The times for running a 5K for a local charity event are Normally distributed. Which standardized time represents the
87th percentile?
Find the z-table here.
-1.34
-1.13
01.13
1.34

Answer:

c

Step-by-step explanation:

i just took a test on it

The sequence converges to 0.

"It is a type of sequence where the ratio of every two consecutive terms is a constant."

"[tex]a_n=a_1\times r^{n-1}[/tex]

where [tex]a_1[/tex] is the first term, and r is the common ratio."

"If [tex]\lim_{n \to \infty} a_n[/tex]⁡ exists and is finite we say that the sequence is convergent.

where [tex]a_n[/tex] is the n-th term of the sequence."

" If [tex]\lim_{n \to \infty} a_n[/tex]doesn't exist or is infinite we say the sequence diverges.

where [tex]a_n[/tex] is the n-th term of the sequence."

For given question,

We have been given a sequence.

36, - 6, 1, - , . . .

The first term of the sequence is [tex]a_1=36[/tex]

[tex]\frac{-6}{36}=-\frac{1}{6}\\\\ \frac{1}{-6}=-\frac{1}{6}[/tex]

The ratio of every two consecutive terms is a constant.

⇒ [tex]r=-\frac{1}{6}[/tex]

So, the n-th term of given geometric sequence would be,

[tex]a_n=36\times (-\frac{1}{6})^{n-1}[/tex]

Now we determine whether the sequence is convergent or divergent.

[tex]\lim_{n \to \infty} a_n \\\\= \lim_{n \to \infty}36\times (-\frac{1}{6} )^{n-1}\\\\=36\times \lim_{n \to \infty} (-\frac{1}{6} )^{n-1}\\\\=36\times 0\\\\=0[/tex]

Since [tex]\lim_{n \to \infty} a_n[/tex] exists and is finite we say that the sequence is convergent.

Therefore, the sequence converges to 0.

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Answer:

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

Step-by-step explanation:

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 zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

Normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes.

This means that [tex]\mu = 90, \sigma = 18[/tex]

The proportion of new typists that take at most two hours to learn the computer system is

This is the pvalue of Z when X = 120 minutes = 2 hours. So

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

[tex]Z = \frac{120 - 90}{18}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a pvalue of 0.9525.

The proportion of new typists that take at most two hours to learn the computer system is 0.9525 = 95.25%.

Answer:

Step-by-step explanation:

She poured ⅔×2 = 4/3 qt into the second bottle.

Her bottle holds 2×4/3 = 8/3 qt

Answer:

0 and 1

Step-by-step explanation:

"The probability ot an event lies between 0 and 1"

Answer: 0.089

Step-by-step explanation:

Math

Answer:

12 50 I don't know

Step-by-step explanation:

Answer:

Step-by-step explanation:

Linear

The solutions of x in the equation are -5 and -1

Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The equation is given as

(x + 3)^2 - 4 = 0

Add 4 to both sides of the equation

So, we have

(x + 3)^2 = 4

Take the square root of both sides

x + 3 = ±2

Subtract 3 from both sides

x = - 3 ± 2

Evaluate

x = (-3 - 2, -3 + 2)

This gives

x = (-5, -1)

Hence, the solutions of x in the equation are -5 and -1

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Answer:

disappoint

recall

disgusted

reunited

prepare

Answer:

b. 59

Step-by-step explanation:

cosΘ = 42/82

Θ ~= 59.1898

Answer:

y = 55

x = 6

∠E = 70

Step-by-step explanation:

Hello There!

Segment DE and segment EF are congruent meaning that there opposite angles are congruent

So angle D and angle F are congruent

Because ∠D = 55 ∠F also equals 55

now we can solve for x

Remember all of the angles in a triangle add up to equal 180 so we use this equation to solve for x

180=55+55+11x+4

step 1 combine like terms

55+55+4=114

now we have

180=11x+114

step 2 subtract 114 from each side

180-114=66

now we have

66=11x

step 3 divide each side by 11

66/11=6

11x/11=x

we´re left with

x=6

Now we can plug in 6 to x to find the measure of angle E

6x11=66

66+4=70 so angle E = 70

Step-by-step explanation:

i) Capacity(Volume) = length x breadth x depth

= 3.2 x 2.9 x 1.5

= 13.92 m³

In litres, 13.92 x 1000 = 139,20 litres

ii) Capacity(Volume) = length x breadth x depth

= 2.5 x 1.6 x 1.3

= 5.2 m³

In litres, 5.2 x 1000 = 5200 litres

iii) Capacity(Volume) = length x breadth x depth

= 7.3 x 3.6 x 1.4

= 36.792 m³

In litres, 36.792 x 1000 = 36,792 litres

Answer:

IT SAYS IT 27 PEOPLE WOULD BE SEATED

Step-by-step explanation:

Step-by-step explanation:

let Rita = R

Let Gabriela = G

so we have

G ×R = 21

G= R + 4

(R+4)(R) = 21

R^2+4R -21=0

Answer:

448

Step-by-step explanation:

Answer:

The time it will take is approximately 104,128 seconds

Step-by-step explanation:

The given parameters are;

The diameter of the tank, D = 24 ft.

Therefore, the tank radius, R = D/2 = 24 ft./2 = 12 ft.

The height of the tower on which the tank sits, h = 60 ft.

The hose through which the tank is filled is attached at the bottom of the tank

The radius of a slice of sphere, r = √(R² - y²) = √(12² - y²)

The power of the pump which is used to deliver the water = 1.5 horsepower

The volume of a slice of water in the tank, V = π·r²·Δx = π·(√(12² - y²))²·Δx ft³ = (144 - y²)·π·Δx ft³

The force of the slice, F = V·g·ρ = (144 - x²)·π·Δx ft³ × 62.5 lb/ft³

Let '[tex]y_i[/tex]' represent the height to which each slice is pumped in  the tank, we have;

y = R - (√(R² - x²)) = 12 - (√(144 - x²)

[tex]\lim\limits_{n \to \infty}\ \sum\limits_{i=0}^n (144 - x^2) \cdot \pi \times 62.5 \cdot y_i\ \Delta x \ lb[/tex]

The work done is therefore;

[tex]W = 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \cdot(12-(\sqrt{144-x^2} ) \ } \, dx = 632044.366475 \ ft. \cdot lb[/tex]

The work done in filling the tank, W = 632,044.366475 ft·lb

The work done in lifting the water to the base of the tank, W₂ = V·ρ·g×h

[tex]\therefore W_2 = 60 \times 62.5\times\pi \times \int\limits^{12}_{-12} {(144 - x^2) \ } \, dx = 632044.366475 \ ft. \cdot lb = 85273382.0257[/tex]

Therefore, W₂ = 85,273,382.0257 ft.lb

The total work done by the pump,

W = 85,273,382.0257 ft.lb + 632,044.366475 ft·lb = 85,905,426.3922 ft.lb

The time it will take the pump to fill the tank, 't', is given as follows;

1

Power, P = Work, W/(Time, t)

∴ t = W/P

P = 1.5 HP = 550 × 1.5 ft·lb/s = 825 ft·lb/s

t = 85,905,426.3922 ft.lb/(825 ft·lb/s) = 104,127.789566 s

The time it will take, t ≈ 104,128 seconds

Answer:

I think that the answer is 2.5 , the second item .

Answer:

 parallelogram

options D

I took the test and got it right.

Answer:

25 in²

Step-by-step explanation:

formula for area of a triangle:

1/2(bxh)

1/2(5x10)

1/2(50)

25

Answer:

D. [tex]25^{2}[/tex]

Step-by-step explanation:

Ans.......

YTC ...................................

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

19 < x < 25

x had to be higher than 19 but lower than 25

18 cant be the answer because it is less than 19

27 cant be the answer because it is higher than 25

that leaves 20, which is the right answer

19 < 20 < 25

Answer:

i need help with this so you can ready

Answer:

y-12=1/3(x-6)

Step-by-step explanation:

Using the slope intercept form:

[tex]y - yo = m(x - xo) [/tex]

We can see from the given point (6,12) that yo = 12 and xo = 6. The slope, m, is 1/3. Plugging in the values gives us this equation in slope-intercept form that can then be converted to any other form.

Answer:

5/13

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

Joe Mok

Step-by-step explanation:

Joe MAMA

Answer:14127

Step-by-step explanation:

Po=2100

T=11

D=4

Pt=po•2 t/d

Pt=2100•2 11/4

Pt=14127.0598=14127

Answer:

The area of this is 28.67 meters squared

Step-by-step explanation:

You must use division in order to complete the question

Answer:

28

Step-by-step explanation:

Steps 1 : for the top numerator 7!4! =

7! = 7×6×5×4×3×2×1

4!=4×3×2×1

step 2 : for the bottom denominator 3!6!

3!= 3×2×1

6!=6×5×4×3×2×1

step 3 : is to cancel out all number that looks like on numerator over denominator

it will leave you with 7 × 4 only on the numerator = 28

because all the number in the denominator will cancel out with some on the numerator .

I hope it helps

The simplified solution of the factorial expression (7!4!)/(3!6!) is 14/3.

The given expression is

(7!4!)/(3!6!)  

We can simplify it using properties of factorials.

First, let's expand each factorial:

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1

4! = 4 x 3 x 2 x 1

3! = 3 x 2 x 1

6! = 6 x 5 x 4 x 3 x 2 x 1

Now, we can substitute these factorials into the original expression:

(7!4!)/(3!6!) = (7 x 6 x 5 x 4 x 3 x 2 x 1 x 4 x 3 x 2 x 1) / (3 x 2 x 1 x 6 x 5 x 4 x 3 x 2 x 1)

Next, we can cancel out common factors from the numerator and denominator:

(7 x 4)/(3 x 2 x 1) = 28/6

Simplifying:

28/6 = 14/3

Therefore, the simplified solution to (7!4!)/(3!6!) is 14/3.

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Answer:

B

Step-by-step explanation:

just divide 152 by 328 and youll get 0.463