The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=553.8 and standard deviation σ=28.
(a) What is the probability that a single student randomly chosen from all those taking the test scores 559 or higher? For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test. (b) What are the mean and standard deviation of the sample mean score 7, of 25 students? The mean of the sampling distribution for x is: ___ The standard deviation of the sampling distribution for x is: ___
(c) What z-score corresponds to the mean score x of 559? (d) What is the probability that the mean score o of these students is 559 or higher?

Answer:

The 2nd answer is the correct answer

Step-by-step explanation:

Hope this helps:)

Answer:

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

First, plot the points and connect together in the given order.

See attached.

As we can see all sides are of different length but two sides seem to be parallel.

Let's find the slopes of segments BC and AD and compare:

As se see the slopes are same, so BC and AD are parallel.

Since we have a pair of parallel sides, the quadrilateral is a trapezoid.

Answer:

The truck driver travels 2310 miles every day

Step-by-step explanation:

To make this more understandable (maybe not more simpler but still works lol) we will add 385 onto itself until we have done it 6 times

385 (1) + 385 (2) = 770

770 + 385 (3) = 1155

1155 + 385 (4) = 1540

1540 + 385 (5) = 1925

1925 + 385 (6) = 2310

Answer:

2,310 miles

Step-by-step explanation:

385 miles= 1 day

Multiply: 385 times 6 (to be able to know how much in 6 days)= 2,310

Hope this helped!!! :)

Brainliest?!?!

Stay safe and have a wonderful day/afternoon/night!!!

Answer:

c. non-linear and increasing

Step-by-step explanation:

Answer:

x = 52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

Combine like terms

5x+100 =360

Subtract 100 from each side

5x+100-100 = 360 -100

5x = 260

Divide by 5

5x/5  = 260/5

x = 52

Answer:

x=52

Step-by-step explanation:

50+(2x +30)+ (2x +20) + X=360

First combine like terms

50+30+20=100

2x+2x+x=5x

combine

5x+100=360

subtract 100

5x=260

divide by GCF (5)

x=52

Hope this helps! Plz award Brainliest : )

The circle centered at C(-5,4) intersects the line y = 3x + 2 at the point Q, with coordinates (-1/10, 17/10). This point Q serves as the tangent point between the line and the circle.

To find the coordinates of the point Q where the line y = 3x + 2 is tangent to the circle with center C(-5,4), we can use the concept of the slope of a tangent line.

First, we need to find the slope of the tangent line. The slope of the line y = 3x + 2 is 3. For a tangent line to a circle, the radius drawn from the center of the circle to the point of tangency is perpendicular to the tangent line. Since the slope of the radius is the negative reciprocal of the tangent line's slope, the slope of the radius is -1/3.

Next, we find the equation of the radius line passing through the center C(-5,4) with a slope of -1/3. Using the point-slope form, we have:

y - 4 = (-1/3)(x + 5)

To find the point of tangency, we solve the system of equations formed by the line y = 3x + 2 and the radius line:

y = 3x + 2

y - 4 = (-1/3)(x + 5)

Substituting the value of y from the first equation into the second equation:

3x + 2 - 4 = (-1/3)(x + 5)

3x - 2 = (-1/3)x - 5/3

3x + (1/3)x = 5/3 - 2

(10/3)x = -1/3

x = -1/10

Substituting this value of x back into the first equation:

y = 3(-1/10) + 2

y = -3/10 + 20/10

y = 17/10

Therefore, the coordinates of the point Q, where the line y = 3x + 2 is tangent to the circle with center C(-5,4), are (-1/10, 17/10)

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Answer:

The answer is B

Step-by-step explanation:

b.

$26.83

Answer:

the interger would be 15 because you earn 15 so therfore it would be 15.

Step-by-step explanation:

Answer:

m= 11/ 12

Step-by-step explanation:

hope that really helps

a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.

b) Nearly normal according to the central limit theorem.

c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.

Normal probability distribution:

The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.

Central Limit Theorem:

The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.

According to the Question:

The average monthly charge is $142 with a standard deviation of $29.

This is μ = 142 and σ = 29

Part a:

The mean and standard deviation of the sampling distribution of x to show your research and support your argument:

1500 samples (over 30).

According to the Central Limit Theorem

The mean is 142 $

The standard deviation is s = \(\frac{29}{\sqrt{1500} }\) = 0.7488

Part b:

Shape of sampling distribution of X.

Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)

Part C:

The probability that the average cable service paid by a sample of cable service customers exceeds $170.

Therefore, by the central limit theorem, the p-value of Z when X= 170

                         Z =  x - μ/ σ

By the Central Limit Theorem:

   Z = 170 - 142 / 0.7488

      = 28/ 0.7488

      = 37.34 exceeds 0.9099

Using the Z probability calculator :

P(Z > 1.335) = 0.09093

Complete Question:

The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.

Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.

Part b: what is the shape of the sampling distribution of x hat justify your answer.

Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.

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Answer: x = 8

Step-by-step explanation:

because x + 7 = 15, you can subtract 7 from both sides to get x = 8.

Hope it helps <3

Answer:

8

Step-by-step explanation:

x + 7 = 15

x = 15 - 7

x = 8

Thus, the value of x is 8

2 hours will pass before they meet.

"Information available from the question"

In the question:

Aaron starts riding a bike at a rate of 3 mi/h on a road toward a store 20 mi away.

Zhang leaves the store when Aaron starts riding his bike, and he rides his bike toward Aaron along the same road at 2 mi/h.

Now, According to the question:

Total distance = 20mi

Aaron starts riding a bike at a rate of  = 3mi/h

Zhang rides his bike toward Aaron along the same road at  = 2mi/h

Let y be the number of hours for them to meet.

The expression is given as

3y + 2y = 20

solving for y, we have

5y = 20

y = 20/5

y = 4hrs

Therefore, 2 hours will pass before they meet.

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Using mathematical operations, the standard form of the following operations are:

(A) (7 – 18i) – (5 – √-81): 12 - 9i

(B) (9 + 2√(6)i) (9 – 2√(6)i): 105

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).

(A) (7 – 18i) – (5 – ROOT(-81):

(7 – 18i) – (5 – √-81)

7 – 18i – (5 – √-81)

– (5 – √-81) = -5 + i9

17 - 18i - 5 + i9

- 18 + i9 + 17 - 5

- 9i + 17 - 5

-9i + 12

12 - 9i

(B) (9 + 2 ROOT(6)i) (9 – 2 ROOT(6)i)

(9 + 2√(6)i) (9 – 2√(6)i)

Complex arithmetic rule: (a+bi)(a-bi) = a²+b²

9² + (2√6)² = 105

105

Therefore, using mathematical operations, the standard form of the following operations are:

(A) (7 – 18i) – (5 – √-81): 12 - 9i

(B) (9 + 2√(6)i) (9 – 2√(6)i): 105

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To find the equivalent nominal interest rate with daily compounding, we can use the formula: Nominal Interest Rate =\((1 + Effective Annual Rate)^(1/n) - 1\) Where: Effective Annual Rate is the rate quoted by the bank (in decimal form) n is the number of compounding periods per year

In this case, the quoted rate by the bank is 15.6% (or 0.156 in decimal form), and the compounding is done annually, so there is one compounding period per year.

Plugging in these values into the formula, we get:

Nominal Interest Rate = (1 + 0.156)^(1/365) - 1

Calculating the expression inside parentheses:

Nominal Interest Rate = (1.156)^(1/365) - 1

Calculating the exponent:

Nominal Interest Rate = 1.000427313 - 1

Subtracting:

Nominal Interest Rate = 0.000427313

Converting to a percentage to 2 decimal places:

Nominal Interest Rate = 0.0427%

Therefore, the equivalent nominal interest rate with daily compounding is approximately 0.0427%.

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The percentage of Venus's year to mercury's year is 39.1%

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction - three for the price of one! To change the percentage to a fraction, just put the percentage number in the numerator and 100 in the denominator.

Venus year is 88 earth days and mercury is 225 earth days.

To find the percentage of venus's year to mercury's we divide the Venus's year by mercury and multiply by 100

Then , 88/225 ×100 = 39.1 %

Therefore Venus length of year is 39% of mercury's year.

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Answer:

24m

Step-by-step explanation:

l=8m

b=4m=w

p=2(l+b)

p=2(8+4)m

p=2(12m)

p=24m

Answer:

24 cm

Step-by-step explanation:

\(\boxed{\begin{minipage}{5 cm}\underline{Perimeter of a rectangle} \\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width.\\ \phantom{ww}$\bullet$ $l$ is the length. \\\end{minipage}}\)

Given values:

Substitute the given values into the formula:

\(\begin{aligned}P&=2(w+l)\\\implies P&=2(4+8)\\&=2(12)\\&=24\;\; \sf cm\end{aligned}\)

Therefore, the perimeter of the rectangle is 24 cm.

For a normal distribution, a negative value of z indicates D. the z is to the left of the mean.

A continuous probability distribution known as the "normal distribution" has values that are symmetrically distributed mostly around the mean.

The standard deviation determines the width of the curve in a normal distribution, which depicts a symmetrical plot of data around its mean value. It is represented graphically by the "bell curve.

Z is the number of standard deviations from the mean given by the formula:

z = ( X - μ ) ÷ ( σ )

where

x is the raw score,

μ is the population mean, and

σ is the population standard deviation

A negative value means that the number of standard deviations of an observation is to the left of the mean.

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Answer:

D

Step-by-step explanation:

Hey there! I'm happy to help!

Sum means to add. Let's call our number n.

n+15

We multiply this whole thing by 6.

6(n+15)

And this is -42.

6(n+15)=-42

We use distributive property to undo the parentheses.

6n+90=-42

We subtract 90 from both sides.

6n=-132

We divide both sides by 6.

n=-22.

Have a wonderful day! :D

The optimal solution for the amount of cash to withdraw each time to minimize transportation costs and maximize interest earnings is determined by calculating the Economic Order Quantity (EOQ) using the formula Q = √((2 * C * T) / r), and rounding the result to a convenient amount.

The Economic Order Quantity (EOQ) model is typically used for inventory management, not for optimizing cash withdrawals. However, if we assume that the question is seeking an optimal withdrawal strategy to minimize transportation costs and maximize interest earnings, we can approach it as follows:

Let's denote:

C = Annual cash need ($5,000)

T = Transportation cost per visit ($5)

r = Annual interest rate (5%)

To find the optimal solution for the amount of cash to withdraw each time, we can consider the trade-off between transportation costs and interest earnings. The objective is to minimize the total cost.

Calculate the optimal order quantity (Q) using the EOQ formula:

Q = √((2 * C * T) / r)

Round the calculated Q to the nearest convenient amount, such as multiples of $100 or $500.

The optimal solution would be to withdraw the rounded Q amount each time to minimize transportation costs while still meeting the annual cash need.

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Answer:

The correct answer is X = 38.

Answer: 48

Step-by-step explanation:

So as we can see it’s a straight line (180 degrees) and we have a right angle (90 degrees) and 42, so we subtract 180 by 90 and 42,

180 - 132 = 48!

There’s your answer!

Answer:

7

Step-by-step explanation:

When dividing numbers with exponents that have the same base (in this case it’s 5), you can subtract the two exponents to simplify it.

I’m just going to show you how to solve it for you to understand:

\(\frac{5^{11} }{5^{x} }=5^{4}\) This means that what can you subtract from 11 (the exponent) to get to 4 (the other exponent). You can notice that 11 - 7 = 4.

So,

\(\frac{5^{11} }{5^{7} }=5^{4}\)

Answer: 7

You have a good day too!

Hope this helps! :)

a) i - The ingredient that Paige can increase to make the smoothie more pumpkin-Y is pumpkin puree and pumpkin pie spice.

b) ii - She can also reduce pumpkin puree to make the smoothie less pumpkin-y.

b) i - If she follows the recipe, the smoothie will be 20.48% pumpkin. Thus, the unit rate of pumpkin/cup of smoothy is 20.48% percent.

Note that the term pumpkin-y is an adjective used to denote how much pumpkin is in a coup of smoothie.

a( 1-11) As already indicated above, The ingredient that Paige can increase to make the smoothie more pumpkin-Y is pumpkin puree and pumpkin pie spice given that both are derived from or related to pumpkin.

Hence to make the smoothie more or less pumpkin-y, you must either increase or decrease both ingredients.

b) To derive the unit rate to represent the amount of pumpkin-y ingredients per cup of smoothy, given that there are 48 teaspoons in a cup, we must convert all unit of the ingredients into teaspoon measures then work the percentage of pumkin-y ingredients against the total.

We know that:

Since there are 48 teaspoons in a cup,

Banana is:

= 3/4 x 48

= 144/4

= 36 teaspoons

Using the above computation we can also derive the rest to get:

When all the above ingredients are mixed we have

Smoothie = 36 + 24 + 48 + 32 + 24 + 2

= 166 teaspoons

Recall that the ingredients that are "Pumpkin-y" are:

Total pumkin-y ingredients = 34 teaspoons

Thus, the unit rate to represent the amount of pumkin-y ingredients per cup will be:

= (34/166) * 100

= 0.20482 or

= 20.48%

Thus, it is correct to state that a unit rate to represent the amount of pumpkin-y ingredients per cup of smoothie is 20.48%.

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Full Question:

a) i- Paige is trying to make the perfect pumpkin smoothie n. What ingredients can Paige increase to make the smoothie more pumpkin-y?

ii- Less pumpkin-?

b) i- How pumpkin-y are Paige's smoothies if she follows the recipe?

ii- Write a unit rate to represent the amount of pumpkin- ingredients per cup of smoothie. (Hint: There are 48 teaspoons in a cup.)

See attached image.

Answe

Step-by-step explanation:

The missing blanks have been filled .

A permutation is an act of arranging the objects or numbers in order. Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

A bag contains one green ball, one yellow ball, one red ball, and one blue ball.

Jerome picks a ball from the bag, replaces it, and then picks another ball.

Order matters since the ball is being replaced each time.

This is all the possible combinations to take 2 balls with replacement,

GY YY RY BY GR YR RR BR GB YB RB BB GG YG RG BG

For  the first missing blank , RR, RB, and RG are listed and the only other combination when choosing a red first would be to pick a yellow, so RY.

This is the same pattern for the others also.

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The dimensions of the vertical cross section of the prism is D = 5 in x 4 in

Given data ,

Let the prism be represented as A

Now , the value of A is

The formula for the surface area of a prism is SA=2B+ph, where B, is the area of the base, p represents the perimeter of the base, and h stands for the height of the prism

Surface Area of the prism = 2B + ph

The area of the triangular prism is A = ph + ( 1/2 ) bh

Now , the length of the cross section of prism is L = 5 inches

And , the height of the cross section = height of the prism

where the height of the prism H = 4 inches

Hence , the dimension of the cross section is D = 5 in x 4 in

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