What is the length of the line?Answers:A. 6.5 B. 7C. 35 *square root symbol*D. 37 *square root symbol*

Answer:

0.0548

Step-by-step explanation:

Given that:

Mean (m) life expactancy of product = 14 years

Standard deviation (σ) = 2.5 years

Probability of buying a product which will last more than 18 years ;

x = 18 years

Using empirical formula:

Zscore = (x - mean) / standard deviation

Zscore = (18 - 14) / 2.5

Zscore = 4 /2.5

Zscore = 1.6

Hence ;

P(Z > 1.6)

P(Z > 1.6) = 1 - P(Z < 1.6)

P(Z < 1.6) = 0.9452

P(Z > 1.6) = 1 - 0.9452

P(Z > 1.6) = 0.0548

Hence, probability = 0.0548 OR 5.48%

Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Bill Murray has 16 3/4 days in total.

(16×4 + 3)/4 = 67/4 days.

Then;

1 3/4 = (1×4 + 3)/4 = 7/4 days

4 2/3 = (4×3 + 2)/3 = 14/3 days

2 1/6 = (2×6 + 1) = 13/6 days

To add and then subtract them directly, we need to bring all fractions to the same denominator.

we have to multiply each fraction by a fitting n/n factor to bring the denominators to 12

67/4 = 67/4 × 3/3 = 201/12

7/4 = 7/4 × 3/3 = 21/12

14/3 = 14/3 × 4/4 = 56/12

13/6 = 13/6 × 2/2 = 26/12

Thus the remaining vacation time will be

201/12 - 21/12 - 56/12 - 26/12 = 98/12 = 49/6

49/6 = 8 and remainder 1 = (8×6 + 1)/6 = 8 1/6 days

Hence, Bill Murray has 16 3/4 days in total of vacation per year.  Bill entitled to  8 1/6 days more vacation time.

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The calculated area of the quadrilateral is 35.82 square units.

Given that

BAse = 6.5

Height = 5.51

To find the area of a quadrilateral, we need to multiply the base by the height.

Area of quadrilateral = base x height

Substituting the given values, we get:

Area = 6.5 x 5.51

Area = 35.815

Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.

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We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.

The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.

Therefore, the speed upstream is: (14 mi/h - S)

The speed downstream is (14 mph + S), where S is the stream's current flow rate.

We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:

14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.

In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:

T = (12 miles)/(14 miles per hour Plus S)

By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.

Taking only the favorable outcome, we obtain:

S = (24 - 25)/(-0.5) = 2 mph

2 mi/hr is the stream's current velocity.

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Answer:

195

Step-by-step explanation:

Answer:1  pound

Step-by-step explanation:

Directly you see  from Qestion Sarah picked 4  pounds and Nathan 3...for difference  4-3=1

Answer:

A: 1 pound

Step-by-step explanation:

4lbs -- 3lbs = 1lbs

Answer:

\(y = 9x + 7\)

Step-by-step explanation:

To solve for y, our goal is to get it isolated on one side of the equation.

\(4y - 36x = 28\)

Let's add \(36x\) to both sides of the equation.

\(4y = 36x + 28\)

Now divide both sides by 4.

\(y = 9x + 7\)

Hope this helped!

Answer:

4y-36x = 28........... :4

y-9x = 7

y = 7+9x or y = 9x+7

Answer: The answer is 171.2 Miles

Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.

Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.

The solution to the equation 3 / 5x-2 = 2 / 3x-1 is x = 1.

Given the equation in the question;

3 / 5x-2 = 2 / 3x-1

To solve for x, cross multiply the equation

3 / 5x-2 = 2 / 3x-1

3( 3x - 1 ) = 2( 5x - 2 )

Apply distributive property

3( 3x - 1 ) = 2( 5x - 2 )

3×3x + 3×-1 = 2×5x + 2×-2

9x - 3 = 10x - 4

Subtract 10x from both sides

9x - 10x - 3 = 10x - 10x - 4

9x - 10x - 3 = - 4

Add 3 to both sides

9x - 10x - 3 + 3 = - 4 + 3

9x - 10x  = - 4 + 3

-x = -1

Divide both sides by -1

-x/-1 = -1/-1

x = 1

Therefore, the value of x is 1.

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The smaller number = 12

The larger number = 51

Let the larger number be y

Let the smaller number be x

The larger number is 15 more than three times the smaller number

y = 3x + 15.....................................(1)

The sum of the two numbers is 63

x + y = 63.....................................(2)

Substitute equation (1) into equation (2)

x + 3x + 15 = 63

4x + 15 = 63

4x = 63 - 15

4x = 48

x = 48/4

x = 12

Substitute the value of x into equation (1)

y = 3(12) + 15

y = 36 + 15

y = 51

Therefore:

The smaller number = 12

The larger number = 51

Step-by-step explanation:

how much of an 80% orange juice drink must be mized with 20 gallons of a 20% orange juice drink to obtain a mixture that is 50% orange juice

Answer by mananth(16075) (Show Source): You can put this solution on YOUR website!

--------percent ---------------- quantity

Orange juice 20 ---------------- 20 gal

Orange juice 80 ---------------- x gal

Mixture 50 ---------------- 20 + x gal

20 * 20 + 80 x = 50 ( 20 + x )

400 + 80 x = 1000 + 50 x

80 x + -50 x = 1000 - -400

30 x = 600

/ 30

x = 20

20 gal of 80 % Orange juice

Answer:

A' (7,7)

B' (10,4)

C' (6,5)

Step-by-step explanation:

Add 9 to every x value and 3 to every y value.

Answer:

A'(7,7)

B'(10,4)

C'(6,5)

Step-by-step explanation:

⭐What is a translation?

⭐What is the translation notation?

The problem tells us to translate ΔABC 9 units to the right, and 3 units up because it is inside the <>, and the numbers are positive.

To translate the vertices of ΔABC, we have to add the respective x and y coordinates of the translation rule to each vertecie of ΔABC.

A(-2,4):

B(1,1):

C(-3,2):

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

Length = 17

Step-by-step explanation:

So the width is w

The length is w + 11

2w + 2w + 22 = 46

4w = 24

w = 6

l = 17

The length of the rectangle is 17 ft.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

Answer:

∠1 = 50

∠2 = 50

∠3 = 80

∠4 = 130

∠5 = 130

Step-by-step explanation:

∠1 = 180 - 130 = 50

∠2 = ∠1 = 50

∠3 = 180 - ∠1 - ∠2 = 180 - 50 - 50 = 80

∠4 = 180 - ∠2 = 180 - 50 = 130

∠5 = ∠4 = 130

Answer:

-ab

Step-by-step explanation:

Answer:

Negative

Step-by-step explanation:

Positive * negative = negative

Answer:

The 95% confidence interval for the population variance is (8.80, 32.45).

Step-by-step explanation:

The (1 - α)% confidence interval for the population variance is given as follows:

\(\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}\)

It is provided that:

n = 20

s = 3.9

Confidence level = 95%

⇒ α = 0.05

Compute the critical values of Chi-square:

\(\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2, (20-1)}=\chi^{2}_{0.025,19}=32.852\\\\\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.05/2, (20-1)}=\chi^{2}_{0.975,19}=8.907\)

*Use a Chi-square table.

Compute the 95% confidence interval for the population variance as follows:

\(\frac{(n-1)\cdot s^{2}}{\chi^{2}_{\alpha/2}}\leq \sigma^{2}\leq \frac{(n-1)\cdot s^{2}}{\chi^{2}_{1-\alpha/2}}\)

\(\frac{(20-1)\cdot (3.9)^{2}}{32.852}\leq \sigma^{2}\leq \frac{(20-1)\cdot (3.9)^{2}}{8.907}\\\\8.7967\leq \sigma^{2}\leq 32.4453\\\\8.80\leq \sigma^{2}\leq 32.45\)

Thus, the 95% confidence interval for the population variance is (8.80, 32.45).

Answer:150?

Step-by-step explanation:

Answer:

b = 19

Step-by-step explanation:

- 2(b-1)=3(7-b) (distributive property)

-2b+2 = 21 - 3b

-2b+3b = 21-2

b = 19

The true statement for the function p(x) is p(-2) and p(0) cannot be compared as p(0) is undefined. Option D is correct.

The given function is a logarithmic function and it is undefined at x = 0.

First, let us understand the logarithmic function:

A logarithmic function is a function of the form which is read as “ y equals the log of x, base b” or “ y equals the log, base b, of x.” In both forms, x > 0 and b > 0, b ≠ 1.

We are given:

p(x) = log 5x

substitute x = 0 in the above equation, we will get;

p(0) = log 5 × 0

p(0) = log 0

p(0) = undefined

Thus, the true statement for the function p(x) is p(-2) and p(0) cannot be compared because p(0) is undefined. Option D is correct.

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Using the equation of the function p(x) below, determine which of the statements below is true. Show your work.

Captionless Image

p(-2) > p(0)

p(-2) < p(0)

p(-2) and p(0) cannot be compared because p(-2) is undefined.

p(-2) and p(0) cannot be compared because p(0) is undefined.

The ratio of the length to the width that is- length:width = 5:3

Take x as a common value,

5x= length

3x= width

Width of the rectangle= 1500 cm

3x= 1500 cm

x= 1500/3

x= 500 cm

Length of the rectangle= 5x

x=500 cm

Length= 5*500

=2500 cm

Length of the rectangle= 2500 cm

Answer:

a) 0.0031 = 0.31% probability of marking exactly 3 incorrect answers.

b) 0.0035 = 0.35% probability of passing.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student chooses the correct answer, or he does not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

10 multiple choice questions

This means that \(n = 10\)

4 answers that are equally likely to be the correct one. The quiz taker selects the answers randomly.

This means that \(p = \frac{1}{4} = 0.25\)

a) Probability of marking exactly 3 incorrect answers.

3 incorrectly = 7 correctly, so this is P(X = 7).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031\)

0.0031 = 0.31% probability of marking exactly 3 incorrect answers.

b) Probability of passing

At least 7 correct, so

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031\)

\(P(X = 8) = C_{10,8}.(0.25)^{8}.(0.75)^{2} = 0.0004\)

\(P(X = 9) = C_{10,9}.(0.25)^{9}.(0.75)^{1} \approx 0\)

\(P(X = 10) = C_{10,10}.(0.25)^{10}.(0.75)^{0} \approx 0\)

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0031 + 0.0004 + 0 + 0 = 0.0035\)

0.0035 = 0.35% probability of passing.

Answer:

\((x-4)^2+(y+1)^2=162\)

Step-by-step explanation:

Determine r² by using the equation of a circle and plugging in the center (h,k)->(4,-1) as well as (x,y)->(13,8):

\((x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-(-1))^2=r^2\\(13-4)^2+(8+1)^2=r^2\\9^2+9^2=r^2\\81+81=r^2\\162=r^2\\\)

Hence, the equation of the circle that meets these criteria is\((x-4)^2+(y+1)^2=162\)

Answer:

100%

Step-by-step explanation:

Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

S₂₇ = 1188

Step-by-step explanation:

using the given formula for \(S_{n}\) , that is

\(S_{n}\) = \(\frac{n}{2}\) (a₁ + \(a_{n}\) )

with a₁ = 5 and \(a_{n}\) = a₂₇ = 83 , then

S₂₇ = \(\frac{27}{2}\) (5 + 83) = 13.5 × 88 = 1188

Answer:

  Left to right: Zoe, Johana, Kami, Craig

Step-by-step explanation:

The values of x can be found by solving each of the equations.

A) x/-12 -2 = -22  ⇒  x = -12(-22 +2) = 240 . . . (first step: add 2)

B) 3x -21 = 15  ⇒  x = (15 +21)/3 = 12

C) -12x +2 = -22  ⇒  x = (-22 -2)/-12 = 2 . . . (first step: subtract 2)

D) 1/2x +66 = 126  ⇒  x = 2(126 -66) = 120

__

Zoe's equation requires adding 2 as the first step. It is equation A.

Craig's equation's solution is half that of Zoe's. 240/2 = 120. Craig's is equation  D.

Kami's equation requires subtracting 2 as the first step. It is equation C.

Johana's equation's solution is 6 times that of Kami's. 6·2 = 12. Johana's is equation B.

The names that go in the blanks, left-to-right, are ...

  Zoe, Johana, Kami, Craig

Answer:

16.6

Step-by-step explanation:

Edge

\(\begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( \frac{x}{y}\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\[-0.35em] ~\dotfill\\\\ \log_8(x)-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\implies \log_8(\stackrel{x }{5})-\log_8(7)=\log_8\left( \cfrac{5}{7} \right)\)