The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected. a) What is the probability that the sample mean will be larger than 1224

Answer:

86.9

Step-by-step explanation:

Find the number in the tenth place 9 and look one place to the right for the rounding digit 4 Round up if this number is greater than or equal to 5 and round down if it is less than 5

Hope this can help

The correct graph will be the first one (A)

Answer:

(i) 520

(ii) 2

Step-by-step explanation:

(i) x³ + y³

Plug x as 2, and y as 8.

(2)³ + (8)³

Solve for exponents.

8 + 512

Add.

= 520

(ii) ∛y

Plug y as 8.

∛(8)

Solve for cube root.

= 2

Answer:

( i ) 520

( ii ) 2

Step-by-step explanation:

We can find this solution by plugging in known values -

If x = 2, y = 8

x³+y³ = ( 2 )³ + ( 8 )³ = 8 + 512

= 520

Know let us move on to the second half -

We only need one part of this information now, y = 8. If so,

∛y = ∛8

2 x 2 x 2 = 8 - and thus 2 should be our solution for this portion.

Answer:

The geometric mean of the measures of the line segments AD and DC is  60/13

Step-by-step explanation:

Geometric mean: BD² = AD×DC

BD = √(AD×DC)

hypotenuse/leg = leg/part

ΔADB: AC/12 = 12/AD

AC×AD = 12×12 = 144

AD = 144/AC

ΔBDC: AC/5 = 5/DC

AC×DC = 5×5 = 25

DC = 25/AC

BD = √[(144/AC)(25/AC)]

BD = (12×5)/AC

BD= 60/AC

Apply Pythagoras theorem in ΔABC

AC² = 12² + 5²

AC² = 144+ 25 = 169

AC = √169 = 13

BD = 60/13

The geometric mean of the measures of the line segments AD and DC is BD = 60/13

Answer:

C

Step-by-step explanation:

So you can use the 30, 60, 90 degree triangle ratio of x: 2x: x√3

The 3 is the x, and the hypotenuse is the 2x, so it's 6

Answer:

C. 6

Step-by-step explanation:

I just finished the test and I got 100 percent

Answer:

B

Step-by-step explanation:

It can't be A because of the fact that by multiplying 445 by "x" you'll get a higher, postitive number. Meaning that if adding that positive number, you'll get something higher than 18,259. Which isn't our goal. In addition, the key word is "depreciates" which is another word for subtracting. However, that only applies in some circumstances. It can't be D either since you're basically adding a negative number by another negative number. However, "18,259" has to be a positive in this problem. By that you can also eliminate C as well. Meaning that B would be the correct answer.

Answer:

The infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} \frac{8/k}{\sqrt{k + 7}}[/tex] indeed converges.

Step-by-step explanation:

The limit comparison test for infinite series of positive terms compares the convergence of an infinite sequence (where all terms are greater than zero) to that of a similar-looking and better-known sequence (for example, a power series.)

For example, assume that it is known whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges or not. Compute the following limit to study whether [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] converges:

[tex]\displaystyle \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}[/tex].

Let [tex]a_k[/tex] denote each term of this infinite Rewrite the infinite sequence in this question:

[tex]\begin{aligned}a_k &= \frac{8/k}{\sqrt{k + 7}}\\ &= \frac{8}{k\cdot \sqrt{k + 7}} = \frac{8}{\sqrt{k^2\, (k + 7)}} = \frac{8}{\sqrt{k^3 + 7\, k^2}} \end{aligned}[/tex].

Compare that to the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] where [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}} = \frac{1}{k^{3/2}} = k^{-3/2}[/tex]. Note that this

Verify that all terms of [tex]a_k[/tex] are indeed greater than zero. Apply the limit comparison test:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\; \begin{tabular}{l}\\ $\leftarrow$ Series whose convergence is known\end{tabular}\\ &= \lim\limits_{k \to \infty} \frac{\displaystyle \frac{8}{\sqrt{k^3 + 7\, k^2}}}{\displaystyle \frac{1}{{\sqrt{k^3}}}}\\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{k^3}{k^3 + 7\, k^2}}\right) = 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\end{aligned}[/tex].

Note, that both the square root function and fractions are continuous over all real numbers. Therefore, it is possible to move the limit inside these two functions. That is:

[tex]\begin{aligned}& \lim\limits_{k \to \infty} \frac{a_k}{b_k}\\ &= \cdots \\ &= 8\left(\lim\limits_{k \to \infty} \sqrt{\frac{1}{\displaystyle 1 + (7/k)}}\right)\\ &= 8\left(\sqrt{\frac{1}{\displaystyle 1 + \lim\limits_{k \to \infty} (7/k)}}\right) \\ &= 8\left(\sqrt{\frac{1}{1 + 0}}\right) \\ &= 8 \end{aligned}[/tex].

Because the limit of this ratio is a finite positive number, it can be concluded that the convergence of [tex]\displaystyle a_k &= \frac{8/k}{\sqrt{k + 7}}[/tex] and [tex]\displaystyle b_k = \frac{1}{\sqrt{k^3}}[/tex] are the same. Because the power series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} b_k[/tex] converges, (by the limit comparison test) the infinite series [tex]\displaystyle \sum\limits_{k = 1}^{\infty} a_k[/tex] should also converge.

Answer:

[tex]\large \boxed{\sf \begin{aligned}9567&\\+1085&\\----&-\\10652&\\\end{aligned}}[/tex]

Step-by-step explanation:

Hello, let's do it step by step and see what we can find.

[tex]\begin{aligned}\text{ SEND}&\\+\text{ MORE}&\\-----&-\\\text{ MONEY}&\\\end{aligned}[/tex]

We assume that M is different from 0, otherwise we could find several different solutions I would think.

It means that S + M is greater than 10, otherwise the number of digit of the result would have been 4 and not 5.

The only possible number for M is then 1. M = 1

[tex]\begin{aligned}\text{ SEND}&\\+\text{ \boxed{1}ORE}&\\-----&-\\\text{ \boxed{1}ONEY}&\\\end{aligned}[/tex]

But then, S can only by 9, otherwise S + 1 < 10. S = 9

S + 1 = 10 + O if there is no carry over, so S = 9 + O

1 + S + 1 = 10 + O if there is a carry, so S = 8 + O

So O = 0 or O = 1. Wait !? M is already equal to 1 so O must be 0

E cannot be equal to N so 1 + E = N, meaning that there must be a carry over from column second from the right.

and E < 9 as we know that there is no carry over from column 3 from the right.

N + R = 10 + E => 1 + E + R = 10 + E => R = 9, impossible, as S=9

or 1 + N + R = 10 + E => 1 + 1 + E + R = 10 + E => R = 8

And there is a carry over from the column 1 from the right, so:

Y cannot be 0 or 1, as already used so D + E > 11

8 and 9 are already taken so we could have 7 + 5 = 12, 7 + 6 = 13 and that's it.

It means that E is 7 or D is 7.

If E is 7 then E+1=9=N, impossible, so D = 7

Then, E is 5 or 6

if E = 6 E + 1 = N = 7, impossible, so E = 5 and N = 6.

And 7 + 5 = 12 so Y = 2.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Complete question:

If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

a) The discriminant is negative.

b) The discriminant is –3.

c) The discriminant is 0.

d) The discriminant is positive.

Answer:

c) The discriminant is 0.

Step-by-step explanation:

Here, x = -3 is the only x intercept of graph of a quadrant equation.

In this case the determinant of the quadrant equation will be 0.

i.e, x = 0

The determinant of the quadrant equation will be zero because, since x = -3 is the only x intercept of the graph, the quadrant equation will have equal roots. Also, when there are equal roots in a quadrant equation, the discriminant tends to zero.

Therefore the correct answer is (c) The discriminant is 0.

D = 0

Answer:

C

Step-by-step explanation:

taking the quiz rn

Answer:

6.2* 10 ^-24

Step-by-step explanation:

(2.0 ⋅ 10−4) ⋅ (3.1 ⋅ 10−20)

Multiply the numbers

2.0 * 3.1 =6.2

Add the exponents

10 ^-4 * 10 ^-20 = 10 ^( -4+-20) = 10 ^ -24

Put back together

6.2* 10 ^-24

The number is in scientific notation since there is one nonzero digit in front of the decimal

Answer:

B, now give the other person brainlist

Answer:

4.87

Step-by-step explanation:

According to the given situation, for calculation of standard deviation for the number of people first we need to calculate the variance which is shown below:-

Variance is

[tex]np(1 - p)\\\\ = 500\times (0.05)\times (1 - 0.05)[/tex]

After solving the above equation we will get

= 23.75

Now the standard deviation is

[tex]= \sqrt{\sigma} \\\\ = \sqrt{23.75}[/tex]

= 4.873397172

or

= 4.87

Therefore for computing the standard variation we simply applied the above formula.

Answer:

[tex] S.A = 246.6 in^2 [/tex]

Step-by-step explanation:

The figure given above is a square pyramid, having a square base and 4 triangular faces on the sides that are of the same dimensions.

Surface area of the square pyramid is given as: [tex] B.A + \frac{1}{2}*P*L [/tex]

Where,

B.A = Base Area of the pyramid = 9*9 = 81 in²

P = perimeter of the base = 4(9) = 36 in

L = slant height of pyramid = 9.2 in

Plug in the values into the given formula to find the surface area

[tex] S.A = 81 + \frac{1}{2}*36*9.2 [/tex]

[tex] = 81 + 18*9.2 [/tex]

[tex] = 81 + 165.6 [/tex]

[tex] S.A = 246.6 in^2 [/tex]

Answer:

Step-by-step explanation:

Given that:

Mean μ= 100

standard deviation σ = 2.6

sample size n = 9

sample mean X = 100.6

The null hypothesis and the alternative hypothesis can be computed as follows:

[tex]H_o : \mu \leq 100[/tex]

[tex]H_1 :\mu > 100[/tex]

The numerical value for the test statistics is :

[tex]z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{100.6- 100}{\dfrac{2.6}{\sqrt{9}}}[/tex]

[tex]z = \dfrac{0.6}{0.8667}[/tex]

z = 0.6923

At  ∝ = 0.05

[tex]t_{\alpha/2 } = 0.025[/tex]

The critical value for the z score = 0.2443

From the z table, area under the curve, the corresponding value which is less than the significant level of 0.05 is 1.64

P- value =  0.244

c> If the true population mean is 101.3 ;

Then:

[tex]z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{101.3- 100.6}{\dfrac{2.6}{\sqrt{9}}}[/tex]

[tex]z = \dfrac{0.7}{0.8667}[/tex]

z = 0.808

From the normal z tables

P value  =  0.2096

Answer:

The probability that no more than 70% would prefer to start their own business is 0.1423.

Step-by-step explanation:

We are given that a Gallup survey indicated that 72% of 18- to 29-year-olds, if given choice, would prefer to start their own business rather than work for someone else.

Let [tex]\hat p[/tex] = sample proportion of people who prefer to start their own business

The z-score probability distribution for the sample proportion is given by;

                               Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, p = population proportion who would prefer to start their own business = 72%

            n = sample of 18-29 year-olds = 600

Now, the probability that no more than 70% would prefer to start their own business is given by = P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%)

       P( [tex]\hat p[/tex] [tex]\leq[/tex] 70%) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{0.70-0.72}{\sqrt{\frac{0.70(1-0.70)}{600} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.07) = 1 - P(Z < 1.07)

                                                                       = 1 - 0.8577 = 0.1423

The above probability is calculated by looking at the value of x = 1.07 in the z table which has an area of 0.8577.

Answer:

it does work

i think u mean why is it not whole

but it is not a whole number

Step-by-step explanation:

200/3=66.6(6 is repeating)

for example if u have 200 chocolates and u give them to 3 people

everyone will have 66

and u will have 2 left

2/3 is also 0.66(6 repeating)

66+0.66(6repeating)

=66.66(6repeating0

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

            -ZYLYNN JADE ARDENNE

Answer:

Step-by-step explanation:

it does not work as a whole number.

but it does work in simple division with fraction.

200 / 3 = 66 and [tex]\frac{2}{3}[/tex]

Answer:

$4,866.61

Step-by-step explanation:

Using the formular, A = P(1 + R/100)^n

Where, A = Amount; P = Principal; n = Time(year) and R = Rate

Hence, A = $4000(1 + 4/100)^5 = $4,866.61

Amount = Principal + Compound Interest

∴ Compund Interest = Amount - Principal = $(4,866.61 - 4,000) = $866.61

Answer:

The new extra processor would take 20 hours to download the movie.

Step-by-step explanation:

This word problem presents two variables: [tex]n[/tex] - Processing capacity, dimensionless; [tex]t[/tex] - Download time, measured in hours. Both variables exhibit a relationship of inverse proportionality, that is:

[tex]t \propto \frac{1}{n}[/tex]

[tex]t = \frac{k}{n}[/tex]

Where [tex]k[/tex] is the proportionality constant.

Now, let suppose that original processor has a capacity of 1 ([tex]n = 1[/tex]), the proportionality constant is: ([tex]t = 5\,h[/tex])

[tex]k = n\cdot t[/tex]

[tex]k = (1)\cdot (5\,h)[/tex]

[tex]k = 5\,h[/tex]

The equation is [tex]t = \frac{5}{n}[/tex] and if time is reduced to 4 hours by adding an extra processor, the processing capacity associated with this operation is: ([tex]t = 4\,h[/tex])

[tex]n = \frac{5}{t}[/tex]

[tex]n = \frac{5\,h}{4\,h}[/tex]

[tex]n = 1.25[/tex]

Then, the extra processor has a capacity of 0.25. The time required for the new extra processor to download the movie is: ([tex]n = 0.25[/tex])

[tex]t = \frac{5\,h}{0.25}[/tex]

[tex]t = 20\,h[/tex]

The new extra processor would take 20 hours to download the movie.

Answer:

Infinitely many solutions

Step-by-step explanation:

Any value of x will make this inequality true, hence there are infinitely many solutions.  Another way to say this is True for all x on the interval [-infinite,+infinite]

The reason this is true, is because all values of an absolute value will be greater than or equal to 0.

Cheers.

That's weird !

X is ANY NUMBER !

-∞  ≤  X  ≤  ∞

Answer:

Step-by-step explanation:

Let's create an equation:

[tex]5y = 135[/tex]

( Being vertically opposite angles)

Now, let's solve

Divide both sides of the equation by 5

[tex] \frac{5y}{5} = \frac{135}{5} [/tex]

Calculate

[tex] y = 27[/tex]

Hope this helps...

Best regards!!

Answer:

VY

Step-by-step explanation:

Coz they all look the same on the sides

Answer:

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]

Step-by-step explanation:

Given

[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]

Required

Determine the

- sin

- cosine

- tangent

of an angle

The given expression can be represented as follows;

[tex]cosAcosB + sinAsinB[/tex]

Where A = 94 and B = 37

In trigonometry:

[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]

Substitute 94 for A and 37 for B

[tex]cos(A - B) = cos(94 - 37)[/tex]

[tex]cos(A - B) = cos(57)[/tex]

Hence, the angle is 57;

Since 57 is not a special angle; I'll solve using a calculator

[tex]cos57 = 0.5446[/tex]

[tex]sin57 = 0.8387[/tex]

[tex]tan57 = 1.5399[/tex]

Answer:

8/5

Step-by-step explanation:

w = k / √x

4 = k / √4

k = 8

w = 8 / √x

w = 8 / √25

w = 8/5

Answer:

Step-by-step explanation:

The null hypothesis is usually the default statement while the alternative hypothesis is its opposite and usually tested against the null hypothesis.

In this case study, the null hypothesis is u = 21%/0.21, the percentage is not different among residents in Sonoma County and is equal to 0.21.

While the alternative hypothesis is u =/ 0.21, the percentage is different among residents in Sonoma County; not equal to 0.21

Answer:

Step-by-step explanation:

The null hypothesis is mostly of the time the default hypothesis while the alternative hypothesis is the opposite of the null hypothesis and always tested against the null.

In this case study, the null hypothesis is: mean mass of vitamin c tab = to 248 milligrams

The alternative hypothesis is: mean mass of vitamin c tab =/ 248 milligrams

Answer:

150 m²

Step-by-step explanation:

area of triangle is 1/2(6)(9.5) = 28.5

there are 4 triangles

28.5 x 4 = 114

bottom is 6 x 6 = 36

114 + 36 = 150 m²

Answer: hundredths place

Step-by-step explanation:

option A is correct answer.

because angle JKL is half of of arc JL .

so, angle JK is equal to 64°.

hope it helps...

Answer:

The answer is below

Step-by-step explanation:

The corresponding data are missing, which are the following:

Strikes (pre):

29

32

44

34

19

Strikes (post):

51

45

68

92

64

We have to say the difference between the post-pre values of the strike. The d will be the average of the differences between the post and pre values. If Kara is to show improvement, her post-workout attacks should be more than the pre-workout values. Let m be the population mean of the difference:

H0: m = 0 the mean difference in Strikes between post and pre is zero.

H0: m>0, the mean difference in strikes between post and pre is more than zero.

Answer: 4 miles

Step-by-step explanation:

If Ashley ran 1 mile 4 times, she ran 1+1+1+1, or 1*4, or 4 miles.

Hope it helps <3