Which inequality is shown in this graph?
(0, 2) (-1,-2)

a) y>=-4x+2
b) y>=4x+2
c) y<=-4x+2
d) y<=4x+2

Answer:

4.647 to the nearest thousandth.

Step-by-step explanation:

The formula for the length of an arc between  x = a and x = b is

  a

    ∫  √( 1 + (f'(x))^2) dx

  b

Here f(x) = √x so

we have  ∫  (√( 1 + (1/2 x^-1/2))^2 )   between x = 0 and x = 4.

=   ∫ ( √( 1 + 1/(4x)) dx   between  x = 0 and x = 4.

This is not easy to integrate  but some software I have gives me the following

length =  √17 + 1/8 log(33 + 1/8 √17)

= 4.647.

Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.

Step-by-step explanation:

Given, Farmer has 240 apples and 150 pears.

The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)

Prime factorization of 240 and 150 :

[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]

Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]

Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.

Answer:

38.68 cm

Step-by-step explanation:

Perimeter of an equilateral triangle : P = 3a

Area of an equilateral triangle : A = [tex]\frac{\sqrt{3} }{4}a^2[/tex]

a = side length

The area is given, solve for a.

[tex]72= \frac{\sqrt{3} }{4}a^2[/tex]

[tex]a = 12.894839[/tex]

The side length is 12.894839 centimeters.

Find the perimeter.

P = 3a

P = 3(12.894839)

P = 38.684517 ≈ 38.68

The perimeter is 38.68 centimeters.

Answer:

The correct answer will be "56".

Step-by-step explanation:

Use a combination of 8 things taken 3 at a time :

⇒  [tex]8_{C_{3}}[/tex]

⇒  [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]

⇒  [tex]\frac{8!}{(3!5!)}[/tex]

⇒  [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]

⇒  [tex]8\times 7[/tex]

⇒  [tex]56[/tex]

Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.

Using the principle of combination :

Hence, we have ;

8C3 = [8! ÷ (8 - 3)! 3!]

8C3 = [8! ÷ 5!3!]

8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)

8C3 = 8 × 7

8C3 = 56

Hence, there are 56 different possible samples.

Learn more : https://brainly.com/question/25581049

Answer:

x = -7/5

Step-by-step explanation:

If we square both sides of the equation, we get:

[tex]\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\[/tex]

Then, solving for x, we get:

[tex]x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x[/tex]

So, x is equal to -7/5

Answer:

its -7

Step-by-step explanation:

gots it right!

Answer:

6 units

Step-by-step explanation:

Distance between 2 points

[tex] = \sqrt{(x1 - x2)^{2} + (y1 - y2)^{2} } [/tex]

Thus, distance between (-3, 5) and (-9, 5)

[tex] = \sqrt{( - 3 - ( - 9))^{2} + (5 - 5)^{2} } \\ = \sqrt{( - 3 + 9)^{2} } \\ = \sqrt{6 ^{2} } \\ = 6[/tex]

Alternatively, notice that this line is a horizontal line as both points have the same y-coordinate of 5.

Thus, distance between the 2 points

= -3 -(-9)

= -3 +9

= 6 units

Answer:

15

Step-by-step explanation:

Answer:

12 people heard the joke?

Step-by-step explanation:

Answer:

O (1,-1)  is collinear with (2, 1) and (3, 3).

Step-by-step explanation:

equation of line in point slope form is

y-y1/x-x1 = m

where m is the slope of line

slope of line is given by

m = (y2-y1)/(x2-x1)

where(x1,x2) and (y1,y2) are points on the given line

_______________________________________

Given point

(2, 1) and (3, 3)?

m = 3-1/3-2 = 2

Equation of line

y-1/x-2 = 2

=> y-1 = 2(x-2)

=> y-1 = 2x-4

=> y= 2x-4+1

=> y = 2x-3

col-linear points are one which lie on the same line

To solve the problem we will check which  of the given points satisfy the equation of line derived above.

y = 2x-3

(0,0)

if we put value of x = 0 the above equation we should get y =0

y = 2*0 -3 = -3

since -3 is not equal to 0, hence (0,0) is not collinear with  (2, 1) and (3, 3).

1,-1

y = 2*1 -3 = -1

since -1 is  equal to -1, hence (1,-1) is collinear with  (2, 1) and (3, 3).

(4,4)

y = 2*4-3 = 5

since 5 is not equal to 4 , hence (4,4) is not collinear with  (2, 1) and (3, 3).

(-1,2)

y = 2*-1 -3 = -5

since -5 is not equal to 2, hence (-1,2) is not collinear with  (2, 1) and (3, 3).

Hence answer is O (1,-1)  s collinear with (2, 1) and (3, 3).

Answer:

52 minutes

Step-by-step explanation:

This should be a proportional statement, because if each individual person painted there own wall it should still take 52 minutes.

Answer:

p=2m

p+m=51

take the 2m and plug that in for p -> 2m+m=51

3m=51

m=51/3

m=17 then plu the value of m into Paula's points

p=2(17)

p=34

Answer:

[tex]\approx[/tex] 17.5% per annum

Step-by-step explanation:

Given:

Money invested = $20,000 at the age of 20 years.

Money expected to be $500,000 at the age of 40.

Time = 40 - 20 = 20 years

Interest is compounded annually.

To find:

Rate of growth = ?

Solution:

First of all, let us have a look at the formula for compound interest.

[tex]A = P \times (1+\frac{R}{100})^T[/tex]

Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.

Here, We are given:

P = $20,000

A = $500,000

T = 20 years

R = ?

Putting all the values in the formula:

[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]

So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.

Answer:

16.1%

Step-by-step explanation:

(the other person is wrong, trust me)

Answer:

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Step-by-step explanation:

Mean is the averaage of all the values.

Median is the value of the data which gives an estimate of the middle value. Middle values can be different than the average values.

The mean is

1) rigorously defined by a mathematical formula.

2) based on all the observations of the data

3) affected by extreme values

The meadian is

1) computed for open end classes like income etc.

2) not rigorously defined

3) is located when the values are not capable of quantitative measurment.

4) is not affected by extreme values.

The mean is more useful in this case because it would give an average value of the accidents for example 3 accidents per year but the median would give the middle value which may be 5  or greater or much lesser than the average. It would not give an approximate value of occurrences.

Answer:

10 miles

Step-by-step explanation:

1 inch = 4 miles

3 - 0.5  = 2.5

2.5 * 4 = 10 miles

Answer:

x = -8 and x= 7

Step-by-step explanation:

recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.

Hence the asymptototes will occur in x-locations where the denominator , i.e

(x+8)(x-7) = 0

solving this, we get

(x+8) = 0 ----> x = -8

or

(x-7) = 0 ------> x = 7

hence the asymptotes occur x = -8 and x= 7

Answer:

x = -8 and x = 7.

Step-by-step explanation:

The vertical asymptotes are lines that the function will never touch.

Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.

[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.

x + 8 = 0

x = -8

x - 7 = 0

x = 7

The vertical asymptotes are at x = -8 and x = 7.

Hope this helps!

Answer:

The statement

the product of 60 and the number of seconds is written as

60 * s

Hope this helps you

Answer:

Hey! The answer will be below!! :)

Step-by-step explanation:

In least to greatest the answer will be....

0.652, 6.52, 65.2

0.652 comes first because since the decimal point is between the 0 and 6

It’s also because 0 is less than 6 and 65.

Here is a easy way to do this, when you have this kind of question.

First look where the decimal is.

Pretend it’s a whole number like, 0.652 becomes 0

And 6.52 becomes 6, also 65.2 becomes 65

You have to use the decimal to find out least to greatest, also you will have to round the number.

So remember, when ever you have this kind of question...after the decimal point like 65.2 you take away the .2 and just have 65....this will help you do least to greatest faster! :)

Hope this helps!

Answer:

0.652, 6.52, 65.2

Step-by-step explanation:

You have to round to find the answer in a easy way.

Least to greatest would be 0.652, 6.52, 65.2

Hop it will help u

Answer:

14v - 5

Step-by-step explanation:

The product of 14 and v is 14v. 5 less than that is 14v - 5.

Answer:

7v = 119

Step-by-step explanation:

Answer:

A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.

Step-by-step explanation:

add everyone who prefers plan 1 = 60

age 36-45 / total of plan 1 = 14/60 = .23 or 23%

add everyone in age group 46-55 = 50

in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%

Answer:

[tex]\boxed{\mathrm{Option \ B}}[/tex]

Step-by-step explanation:

Total people in 36 - 45 age group = 50

Who prefer plan I = 14

%age of people preferring plan 1 among 36-45 age group:

=> [tex]\frac{14}{50} * 100[/tex]

=> 0.28 * 100%

=> 28%

Now,

Total People in 46-55 age group = 50

Those who prefer plan II = 21

%age of people preferring plan II among 46-55 age group:

=> [tex]\frac{21}{50} * 100[/tex]

=> 0.42 * 100%

=> 42%

Answer:

[tex]\large \boxed{\sf \ \ x \geq -9 \ \ }[/tex]

Step-by-step explanation:

Hello, please find below.

[tex]6\leq x+15\\\\\text{*** subtract 15 from both sides ***}\\\\6-15=-9\leq x \\\\x \geq -9[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: it should be b, 1. :)

Step-by-step explanation:

Answer:

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Step-by-step explanation:

Step(i):-

Given Population proportion P = 0.06

Sample size 'n' = 500

A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.

Sample proportion

                                  [tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]

Null hypothesis :H₀: P = 0.06

Alternative Hypothesis :H₁:P<0.06

Level of significance = 0.05

Z₀.₀₅ = 1.96

Step(ii):-

       Test statistic

                          [tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]

                         [tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]

                        Z =  - 2

                    |Z|= |-2| = 2

Step(iii):-

The calculated value Z = 2 > 1.96 at 0.05 level of significance

Null hypothesis is rejected

Alternative Hypothesis is accepted

The proportion of defective tablets manufactured in this factory is less than 6%."

Answer: B. 1.414

Step-by-step explanation:

let x be the random variable denotes the number of die.

Numbers on 5-faced die = 1,2,3,4,5

Probability of getting any number = [tex]\dfrac{1}{5}[/tex]

Mean = [tex]\bar {x}=\sum p_ix_i[/tex]

[tex]\\\\\Rightarrow\bar{x}=\dfrac{1}{5}(1)+\dfrac{1}{5}(2)+\dfrac{1}{5}(3)+\dfrac{1}{5}(4)+\dfrac{1}{5}(5)\\\\=\dfrac{1}{5}(1+2+3+4+5)\\\\=\dfrac{1}{5}(15)=3[/tex]

Standard deviation: [tex]\sigma=\sum \sqrt{\dfrac{(x_i-\bar{x})^2}{N}}[/tex]

[tex]=\sqrt{\dfrac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}}\\\\=\sqrt{\dfrac{4+1+0+1+4}{5}}\\\\=\sqrt{\dfrac{10}{5}}\\\\=\sqrt{2}\approx1.414[/tex]

Hence, the standard deviation of the random variable x is 1.414.

Thus, the correct option is B.

Answer:

0.6921 (69.21%)

Step-by-step explanation:

The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)

So the area we want to determine in this case is as follows;

P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)

What we use to calculate this finally is the standard normal distribution table

We use this to get these values so we can calculate the probability.

Using the standard normal distribution table;

P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921

Answer:

a

    [tex]0.5043 < p <0.9075[/tex]

b

   [tex]n = 24[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  34

    The  number of damaged helmets is  x  =  24

Now the proportion of damaged helmets is mathematically represented as

      [tex]\r p = \frac{k}{n }[/tex]

substituting values

     [tex]\r p = \frac{24}{34 }[/tex]

    [tex]\r p = 0.7059[/tex]

Given that the confidence level is 99% the level of significance can be evaluated as

     [tex]\alpha = 100 - 99[/tex]

     [tex]\alpha = 1[/tex]%

    [tex]\alpha = 0.01[/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} } = 2.58[/tex]

The reason we are obtaining critical values of   [tex]\frac{\alpha }{2}[/tex] instead of   [tex]\alpha[/tex] is because  

[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval (  [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while  

[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error

   The margin of error is mathematically represented as

     [tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p ( 1 - \r p)}{n} }[/tex]

substituting values

      [tex]MOE = 2.58 * \sqrt{\frac{ 0.7059 ( 1 - 0.7059)}{34} }[/tex]

     [tex]MOE =0.2016[/tex]

The 99% confidence interval for p is mathematically represented as

      [tex]p-MOE < p < p + MOE[/tex]

substituting values

       [tex]0.7059 - 0.2016 < p <0.7059 + 0.2016[/tex]

      [tex]0.5043 < p <0.9075[/tex]

The  sample size required for the width of a 99% Cl to beat most 0.10, irrespective of p ? is mathematically represented as  

     [tex]n \ge \frac{ Z_{\frac{\alpha }{2} } * \sqrt{\r p (1- \r p )} }{\frac{\sigma }{2} }[/tex]

Here  [tex]\sigma = 0.10[/tex]  telling  us that the deviation from the sample proportion is  set to 0.10 irrespective of the value of  [tex]\r p[/tex]

so the  sample size for this condition is

    [tex]n \ge \frac{ 2.58 * \sqrt{ 0.7059 (1- 0.7059)} }{\frac{0.10 }{2} }[/tex]

    [tex]n \ge 23.51[/tex]

=>   [tex]n = 24[/tex]

Answer:

Step-by-step explanation:

If [tex]\sum a_n[/tex] is a series, for the series to converge/diverge according to ratio test, the following conditions must be met.

[tex]\lim_{n \to \infty} |\frac{a_n_+_1}{a_n}| = \rho[/tex]

If [tex]\rho[/tex] < 1, the series converges absolutely

If [tex]\rho > 1[/tex], the series diverges

If [tex]\rho = 1[/tex], the test fails.

Given the series [tex]\sum\left\ {\infty} \atop {1} \right \frac{n^2}{5^n}[/tex]

To test for convergence or divergence using ratio test, we will use the condition above.

[tex]a_n = \frac{n^2}{5^n} \\a_n_+_1 = \frac{(n+1)^2}{5^{n+1}}[/tex]

[tex]\frac{a_n_+_1}{a_n} = \frac{{\frac{(n+1)^2}{5^{n+1}}}}{\frac{n^2}{5^n} }\\\\ \frac{a_n_+_1}{a_n} = {{\frac{(n+1)^2}{5^{n+1}} * \frac{5^n}{n^2}\[/tex]

[tex]\frac{a_n_+_1}{a_n} = {{\frac{(n^2+2n+1)}{5^n*5^1}} * \frac{5^n}{n^2}\\[/tex]

aₙ₊₁/aₙ =

[tex]\lim_{n \to \infty} |\frac{ n^2+2n+1}{5n^2}| \\\\Dividing\ through\ by \ n^2\\\\\lim_{n \to \infty} |\frac{ n^2/n^2+2n/n^2+1/n^2}{5n^2/n^2}|\\\\\lim_{n \to \infty} |\frac{1+2/n+1/n^2}{5}|\\\\[/tex]

note that any constant dividing infinity is equal to zero

[tex]|\frac{1+2/\infty+1/\infty^2}{5}|\\\\[/tex]

[tex]\frac{1+0+0}{5}\\ = 1/5[/tex]

[tex]\rho = 1/5[/tex]

Since The limit of the sequence given is less than 1, hence the series converges.

Answer:

[tex]\boxed{D = 6.4 units}[/tex]

Step-by-step explanation:

She stops by (0,0)

She further needs to travel to (5,-4)

Let's calculate the distance using the Distance Formula:

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(5-0)^2+(-4-0)^2}[/tex]

D = [tex]\sqrt{(5)^2+(-4)^2}[/tex]

D = [tex]\sqrt{25+16}[/tex]

D = [tex]\sqrt{41}[/tex]

D = 6.4 units

She needs to travel 6.4 units more.

Answer:

2sqrt41

Step-by-step explanation:

Origin=(0,0)

Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).

The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.

So: sqrt (5-0)^2+(-4-0)^2

sqrt (5^2+-4^2)

sqrt 25+16

sqrt 41

Now we need to figure out the distance from (0,0) to (5,-4)

sqrt(0-5)^2+(0-(-4))^2

sqrt(-5^2+4^2)

sqrt 25+16

sqrt 41

sqrt 41+sqrt 41

2sqrt41

Answer:

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

Step-by-step explanation:

Given that:

f(x, y) = xy

subject to x + 2y = 52

So;

x = 52 - 2y

and;

f(x, y) = xy

f(x, y) = (52- 2y) y

f(x, y) =  52y - 2y²

In order to maximize this function;

52y - 2y² = 0

26 y - y² = 0

26 - 2y = 0

-2y = -26

y = -26/-2

y = 13

Again:

x = 52 - 2y

x = 52 - 2(13)

x = 52 - 26

x = 26

fmax = xy =  26 × 13 = 338

(x,y) = (26,13)

Answer:

The total amount is $2250.

Step-by-step explanation:

Given that each person pays $5 and there is 450 people so you have to multiply :

$5 × 450 = $2250

Answer: The answer is two

Step-by-step explanation: If you look for opposites of a number its either negative or positive. So when the answer is negative, the opposite is positive and if the answer is positive, the opposite is negative.

Answer:

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

Step-by-step explanation:

The opposite of a number is the number that is the same distance from 0 on the number line.

-2 opposite is 2.

Answer:

Number of shares = 32 shares

Accountant total expenses= $254000

Step by step explanation:

The accountant salary is $262000

He spends $99000 on mortage

Spends $54000 on foods

Spends $32000 on clothing

Spends $41000 on household

Spends $28000 on others

Total expenses= 99000+54000+32000+41000+28000

Total expenses =$254000

Remaining money = 262000-254000

Remaining money= $8000

If shares = $250 for one

To know the amount he buys with the remaining money

We divide remaining money by shares cost

= $8000/$250

= 32 shares