Convert the given base ten numeral into a numeral in base eight.

Answer:

The two values of X that delineate the "82% middle pack" of this random variable are 9480 and 27520.

0.4017 = 40.17% probability that the sample average that you calculated will lie between 1,702 and 1,948.

Step-by-step explanation:

To solve the first question, we use the normal distribution, while for the second quetion, it is used with the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

First question:

Mean of 18,500:

This means that [tex]\mu = 18500[/tex]

You are told that P(X ≥ 15,000) = 0.6981.

This means that when [tex]X = 15000[/tex], Z has a o-value of 1 - 0.6981 = 0.3019, which means that when [tex]X = 15000, Z = -0.52[/tex]. We use this to find [tex]\sigma[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.52 = \frac{15000 - 18500}{\sigma}[/tex]

[tex]0.52\sigma = 3500[/tex]

[tex]\sigma = \frac{3500}{0.52}[/tex]

[tex]\sigma = 6731[/tex]

What are the two values of X that delineate the "82% middle pack" of this random variable?

Between the 50 - (82/2) = 9th percentile and the 50 + (82/2) = 91st percentile.

9th percentile:

X when Z has a p-value of 0.09, so X when Z = -1.34.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.34 = \frac{X - 18500}{6731}[/tex]

[tex]X - 18500 = -1.34*6731[/tex]

[tex]X = 9480[/tex]

91st percentile:

X when Z has a p-value of 0.91, so X when Z = 1.34.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.34 = \frac{X - 18500}{6731}[/tex]

[tex]X - 18500 = 1.34*6731[/tex]

[tex]X = 27520[/tex]

The two values of X that delineate the "82% middle pack" of this random variable are 9480 and 27520.

Question 2:

A random variable has a population mean equal to 1,973 and population variance equal to 892,021.

This means that [tex]\mu = 1973, \sigma = \sqrt{892021} = 944.5[/tex]

Sample of 79:

This means that [tex]n = 79, s = \frac{944.5}{\sqrt{79}}[/tex]

What is the probability that the sample average that you calculated will lie between 1,702 and 1,948?

This is the p-value of Z when X = 1948 subtracted by the p-value of Z when X = 1702. So

X = 1948

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1948 - 1973}{\frac{944.5}{\sqrt{79}}}[/tex]

[tex]Z = -0.235[/tex]

[tex]Z = -0.235[/tex] has a p-value of 0.4071

X = 1702

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{1702 - 1973}{\frac{944.5}{\sqrt{79}}}[/tex]

[tex]Z = -2.55[/tex]

[tex]Z = -2.55[/tex] has a p-value of 0.0054

0.4071 - 0.0054 = 0.4017

0.4017 = 40.17% probability that the sample average that you calculated will lie between 1,702 and 1,948.

Answer:

The numbers are 31 and 44.

Step-by-step explanation:

Given that the difference of two numbers is 13, and the sum of two numbers is 75, to determine what these numbers are, the following calculations must be performed:

(75 - 13) / 2 = X

62/2 = X

31 = X

31 + (31 + 13) = X

31 + 44 = X

75 = X

Therefore, the numbers are 31 and 44.

Answer:

1

Step-by-step explanation:

take the -2 and divide it by 2

that gives you -1

then square it

now its positive 1

formula is [tex](b/2)^{2}[/tex]

where b is the term next to the x

Answer:

the last option is coorect

Answer:

[tex]-18\sqrt{10}[/tex]

Step-by-step explanation:

[tex](6\sqrt{2})(-3\sqrt{5} )[/tex]

[tex]6\sqrt{2} * -3\sqrt{5}[/tex]

[tex](6*-3)\sqrt{2*5}[/tex]

[tex]-18\sqrt{10}[/tex]

Answer:

A

Step-by-step explanation:

The function that is  shown in the graph is strictly decreasing

"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."

The given function has a value of (- 5) at a certain point.

After that the function is decreased to a value of (- 10).

Therefore, we can conclude that the function is strictly decreasing.

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Answer:

that's right B) 3 - √3i

Step-by-step explanation:

(12 - √-48) / 4 =

12/4 - √-48 /4

= 3 - √(-48/16)

= 3 - √-3

= 3 - √ 3i

[tex]\\ \rm\Rrightarrow \dfrac{12-\sqrt{-48}}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{12}{4}-\dfrac{\sqrt{48}i}{4}[/tex]

[tex]\\ \rm\Rrightarrow 3-4\sqrt{3}i/4[/tex]

[tex]\\ \rm\Rrightarrow 3-\sqrt{3}i[/tex]

Answer:

Step-by-step explanation:

Based on this information, you could conclude that the annual rainfall in Falls City is generally more than that of the annual rainfall in Rockaway Beach. This is based on the information provided since the numbers given are the mean annual rainfall. Meaning that this is the average amount of rain that falls in any given year in that specific location. Since the amount provided for Falls City is a larger number then it means it gets more rainfall than Rockaway Beach on average and would therefore be the safest conclusion that can be made.

Answer:

I hope this helps

Step-by-step explanation:

Answer:

9^8

Step-by-step explanation:

9²•9⁶​ = 9^(2+6) = 9^8

Answer:

IF the 6 is negative : [tex]9^{2}[/tex] · [tex]9^{-6}[/tex] then the answer is 1/[tex]9^{4}[/tex]

If the 6 is positive then the answer is [tex]9^{8}[/tex]

Step-by-step explanation:

Exponents are add when their bases are similar.

Answer:

7

Step-by-step explanation:

Step-by-step explanation:  

AB//CD (Opposite sides of parallelogram are parallel)  

Angle A + Angle B = 180 (Sum of interior angles=180)  

179 + 3x - 20 = 180  

3x - 20 = 180 - 179

3x - 20 = 1

3x = 1 + 20

3x = 21

x = 21/3  

x = 7

Answer:

Step-by-step explanation:

∡1 = 180-30-90 = 60°, because sum of all interior angles of a triangle is 180°

∡2 =30°, because vertical angles are congruent

∡3 =180-70-30 = 80°, because sum of all interior angles of a triangle is 180°

Answer:

28.7

Step-by-step explanation:

12.7% = 0.127

226 * 0.127 = 28.702

Rounded

28.7

Answer:

the 3 numbers are 20,22,and 24 and the smallest of which is 20

Step-by-step explanation:

Hope this helped

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

When p and q are roots, (x -p) and (x -q) are factors. The quadratic equation is then ...

  0 = (x -p)(x -q) = x^2 -(p+q)x +pq

That is, the constant term is the product of the roots and the linear term coefficient is the opposite of the sum of the roots.

Using the given sum and product, the equation can be written ...

  0 = x^2 -(-5/4)x +3/4

Multiplying by -8 gives ...

  0 = -8x^2 -10x -6 . . . . . matches lower right choice

_____

Check

The product of roots is positive, so both roots have the same sign. The sum of roots is negative, so both roots are negative. That means there are no positive real roots to the equation. Descartes' Rule of Signs tells you this means the sequence of coefficients has no sign changes. Only the choice shown below has no sign changes. All of the others have at least 1 sign change.

Answer:

10 oz: 7

14 oz: 8

20 oz: 6

Answer:

Kyle filled  4 servings of 10oz   16 servings of 14 oz  9 servings of 20 oz

Step-by-step explanation:

10oz  95c = x

14oz 1.15c = y

20oz 1.50c = z

444 given divided by 29 cups

= 444/29 = 15.3103448 average cup weight so the higher size were used more.  

9 servings of 20 oz cups = 180 = cost check at 1.50 x 9 = $13.50

16 servings of 14 oz cups = 224 = cost check at 16 x 1.15 = $18.40

4 servings of 10 oz cups = 40 = cost check at 4 x 0.95 = $3.80

Where given collection total said to be $35.90 we total 13.5+18.4+3.8 = 35.7 so we are 0.20 out and can try again.

OR just submit this.  4 servings of 10oz   16 servings of 14 oz  9 servings of 20 oz

Answer: 86 degrees

Step-by-step explanation:

Answer:

14d + 21 = 7(2d + 3)

16 + 4w = 2(2w + 8)

Step-by-step explanation:

14d + 21

7(2d + 3)

14d + 21

14d + 21 = 7(2d + 3)

9(5r - 2)

45r - 18

14r - 7

9(5r - 2) ≠ 14r - 7

8(69 - 9)

552 - 72

489 - 72

8(69 - 9) ≠ 489 - 72

16 + 4w

2(2w + 8)

4w + 16

16 + 4w = 2(2w + 8)

32t + 16

16(2 - t)

32 - 16t

32t + 16 ≠ 16(2 - t)

The pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

To do this, we test each pair of expression.

This is done as follows

14d + 21 = 7(2d + 3)

Expand

14d + 21 = 14d + 21 --- this is true

9(5r - 2) = 14r - 7

Expand

45r - 18 = 14r - 7 --- this is false

8(69 - 9) = 489 - 72

Expand

552 - 72 = 489 - 72 --- this is false

16 + 4w = 2(2w + 8)

Expand

16 + 4w = 4w + 16 ---- this is true

32t + 16 = 16(2 – t)

Expand

32t + 16 = 32 - 16t --- this is false

Hence, the pairs of expressions that are equivalent are 14d + 21 and 7(2d + 3) and 16 + 4w and 2(2w + 8)

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Answer:

12 2/3

Step-by-step explanation:

add the integers to get 6+3 + 4 = 13

Now subtract 1/3

13 = 12 + 1 - 1/3

but one is equal to 3/3

12 + 3/3 - 1/3

12 2/3

Answer:

y=1/2x-6

Step-by-step explanation:

slope=1/2, (6,-3)

plug in the x and y coordinates into the equation

-3= 1/2 (6) +b

-3=3+b

subtract 3 from both sides

b=-6

y=1/2x-6

Answer:

A = 190 inches^2

Step-by-step explanation:

The total area would be area for a rectangle + half the area of a circle:

Area for a rectangle:

A = l x w

A = 12 x 15

A = 180 [tex]inches^{2}[/tex]

Area for half of the circle:

A = [tex]\frac{\pi r^{2} }{2}[/tex]

[tex]A = \frac{\pi 2.5^{2} }{2} \\\\= \frac{19.63}{2} \\\\= 9.8 inches^{2}[/tex]

Total area: Rectangle area + half of the circle area

= 180 + 9.8 = 189.8 = 190 inches^2

Step-by-step explanation:

Find the rectangle area first by using the formula A=length * width then find the semicircle area by using the formula A=pi*r²/2

Answer:

X = 4

UV = 24

Step-by-step explanation:

Opposite sides are equal

5x+4=6x

subtract 5x from both sides

4 = x

then substitute the 4 into 5x+4

5(4) + 4 = 24

[tex]\sf{3. \ \ Given : \dfrac{2}{3} - \dfrac{5}{4} + \dfrac{7}{2}}[/tex]

Let us solve the first two fractions : The LCM of 3 and 4 is 12

[tex]\sf{\implies \dfrac{4(2) - 5(3)}{12} + \dfrac{7}{2}}[/tex]

[tex]\sf{\implies \dfrac{8 - 15}{12} + \dfrac{7}{2}}[/tex]

[tex]\sf{\implies \dfrac{-7}{12} + \dfrac{7}{2}}[/tex]

LCM of 2 and 12 is 12

[tex]\sf{\implies \dfrac{-7 + 7(6) }{12}}[/tex]

[tex]\sf{\implies \dfrac{-7 + 42}{12}}[/tex]

[tex]\sf{\implies \dfrac{35}{12}}[/tex]

[tex]\sf{\implies 2 +\dfrac{11}{12}}[/tex]

[tex]\sf{\implies 2 \dfrac{11}{12}}[/tex]

---------------------------------------------------------------------------------------

[tex]\sf{4. \ \ Given : \dfrac{(2 - 7)^2 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{(-5)^2 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{25 + 5}{3}}[/tex]

[tex]\sf{\implies \dfrac{30}{3}}[/tex]

[tex]\sf{\implies 10}[/tex]

Answer:

2/3-5/4+7/2

Step-by-step explanation:

Answer:

0.51

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

squaring both sides first gives 2x-5=x-3+1 hence simplifying further give x=3

Answer:

% of unoccupied seats = 63.2 %

Step-by-step explanation:

Total seats = 80, 000

VIP seats = 12 % of 80, 000

              [tex]= \frac{12}{100} \times 80000\\\\= 9600[/tex]

General Seats = 39040

Remaining seats = 80000 - 9600 - 39040 = 50, 560

Percentage of un-occupied seats,

                                                 [tex]= \frac{50560}{80000} \times 100 = 63.2 \%[/tex]

Answer:

THE NUMBER OF SEATS OCCUPIED BY VIPS=80000×12/100

=9600

occupied seats=9600+39040

=48640

number of unoccupied seats=80000-48640

=31360

percentage of unoccupied seats=31360/80000×100%

=39.2%

Answer:

hope this will help u

Step-by-step explanation:

⇒  Given zeros are α=2 and β=−6.

⇒  Sum of zeros =α+β=2+(−6)=−4

⇒  Product of zeros =α×β=2×(−6)=−12

⇒  Quadratic polynomial =x  

2

−(α+β)x+(α×β)

⇒  Quadratic polynomial =x  

2

−(−4)x+(−12)

∴   Quadratic polynomial =x  

2

+4x−12

The quadratic function having 2 and -6 as zeros is f(x) = x² + 4x - 12.

Given the parameters:
Zeros of the function: 2 and -6.

To find the quadratic function f(x) with zeros at 2 and -6, first set up the equation:

x = 2 and x = -6

These are the real solutions to the quadratic equation:

This means that; ( x - 2 ) and ( x + 6 ) are the factors of the quadratic equation:

Hence:

( x - 2 )( x + 6 ) = 0

Expand using distributive property:

x( x + 6 ) - 2(x + 6 )  = 0

x² + 6x - 2x - 12 = 0

Collect and add like terms:

x² + 4x - 12 = 0

Therefore, the function will be:
f(x) = x² + 4x - 12.

The quadratic function is f(x) = x² + 4x - 12.

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Explanation:

Choice A can be ruled out because the three angles shown add up to 360 degrees (which is a full circle rotation). The three angles of any triangle always add to 180.

Choice C can be ruled out because angles 'a' and 'b' are supplementary, as they same side interior angles. Because a+b = 180, there isn't any way to have c be a positive number and have a+b+c = 180 to be true. In other words, angles a,b,c add up to something over 180 degrees.

Choice D is a similar story to choice C. The three angles a,b,c add up to something over 180 degrees, but less than 360.

Choice B is the only thing left. We can see that the three angles form a straight angle, so a+b+c = 180 is true and all three variables are positive numbers. If b = c were true, then the triangle is isosceles. This is because the base angles are always congruent for any isosceles triangle.

That's why choice B is the answer.

Answer:

Step-by-step explanation:

Answer:

BCA is obtuse

Step-by-step explanation:

BCA = 98 degrees

greater than 0 to less than 90 is acute angles

90 - right angle

greater than 90 to less than 180 is obtuse

98 is obtuse