the question we are given

           a set of  data  

                               20  18  17  22  18

       The confidence level is 90%

       The  sample  size  is  n =  5  

Generally the mean of the sample  is  mathematically evaluated as

        [tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]

       [tex]\= x = 19[/tex]

The standard deviation is evaluated as

        [tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]

         [tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]

         [tex]\sigma = 2[/tex]

Now the confidence level is given as  90 %  hence the level of significance can be evaluated as

         [tex]\alpha = 100 - 90[/tex]

        [tex]\alpha = 10[/tex]%

         [tex]\alpha =0.10[/tex]

Now the null hypothesis is  

         [tex]H_o : \mu = 21[/tex]

the Alternative  hypothesis is  

           [tex]H_a : \mu< 21[/tex]

The  standard error of mean is mathematically evaluated as

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

substituting values

         [tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]

        [tex]\sigma_{\= x} = 0.8944[/tex]

The test statistic is  evaluated as  

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

substituting values

              [tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]

              [tex]t = -2.236[/tex]

The  critical value of the level of significance is  obtained from the critical value table for z values as  

                   [tex]z_{0.10} = 1.28[/tex]

Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected

Answer:

[tex]B'(x,y) = (0,-2)[/tex]

Step-by-step explanation:

Given

The attached grid

Translation rule: [tex](x,y) = (x + 5, y - 2)[/tex]

Required

Determine the coordinates of B'

First, we have to write out the coordinates of B

[tex]B(x,y) = (-5,0)[/tex]

Next is to apply the translation rule [tex](x,y) = (x + 5, y - 2)[/tex]

[tex]B(x,y) = (-5,0)[/tex] becomes

[tex]B'(x,y) = B(x+5,y-2)[/tex]

Substitute -5 for x and 0 for y

[tex]B'(x,y) = (-5+5,0-2)[/tex]

[tex]B'(x,y) = (0,-2)[/tex]

Answer:

1) [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2+i^2b[/tex]

Step-by-step explanation:

1) [tex]a^2+b^2[/tex]

=> [tex]a^2 - (-1)b^2[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2-i^2b^2[/tex]

=> [tex](a)^2-(ib)^2[/tex]

Using Formula [tex]a^2 -b^2 = (a+b)(a-b)[/tex]

=> [tex](a+ib)(a-ib)[/tex]

2) [tex]a^2-b[/tex]

=> [tex]a^2+(-1)b[/tex]      (We know that -1 = [tex]i^2[/tex] )

=> [tex]a^2+i^2b[/tex]  (It cannot be simplified further)

Answer:

[tex]\boxed{(a+ib)(a-ib)}[/tex]

[tex]\boxed{a^2+i^2b}[/tex]

Step-by-step explanation:

[tex]a^2 + b^2[/tex]

Rewrite expression.

[tex]a^2- (-1)b^2[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2- i^2 b^2[/tex]

Factor out square.

[tex]a^2-(ib)^2[/tex]

Apply difference of two squares formula : [tex]a^2-b^2 =(a+b)(a-b)[/tex]

[tex](a+ib)(a-ib)[/tex]

[tex]a^2-b[/tex]

Rewrite expression.

[tex]a^2+(-1)b[/tex]

Use identity :  [tex]-1=i^2[/tex]

[tex]a^2+i^2b[/tex]

Answer:

Proper: 15/4

Improper: 3 3/4

Step-by-step explanation:

Well to solve the following question,

5/12 + (5/12 + 3/4)

We solve the part in the parenthesis first,

5/12 + 3/4 = 14/4

Simplified -> 7/2

5/12 + 7/2

= 45/12

Simplified -> 15/4

Thus,

the answer is 15/4 or 3 3/4.

Hope this helps :)

Answer:

Step-by-step explanation:

[tex]\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\\\\=\frac{5}{12}+\frac{5}{12}+\frac{3}{4}\\\\\mathrm{Add\:similar\:elements:}\:\frac{5}{12}+\frac{5}{12}=2\times \frac{5}{12}\\=2\times \frac{5}{12}+\frac{3}{4}\\\\=\frac{5\times \:2}{12}\\\\=\frac{10}{12}\\\\=\frac{10}{12}\\\\=\frac{5}{6}+\frac{3}{4}\\L.C.M =12\\\mathrm{Adjust\:Fractions\:based\:on\:the\:LCM}\\\\\frac{5}{6}=\frac{5\cdot \:2}{6\times \:2}=\frac{10}{12}\\\\\frac{3}{4}=\frac{3\times \:3}{4\times \:3}=\frac{9}{12}\\[/tex]

[tex]\\=\frac{10}{12}+\frac{9}{12}\\\mathrm{Since\:the\:denominators\:are\:equal\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\=\frac{10+9}{12}\\\\=\frac{19}{12}[/tex]

Answer:

θ ≈ 40°

Step-by-step explanation:

Since, sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

In the picture attached,

Measures of adjacent side and opposite side of the triangle have been given. Therefore, tangent rule will be applied in the given triangle.

tanθ = [tex]\frac{19}{23}[/tex]

θ = [tex]\text{tan}^{-1}(\frac{19}{23})[/tex]

θ = 39.56

θ ≈ 40°

Answer:

x=1

y=1

Step-by-step explanation:

Please look at the image below for solutions⬇️

Answer:

Step-by-step explanation:

Add the equations in order to solve for the first variable . Plug this value into the equations in order to solve for the remaining variables.

Point form

(x, 2-x)

Answer:

8n6

step by step explanation.

Answer:

linear

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

since the number is relatively prime to the product of the first 20 positive numbers

It number must not have factor of (1-20)

Therefore the smallest possible number is the next prime after 20

Answer is 23

The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Since, The number is relatively prime to the product of the first 20 positive numbers means a number which must not have factor of (1 - 20).

Hence, The smallest possible number is the next prime after 20 is, 23

Therefore, The smallest positive integer that is greater than 1 and relatively prime to the product of the first 20 positive integers is,

⇒ 23

Learn more about the Greatest common factors visit:

https://brainly.com/question/219464

#SPJ2

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I think. I just multiplies the 3 numbers. Hope this helps (:

Answer:

8*4*3=96 boxes in total

Step-by-step explanation:

I just multiplies the 3 numbers.

Answer:

C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.

Step-by-step explanation:

Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.

Answer

[tex]P= 0.144[/tex] ways

the coin can land tails either exactly 8 times or exactly 5 times in

[tex]0.144[/tex] ways

Step by step explanation:

THis is a binomial distribution

Binomial distribution gives summary of the number of trials as well as observations as each trial has the same probability of attaining one particular value.

P(9)=(14,9).(0.5)⁹.(0.5)¹⁴⁻⁹

p(3)=(14,3).(0.5)⁹.(0.5)¹⁴⁻³

p=(9)+p(3)

p=C(14,9)(0.5)¹⁴ + C(14,3). (0.5)¹⁴

P= (0.5)¹⁴ [C(14,9) + C(14,3)]

P= (0.5)¹⁴ [2002 * 364]

P= 1/16384 * (2002 +364)

P= 91091/2048

P= 0.144

Hence,the coin can land tails either exactly 8 times or exactly 5 times in

[tex] 0.144[/tex] ways

Answer:

251 inches

Step-by-step explanation:

c = 2πr

c = 2(3.14)(5) = 31.4

31.4 x 8 rev. = 251 inches

Answer:

x=2

Step-by-step explanation:

12-10=2

Answer:

x=2

Step-by-step explanation:

10=12-x

Subtract 12 from each side

10-12 = 12-12-x

-2 =-x

Multiply by -1

2 = x

Answer:

Her eye discourses; I will answer it.

I am too bold; ’tis not to me she speaks:

Two of the fairest stars in all the heaven,

Having some business, do entreat her eyes

To twinkle in their spheres till they return.

Step-by-step explanation:

Answer:

  52/3.

Step-by-step explanation:

There are (54·53)/2 = 1431 ways the 2 jokers can be placed in the 54-card deck. We can consider those to see how the number of cards between them might work out.

Suppose we let J represent a joker, and - represent any other card. The numbers of interest can be found as follows:

For jokers: JJ---... there are 0 cards between. This will be the case also for ...

  -JJ---...

  --JJ---...

and so on, down to ...

 ...---JJ

The first of these adjacent jokers can be in any of 53 positions. So, the probability of 0 cards between is 53/1431.

__

For jokers: J-J---..., there is 1 card between. The first of these jokers can be in any of 52 positions, so the probability of 1 card between is 52/1431.

__

Continuing in like fashion, we find the probability of n cards between is (53-n)/1431. So, the expected number of cards between is ...

  [tex]E(n)=\sum\limits_{n=0}^{53}{\dfrac{n(53-n)}{1431}}=\dfrac{53}{1431}\sum\limits_{n=0}^{53}{n}-\dfrac{1}{1431}\sum\limits_{n=0}^{53}{n^2}\\\\=\dfrac{53(53\cdot 54)}{1431(2)}-\dfrac{1(53)(54)(107)}{1431(6)}=53-\dfrac{107}{3}\\\\\boxed{E(n)=\dfrac{52}{3}}[/tex]

Answer:  C

Step-by-step explanation:

h · k(x) = 2(3x - 5)(-2x + 1)

           = (6x - 10)(-2x + 1)

           = -12x² + 6x + 20x - 10

           = -12x² + 26x - 10

Answer:

C

Step-by-step explanation:

h(x) × k(x)

= 2(3x - 5)(- 2x + 1) ← expand factors using FOIL

= 2(- 6x² + 3x + 10x - 5)

= 2(- 6x² + 13x - 5) ← distribute parenthesis by 2

= - 12x² + 26x - 10 → C

Answer:

I think it is [tex]\frac{6x-18}{x^{4} }[/tex]

Step-by-step explanation:

Answer:

95% confidensce interval of the mean (two-tail) =  [132.2, 139.2]

Step-by-step explanation:

Given:

N = size of sample = 61

m = sample mean = 135.7

s = sample standard deviation 13.7

Need 95% confidence interval

Solution.

alpha (95% confidence interval) = 0.05

(1-alpha/2) = 0.975   [two sided]

Equation for confidence interval of the mean

= m +/- t(1-alpha/2,N-1) * s / sqrt(N)

= 135.7 +/- 2.0003 * 13.7 / sqrt(60)

= [132.16, 139.24]

Answer:

65 dinners are expected to show up

The standard deviation of the distribution is 3.13

Step-by-step explanation:

Given

Proportion = 15%

Population = 77

Required

Expected Number that'll show up

Standard Deviation

If 15% won't show up; then

100% - 15% = 85% will show up

Expected Number, E(x) of Dinner is calculated as thus;

[tex]E(x) = np[/tex]

Where [tex]p = 85\%[/tex] (calculated above)

and [tex]n = 77[/tex]

Convert p to decimal

[tex]p = 0.85[/tex]

So;

[tex]E(x) = 0.85 * 77[/tex]

[tex]E(x) = 65.45[/tex]

[tex]E(x) = 65[/tex]

65 dinners are expected to show up

Calculating Standard Deviation, SD

Standard Deviation is calculated as;

[tex]SD = \sqrt{np(1-p)}[/tex]

Substitute 0.85 for p and 77 for n

[tex]SD = \sqrt{77 * 0.85 * (1-0.85)}[/tex]

[tex]SD = \sqrt{77 * 0.85 * 0.15}[/tex]

[tex]SD = \sqrt{9.8175}[/tex]

[tex]SD = 3.13328900678[/tex]

[tex]SD = 3.13[/tex] (Approximated)

The standard deviation of the distribution is 3.13

Answer:

The answer is below

Step-by-step explanation:

Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to

Answer:

Given:

Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05

From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645

The margin of error (E) is given by:

[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]

The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)

The 90% confidence interval is from 7.3442 to 9.9278

Answer:

x = ±sqrt(7)

Step-by-step explanation:

x^2 - 8 = -1

Add 8 to each side

x^2 - 8+8 = -1+8

x^2 = 7

Take the square root of each side

sqrt(x^2) = ±sqrt(7)

x = ±sqrt(7)

Answer:

$0.558

Step-by-step explanation:

The expected value is the sum of the value of each outcome times the chance that it happens. In this case, there are two outcomes:

Then our expected value can be calculated as:

[tex]EV=(31,000,000)(0.000000018)+(0)(1-0.000000018)=0.558[/tex]

Answer:

Side length: 3 cm.

Surface area: 54 cm squared.

Step-by-step explanation:

The formula for a cube is the side length cubed, since the formula for a rectangular prism is length times width times height. Those three measurements are the same for a cube.

So, since the volume is 27 cm cubed, we can say that the side length of the cube is the cube root of 27 cm cubed, or 3 cm.

There are 6 sides on a cube, and every cube has the same area. Since the side length of the cube is 3 cm, the area of one side of the cube is 3 * 3 = 9 cm squared. 9 * 6 = 54 cm squared.

Hope this helps!

Answer:

n = 13

Step-by-step explanation:

24 = 3 (n-5)

3n  - 15 = 24

3n = 24 +15

3n = 39

n = 39/3

n = 13

Answer:

[tex]\boxed{\sf n=13}[/tex]

Step-by-step explanation:

[tex]\sf 24=3(n-5)[/tex]

[tex]\sf Expand \ brackets.[/tex]

[tex]\sf 24=3n-15[/tex]

[tex]\sf Add \ 15 \ to \ both \ sides.[/tex]

[tex]\sf 24+15=3n-15+15[/tex]

[tex]\sf 39=3n[/tex]

[tex]\sf Divide \ both \ sides \ by \ 3.[/tex]

[tex]\sf \frac{39}{3} =\frac{3n}{3}[/tex]

[tex]\sf 13=n[/tex]

Answer: $951,064.06 would be your answer.

Step-by-step explanation: Hope that helped!

Answer:

a=11/5 OR 5.5

Step-by-step explanation: