Use the normal distribution of SAT critical reading scores for which the mean is 515 and the standard deviation is 125. Assume the variable x is normally distributed. What percent of the SAT verbal scores are less than ​675? If 1000 SAT verbal scores are randomly​ selected, about how many would you expect to be greater than ​550?

Answer:

We use the binomial distribution to describe this situation.

The mean number of phone sales is 749.7 with a standard deviation of 15.

Step-by-step explanation:

For each shopper, there are only two possible outcomes. Either they plan to purchase the newly released smart phone, or they do not. Each customer is independent of other customers. So we use the binomial distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Fifty random shoppers at an electronics store have been interviewed and 35 of them intend to purchase a newly released smart phone.

This means that \(p = \frac{35}{50} = 0.7\)

What are its mean and standard deviation of phone sales if we are concerned about 1071 shoppers that day

1071 shoppers, so \(n = 1071\)

Mean

\(E(X) = 1071*0.7 = 749.7\)

Standard deviation

\(\sqrt{V(X)} = \sqrt{1071*0.7*0.3} = 15\)

The mean number of phone sales is 749.7 with a standard deviation of 15.

In order to achieve the shortest distance from starting vertex (A) to F on a network, utilize Dijkstra's algorithm following these steps:

Initiate every vertex with a tentative distance value: assign zero to the starting point and infinity to other vertices.

Establish the initiating vertex as the current vertex.

Analyze all neighboring vertices of the current vertex and determine their respective tentative path length via current vertex. Proceed to compare it with its already assigned value; upgrade such distance if shorter than before.

Subsequent to analyzing adjacent points of the present node, designate it as 'visited'. Futuristic reference will disregard this chosen and visited vertex altogether.

Examine unexplored vertices marked as having the most reduced tentative distances, declare them 'current' while formulating new calculations for other contenders until pertinent conclusion is reached.

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The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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Some things you can do to help you decide on a bank include:

When trying to locate a bank that offers competitive returns on savings and favorable borrowing costs, consider comparing interest rates.

To gather additional information about certain banks, why not solicit feedback from acquaintances? People who have personal experience with a particular bank can provide valuable insights into their satisfaction levels with regards to customer service, for example.

Finally, taking the time to visit branch offices can offer valuable clues regarding convenience level and overall atmosphere.

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Answer:

y=6x

Step-by-step explanation:

y-y1=m(x-x1)

y-0=6(x-0)

y=6(x)

y=6x

Answer: f(3) = g(6)

Step-by-step explanation: if you plug them in we see that f of 3 on the y axis intercept g of x so we then go up and see that g of 6 intercepts f of 3 so therefore that is the answer

Answer:

-1<x<4

BLUE

Step-by-step explanation:

Answer:

5/7=W/28

Step-by-step explanation

They won 5 out of 7 played games so that's their win rate. If the same team continued to do this for 28 games then they would win 20 times.

Answer:

0.18km

Step-by-step explanation:

Lateral Surface Area = 2πrh

= 2 × 22 × 21 × 75

7

= 9900m^2

Area taken by revolution = 9900 × 800

= 7920000m^2

= 7.92 km^2

breadth = 7.92km^2 ÷ 44

= 0.18km

A swimming pool has a volume of 256 yd³.The amount of water in gallons needed to completely fill the pool is 51705.344 gallons.

Given that,

A swimming pool has a volume of 256 yd³.

We have to find The amount of water in gallons needed to completely fill the pool.

What is the conversion factor defined as?

An amount is used as a conversion factor when multiplying or dividing one set of units by another.

The appropriate conversion factor must be applied when converting to an equivalent value.

For instance, 12 inches equals 1 foot when converting between inches and feet.

Regarding the given problem;

The pool has a volume of 256 yd³.

Convert the yd³ volume to gallons.

201.976 gallons are in 1 yd³.

As a result, multiply both sides by 256 to get the total volume, which is 256 yd³.

201.976 yd³ are equal to 256 gallons.

51705.344 gallons are equal to 256 yd³.

Consequently, 51705.344 gallons of water are needed to completely fill the pool.

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Given that, one digit of a two digit number is three times the other digit.

Let assume that digit at ones place be x.

digit at ones place be x.So, digit at tens place be 3x.

digit at ones place be x.So, digit at tens place be 3x.So, two digit original number = 10 × 3x + 1 × x = 30x + x = 31x

Now, number formed on interchanging its digits, i.e.

Reverse number = 10 × x + 1 × 3x = 10x + 3x = 13x

According to statement, if we interchange the digits of this two digit number and add the resulting number to the original number, we get 88.

\(\begin{gathered}\sf \: 31x + 13x = 88 \\ \\ \end{gathered}\)

\(\begin{gathered}\sf \: 44x = 88 \\ \\ \end{gathered}\)

\(\begin{gathered}\sf \: x = \dfrac{88}{44} \\ \\ \end{gathered}\)

\(\begin{gathered}\sf\implies \: x = 2 \\ \\ \end{gathered}\)

So, two digit number is 31 × 2 = 62

Hence,

\(\begin{gathered}\sf\implies \: \boxed{ \bf{ \:Original \: number \: = \: 62 \: \: }} \\ \\ \end{gathered}\)

\(\rule{190pt}{2pt}\)

Answer:

26 or 62

Step-by-step explanation:

If one of the two digits of a two-digit number is three times the other digit, then the options for the two-digit number are:

If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88.

From inspection of the listed pairs of numbers, the only pair that sums to 88 is 26 and 62:

⇒ 26 + 62 = 88

Therefore, the original number is either 26 or 62.

In order to calculate continuous interest, we can use the formula below:

Where A is the amount after t years, P is the principal (initial value) and r is the interest rate.

So, using A = 2P and r = 0.0475, we have:

Therefore it will take 14.59 years to double the investment.

We know the volume is 24, we can rearrange the formula to find the height: h = V/A. Plugging in the given values, we get h = 24/πr^2.

If the volume of a cylinder B2 is 24 cubic centimeters, there are a few things we can determine about the cylinder's dimensions. To find the radius of the cylinder, we first need to calculate the area of the base.

We can use the formula A = πr^2, where A is the area and r is the radius. If we know the volume of the cylinder, we can use the formula V = Ah, where V is the volume,

A is the area of the base, and h is the height of the cylinder. However, we do not have enough information to find the radius, as there are infinite combinations of radius and height that can give us a volume of 24 cubic centimeters.

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Step-by-step explanation:

||-514||,||-47||,||67||

Answer:

x = 20, y = -3

Step-by-step explanation:

Set both equations equal to each other

\(\displaystyle y=\frac{3}{5}x-15\\\\y=-\frac{3}{4}x+12\\\\\\\\\frac{3}{5}x-15=-\frac{3}{4}x+12\\\\\frac{12}{20}x-15=-\frac{15}{20}x+12\\\\\frac{27}{20}x-15=12\\\\\frac{27}{20}x=27\\\\x=20\\\\y=\frac{3}{5}x-15\\\\y=\frac{3}{5}(20)-15\\\\y=\frac{60}{5}-15\\\\y=12-15\\\\y=-3\)

Answer:

Step-by-step explanation:

The curve is symmetric about x = 1

so does not qualify for y-axis symmetry, nor the others.

Answer:

8

Step-by-step explanation:

let x be the number , then

\(\frac{3}{4}\) x = 27 ( multiply both sides by 4 to clear the fraction )

3x = 108 ( divide both sides by 3 )

x = 36

the number is 36, so

\(\frac{2}{9}\) × 36 = 2 × 4 = 8

The two ninths of the number is 8

We know that Three quarters of a number is  \(\frac{3}{4}\)  times of a number

Hence we will assume the number x ,

                     \(\frac{3}{4} of x = 27\)

                     \(x = 27 X \frac{4}{3}\)

                       \(x = 36\)

Now as we know the number is 36

Therefore , the two ninths of the number assumed as y

We will multiply the number 36 by 2 and then divide by 9

Hence,

                           \(y = 36 X \frac{2}{9}\)

                               \(y = 8\)

Thus, the two ninths of the number 36  is 8                            

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Answer:

x is 0 or -7

Step-by-step explanation:

\(4x^{2} +28x=0\\4x(x} +7)=0\\4x=0 x=0\\x+7=0\\x=-7\)

Answer:

x = {-7, 0}

Step-by-step explanation:

4x^2 + 28x = 0

Divide both sides by 4

x^2 + 7x = 0

Factor out x

x(x + 7) = 0

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

From the zero product rule

x = 0

and

x + 7 = 0

subtract 7 from both sides

x = -7

x = {-7, 0}

Answer:

The correct answer is:

D. Action: Divide both sides by 4.

E. Property: Division property of equality.

Answer:

1/2

Step-by-step explanation:

We are given the expression 3b²-c, and we want to evaluate it if b is 1/2 and c is 1/4.

Because b and c are given values, we can substitute them into the expression as so:

Replace b with 1/2 in the expression.

3(1/2)²-c

Now replace c with 1/4 in the expression.

3(1/2)²-1/4

Now to solve this, we need to use the order of operations, which is usually known as PEMDAS (parentheses, exponents, multiplication, division, addition, subtraction) in the United States, although other countries have different abbreviations.

Regardless, the order of operations tells us that we should start with what is inside parentheses (i.e. if we need to do anything, like multiplying or dividing any numbers that are inside parentheses).

In this case, we don't have anything. So, we should go next to exponents, and we do have an exponent here (1/2 is raised to the second power).

So let's evaluate that.

Raise 1/2 to the second power (multiply it by itself).

1/2 * 1/2 = 1/4

We can substitute (1/2)² with 1/4:

3(1/4) - 1/4

Next, we should take care of any multiplication / division, making sure that we should work left to right

There is one multiplication thing to do: the 3(1/4), which will be 3/4

Replace 3(1/4) with 3/4.

3/4 - 1/4

Now, we can subtract 1/4 from 3/4, as the final two things in PEMDAS are addition and subtraction (A and S). Note that even though while addition is written first, we should always be working left to right, so for example if we had 3 - 4 + 6, we should do 3 - 4 first, THEN add 6 to the result of that. The same is true for multiplication and division.  

3/4 - 1/4 = 2/4 = 1/2

Answer:

The answer will be in the form y=mx+b

y= - \(\frac{2}{5}\) x + \(\frac{7}{10}\)

Brainliest please

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of -4x - 10y = -7 in slope-intercept form is

y = (-2/5)x + (-7/10)

The equation of a line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

The equation of a line in slope intercept form is given by:

y = mx + c

m = slope

c = y-intercept

We have,

-4x - 10y = -7

Add 4x on both sides.

-4x - 10y + 4x = 7 + 4x

-10y = 7 + 4x

Multiply -1/10 on both sides.

y = -1/10 ( 7 + 4x )

y = -7/10 - (4/10)x

y = (-2/5)x + (-7/10)

Thus the equation of -4x - 10y = -7 in slope-intercept form is

y = (-2/5)x + (-7/10)

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Answer:

ab(3a + 4b)

Step-by-step explanation:

Here are the steps on how to write the expression

3a^2 b + 4ab^2 as an equivalent algebraic expression:

1. Factor out the greatest common factor, which is ab.

2. The expression becomes ab(3a + 4b).

3. This is an equivalent algebraic expression to 3a^2 b + 4ab^2.

steps:

I hope this helps! Let me know if you have any other questions.

Answer:

Step-by-step explanation:

To simplify the expression 3a^2b + 4ab^2, [ we can factor out the common factor of ab from both terms: Step 1: Take out the common factor of ab. 3a^2b + 4ab^2 = ab(3a + 4b) Now the expression is in its factored form.

The probability that the mean amount of cereal in 5 randomly selected boxes is at most 9.65 ounces is 0.4808.

The Central limit theorem is used to find the probability

Data given:

sample size = 5.

mean, μ = 9.70 ounces

standard deviation, σ = 0.03 ounce.

To calculate the probability, we determine the z-score corresponding to the sample mean of 9.65 ounces using the z-score formula.

x is the sample mean,

μ is the population mean,

σ is the population standard deviation, and

n is the sample size.

For the sample mean of 9.65 ounces in 5 boxes:

z = (9.65 - 9.70) / (0.03 / √5)

z ≈ -0.05 / (0.03 / √5)

Using a calculator, we find that the probability is approximately 0.4801.

Therefore, the probability that the mean amount of cereal in 5 randomly selected boxes is less than 9.65 ounces is approximately 0.4801.

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Answer: 131.36363 pints of the first type of drink, and 38.63636 pints of the second type of drink.

Step-by-step explanation:

We can use the principle of linear equations. Let's say that the first type of drink is represented by x, and the second type is represented by y. We can then set up the following system of equations:

x + y = 170 (1)

0.4x + 0.9y = 0.45 * 170 (2)

We can solve for x and y using the methods of linear algebra. To do this, we can multiply equation (1) by 0.9, and equation (2) by 0.4, and then subtract the two equations to get the following equation:

0.9x - 0.4y = 0.45 * 170 - 0.4x - 0.9y

0.5x = 0.45 * 170 - 0.9y

x = (0.45 * 170 - 0.9y) / 0.5

We can substitute this expression for x into equation (1) and solve for y:

y = 170 - x

y = 170 - (0.45 * 170 - 0.9y) / 0.5

2.2y = 170 - 0.45 * 170

y = (170 - 0.45 * 170) / 2.2

y = 85 / 2.2

We can then substitute this value for y back into equation (1) to solve for x:

x = 170 - y

x = 170 - (85 / 2.2)

x = 170 - 38.63636

x = 131.36363

Therefore, the Royal Fruit Company needs to use 131.36363 pints of the first type of drink, and 38.63636 pints of the second type of drink, in order to produce 170 pints of a mixture that is 45% pure fruit juice.

Answer: 18

6 containers of yogurt is 4 dollars, that means every 4 dollars is 6 containers.

Now, divide 12 by 3, and you will get the factor you need.

12 ÷ 4 = 3

Now, multiply this number by 6 and get the answer.

3 x 6 = 18.

Hope this helped you!

Answer:

(a)\(\dfrac{15}{32}\)

(b) 17:15

Step-by-step explanation:

(a)

The roulette wheel has 32 slots (inclusive of 0 and 00)

Number of Odd Numbers between 1 to 30 =15

Since you are placing a bet that the outcome is an odd number.

\(P(\text{Winning})=\dfrac{\text{Number of Odd Numbers}}{\text{Total Number of Slots}} \\=\dfrac{15}{32}\)

(b) The actual odds against​ winning

\(\text{Actual Odds against Winning})=\dfrac{32-15}{15}\\=\dfrac{17}{15}\)

Therefore, the actual odds against​ winning are 17:15

The fence in dead center is about 399 feet from the third base.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

For the triangle in this problem, we have that:

Hence the distance is obtained as follows:

d² + 90² = 409²

\(d = \sqrt{409^2 - 90^2}\)

d = 399 ft.

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