Write one to two paragraphs about what you have learned from this process. When you read, see, or hear a statistic in the future, what skills will you apply to know whether you can trust the result?

Answer:

B

Step-by-step explanation:

Adding the 7 to the input (x) will increase the output (y) by 7. Therefore, the graph is translated 7 units up.

Answer:

The answer is B

Step-by-step explanation:

well the equation of a line is : y = mx + b

in this question the equation is y = x

so the line y = x +7  will be 7 units up than y = x

Answer:

16

Step-by-step explanation:

X^2 + 8x= 11

Take the coefficient of x

8

Divide by 2

8/2 =4

Square it

4^2 = 16

Add 16 to each side

Answer: f(f(f(x)))=8x-7

Step-by-step explanation:

Since we were given f(x) and f(f(x)), We plug that into f(x) again to get f(f(f(x))).

2(4x-3)-1                          [distribute]

8x-6-1                              [combine like terms]

8x-7

Answer:

15.48 ft^2

Step-by-step explanation:

According to the image we have the following information:

the length of the rectangle = diameter of the semicircle, therefore it is 12 feet

, the radius of the semicircle (half the diameter) = width of the rectangle = 12/2 ft = 6 ft

We also know that the area of the shaded region would be equal to the area of the rectangle minus the area of the semicircle.

Therefore, we replace:

Area of the rectangle = width * length

Ar = 6 ft * 12 ft = 72 ft ^ 2

Area of the semicircle = [1/2] * π * (r ^ 2)

As = [1/2] * 3.14 * (6 feet) ^ 2 = 56.52 ft ^ 2

We replace in the area of the shaded region

shaded region area = 72 ft ^ 2 - 56.52 ft ^ 2 =

Shaded region area = 15.48 ft ^ 2

Answer:

The length of the third side of fence is 11.4 m

Step-by-step explanation:

Solution:-

- We are to mow a triangular piece of land. We are given the description of motion and the orientation of land-mower while fencing.

- From one corner of the triangular land, the land-mower travels H1 = 5.7 m at θ1 = 0.3 radians north of east. We will use trigonometric ratios to determine the amount traveled ( B1 ) in the east direction.

                                  [tex]cos ( theta_1 ) = \frac{B_1}{H_1}[/tex]

Where,

                          B1: Is the base length of the right angle triangle

                          H1: Hypotenuse of the right angle triangle

Therefore,

                                [tex]B_1 = H_1*cos ( theta_1 )\\\\B_1 = 5.7*cos ( 0.3 )\\\\B_1 = 5.44541 m[/tex]

- Similarly, from the other corner of the triangular land. The land-mower moves a lateral distance of H2 = 9m and directed θ2 = 0.9 radians north of west. We will use trigonometric ratios to determine the amount traveled ( B2 ) in the west direction.

                                [tex]cos ( theta_2 ) = \frac{B_2}{H_2} \\[/tex]

Where,

                          B2: Is the base length of the right angle triangle

                          H2: Hypotenuse of the right angle triangle

Therefore,

                                 [tex]B_2 = H_2*cos ( theta_2 )\\\\B_2 = 9*cos(0.9)\\\\B_2 = 5.59448 m[/tex]

- The total length of the third side of the fence would be the sum of bases of the two right angles formed by the land-mower motion at each corner.

                                [tex]L = B_1 + B_2\\\\L = 5.44541 + 5.59448\\\\L = 11.4 m[/tex]

Answer:

Point A

Step-by-step explanation:

We know that on a coordinate plane, negative numbers can be found by moving down or moving to the left. This point must be found by moving down and left. To establish whether it is point A or point Y, we can remember that x coordinates move left and right and y coordinates move up and down. So, we would need to move 3.5 units left for x and then 4.5 units down for y. This leads us to point A.

hope this helps!

Answer:

it is point A

Step-by-step explanation:

Answer:

1) Option B is correct.

Expected frequency of satisfied customers from the Berwick sample = 75

2) Option D is correct.

Expected frequency of satisfied customers from the Milton sample = 90

3) Option A is correct.

Expected frequency of satisfied customers from the Leesburg sample = 60

4) Option B is correct.

The chi-square test statistic for these samples = 2.44

5) Option B is correct.

The degrees of freedom for the chi-square critical value = 2

6) Option C is correct.

The chi-square critical value using alpha = 0.05 is 5.991

7) Option D is correct.

The conclusion for this chi-square test would be that because the test statistic is less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.

Step-by-step explanation:

Berwick Milton Leesburg

Number Satisfied 80 85 60

Unsatisfied 20 35 20

Sample Size 100 120 80

Since this is a chi test that aims to check if there are differences in the proportion of expected number of customers for each location, we state the null and alternative hypothesis first.

The null hypothesis usually counters the claim we hope to test and would be that there is no difference between the proportion of expected frequency of satisfied customers at the three locations.

The alternative hypothesis confirms the claim we want to test and is that there is a significant difference between the proportion of expected frequency of satisfied customers at the three locations.

So, the total proportion of satisfied customers is used to calculate the expected number of satisfied customers for each of the three locations.

80+85+60= 225

Total number of customers = 100 + 120 + 80 = 300

Proportion of satisfied customers = (225/300) = 0.75

1) Expected frequency of satisfied customers from the Berwick sample = np = 100 × 0.75 = 75

2) Expected frequency of satisfied customers from the Milton sample = np = 120 × 0.75 = 90

3) Expected frequency of satisfied customers from the Leesburg sample = np = 80 × 0.75 = 60

4) Berwick Milton Leesburg

Number Satisfied 80 85 60

Unsatisfied 20 35 20

Sample Size 100 120 80

Proportion for unsatisfied ccustomers = 0.25

So, expected number of unsatisfied customers for the three branches are 25, 30 and 20 respectively.

Chi square test statistic is a sum of the square of deviations from the each expected value divided by the expected value.

χ² = [(X₁ - ε₁)²/ε₁] + [(X₂ - ε₂)²/ε₂] + [(X₃ - ε₃)²/ε₃] + [(X₄ - ε₄)²/ε₄] + [(X₅ - ε₅)²/ε₅] + [(X₆ - ε₆)²/ε₆]

X₁ = 80, ε₁ = 75

X₂ = 85, ε₂ = 90

X₃ = 60, ε₃ = 60

X₄ = 20, ε₄ = 25

X₅ = 35, ε₅ = 30

X₆ = 20, ε₆ = 20

χ² = [(80 - 75)²/75] + [(85 - 90)²/90] + [(60 - 60)²/60] + [(20 - 25)²/25] + [(35 - 30)²/30] + [(20 - 20)²/20]

χ² = 0.3333 + 0.2778 + 0 + 1 + 0.8333 + 0 = 2.4444 = 2.44

5) The degree of freedom for a chi-square test is

(number of rows - 1) × (number of columns - 1)

= (2 - 1) × (3 - 1) = 1 × 2 = 2

6) Using the Chi-square critical value calculator for a degree of freedom of 2 and a significance level of 0.05, the chi-square critical value is 5.991.

7) Interpretation of results.

If the Chi-square test statistic is less than the critical value, we fail to reject the null hypothesis.

If the Chi-square test statistic is unusually large and is greater than the critical value, we reject the null hypothesis.

For this question,

Chi-square test statistic = 2.44

Critical value = 5.991

2.44 < 5.991

test statistic < critical value

The test statistic is Less than the critical value, we fail to reject the null hypothesis and conclude that there is no difference in proportion of satisfied customers between these three locations.

Hope this Helps!!!

Answer:

  see attached

Step-by-step explanation:

The limit as x gets large is the ratio of the highest-degree terms. In most cases, the limit can be found by evaluating that ratio. Where an absolute value is involved, the absolute value of the highest-degree term is used.

If the ratio gives x to a positive power, the limit does not exist. If the ratio gives x to a negative power, the limit is zero.

The arrangement of functions according to the given condition

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

[tex]h(x)=\frac{x^{3} -x^{2} +4}{1-3x^{2} }[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]i(x)=\frac{x-1}{|1-4x| }[/tex]

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

[tex]f(x)=\frac{x^{2} -1000}{x-5}[/tex]

[tex]j(x)=\frac{x^{2}-1 }{|7x-1|}[/tex]

A limit is the value that  a function approaches as the input approaches some value.

According to the given question

[tex]l(x)=\frac{5x^{2} -4}{x^{2} +1}[/tex]

⇒[tex]\lim_{nx\to \infty} \frac{5x^{2} -1}{x^{2} +1}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} }{x^{2} } \frac{5-\frac{1}{x^{2} } }{1+\frac{1}{x^{2} } }[/tex]

= 5           ([tex]\frac{1}{x^{2} } = 0[/tex] ,as x tends to infinity  [tex]\frac{1}{x^{2} }[/tex] tends to 0)

[tex]i(x)=\frac{x-1}{|1-4x|}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x-1}{|1-4x|}[/tex] =  [tex]\lim_{x \to \infty} \frac{x}{x} \frac{1-\frac{1}{x} }{|\frac{-1}{4}+\frac{1}{x} | }[/tex]  =[tex]\frac{1}{\frac{1}{4} }[/tex] =[tex]\frac{1}{4}[/tex]

As x tends to infinity 1/x tends to 0, and |[tex]\frac{-1}{4}[/tex]| gives 1/4

[tex]f(x)= \frac{x^{2} -1000}{x--5}[/tex]

⇒[tex]\lim_{x \to \infty} \frac{x^{2} -1000}{x-5}[/tex]= [tex]\lim_{x \to \infty} \frac{x^{2} }{x} \frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex]= [tex]\lim_{x \to \infty} x\frac{1-\frac{1000}{x^{2} } }{1-\frac{5}{x} }[/tex] ⇒ limit doesn't exist.

[tex]m(x)=\frac{4x^{2}-6 }{1-4x^{2} }[/tex]

⇒[tex]\lim_{x\to \infty} \frac{4x^{2} -6}{1-4x^{2} }[/tex]=[tex]\lim_{x\to \infty} \frac{x^{2} }{x^{2} } \frac{4-\frac{6}{x^{2} } }{\frac{1}{x^{2} } -4}[/tex]  [tex]= \lim_{n \to \infty} \frac{4}{-4}[/tex] = -1

As x tends to infinity [tex]\frac{1}{x^{2} }[/tex] tends to 0.

[tex]g(x)=\frac{|4x-1|}{x-4}[/tex]

⇒[tex]\lim_{x\to \infty} \frac{|4x-1|}{x-4}[/tex] = [tex]\lim_{x \to \infty} \frac{|x|}{x} \frac{4-\frac{1}{x} }{1 -\frac{4}{x} } }[/tex] = 4

as x tends to infinity 1/x tends to 0

and |x|=x ⇒[tex]\frac{|x|}{x}=1[/tex]

[tex]h(x)=\frac{x^{3}-x^{2} +4 }{1-3x^{3} }[/tex][tex]\lim_{x \to \infty} \frac{x^{3} -x^{2} +4}{1-3x^{3} }[/tex][tex]= \lim_{x \to \infty} \frac{x^{3} }{x^{3} } \frac{1-\frac{1}{x}+\frac{4}{x^{3} } }{\frac{1}{x^{3} -3} }[/tex]  = [tex]\frac{1}{-3}[/tex] =[tex]-\frac{1}{3}[/tex]

[tex]k(x)=\frac{5x+1000}{x^{2} }[/tex]

[tex]\lim_{x \to \infty} \frac{5x+1000}{x^{2} }[/tex] = [tex]\lim_{x \to \infty} \frac{x}{x} \frac{5+\frac{1000}{x} }{x}[/tex] =0

As x tends to infinity 1/x tends to 0

[tex]j(x)= \frac{x^{2}-1 }{|7x-1|}[/tex]

[tex]\lim_{x \to \infty} \frac{x^{2}-1 }{|7x-1|}[/tex] = [tex]\lim_{x \to \infty} \frac{x}{|x|}\frac{x-\frac{1}{x} }{|7-\frac{1}{x}| }[/tex]  = [tex]\lim_{x \to \infty} 7x[/tex] = limit doesn't exist.

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Answer:

A 1,296

B 1,369

36 answer

Answer:

$36,241.20

Step-by-step explanation:

Compounded Interest Rate Formula: A = P(1 + r/n)^nt

Since we are given P, r, n, and t, simply plug it into the formula:

A = 35000(1 + 0.035/4)⁴⁽¹⁾

A = 35000(1 + 0.00875)⁴

A = 35000(1.00875)⁴

A = 35000(1.03546)

A = 36241.2

Answer:

He should accept contract 2 because it has a higher present value.

Step-by-step explanation:

we need to find the present value of each contract:

Contract 1 = $3,000,000/1.1 + $3,000,000/1.1² + $3,000,000/1.1³ + $3,000,000/1.1⁴  = $2,727,273 + $2,479,339 + $2,253,944 + $2,049,040 = $9,509,596

Contract 2 $2,000,000/1.1 + $3,000,000/1.1² $4,000,000/1.1³ + $5,000,000 /1.1⁴  = $1,818,182 + $2,479,339 + $3,005,259 + $3,415,067 = $10,717,847

Contract 3 $7,000,000/1.1 + $1,000,000/1.1² + $1,000,000/1.1³ + $1,000,000/1.1⁴  = $6,363,636 + $826,446 + $751,315 + $683,013 = $8,624,410

Answer:

false

Step-by-step explanation:

hello

this is false

FOREX means Foreign Exchange

it refers to the foreign exchange market

hope this helps

Answer:

true, forex trading is a profitable than staking cryptocurrency. forex trading is the best thing I will refer someone I love because learning never stops and no on is above blowing accounts when beginning Forex

Part A

g(x) = 3x+1

g(-4) = 3(-4)+1 ... every x replaced with -4

g(-4) = -12+1

g(-4) = -11

Plug this into the f(x) function

f(x) = x^2 - 2x

f( g(-4) ) = (g(-4))^2 - 2( g(-4) )

f( g(-4) ) = (-11)^2 - 2(-11)

f( g(-4) ) = 121 + 22

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

Part B

Plug the g(x) function into the f(x) function

f(x) = x^2 - 2x

f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)

f( g(x) ) = (3x+1)^2 - 2(3x+1)

f( g(x) ) = (9x^2+6x+1) + (-6x-2)

f( g(x) ) = 9x^2+6x+1-6x-2

Note that we can plug x = -4 into this result and we would get

f( g(x) ) = 9x^2-1

f( g(-4) ) = 9(-4)^2-1

f( g(-4) ) = 9(16)-1

f( g(-4) ) = 144-1

f( g(-4) ) = 143 which was the result from part A

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

Part C

Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.

[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]

Answer:

20

Step-by-step explanation:

The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

As per the given pair of (number of units sold y, profit x)

Linear equation slope and y-intercept

A linear equation or function is given as ;

y = mx + c

Here, c is the y-intercept and m is the slope.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope m  = (y₂ - y₁)/(x₂ - x₁)

Therefore slope of (46,250), (48, 305)

m = (305 - 250)/(48 - 46) = 27.5

Put, m = 27.5 and (46,250)

250 = 27.5(46) + c

c = -1015

y = 27.5x - 1015

Hence "The linear function represents the number of units sold y in terms of profit x is y = 27.5x - 1015".

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Answer:

The predicted sales for the new set of advertising budgets is 14.

Step-by-step explanation:

The linear regression model is:

[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]

Compute the value of sales for:

TV = 200,

Radio = 10,

Newspaper = 20

[tex]\text{Sales}=2.9389+0.0458\cdot(\text{TV})+0.1885\cdot(\text{Radio})-0.0010\cdot(\text{Newspaper})[/tex]

        [tex]=2.9389+0.0458\cdot(200)+0.1885\cdot(10)-0.0010\cdot(20)\\=2.9389+9.16+1.885-0.0002\\=13.9837\\\approx 14[/tex]

Thus, the predicted sales for the new set of advertising budgets is 14.

Answer:  24

Step-by-step explanation:

Let's find one solution:

3x² + 7x + c = 0

a=3 b=7  c=c

First, let's find c so that it has REAL ROOTS.

⇒ Discriminant (b² - 4ac) ≥ 0

                         7² - 4(3)c ≥ 0

                         49 - 12c ≥ 0

                               -12c  ≥ -49

                                [tex]c\leq\dfrac{-49}{-12}\quad \rightarrow c\leq \dfrac{49}{12}[/tex]      

Since c must be a positive integer, 1 ≤ c ≤ 4

Example: c = 4

3x² + 7x + 4 = 0

(3x + 4)(x + 1) = 0

x = -4/3, x = -1         Real Roots!

You need to use Quadratic Formula to solve for c = {1, 2, 3}

Valid solutions for c are: {1, 2, 3, 4)

Their product is: 1 x 2 x 3 x 4 = 24

Answer:

$3x^2+7x+c=0$

comparing above equation with ax²+bx+c

a=3

b=7

c=1

using quadratic equation formula

[tex]x = \frac{ - b + - \sqrt{b {}^{2} - 4ac} }{ 2a} [/tex]

x=(-7+-√(7²-4×3×1))/(2×3)

x=(-7+-√13)/6

taking positive

x=(-7+√13)/6=

taking negative

x=(-7-√13)/6=

Answer:

Federal income taxes, health insurance premium, state income tax

Step-by-step explanation:

Commission may be a bonus from a sale you made and overtime hours are extra hours over 40.00 that you worked during the week

2  things are certain in life death and taxes

Answer:

[tex]n = \frac{k}{ {d}^{2} } [/tex]

[tex] {d}^{2} = \frac{k}{n} [/tex]

[tex]d = \sqrt{ \frac{k}{n} } [/tex]

Answer:

d = √(k/n)

Step-by-step explanation:

n = k/d²

n/1 = k/d²

Cross multiply.

k = nd²

Divide both sides by n.

k/n = nd²/n

k/n = d²

Take the square root on both sides.

√(k/n) = √(d²)

√(k/n) = d

Answer:

(a)[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]

(b)13.3 kg

Step-by-step explanation:

The volume of brine in the tank = 4000L

Initial Amount of salt, A(0)=18 kg

The rate of change in the amount of salt in the tank at any time t is represented by the equation:

[tex]\dfrac{dA}{dt}=$Rate In$-$Rate Out[/tex]

Rate In = (concentration of salt in inflow)(input rate of brine)

Since pure water enters the tank, concentration of salt in inflow =0

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]=\frac{A(t)}{4000}\times 40\\ =\frac{A(t)}{100}[/tex]

Therefore:

[tex]\dfrac{dA}{dt}=-\dfrac{A(t)}{100}\\\dfrac{dA}{dt}+\dfrac{A(t)}{100}=0[/tex]

This is a linear D.E. which we can then solve for A(t).

Integrating Factor: [tex]e^{\int \frac{1}{100}d}t =e^{ \frac{t}{100}[/tex]

Multiplying all through by the I.F.

[tex]\dfrac{dA}{dt}e^{ \frac{t}{100}}+\dfrac{A(t)}{100}e^{ \frac{t}{100}}=0e^{ \frac{t}{100}}\\(Ae^{ \frac{t}{100}})'=0[/tex]

Taking integral of both sides

[tex]Ae^{ \frac{t}{100}}=C\\A(t)=Ce^{ -\frac{t}{100}}[/tex]

Recall our initial condition

A(0)=18 kg

[tex]18=Ce^{ -\frac{0}{100}}\\C=18[/tex]

Therefore, the amount of salt in the tank after t minutes is:

[tex]A(t)=18e^{ -\frac{t}{100}}[/tex]

(b)When t=30 mins

[tex]A(30)=18e^{ -\frac{30}{100}}\\=18e^{ -0.3}\\=13.3 $kg(correct to 1 decimal place)[/tex]

The amount of salt in the tank after 30 minutes is 13.3kg

In this exercise we have to use the integral to calculate the salt concentration:

(a)[tex]A(t)=18e^{-\frac{t}{100} }[/tex]

(b)[tex]13.3 kg[/tex]

Knowing that the volume of brine in the tank = 4000L, the initial Amount of salt, A(0)=18 kg. The rate of change in the amount of salt in the tank at any time t is represented by the equation:

[tex]\frac{dA}{dt} = Rate \ in - Rate \ out[/tex]

Rate In = (concentration of salt in inflow)(input rate of brine). Since pure water enters the tank, concentration of salt in inflow =0.

Rate In = 0

Rate Out=(concentration of salt in outflow)(output rate of brine)

[tex]\frac{A(t)}{4000}*(40)[/tex]

[tex]= \frac{A(t)}{100}[/tex]

Therefore:

[tex]\frac{dA}{dt} = \frac{A(t)}{100}\\\frac{dA}{dt} + \frac{A(t)}{100} = 0[/tex]

This is a linear D.E. which we can then solve for A(t). Integrating Factor:  [tex]e^{\int\limits {\frac{t}{100} } \, dt\\e^{t/100}[/tex] . Multiplying all through by the Integrating Factor:  

[tex]\frac{dA}{dt} = e^{t/100}+\frac{A(t)}{100}e^{t/100}\\(Ae^{1/100})'=0[/tex]

Taking integral of both sides:

[tex]Ae^{t/100}=C\\A(t)=Ce^{-t/100}[/tex]

Recall our initial condition:

[tex]A(0)=18 kg\\18=Ce^{0}\\C=18[/tex]

Therefore, the amount of salt in the tank after t minutes is:

[tex]A(t)=18e^{-t/100}[/tex]

(b)When t=30 mins

[tex]A(30)=18e^{-30/100}\\=18e^{-0.3}\\=13.3[/tex]

The amount of salt in the tank after 30 minutes is 13.3kg.

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Answer:

A discrete data set because there are a finite number of possible values.

Step-by-step explanation:

We are given the following data set below;

When a car is randomly selected, it is found to have 8 windows.

Firstly, as we know that the discrete data is that data that have countable or finite values, and also we can observe at a point value.

On the other hand, the continuous data is that data in which there is a range of values and we can't count or observe each and every value.

So, in our question; as we can observe that we can count all the windows and it is also a finite number which means that the given data set is a discrete data set because there are a finite number of possible values.

Answer:

2. Precise but not accurate

Step-by-step explanation:

In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)

Answer:

a =5/9 b=1/3 c=1/9 d=8/9

Step-by-step explanation:

there are total 9 numbers

in a

there are 5 odd numbers

in b

there are 3 multiplier of 3

in c

there is only one 5

in d

there are 8 numbers except 7

a) 5/9 b) 1/3 c) 1/9 d) 8/9

Step-by-step explanation:

a) odd numbers between 1 to 9 are 1,3,5,7,9. so there are 5 odd numbers.

total balls are 9

=> probability is 5/9

b) multiples of 3 = 3, 6,9 there are 3 numbers.

=> probability is = 3/9 = 1/3

c) 5. only one 5 is there between 1 to 9 numbers.

=> probability is 1/9

d) not a 7.

removing 7. there will 8 numbers.

=> probability is 8/9

We multiply the numerators together to get x*2x = 2x^2 as the numerator for the answer.

The denominators pair up and multiply to get (x-5)(x+4) = x^2+4x-5x-20 = x^2-x-20. You can use the distributive property, FOIL, or the box method to expand out (x-5)(x+4)

So that's how we end up with (2x^2) all over (x^2-x-20) as the answer.

Answer:

13 Compute using the 2 right angles, we know that m<FIG=90* and

Answer:

The second question

Step-by-step explanation:

The orca starts at -25 meters. She goes up 25 meters.

up 25 = +25

-25+25=0

Answer:

Option 2

Step-by-step explanation:

The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.

-25 + 25 = 0

Answer:

Therefore the x - coordinate of the minimum is x = -8

Step-by-step explanation:

[tex]y = 2x^2 + 32x + 56 = 2(x^2 + 16x ) + 56 = 2(x^2 + 16x +64 - 64) + 56 \\= 2(x^2 + 16x +64) - 128 + 56 = 2(x+8)^2 - 72[/tex]

Therefore the x - coordinate of the minimum is x = -8

Answer:

104.93 in

Step-by-step explanation:

When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:

sin23° = 41/x

xsin23° = 41

x = 41/sin23°

x = 104.931

Answer:

c = 5.5

Step-by-step explanation:

We can find the slope of the line using the given points (5,5) and (-3,1) using rise over run:

-4/-8 = 1/2

Now, we can plug in the slope and a point into the equation y = mx + b to find b:

5 = 1/2(5) + b

5 = 2.5 + b

2.5 = b

Then, we can plug in 6 in the point (6,c) to find c:

y = (1/2)(6) + 2.5

y = 3 + 2.5

y = 5.5

c = 5.5

Answer:

c = 5.5

Step-by-step explanation:

Find the slope with two points

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

m = (1-5)/(-3-5)

   = -4/-8

   = 1/2

If all the points are on the same line, then they have the same slope

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

Using the first and third points

1/2 = (c-5)/(6-5)

1/2 =  (c-5)/1

1/2 = c-5

Add 5 to each side

5+1/2 = c

5.5 =c

Answer:

452.4

Step-by-step equation:

surface area of a sphere formula= 4πr²

plug 6 in for r

4π(6)² =452.389 rounded  to 452.4

Answer:

b. The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

Step-by-step explanation:

A square matrix is said to be invertible if the product of the matrix and its inverse result into an identity matrix.

3  0 -4

2  0  6

-3 0  8

Since the second column elements are all zero, the determinant of the matrix is zero ad this implies that the inverse of the matrix does not exist(i.e it is not invertible )

A square matrix is said to be invertible if it has an inverse.

The matrix is not invertible. If the given matrix is A, the columns of A do not form a linearly independent set.

The matrix is given as:

[tex]\left[\begin{array}{ccc}3&0&-4\\2&0&6\\-3&0&8\end{array}\right][/tex]

Calculate the determinant

The determinant of the matrix calculate as:

[tex]|A| = 3 \times(0 \times 8- 6 \times 0) - 0(2 \times 8 - 6 \times -3) -4(2 \times 0 - 0 \times -3)[/tex]

[tex]|A| = 3 \times(0) - 0(34) -4(0)[/tex]

[tex]|A| = 0 - 0 -0[/tex]

[tex]|A| = 0[/tex]

When a matrix has its determinant to be 0, then

Hence, the correct option is (b)

Read more about matrix at:

https://brainly.com/question/19759946