check all that apply

Answer:

The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490 .

Step-by-step explanation:

Z-score:

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.

A. The ACT score gt 17.0 is relatively better than the SAT score of 1490 a relatively better then the SAT score of 1490.

We find the z-score for each of these options. Whichever has the higher z-score is the better grade.

ACT:

Mean 21.1, standard deviation of 4.8. Score of 17. So [tex]\mu = 21.1, \sigma = 4.8, X = 17[/tex]

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

[tex]Z = \frac{17 - 21.1}{4.8}[/tex]

[tex]Z = -0.85[/tex]

SAT:

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Score of 1490. So [tex]\mu = 1518, \sigma = 325, X = 1490[/tex]

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

[tex]Z = \frac{1490 - 1518}{325}[/tex]

[tex]Z = -0.09[/tex]

The SAT score of 1490 has the higher z-score, so this is the better score, which means that this statement is false and A. is the answer of this question.

B. An SAT score of 1490 has a z-score of -0.09

From A., this is true

C. The SAT score of 1490 is relatively better than the ACT score of 17.0.

From A., this is true.

Step-by-step explanation:

cos(3x) − 3 cos x = cos(2x) + 1

Use triple and double angle formulas.

(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1

Simplify.

4 cos³x − 6 cos x = 2 cos²x

4 cos³x − 2 cos²x − 6 cos x = 0

2 cos³x − cos²x − 3 cos x = 0

Factor.

cos x (2 cos²x − cos x − 3) = 0

cos x (cos x + 1) (2 cos x − 3) = 0

Solve.

cos x = 0 → x = 90°, 270°

cos x + 1 = 0 → x = 180°

2 cos x − 3 = 0 → no solution

Answer:

a) Calculate the probability that at least one of them suffers from arachnophobia.

x = number of students suffering from arachnophobia

= P(x ≥ 1)

= 1 - P(x = 0)

= 1 - [0.05⁰ x (1 - 0.05)¹¹⁻⁰ ]

= 1 - (0.95)¹¹

= 0.4311999 = 0.4312

b) Calculate the probability that exactly 2 of them suffer from arachnophobia? 0.08666

=  P(x = 2)

=  (¹¹₂) x (0.05)² x (0.95)⁹

where ¹¹₂ = 11! / (2!9!) = (11 x 10) / (2 x 1) = 55

= 55 x 0.0025 x 0.630249409 = 0.086659293 = 0.0867

c) Calculate the probability that at most 1 of them suffers from arachnophobia?

P(x ≤ 1)

= P(x = 0) + P(x = 1)    

= [(¹¹₀) x 0.05⁰ x 0.95¹¹] + [(¹¹₁) x 0.05¹ x 0.95¹⁰]

= (1 x 1 x 0.5688) + (11 x 0.05 x 0.598736939) = 0.5688 + 0.3293 = 0.8981

Answer:

ok I am tellin6 to you

Step-by-step explanation:

ok I will tell to you

Answer:

Step-by-step explanation:

Let x be a random variable representing the flight arrival time from Boston to New York.

For a uniform probability distribution, the notation is

X U(a, b) where a is the lowest value of x and b is the lowest value of x

The probability density function, f(x) = 1/(b - a)

Mean, µ = (a + b)/2

Standard deviation, σ = √(b - a)²/12

From the information given, the time difference in minutes is 9:57 - 9:07 = 50 minutes. Therefore,

a = 0

b = 50

µ = (0 + 50)/2 = 25

σ = √(50 - 0)²/12 = 14.43

b) converting to minutes, it is 9:30 - 9:07 = 23 minutes

the probability that a flight arrives late(later than 9:30 am) is expressed as P(x > 23)

f(x) = 1/(50) = 0.02

P(x > 23) = (50 - 23)0.02 = 0.54

20%

Here's a tip: Always start percentage calculating with dividing the current number by 10.

Answer:

The first answer.

Step-by-step explanation:

The first answer.

What was the temperature of the air?

'was 2C warmer than the surface of the ice'

warmer than= +2c

Temp. of ice=-2c

-2c+2c=0

Answer:

Option 1

Step-by-step explanation:

The temp. was -2 degrees celsius.

The temp. got 2 degrees celsius warmer.

-2 + 2 = 0

Answer:

In a function that is represented by Y=mx+b b would be the y-intercept

Definition of y-intercept. : the y-coordinate of a point where a line, curve, or surface intersects the y-axis.

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: Number of people that support the candidate.

You need to calculate the sample size to estimate the population proportion of supporters given a confidence level of 99% and a margin of error of 4%

The margin of error of the confidence level for the population proportion is

d= [tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]

From this formula you have to clear the value of n:

[tex]\frac{d}{Z_{1-\alpha /2}}[/tex]= [tex]\sqrt{\frac{p'(1-p')}{n} }[/tex]

[tex](\frac{d}{Z_{1-\alpha /2}})^2[/tex]= [tex]\frac{p'(1-p')}{n}[/tex]

[tex]n*(\frac{d}{Z_{1-\alpha /2}})^2[/tex]= [tex]p'(1-p')[/tex]

n= [tex]p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2[/tex]

[tex]Z_{1-\alpha/2}= Z_{0.995}= 2.586[/tex]

sample proportion "p'" since there is no sample information, nor any previous information is known, you have to consider it as the "worse case scenario" and use the value of p'= 0.50

d= 0.04

[tex]n= p'(1-p') * (\frac{Z_{1-\alpha/2}}{d} )^2= 0.5*0.5*(\frac{2.586}{0.04} )^2= 1044.9= 1045[/tex]

She has to take a sample of 1045 people to estimate the population proportion of her supporters with a confidence level of 99% and a margin of error of 4%

I hope this helps!

Answer:

Option 2

Step-by-step explanation:

The average temperature in January is -1 degrees celsius. Last year, it was 1 degrees celsius higher than the average.

-1 + 1 = 0

Answer:

The second answer.

Step-by-step explanation:

The average temp. is -1C.

'was 1C warmer' = +1

-1+1=0

Step-by-step explanation:

let us keep the price of pants as x

and price of necklace as y

Simultaneous equations comes as follows:

4x + 3y = 216 for Alexis

7x + 2y = 300 for Jess

we'll make either x or y equal

here let's make y equal

2 ( 4x + 3y = 216)

3 ( 7x + 2y = 300)

8x + 6y = 432

21x + 6y = 900

21x - 8x = 900 - 432

13x = 468

x = $36

so a pant costs $36

And

3y = 72

y = $ 24

so a necklace costs $36

Answer:

21/5

Step-by-step explanation:

if a/b = c, then b=a/c

in other words:

divide -7/25 by -1/15 to get the answer

It also helps to use the fact that a/b / c/d = a/b * d/c

-7/25 / -1/15 = -7/25 * -15/1

= 105 / 25

= 21 / 5

Answer:

[tex]4 \frac{1}{5} [/tex]

Step-by-step explanation:

[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]

[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]

[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]

[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]

Answer:   y=1/8*x+2

Step-by-step explanation:

The equation of any tangent line is y=a*x+b  (1)

To the equation of the tangent line we have to find the coefficients a and b   and the to substitute them to equation (1).

As we know  a=y'(x0) ( where x0=16)

So y'(x)= (√ (x) )' = 1/(2*√x)

a=y'(x0)= 1/(2*√16)=1/(2*4)=1/8

So lets substitute a in equation (1):

y=1/8 *x+b

Now we have to find b

We know that the point (16, 4) belongs to the tangent line.

That means

4=1/8*16+b => 4=2+b => b=2

SO the equation of the tangent line is y=1/8*x+2

Answer:

[tex]-24a^3b^2 -8ab^5\\[/tex]

Step-by-step explanation:

Given the two expression (6a²+2b³) and -4ab², to find their product, the following steps are valid;

[tex]= (6a^2+2b^3) *-4ab^2\\= (6a^2+2b^3)(-4ab^2)\\= (6a^2)(-4ab^2)+(2b^3)(-4ab^2) \\= -24a^3b^2 + (-8ab^5)\\= -24a^3b^2 -8ab^5\\[/tex]

The final expression gives the required product

Simple interest formula = I = PRT where I = interest, P = principal, r = interest rate and t = time.

i = 806.20, p = 14,000 t = 250 days.

Change t to be fraction of a full year: t = 250/365

Now solve for r:

806.20 = 14000 x r x 250/365

Simplify :

806.20 = r x 9589.04

Divide both sides by 9589.04:

r = 806.20 / 9589.04

r = 0.08407

Multiply by 100 to get percent:

r = 8.41% (rounded to nearest hundredth)

Answer:

Step-by-step explanation:

The question is incomplete. Find the complete question in the attached file.

a) Given the expression 9x^2 - y^2 = 1

Differentiating implicitly will give;

[tex]18x-2y\frac{dy}{dx} = 0\\[/tex]

We can then make dy/dx the subject of the formula as shown;

[tex]18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}[/tex]

b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.

[tex]9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\[/tex]

Using chain rule to solve the equation;

let;

[tex]u = 9x^{2} -1\\ y = u^{1/2}[/tex]  

du/dx = 18x

dy/du = [tex]1/2u^{-1/2}[/tex]

dy/dx = dy/du * du/dx

dy/dx = [tex]1/2u^{-1/2} * 18x[/tex]

[tex]\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }[/tex]

c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute [tex]y = \sqrt{9x^{2} - 1 } \\[/tex] into the answer in (a) as shown;

From (a) [tex]\frac{dy}{dx} = \frac{9x}{y} \\[/tex]

[tex]y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}[/tex]

This shows that they are consistent

Answer: True

Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.

Answer:

  45°

Step-by-step explanation:

It is useful to have some idea what angles of different measures look like. The attachment may help you match the angle to an appropriate measure.

To me, it looks like a 45° angle.

__

Of course, you can always use a protractor and measure it. Make sure your screen or printer does not distort the image. (Printable versions of protractors are available on-line.)

Answer:

it would be 3/5*4/1

Step-by-step explanation:

To divide you multiply the first number by the reciprocal of the second number. Check and you'll see that the answer is the same. Hope this helps!

Answer:

The answer is 3/5 x 4/1

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

It is D. because there are lines on top of the letters meaning that the points PQ, QR, and PR are lines/sides.

You chose the answer already!

Answer:

The correct answer is -  Substitution method

Step-by-step explanation:

substitution method or strategy where an individual solve for one variable first and afterward substitute that articulation into the other equation. The significant thing here is that you are consistently substituting values that are the same.  

Steps :

- Comprehend or solve one of the variables and make an equation.  

- Substitute (module) this articulation into the other equation and comprehend.  

- Resubstitute the value into the first equation to find the value of other variable.

Answer:

the answer is 6x

Step-by-step explanation:

Answer:

A. Pages about Michael Jordan.

Step-by-step explanation:

Michael Jordan, MJ, is a great basketball player, and has achieved one the best records in his career. He is a National Basketball Association (NBA)  player with great skills and energy.

From the search item, the two names Michael OR Jordan is for one person, Michael Jordan. The search would combine the two names because it is a well known one and give an output on Michael Jordan. Thus, the pages that would be favored are pages about Michael Jordan.

Answer:

6.09 * 10 ^-3

Step-by-step explanation:

We want one non zero digit to the left of the decimal

Move the decimal 3 places to the right

6.09

The exponent is 3 and it is negative since we move to the right

6.09 * 10 ^-3

Answer:

6.09(10⁻³)

Step-by-step explanation:

Step 1: Put number into proper scientific decimal form

6.09

Step 2: Figure out how many decimals places it moves

Since it moves to the left 3, our exponent would be -3

Answer:

Anxiety score close to 54.58.

Step-by-step explanation:

When the distribution is normal, we use 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.

In this question:

[tex]\mu = 48, \sigma = 4[/tex]

Approximately what anxiety test score would put someone in the top 5 percent?

We have to find the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

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

[tex]1.645 = \frac{X - 48}{4}[/tex]

[tex]X - 48 = 1.645*4[/tex]

[tex]X = 54.58[/tex]

Anxiety score close to 54.58.

Answer:

D. 66

Step-by-step explanation:

Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.

Answer:

D. 66

Step-by-step explanation:

AD = 100

AC = 34

The whole line is 100. A part of the line is 34. The other part will be 66.

100 - 34 = 66

Answer:

9 mile trip

Step-by-step explanation:

$15 + $15 = $30

$15 + $9 = $24

$15 + $25 = $40

$15 + $12 = $27

$30 > $25

$24 < $25

$40 > $25

$27 > $25