Adriana’s z-score on a given measure is -2.5, where the population mean is 5 and the standard deviation is 1.5. What is Adriana’s raw score?

Answer:

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Step-by-step explanation:

The average salary for public school teachers for a specific year was reported to be $39,385. Test if the mean salary differs from $39,385

At the null hypothesis, we test if the mean is of $39,385, that is:

[tex]H_0: \mu = 39385[/tex]

At the alternative hypothesis, we test if the mean differs from this, that is:

[tex]H_1: \mu \neq 39385[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

39385 is tested at the null hypothesis:

This means that [tex]\mu = 39385[/tex]

A random sample of 50 public school teachers in a particular state had a mean of $41,680, and the population standard deviation is $5975.

This means that [tex]n = 50, X = 41680, \sigma = 5975[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{41680 - 39385}{\frac{5975}{\sqrt{50}}}[/tex]

[tex]z = 2.72[/tex]

P-value of the test and decision:

The p-value of the test is the probability that the sample mean differs from 39385 by at least 2295, which is P(|Z| > 2.72), which is 2 multiplied by the p-value of Z = -2.72.

Looking at the z-table, Z = -2.72 has a p-value of 0.0033

2*0.0033 = 0.0066

The p-value of the test is 0.0066 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean salary differs from $39,385

Answer:

three

P A R

A R A D

A D I S E 

P Q R

A B C D

A B C D E

There are three such pairs of letters. 

Answer:

1100 ft³

Step-by-step explanation:

Use the formula for the volume of a cylinder. For height, use the average of the minimum and maximum depths.

V = πr²h

r = d/2 = 20 ft/2 = 10 ft

h = (1 ft + 6 ft)/2 = 3.5 ft

V = π(10 ft)²(3.5 ft)

V = 1100 ft³

Answer:

[tex]90[/tex] [tex]ft^3[/tex]

Step-by-step explanation:

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

The formula to find the volume of a rectangular prism is   [tex]V=lwh[/tex]

Let's substitute the number for the length, width, and height now.

[tex]V=(6)(5)(3)[/tex]

[tex]V=(30)(3)[/tex]

[tex]V=90[/tex]

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

Hope this is helpful.

9514 1404 393

Answer:

  A.  yes

Step-by-step explanation:

The diagonals of a rectangle are congruent and bisect each other.

The diagonals of a parallelogram bisect each other. If they are also congruent, then the parallelogram is a rectangle.

Answer:

Yes.

Step-by-step explanation:

Press option yes

Answer:

73.3333....

Step-by-step explanation:

please mark me brainliest

Answer:

a: t=13.6 cm

b: h=12.9 mm

Step-by-step explanation:

Hi there!

Let's start with a

in a, we are given a right triangle (notice the right angle), the length of the hypotenuse (the side OPPOSITE from the right angle) as 18 cm, one acute angle given as 41° and the length of one of the legs (the legs are the sides that make up the right angle) as t

We're asked to use the primary trigonometric ratios

Those ratios are:

Sine, which is opposite/hypotenuse

Cosine, which is adjacent/hypotenuse

Tangent, which is opposite/adjacent

We will be basing the ratio off of the 41° angle, so let's find out which sides will be which in reference to that angle

The opposite side will be the other leg, the unmarked side

The adjacent side will be t

The hypotenuse will be the side marked as 18 cm

So let's use cos(41) in this case

cos(41)=t/18

Plug cos(41) into your calculator, and remember to have the calculator in degree mode

cos(41)≈0.8 (rounded to the nearest tenth)

0.8=t/18

multiply both sides by 18

13.6 cm=t

It's already rounded to the nearest tenth :)

b.

We are given a right triangle, and the lengths of the legs as h and 9 mm, as well as one acute angle as 35°

We'll be basing our ratio off of the 35 degree angle, so let's find which sides will be which in reference to that angle

The opposite side will be the leg marked as 9 mm

The adjacent side will be the leg marked as h

The hypotenuse will be the unmarked side

Since we are given the lengths of the opposite and the adjacent, let's use tan(35)

tan(35)=9/h

Plug tan(35) into your calculator, and remember to have it in degree mode

tan(35)≈0.7

0.7=9/h

multiply both sides by h

0.7h=9

divide both sides by 0.7

h=12.9 mm (rounded to the nearest tenth)

Hope this helps!

Answer:

Step-by-step explanation:

Since you have this categorized under college math, I'm going to go out on a limb here and assume you're in calculus. We will solve using the position function and its first derivative (velocity) to solve. Remember that at an object's max height, the velocity is 0.

If the position function is

[tex]s(t)=-16t^2+24t+7[/tex] the first derivative, velocity, is

v(t) = -32t + 24. Set this equal to 0 to find the time when the object is at its max height:

0 = -32t + 24 and

-24 = -32t so

t = .75 seconds. Now we can plug that time into the position function to find where it is at that time. This "where" will be the max height:

s(.75) = [tex]-16(.75)^2+24(.75)+7[/tex] so

s(.75) = 16 feet

Answer:

Old number = 150

Step-by-step explanation:

Given information;

Percentage decreased = 22%

New number obtain = 117

Find:

Old number

Computation:

Old number = New number obtain[100 / (100 - 22)]

Old number = 117[100 / (100 - 22)]

Old number = 117[100 / (78)]

Old number = 11,700 / 78

Old number = 150

Answer:

ab=14.4

Step-by-step explanation:

This is going to be tricky to explain over text, so try to bear with me :) You have the information given above. Let's start with just ad = 11.6 for now. since these are variables, it can also be understood be understood as a times d= 11.6.  Knowing this, we can figure out that d = 11.6/a, when you divide both sides by a. You now have d, so plug (11.6/a) into cd=6.7. You have to do the same thing you did last time, except this time you are aiming to get c by itself. So, multiply both sides by a/11.6 and you get c = (6.7a)/ 11.6.  Guess what, you know c now! so you put (6.7a)/11.6 in for c in the equation given to you earlier, bc =8.3. The math gets a bit messy here, but you basically solve for b here, which, when you crunch the numbers down, ends up being ~14.3705 divided by a. You are looking for ab, so just multiply both sides by a, and round to the nearest tenth so that you have ab= 14.4  

9514 1404 393

Answer:

  -4, 0

Step-by-step explanation:

The denominator is x^2+4x. This is zero when ...

  x^2 +4x = 0

  x(x +4) = 0

The zero product rule tells you the product is zero when the factors are zero.

  x = 0

  x +4 = 0   ⇒   x = -4

The denominator is zero for x=0 and x=-4.

Answer:b

Step-by-step explanation:

Ive done this

Answer:

y = 2x

Step-by-step explanation:

Given that , the line passes through the point (0,0) and has a slope of 2. So here we can use the point slope form of the line as ,

[tex]\implies y- y_1 = m( x - x_1) \\\\\implies y - 0 = 2( x - 0 ) \\\\\implies y = 2(x) \\\\\implies \underline{\underline{y = 2x }}[/tex]

Answer:

the answers are on the picture but the numbers may be rounded

Answer:

The answer is below

Step-by-step explanation:

The bar chart to the question is attached below.

The distance traveled by Paolo = 210 m, The distance traveled by Lucas = 150 m, The distance traveled by Jashua = 175 m, The distance traveled by Topher = 190 m

1) The farther distance walk by Paolo = The distance traveled by Paolo - The distance traveled by Topher = 210 m - 190 m = 20 m

2) The farther distance walk by Jasha = The distance traveled by Jashua - The distance traveled by Lucas = 175 m - 150 m = 25 m

3) The farther distance walk by Topher = The distance traveled by Topher - The distance traveled by Lucas = 190 m - 150 m = 40 m

4) Combined distance of Paolo's and Lucas = 210 m + 150 m = 360 m

Combined distance of Jashua and Topher = 175 m + 190 m = 365 m

Therefore the Combined distance of Jashua and Topher is more

5) Average distance = (210 + 150 + 175 + 190)/4 = 181.25 m

Answer:

13

Step-by-step explanation:

1. Round 19.625 up to 20.

2. Round 6.77 up to 7.

3. Calculate the equation. Ans is 13.

Answer:

T = 2.215

df = 7

Critical value = 2.364

Fail to reject the null

Step-by-step explanation:

Swimmer __Spandex __Speedo Fastskin__ d

1 __________31.1 _______29.1 __ 2

2_________ 28.9 ______30.4 __ -1.5

3_________ 31.4 ______ 32.0 __ - 0.6

4_________ 34.9 ______31.7 __ 3.2

5 _________27.7 ______28.2 __ - 0.5

6_________ 36.7 _____ 32.9 ___ 3.8

7 _________ 33.3 _____28.6 ___ 4.7

8_________ 30.8 _____26.2 ___ 4.6

The mean difference = Σd / n

2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6

μd = Σd / n = 15.7 / 8 = 1.9625

Sd = standard deviation of difference = 2.5065 (using calculator)

H0 : μd = 0

H1 : μd ≠ 0

The test statistic:

T = μd / (Sd/√n)

T = 1.9625 / (2.5065/√8)

T = 2.2145574

The degree of freedom, df = n - 1 = 8 - 1 = 7

Using a Pvalue calculator :

α = 0.05

Critical value, Tcritical = 2.364 (T distribution table)

Since Test statistic < Critical value

we fail to reject H0 ;

Answer:

First one , 0.0000805

Step-by-step explanation:

With negative exponents the decimal is moved to the left the amount of the exponent. The spaces are filled with zeros.

With positive exponents the opposite occurs.  The decimal moves to the right.

Answer:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}][/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

Step-by-step explanation:

In order to solve this problem, we must begin by splitting the function into its partial fractions, so we must first factor the denominator.

[tex]\frac{x+6}{2x^2-9x+5}=\frac{x+6}{(2x+1)(x-5)}[/tex]

Next, we can build our partial fractions, like this:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

we can then add the two fraction on the right to get:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A(x-5)+B(2x+1)}{(2x+1)(x-5)}[/tex]

Since we need this equation to be equivalent, we can get rid of the denominators and set the numerators equal to each other, so we get:

[tex]x+6=A(x-5)+B(2x+1)[/tex]

and expand:

[tex]x+6=Ax-5A+2Bx+B[/tex]

we can now group the terms so we get:

[tex]x+6=Ax+2Bx-5A+B[/tex]

[tex]x+6=(Ax+2Bx)+(-5A+B)[/tex]

and factor:

[tex]x+6=(A+2B)x+(-5A+B)[/tex]

so we can now build a system of equations:

A+2B=1

-5A+B=6

and solve simultaneously, this one can be solved by substitution, so we get>

A=1-2B

-5(1-2B)+B=6

-5+10B+B=6

11B=11

B=1

A=1-2(1)

A=-1

So we can use these values to build our partial fractions:

[tex]\frac{x+6}{(2x+1)(x-5)}=\frac{A}{2x+1}+\frac{B}{x-5}[/tex]

[tex]\frac{x+6}{(2x+1)(x-5)}=-\frac{1}{2x+1}+\frac{1}{x-5}[/tex]

and we can now use the partial fractions to build our series. Let's start with the first fraction:

[tex]-\frac{1}{2x+1}[/tex]

We can rewrite this fraction as:

[tex]-\frac{1}{1-(-2x)}[/tex]

We can now use the following rule to build our power fraction:

[tex]\sum_{n=0}^{\infty} ar^{n} = \frac{a}{1-r}[/tex]

when |r|<1

in this case a=1 and r=-2x so:

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2x)^n[/tex]

or

[tex]-\frac{1}{1-(-2x)}=-\sum_{n=0}^{\infty} (-2)^{n} x^{n}[/tex]

for: |-2x|<1

or: [tex] |x|<\frac{1}{2} [/tex]

Next, we can work with the second fraction:

[tex]\frac{1}{x-5}[/tex]

On which we can factor a -5 out so we get:

[tex]-\frac{1}{5(1-\frac{x}{5})}[/tex]

In this case: a=-1/5 and r=x/5

so our series will look like this:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\frac{1}{5}\sum_{n=0}^{\infty} (\frac{x}{5})^n[/tex]

Which can be simplified to:

[tex]-\frac{1}{5(1-\frac{x}{5})}=-\sum_{n=0}^{\infty} \frac{x^n}{5^(n+1)}[/tex]

when:

[tex]|\frac{x}{5}|<1[/tex]

or

|x|<5

So we can now put all the series together to get:

[tex]\frac{x+6}{2x^2-9x+5}=-\sum_{n=0}^{\infty} [(-2)^{n}x^{n} + \frac{x^{n}}{5^{n+1}}}[/tex]

when:

[tex]|x|<\frac{1}{2}[/tex]

We use the smallest interval of convergence for x since that's the one the whole series will be defined for.

Answer:

this is the answer I got! i don't know if it helps, but I hope it does

Answer:

Step-by-step explanation:

50 X 240 = 2700. So you will need 240 packs of 50. They cost 17.95 each, so the multiply. 240 X 17.95 is 4,308. So, 4,308 is your answer.

Answer:

1200

Explanation:

Order does not matter, if we said xyz order, it would still not make a difference if it was zyx or yzx hence we use the combination formula:

nCr = n! / r! * (n - r)!

where n= total number of items

r= number of items chosen at a time

Combinations are used when the order of events do not matter in calculating the outcome.

We calculate using the formula:

(30×20×12)÷3!=1200

There are therefore 1200 ways for the three distinct items to not be in same row or column

Answer:

-37 subtract -53

-53 subtract -37 = -16

Step-by-step explanation:

Answer:

The answer is 16

Step-by-step explanation:

-37-(-53) = -37 + 53

You can flip it to 53 - 37 which equals 16.

Hope this helps! :)

*Heads up you can also search this up* ^^

Answer:

x = 2

Step-by-step explanation:

4x-3 + 3 =  5 + 3

4x = 8

4x ÷ 4 = 8 ÷ 4

x = 2

Hi there!  

»»————-　★　————-««

I believe your answer is:  

"When solving 4x-3=5 the property used in the first step is the addition property of equality."

[tex]\boxed{x = 2}[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

⸻⸻⸻⸻

[tex]\boxed{\text{Solving for 'x'....}}\\\\4x-3=5\\----------\\\text{\textbf{Addition Property of Equality:} Add three on both sides.}}\\\\\rightarrow 4x - 3 = 5 \\\rightarrow 4x -3 + 3 = 5 + 3\\\\\rightarrow \boxed{4x = 8}\\\\\text{\textbf{Division Property of Equality:} Divide both sides by 4.}}\\\\\rightarrow {4x=8}\\\rightarrow \frac{4x=8}{4}\\\\\rightarrow \boxed{x = 2}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

B. -21.012÷ -3.4

its yr correct ans.

hope it helps

Answer:

18

Step-by-step explanation:

1/3 of 27 is 9. 9 times 2 is 18.

Step-by-step explanation:

You can simply plot these points on a graph and see where the line goes. It go

Answer:

w = 5

y = 4

Step-by-step explanation:

w + y = 9

3w - y = 11 ( + )

________

4w + 0 = 20

4w = 20

w = 20 / 4

w = 5

Substitute w = 5 in eq. w + y = 9,

w + y = 9

5 + y = 9

y = 9 - 5

y = 4

Answer:

52nd percentile

Step-by-step explanation:

The sorted data :

36.0, 37.0, 39.5, 40.0, 40.5, 43.0, 44.0, 45.5, 45.5, 46.5, 48.0, 48.00, 49.0, 50.0, 51.5, 52.5, 53.0, 53.5, 54.0, 57.3, 57.5, 58.0, 58.5, 59.0, 59.5, 60.0, 61.0, 61.0, 61.0, 61.5, 62.0, 62.5, 63.0, 63.0, 63.5, 64.0, 64.0, 64.0, 64.5, 65.0, 66.0, 67.5, 67.5, 68.5, 70.0, 70.5, 71.5, 72.0, 72.5, 72.5, 72.5, 73.5, 74.5, 77.5

The total size of the data = 54

The value 61.0 occurs in position ; 27th, 28th and 29th

Taking the position average :

(27+28+29)/3 = 84/3 = 28th position

This means the percentile score of 61 is :

(Position average / total size) * 100%

(28/54) * 100%

0.5185185 * 100%

= 51.85%

This means that 61 inch length falls in the 52nd percentile

Answer:

0.8895 = 88.95% probability that the hockey team wins at least 3 games in November.

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the teams wins, or they do not win. The probability of the team winning a game is independent of any other game, which means that the binomial probability distribution is used 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.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a certain hockey team will win any given game is 0.3773.

This means that [tex]p = 0.3773[/tex]

Their schedule for November contains 12 games.

This means that [tex]n = 12[/tex]

Find the probability that the hockey team wins at least 3 games in November.

This is:

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which:

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.3773)^{0}.(0.6227)^{12} = 0.0034[/tex]

[tex]P(X = 1) = C_{12,1}.(0.3773)^{1}.(0.6227)^{11} = 0.0247[/tex]

[tex]P(X = 2) = C_{12,2}.(0.3773)^{2}.(0.6227)^{10} = 0.0824[/tex]

Then

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0034 + 0.0247 + 0.0824 = 0.1105[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1105 = 0.8895[/tex]

0.8895 = 88.95% probability that the hockey team wins at least 3 games in November.