Calories consumed by members of a track team the day before a race are normally distributed, with a mean of 1,700 calories and a standard deviation of 100 calories. If a normal curve is sketched using these data, what is the range for 3 standard deviations to the right and to the left of the mean?
A.) 1,400-2,000
B.) 0-3,500
C.) 1,600-1,800
D.) 1,500-1,900

To calculate the covariance and correlation coefficient of U and V, we need to first find the expected value and variance of U and V.

The covariance of two variables is a gauge of their relationship. In other words, it is a measure of how much the values of two variables tend to fluctuate together. Positive covariance shows that the values of the two variables tend to rise or decrease together, whereas negative covariance indicates that the values of one variable tend to increase when the values of the other variable drop. In probability theory and statistics, covariance is frequently employed to determine the association between two variables. It is determined by multiplying the variances of the two variables from their respective means and dividing the result by the total number of observations. This metric can be helpful for seeing trends and patterns in data and aiding analysts in forecasting.

How to solve?

The expected value of U is $E[U] = E[2 - X_1 - 2X_2] = 2 - m - 2m = -2m. Similarly, the expected value of V is $E[V] = E[3 + 3X_2 - X_3] = 3 + 3m - m = 4m.

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To calculate the value of covariance and correlation coefficient of U and V, we have to find their expected value along with variance.

A measure of the link between two random variables and how much they fluctuate together is called covariance. Alternately, we may say that it establishes the relationship between the two variables' changes, i.e., that a change in one variable is equivalent to a change in the other.

When one variable changes, covariance shows the link between the other two variables. Both variables are said to have positive covariance if a rise in one causes an increase in the other. Reduced values of one variable also result in reduced values of the other.

for expected value of U ;

= $E[U]

= E[2 - X_1 - 2X_2]

= 2 - m - 2m = -2m.

Similarly, the expected value of V;

= $E[V]

= E[3 + 3X_2 - X_3]

= 3 + 3m - m

= 4m.

now we can easily calculate the covariance and correlation coefficient of U,V.

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Using the concept of probability and the combination formula, it is found that there is a 0.4444 = 44.44% probability  they get to be on the same team.

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

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

Combination formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

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

Finding the number of desired outcomes:

\(D = 2C_{8,3} = 2\frac{8!}{3!5!} = 112\)

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

Finding the number of total outcomes:

\(T = C_{10,5} = \frac{10!}{5!5!} = 252\)

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

The probability is:

\(p = \frac{D}{T} = \frac{112}{252} = 0.4444\)

0.4444 = 44.44% probability  they get to be on the same team.

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The amount of the radioactive material after 10 years is 390.87 micrograms

Amount of a certain radioactive material = 900 micrograms.

Material decay every year = 8%

      Weight of radioactive material = 900 micrograms

      With 8% decay each year ,\(W(t) =900(0.92)^{t}\)

       W(1) = 900(0.92)

               = 828 micrograms

The amount of the radioactive material after 1 year is 828 micrograms

      W(2) = 900(0.92)²

               = 900(0.8464)

               = 761.76 micrograms

The amount of the radioactive material after 2  years is 761.76 micrograms

        W(10) = 900(0.92\()^{10}\)

                   = 900(0.4343)

                   = 390.87 micrograms (Refer image for complete question)

The amount of the radioactive material after 10 years is 390.87 micrograms.

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Answer:

12. Line F

Step-by-step explanation:

12. It was on the slope

sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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Answer: 27 students

Step-by-step explanation:

First take 45 + 90 = 135 students total

20% = 0.2

Then take 135 times 0.2 = 27 students

The integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

The integrand is 4x - 2.

To evaluate the integral geometrically in terms of area, we can interpret the integral as the area between the x-axis and the function 4x - 2 over the interval [-2, 2]. We can break this area into two parts: the area under the line y = 4x and the area under the line y = 4x - 2.

The area under the line y = 4x is given by the integral ∫4x dx from -2 to 2, which is equal to [2x^2] from -2 to 2, or 2(2^2) - 2(-2^2) = 16.

The area under the line y = 4x - 2 is given by the integral ∫(4x - 2) dx from -2 to 2, which is equal to [2x^2 - 2x] from -2 to 2, or 2(2^2) - 2(2) - [2(-2^2) - 2(-2)] = 8 - (-8) = 16.

Therefore, the total area between the x-axis and the function 4x - 2 over the interval [-2, 2] is 16 + 16 = 32.

So, the integral ∫(4x - 2)dx from [-2, 2] is equal to the area between the x-axis and the function 4x - 2 over the interval [-2, 2], which is 32.

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Answer:

SOH CAH TOA

Step-by-step explanation:

You could use helpful mnemonic called SOH CAH TOA

SOH is for SIN, OPPOSITE, HYPOTENUSE. It basically says that to find Sin of an angle, you must divide the opposite by the hypotenuse

CAH is for COS, says to find COS of an angle you must divide Adjacent by hypotenuse

TOA is for tan, says to find tan of an angle you must divide opposite by adjacent.

I would suggest watching a video to find out more.

I put a lot of thought and effort into my answers, so a brainliest would be much appreciated!

Answer:

3/100

Step-by-step explanation:

1 m = 100 cm

Scale factor = 3/100

Hope it helps you

Answer:

the answer would be 3/100

Let be "x" the amount of coffee that is sold for $1.20 per pound (in pounds) that the grocer should use in the new mix and "y" the other kind of coffee that is sold for $2.35 per pound (in pounds) that the grocer should use in the new mix

Using the information given in the exercise, you can set up the following System of equations:

Simplifying, you get:

You can solve the system as follows:

1. Multiply the first equation by -1.20.

2. Add the equations.

3. Solve for "y".

Then:

4. Substitute the value of "y" into the first equation.

5. Solve for "x".

Then:

Therefore, the answer is: About 14.61 pounds of the kind of coffee that is sold for $1.20 and about 9.39 pounds of the other kind of coffee that is sold for $2.35 per pound.

Hello!

area

= πr²

= 3.14 * (3ft)²

= 3.14 * 9ft²

= 254.34ft²

≈ 254.3ft²

Answer:  \(\bold{\dfrac{1}{6}=16.67\%}\)

Step-by-step explanation:

       First pick    and      Second pick

   \(\dfrac{4\ blue}{9\ total\ marbles}\times\dfrac{3\ green}{8\ remaining\ marbles}\quad =\dfrac{12}{72}\quad =\large\boxed{\dfrac{1}{6}}\)

If the length,breadth, height of cuboid are 16 m, 5 m,4 m , slant height of pyramid is 10m,  height be 6 m then the surface area of composite figure be 444 \(m^{2}\).

Given that the length,breadth,height of cuboid are 16m,5 m, 4m and slant height be 10 m and height be 6 m.

Surface area is basically sum of area of all the sides of a figure.

Surface area of composite figure =  area of cuboid less area of common side + area of 2 slant sides of pyramid+area of two triangles.

=2(lb+bh+hl)-(lb)+2(slant height*breadth of cuboid)+2[1/2* length of cuboid* height of triangle)

=2(16*5+5*4+4*16)-16*5+2(10*5)+2[1/2*16*6]

=2(80+20+64)-80+2*50+2(48)

=2(164)-80+100+96

=328-80+196

=248+196

=444\(m^{2}\)

Hence the surface area of composite figure having a cuboid and pyramid on top is 444\(m^{2}\).

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The expression for the rate of the water leaking out of the tank is: √t+1.

This means that the rate of water leaking out of the tank at any time t between 0 and 120 minutes is given by the square root of t + 1.

It's important to note that this expression assumes that the rate of water leaking out of the tank is directly proportional to the square root of time, which may not always be the case in real-world scenarios. However, for the purposes of this problem, we assume that this is a reasonable approximation.

Complete question: write an expression for the rate of the water leaking out of the tank water is pumped into an underground tank at a constant rate of 8 gallons per minute. water leaks out of the tank at the rate of √t+1 gallons per minute, for 0≤t≤120 minutes. At time t=0, the tank contains 30 gallons of water.

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As per the number of gym machines, the type of data is b. quantitative discrete data.

A discrete quantitative variable has a distinct quantitative meaning but can only take particular integer values rather than any value within a period. The number of needle sticks, the number of births, and the number of hospitalisations are a few examples of discrete numeric factors.

Similarly to that, the information given in the question refers to the quantity of gym equipment, which qualifies as quantitative data because it is a numerical assessment. Furthermore, rather than representing a continuous range of values, the data is discrete, which means that it reflects a limited collection of whole integers such as 10, 12, 15, 20, and 22. These numbers are the total number of gym machines that are available.

Complete Question:

the data are the number of machines in a gym. you sample five gyms. one gym has 12 machines, one gym has 15 machines, one gym has ten machines, one gym has 22 machines, and the other gym has 20 machines. what type of data is this?

a. Qualitative data

b. Quantitative discrete data

c. Discreet data

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The mean of the number of drivers expected not to be wearing seatbelts is approximately 4.35, the variance is approximately 15.62, and the standard deviation is approximately 3.95 and they expect to stop approximately 4.35 cars before finding a driver whose seatbelt is not buckled.

a. To find the mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts, we can model the situation using a geometric distribution.

Let's define a random variable X that represents the number of cars stopped until the first driver without a seatbelt is found. The probability of a driver not wearing a seatbelt is given as p = 0.23.

The mean (μ) of a geometric distribution is given by μ = 1/p.
μ = 1/0.23 ≈ 4.35

The variance (σ^2) of a geometric distribution is given by σ^2 = q/p^2, where q = 1 - p.
σ^2 = (0.77)/(0.23^2) ≈ 15.62

The standard deviation (σ) is the square root of the variance.
σ = √(15.62) ≈ 3.95


b. The expected number of cars they expect to stop before finding a driver whose seatbelt is not buckled is equal to the reciprocal of the probability of success (finding a driver without a seatbelt) in one trial. In this case, the probability of success is p = 0.23.

Expected number of cars = 1/p = 1/0.23 ≈ 4.35

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the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Answer:

85%

Step-by-step explanation:

Method 1: Set up a proportion

Set up an equation of the form:

part

whole

=

whole

part

​

=

percent

100

100

percent

​

Assign the variable

x

x to the unknown value:

x

=

x=

percent

percent

The question asks what

percent

percent of all the students is 323

Substitute the known values with the numbers given in the problem, and the unknown value with

x

x:

323

380

=

380

323

​

=

x

100

100

x

​

Solve for

x

x:

100

⋅

323

=

100⋅323=

380

⋅

x

380⋅x

Cross multiply

32300

380

=

380

32300

​

=

380

x

380

380

380x

​

Divide both sides by 20

85

%

=

85%=

x

x

Simplify

Method 2: Convert to decimal and multiply

Find

323

out of

380

as a decimal:

Find 323 out of 380 as a decimal:

323

380

=

380

323

​

=

0.85

0.85

Convert decimal to percent:

Convert decimal to percent:

0.85

×

100

=

0.85×100=

85

%

85%

Move decimal 2 places to the right

number

percent

323

85%

380

100%

Answer:

a; 3.45 * 10^3

b) 2.34 * 10^18

c) 80%

Step-by-step explanation:

a) 3450 in standard form

To write in standard form, we have to place a decimal at the back of the first non-zero number

we have this as ;

3.450

The count of numbers after the decimal point is 3

This will be the power to which 10 will be raised

We have this as;

3.45 * 10^3

b) 234 * 10^16

Let us write 234 in standard form

That will be;

234 = 2.34 * 10^2

So we have ;

2.34 * 10^2 * 10^16

Using the law of indices, we have;

2.34 * 10^(2 + 16) = 2.34 * 10^18

c) From the question, Kuwait is 4/5 of Hong kong’s population

Let Honk Kong’s population be x

4/5 * x = 2.4 million

4x = 5 * 2.4 million

x = 5 * 2.4/4

x = 5 * 0.6

x = 3 million

so writing the population of Kuwait as a percentage of that of Hong kong, we have

2.4/3 * 100%

= 0.8 * 100% = 80%

Answer:

There is really no answer to this because this is the furtherest you can go to simplify this expression. I can help solve it if you give me more information, or you tell me what the value of a and b is so I can solve it.

Thanks!

Answer:

x = 11

Step-by-step explanation:

Take the fifth root on both sides.

27(x-2) = 3^5

27x-54 = 3^5

27x = 243 + 54

27x = 297

x = 297/27

x = 11

Answer:

\(x = 11 \\ \)

Step-by-step explanation:

\( \sqrt[5]{27(x - 2)} = 3 \\ { (\sqrt[5]{27(x - 2} )}^{5} = {3}^{5} \\ 27(x - 2) = 243 \\ 27x - 54 = 243 \\ 27x = 243 + 54 \\ 27x = 297 \\ \frac{27x}{27} = \frac{297}{27} \\ x = 11\)

To calculate the amount of money a friend's IRA will contain at a given age, we can use the savings plan formula. In this scenario, the IRA has an annual percentage rate (APR) of 7.25%, and monthly deposits of $35 are made.

The objective is to determine the value of the IRA at a specific age. The savings plan formula allows us to calculate the future value of an investment based on regular contributions and a fixed interest rate. Let's break down the information given:

- APR: The IRA has an annual percentage rate of 7.25%, which is the interest rate applied to the account.

- Monthly deposits: A friend makes deposits of $35 per month into the IRA.

- Age: We want to determine the value of the IRA at a specific age.

To calculate the value of the IRA at a given age, we need to consider the time period and the interest earned on the deposits. The savings plan formula is:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value of the IRA

P = Monthly deposit amount ($35)

r = Monthly interest rate (APR divided by 12)

n = Number of months from the start of the IRA until the desired age

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True value received an invoice dated may 08, 2020. the invoice had a $5,800 balance that included $800 freight true value pays the invoice on may 22.  then true value pay amount is $4900

Invoice dated 08/may/2020. Amounting to $5,800 which includes $800 freight.

Terms:

3/10 ; 2/30 ; n/60

The term 3/10 means that True value can avail of 3% discount if it pays within 10 days from date of issuance. The 10th day would be 18/may/2020

The term 2/30 means that True value can avail of 2% discount if it pays from the 11th day up to the 30th day from the date of issuance.

may 22 is beyond the 10th day but within the 30 days discount period. True Value can avail of the 2% discount.

5,800 - 800 = 5,000  The freight can't be subjected to discount thus it is deducted from the total invoice amount.

5,000 * 2% = 100

5,000 - 100 = 4900 amount True Value has to pay.

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a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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To determine if a difference exists in a psychologist's income as a function of residential status (urban vs. rural), the demographer can use the Independent Samples t-test.

The Independent Samples t-test is appropriate when comparing the means of two independent groups. In this case, the demographer has two independent samples: one from psychologists in urban areas and another from psychologists in rural areas.

The test will assess whether there is a statistically significant difference between the mean incomes of psychologists in urban and rural areas. It takes into account the variability within each group and provides a p-value indicating the likelihood of obtaining the observed difference in means by chance.

By conducting an Independent Samples t-test, the demographer can determine if there is evidence to support the hypothesis that residential status has an effect on a psychologist's income.

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Answer:

4x^2\(\sqrt{7x^{2} }\)

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

2. 674

Step-by-step explanation:

6+67+674=747

Answer:

1. 29

2. 674

Step-by-step explanation:

for the second one 6+67+674=747