What is the height of the trapezoid?

b. You're looking for the probability

Pr [72,972 ≤ X ≤ 90,043]

Transform X to Z ∼ Normal(0, 1) using the rule

X = µ + σ Z

with µ = 64,436 and σ = 17,071. Then the probability is

Pr [(72,972 - µ)/σ ≤ (X - µ)/σ ≤ (90,043 - µ)/σ]

≈ Pr [0.5000 ≤ Z ≤ 1.5000]

You probably have a z-score table available, so you can look up the probabilities to be about

Pr [Z ≤ 0.5000] ≈ 0.6915

Pr [Z ≤ 1.5000] ≈ 0.9332

and then

Pr [0.5000 ≤ Z ≤ 1.5000] ≈ 0.9332 - 0.6915 = 0.2417

c. The 75th percentile word count that separates the lower 75% of the distribution from the upper 25%. In other words, its the count x such that

Pr [X ≤ x] = 0.75

Transforming to Z and looking up the z-score for 0.75, we have

Pr [(X - µ)/σ ≤ (x - µ)/σ] ≈ Pr [Z ≤ 0.6745]

so that

(x - µ)/σ ≈ 0.6745

x ≈ µ + 0.6745σ

x ≈ 75,950

d. Because the normal distribution is symmetric, the middle 60% of novels have word counts between µ - k and µ + k, where k is a constant such that

Pr [µ - k ≤ X ≤ µ + k] = 0.6

Also due to symmetry, we have

Pr [µ - k ≤ X ≤ µ + k] = 2 Pr [µ ≤ X ≤ µ + k]

⇒   Pr [µ ≤ X ≤ µ + k] = 0.3

Transform X to Z :

Pr [(µ - µ)/σ ≤ (X - µ)/σ ≤ (µ + k - µ)/σ] = 0.3

⇒   Pr [0 ≤ Z ≤ k/σ] = 0.3

⇒   Pr [Z ≤ k/σ] - Pr [Z ≤ 0] = 0.3

⇒   Pr [Z ≤ k/σ] - 0.5 = 0.3

⇒   Pr [Z ≤ k/σ] = 0.8

Consult a z-score table:

Pr [Z ≤ k/σ] ≈ Pr [Z ≤ 0.8416]

⇒   k/σ ≈ 0.8416

⇒   k ≈ 14,367

Then the middle 60% of novels have between µ - k = 50,069 and µ + k = 78,803 words.

Answer:

Step-by-step explanation:

Rational Number: -9, 5/8, 30/√25

Irrational Number: √70, π

Step-by-step explanation:

We have to find what one share is

we have 3 shares + 2 shares + 5 shares

so he have a total of 10 shares

next, we divide 50 by total shares to get what one share is

50 ÷ 10 = 5

5 is one share

fins what each is

for 3

3 shares so 3 fives

3 × 5 = 15

for 2

2 shares so 2 fives

2 × 5 = 10

and for 5

can you work it out and leave in the comments i will say if it is correct

Answer:

9.24

Step-by-step explanation:

Using exponential function concepts, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, the initial value of the computer is of A(0) = 1500, while it decays at a rate of 15% a year, hence r = 0.15 and the equation is:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = 1500(0.85)^t[/tex]

Or equivalently, as a sequence:

[tex]a_n = 1500(0.85)^{n-1}[/tex]

Hence, it is found that the student error is in the subtraction of the day rate, as he forgot to subtract from 100% = 1.

More can be learned about exponential function concepts at https://brainly.com/question/25537936

Answer:

[tex] \frac{3}{4} [/tex]

Step-by-step explanation:

Slope formula:

[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]

where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope

[tex] = \frac{8 - 5}{ - 4 - ( - 8)} [/tex]

[tex] = \frac{3}{ - 4 + 8} [/tex]

[tex] = \frac{3}{4} [/tex]

Answer:

57753.

Step-by-step explanation:

Basta pm na Lang.

Answer:

D

Step-by-step explanation:

ey/n + k = t

To get y on its own, the first thing we need to do is subtract k from both sides to get ey/n = t - k. Next, we can multiply both sides by n to get ey = n(t - k). Finally, we can divide by e to get y = n(t - k)/e

Hope this helps!

x is the number of bags of chips

1.05x means "1.05 times x". You could write 1.05*x or omit the multiplication symbol all together.

For example, if he bought x = 100 bags then he would spend 1.05*x = 1.05*100 = 105 dollars.

Answer:

a1 = 8

a2 = 6

a3 = 4

a4 = 2

a5 = 0

So it would be: 8, 6, 4, 2, 0,...

Step-by-step explanation:

Just plug the term number into the equation.

an = -2n + 10

First term:

a1 = -2(1) + 10 = 8

Second term:

a2 = -2(2) + 10 = 6

Third term:

a3 = -2(3) + 10 = 4

and so on...

Hope this helped! :)

Formula for permutation is:

[tex] \boxed{ \tt^{n} C_{r} = \frac{n!}{r!(n - r)!} }[/tex]

Plug in the values:

Required number of ways = ²C7

[tex] \sf \frac{7!}{5!(7 - 5)!} [/tex]

[tex] \sf \frac{7 \times 6 \times \cancel{5!}}{ \cancel{5! }\times 2!} [/tex]

[tex] \sf \frac{7 \times 6 }{ 2!} [/tex]

[tex] \sf \frac{42 }{ 2!} [/tex]

[tex] \sf \frac{42 }{ 2} = 21[/tex]

Thus, The players can be selected in 21 different ways!!~

Here one player cannot be repeated so repeating is not allowed.

Total ways

[tex]\\ \rm\hookrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

[tex]\\ \rm\hookrightarrow ^7C_5[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!(7-5)!}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7!}{5!2!}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7\times 6\times 5!}{5!(2)}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{7(6)}{2}[/tex]

[tex]\\ \rm\hookrightarrow \dfrac{42}{2}[/tex]

[tex]\\ \rm\hookrightarrow 21ways[/tex]

Answer:

10

Step-by-step explanation:

Diagonals  of a isosceles trapezoid are congruent

3x - 16 = 10x - 86  Subtract 3x from both sides and add 86 to both sides

70 = 7x     Divide

x = 10

Answer:

I don’t know figure it out

Step-by-step explanation:

Answer:

5/9, 9/12, 6/7, 6/9 are the ones I believe so far

Step-by-step explanation:

Answer:

y = 2x + 3

Step-by-step explanation:

Get any two points on the line, say (0, 3) and (2, 7)

Slope = (7 - 3)/(2 - 0) = 4/2 = 2

y = 2x + b

use (0, 3), x = 0, y = 3

3 = b

so the equation is y = 2x + 3

Answer:

175

Step-by-step explanation:

Divide. 136.50 divided by 78 then times it by 100 and you get it 175

The percent increase is 56.41%.

We first calculate the difference between the original value and the new value when comparing a rise in a quantity over time. The relative increase in comparison to the initial value is then determined using this difference, and it is expressed as a percentage. The percentage increase formula is provided by:

percentage increase = (increase in amount /original amount ) x 100

Given:

Bill in may month- 78

Bill in June month = 122

So, change in amount= 122 - 78 = 44

So, percent increase = 44/ 78 x 100

percent increase = 0.5641 x 100

percent increase = 56.41%

Hence, the percent increase is 56.41%.

Learn more about percent increase here:

https://brainly.com/question/13533684

#SPJ2

Answer:

[tex]\bold{K = 5n {}^{2} + w} [/tex]

Given ,

value of n = 4

value of w = - 6

Then ,

[tex]\bold{K = 5(4) {}^{2} + ( - 6)} \\\bold{ K = 5(16) - 6} \\\bold{ K = 80 - 6} \\ \fbox\pink{K = 74}[/tex]

hope helpful~

Answer:

Step-by-step explanation:

Here we have been provided with the values of n and w that is 4 and -6 respectively.

Equation that we have,

Substituting the values of n and w in the equation,

[tex] \implies \: \sf{k \: = \: 5(4) {}^{2} \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 5(4 \times 4) \: + \: ( - 6)}[/tex]

[tex] \implies \: \sf{k \: = \: 5 \: (16) \: + \: ( - 6)}[/tex]

Multiplying 16 by 5,

[tex]\implies \: \sf{k \: = \: 5 \: \times 16 \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 80 \: + \: ( - 6)}[/tex]

[tex]\implies \: \sf{k \: = \: 80 \: - \:6)}[/tex]

Subtracting 6 from 80,

[tex]\implies \: \red{\bf{k \: = \: 74}}[/tex]

Therefore, value of k is 74..!!

Answer:

The answer is 47.5 and 72.5

Step-by-step explanation:

So,

Let the number be x and the other number be (x + 25).

Now,

x + (x + 25) = 120

x + x + 25 = 120

2x + 25 = 120

2x + 25 – 25 = 120 – 25

2x = 95

2x/2 = 95/2

x = 47.5

Thus, The number be x is equal to 47.5 and other which is more 25 than other number is (47.5 + 25) = 72.5

-TheUnknownScientist 72

Answer:

The numbers are 47.5 and 72.5

Step-by-step explanation:

Let "x" represent the larger number, then the smaller number would be equivalent to:

[tex]x-25[/tex]

Larger Number + Smaller Number = 120

Therefore...

[tex]x+x-25=120[/tex]

Combine like terms:

[tex]2x-25=120[/tex]

Add 25 to both sides (note we are utilizing the Addition Property of Equality which essentially states that if you add a value to one side of the equation, you must add it to the other side as well):

[tex]2x=120+25\\2x=145[/tex]

Divide both sides by 2 (note we are now utilizing the Division Property of Equality which essentially states that if you divide a value from one side of the equation, you must divide it from the other side as well; the same as the Addition Property of Equality, but with division instead):

[tex]x=\frac{145}{2}\\x=72.5[/tex]

Therefore...

[tex]x-25=72.5-25=47.5[/tex]

Answer:

Option D

Step-by-step explanation:

Given the following question:

Product costs: $90
Monthly bills: $2,300
Manufacturing costs: $75

How much profit did they make in one month if they sold 495 units?

In order to find the answer, we first need to multiply the cost of the product by the units sold last month, then subtract the bills/manufacturing costs.

One unit = 90 dollars
495 units sold last month

[tex]90\times495=44550[/tex]
[tex]=44550[/tex]

The company made 44,550 from the product last month.

Now apply the fees/costs:
2,300 dollars in monthly costs
75 dollars in manufacturing costs PER UNIT

[tex]44550-2300=42250[/tex]
[tex]75\times495=37125[/tex]
[tex]42250-37125=5125[/tex]
[tex]=5125[/tex]

Which means the company made a total profit of "$5,125 dollars" or option D last month.

Hope this helps.

Answer:

Since we assume the variances of the two populations are the same, we can use the pooled variance in the computation of the t-statistic:pooled variance (Sp^2) = (n1-1)s1^2 + (n2-1)*s2^2 / (n1 + n2 - 2) = (13-1)*19.4^2 + (19-1)*12.6^2 / (13 +19- 2) = 245.8Sp = 15.67t-calc = (mean1 - mean2)/ (Sp * sqrt(1/n1 + 1/n2)) = (83.6-72.9)/(15.67 * sqrt(1/13 + 1/19) = 1.897since this is a right tailed test, the p-value = P(t > 1.897) at n1 + n2 - 2 = 30 degrees of freedom = 0.0337so would not reject.

Step-by-step explanation:

mark me brainliest!!

Answer:

The answer is $2

I packet has 4 pencils so 12 pencils is 3 packets

if 3 packets cost $6 1 packet costs $2 and since 1 packet of pencils is the same price as one packet of erasers 1 packet of erasers cost $2

Answer:

45 actual car

Step-by-step explanation:

magaceega faatima

Answer:

The answer is 3

Step-by-step explanation:

I did this quiz before

Answer:

D

Step-by-step explanation:

There is only one vertical asymptote, x = 1.

Only D has vertical asymptote, x = 1.

Answer:

8%

Step-by-step explanation:

The original perimeter is 100cm

The 20cm is representative of the width

30cm is representative of the length

length is increased by 10%

30+(.10 x 30)

(1 + .10) × 30

(100% + 10%) × 30

110% × 30

110 ÷ 100 × 30

110 × 30 ÷ 100

3,300 ÷ 100

= 33

length is increased by 5%

20 + (5% × 20) =

20 + 5% × 20 =

(1 + 5%) × 20 =

(100% + 5%) × 20 =

105% × 20 =

105 ÷ 100 × 20 =

105 × 20 ÷ 100 =

2,100 ÷ 100 =

= 21

New perimeter: 108 cm

Percentage increase:

(108-100):100*100 =

(108:100-1)*100 =

108-100 = 8

= 8%

Answer:

-6 is the correct answer

Step-by-step explanation: