The triglyceride levels for the residents of an assisted living facility are recorded. The levels are normally distributed with a mean of 200 and a standard deviation of 50. If samples of 100 randomly selected residents are taken and the average triglyceride for the sample is recorded between what two values should 95% of all the sample means fall according to the Empirical Rule?Lower value:Upper value:

The constant in the expression represents that the company earned  85 billion dollars in 2008.

The expression given in the question is known as a quadratic function. A quadratic function is a function that usually has a single variable and it is raised to the power of 2. The graph of a quadratic function is a curve called a parabola. Parabolas may curve upward or downward

An example of a quadratic function is ax² + bx + c

Where: a,b, c are real numbers not equal to zero

c = constant.

The constant in this question is 85. It is the amount earned in 2008

Here are the options:

The company earned  85 billion dollars from 2008 to 2018

The company earned  85 billion dollars in 2008

The company earned 14  billion dollars from 2008 to 2018.

The company earned  14 billion dollars in 2008.

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Answer:

Step-by-step explanation:

Using the formula for calculating the length of an arc to get the angle of Maple Street to Elm Street;

Length of an arc = θ/360 * 2Πr  where r is the radius of the circle.

Given r = 10m and length of the arc = 15m

On substituting;

15 =  θ/360 * 2π(10)

15 = θ/360 * 20π

θ/360 = 15/20π

θ/360  = 0.2387

θ = 360* 0.2387

θ = 85.9°

Hence Maple street is at 85.9° to Elm street.

Answer:

\(\approx \bold{85.98^\circ}\)

Step-by-step explanation:

Given that

Radius of circle = 10 metres

Bryan drives 15 metres around the circle.

To find:

The angle of Maple street to Elm street = ?

Solution:

Kindly refer to the image attached.

The Elm street meets the circle at A.

Maple street at B.

Given that arc length AB = 15m

Radius of circle = 10 m

We have to find the angle of arc.

Let us use the formula:

\(\theta = \dfrac{l}{r}\\\Rightarrow \theta = \dfrac{15}{10} \\\Rightarrow \bold{\theta = 1.5\ radians}\)

Converting to degrees:

\(\pi\ rad = 180^\circ\\1.5\ rad = \dfrac{180}{\pi} \times 1.5^\circ\\\theta \approx \bold{85.98^\circ}\)

Answer:

left side:

Range: For all Y inside of Real, y>= -2

Increasing: (-2, inf) For all x inside of Real

Decreasing:(inf, -2)  For all x inside of Real

Right side:

Range: For all Y inside of Real, y<= 1

Increasing: (-1, inf) For all x inside of Real

Decreasing:(inf, 1)  For all x inside of Real

The solution of the equation is (3, 0).

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b. Basically, there are infinitely many solutions to a linear equation with two variables.

Given:

-x+y=-3....................(1)

3x+3y=9...................(2)

Solving Equation (1) and (2) we get

3x + 3(-3 + x) = 9

3x - 9 + 3x= 9

6x = 18

x= 18/ 6

x= 3

and, y= -3+ x

y= -3 + 3

y= 0

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Answer:

3.89

Step-by-step explanation:

To find the price per quart of the window cleaner, we need to first determine how many quarts the 3-gallon container contains. We can do this by converting the number of gallons to quarts using the conversion factor that 1 gallon is equal to 4 quarts.

3 gallons * 4 quarts/gallon = 12 quarts

Next, we need to divide the total cost of the window cleaner, $46.68, by the number of quarts to find the price per quart.

Price per quart = $46.68 / 12 quarts = $3.89/quart

Therefore, the price per quart of the window cleaner is $3.89.

Answer:

350 adult tickets were sold.

Step-by-step explanation:

let x = number of adult tickets

number of student tickets -> x-71

x - 71 + x = 629

2x - 71 = 629

2x = 700

x = 350

Answer:0.0041617435341797

Step-by-step explanation:

j

the probability that exactly 1 out of 10 randomly chosen people favor the new building project is approximately 0.2791, or 27.91%.

To calculate the probability that exactly 1 out of 10 randomly chosen people favor the new building project, we can use the binomial probability formula.

The formula for calculating the probability of getting exactly k successes in n trials, each with a probability of success p, is:

P(X = k) = C(n, k) * \(p^k * (1 - p)^{(n - k)\)

In this case, n = 10 (number of trials), k = 1 (number of successes), and p = 0.55 (probability of success).

Using the binomial coefficient formula C(n, k) = n! / (k!(n - k)!), we can calculate the probability:

P(X = 1) = C(10, 1) * (0.55)¹ * (1 - 0.55)⁽¹⁰⁻¹⁾

P(X = 1) = 10 * (0.55)¹ * (0.45)⁹

P(X = 1) ≈ 0.2791

Therefore, the probability that exactly 1 out of 10 randomly chosen people favor the new building project is approximately 0.2791, or 27.91%.

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In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

The median, a statistician's measure of central tendency, divides a dataset into two equally sized half. When the data is organized from smallest to largest, it is the midway value (or largest to smallest). The median is the average of the two middle values when there are an even number of values. Since it is unaffected by extreme values, the median is frequently employed as a measure of central tendency when a dataset contains outliers or is skewed.

given

None of the claims are untrue.

The mean will be greater than the median if a density curve is tilted to the right.

The mean and median are equal in a density curve that is symmetric.

In a skewed distribution, the long tail pulls the mean toward it. In a density curve, the median is where everything level out.

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Answer:

only C is a function cause a function has only 1 same value.

For a catering company, which used the linear function for calculating the total cost of parties, the cost to cater a dinner party with 90 guests is equals to the $42750.

We have a table form data of total cost of parties for a catering company. There is use of linear function to determine total cost of parties. Table look like as below,

Cost for dinner parties | number of guests

(each guest)

$315 30

$555 60

We have to determine the cost to cater a dinner party with 90 guests. For this we use simple multiplication arithmetic method. As we see in table, cost of cater a dinner party with 30 guests = $315 for each , that is cost for one guest = $315

so, cost of cater a dinner party with 30 guests = 30 × $315 = $ 9450

Similarly, when number of guests is 60 in count, cost of cater a dinner party = $555 for each one

So, total cost of cater a dinner party with 60 guests = 60× $555 = $ 33300

Now, we have total guest = 90

The cost to cater a dinner party with 90 guests

= cost to cater a dinner party with 30 guests + cost to cater a dinner party with 60 guests = $9450+ $33300

= $42750

Hence, required value is $42750.

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Answer:

First, convert minutes and seconds to their degree equivalents and add the results. 25'/60 = 0.4167° 30"/3600 = .0083° ...

Then, add this number to the number of degrees. 39° + 0.425° = 39.425°

So, the final result is: 39° 25' 30" = 39.425°

Step-by-step explanation:

HOPE IT HELPSSS

Answer:

x=1

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

If b = 9, just substitute it into the expression.

4 + (9)

= 13

At t = 2, the velocity is 78 units per time and the acceleration is 74 units per time squared.

To find the velocity and acceleration at a given time, we need to differentiate the position function with respect to time. Given the position function s(t) = 5t^3 + 4t^2 + 2t + 8, we can find the velocity and acceleration by taking the first and second derivatives, respectively.

Taking the derivative of s(t), we have v(t) = 15t^2 + 8t + 2.

To find the velocity at t = 2, we substitute t = 2 into the velocity function:

v(2) = 15(2)^2 + 8(2) + 2 = 78 units per time.

Taking the derivative of v(t), we have a(t) = 30t + 8.

To find the acceleration at t = 2, we substitute t = 2 into the acceleration function:

a(2) = 30(2) + 8 = 74 units per time squared.

Therefore, at t = 2, the velocity is 78 units per time and the acceleration is 74 units per time squared.

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Answer:

x=-3

Step-by-step explanation:

I have a formula

The solution to the equation 3(x + 5) = 30 ÷ 5 is x = -3.

Given that the equation 3(x + 5) = 30 ÷ 5

In the order of operations (PEMDAS/BODMAS), the following steps are given:

Parentheses: There are no parentheses in the expression, so move to the next step.

Exponents: There are no exponents in the expression.

Multiplication and Division: Perform multiplication and division from left to right.

4 × 2 = 8

6 ÷ 3 = 2

After performing the multiplication and division, the expression becomes: 3 + 8 - 2

Addition and Subtraction: Perform addition and subtraction from left to right.

3 + 8 = 11

11 - 2 = 9

Thus, the simplified value of the expression 3 + 4 × 2 - 6 ÷ 3 is 9.

To solve the equation , follow the order of operations (PEMDAS) and simplify both sides step by step.

Let start with the left side of the equation:

3(x + 5)

Using the distributive property, multiply 3 by each term inside the parentheses:

3x + 3 x 5

3x + 15

Now the equation becomes:

3x + 15 = 30 ÷ 5

Next, simplify the right side of the equation:

30 ÷ 5 = 6

Substituting the simplified value, the equation becomes:

3x + 15 = 6

To isolate the variable x, subtract 15 from both sides of the equation:

3x + 15 - 15 = 6 - 15

This simplifies to:

3x = -9

Finally, divide both sides of the equation by 3 to solve for x:

(3x) / 3 = (-9) / 3

This gives :

x = -3

Therefore, the solution to the equation 3(x + 5) = 30 ÷ 5 is x = -3.

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Answer:

There are several steps to this problem, but they are easy steps .  First, determine how many ounces are in one recipe by adding all the ounces of the ingredients together:  8 + 5 + 2 + 3 = 18.

Now multiply that amount by 4, because she made 4 batches:  

18 x 4 = 72

Finally, divide the total amount by 3, because she put it in three bags.  72/3 = 24

To test whether the grades in the instructor's classes are not distributed as claimed, we can conduct a chi-square goodness-of-fit test.

The null hypothesis (H0) states that the observed grade distribution in the sample is consistent with the claimed distribution by the instructor. The alternative hypothesis (Ha) states that the observed grade distribution is not consistent with the claimed distribution.

The expected frequencies for each grade category can be calculated by multiplying the sample size (200, obtained by summing the frequencies) by the claimed proportions: A-40, B-50, C-80, D-20, F-10.

Next, we calculate the chi-square test statistic, which is the sum of the squared differences between the observed and expected frequencies divided by the expected frequencies. The formula is: chi-square = Σ(\((observed - expected)^2 / expected).\)

Plugging in the values, we obtain: chi-square = \(((31-40)^2/40) + ((68-50)^2/50) + ((80-80)^2/80) + ((7-20)^2/20) + ((14-10)^2/10) = 7.38.\)

With four degrees of freedom (number of grade categories - 1), we can compare the calculated chi-square value to the critical chi-square value at a significance level of choice. Assuming a significance level of 0.05, the critical chi-square value is approximately 9.488.

Since the calculated chi-square value (7.38) is less than the critical chi-square value (9.488), we fail to reject the null hypothesis. Therefore, based on the sample data, we do not have sufficient evidence to prove that the grades in the instructor's classes are not distributed as claimed.

In conclusion, we do not have enough evidence to reject the claim made by the instructor regarding the grade distribution in their classes. The observed grade distribution in the sample is consistent with the claimed distribution.

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The appropriate way to state the conclusion of the given statement is:

The results of the statistical test suggest that women have a shorter mean nose length than men (p = 0.04, α = 0.05).

Given:

A null hypothesis is that the mean nose lengths of men and women are the same.

The alternative hypothesis is that women have a shorter mean nose length than men.

Alpha for the problem is.05.

A statistical test is done and the p-value is 0.04.

Hence based on the condition we frame it as:

The results of the statistical test suggest that women have a shorter mean nose length than men (p = 0.04, α = 0.05).

Hence we get the required answer,

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The investment's expected return is 5.95%.

The expected return of an investment is calculated by multiplying the probabilities of each possible return by their respective returns and summing them up. In this case, Gautney Enterprises has provided the probabilities and returns for the investment. By applying the formula, we find that the expected return is 5.95%.

To calculate the standard deviation, we need to determine the variance first. The variance is computed by taking the difference between each possible return and the expected return, squaring those differences, multiplying them by their respective probabilities, and summing them up. Once we have the variance, the standard deviation is simply the square root of the variance. The standard deviation measures the degree of risk associated with an investment.

In this scenario, the expected return of the investment is 5.95%, but we need to consider the standard deviation as well to assess the risk. If the standard deviation is high, it indicates a greater level of uncertainty and potential volatility in returns. A low standard deviation implies a more stable investment.

Without the specific values for each return and their respective probabilities, we cannot calculate the exact standard deviation. However, Gautney Enterprises should compare the calculated expected return and the associated standard deviation to their risk tolerance and investment objectives. If the expected return meets their desired level of return and the standard deviation aligns with their risk appetite, they may consider investing in this security.

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Answer:

Step-by-step explanation:

hmmm

Answer:

Height of cone is 5m

Step-by-step explanation:

To solve a system of linear equations graphically we graph both equations in the same coordinate system. The solution to the system will be in the point where the two lines intersect. The two lines intersect in (-3, -4) which is the solution to this system of equations.

Answer:

equation: y=2x+3

graph with points:

Answer:

Step-by-step explanation:

y = 2x - 3

The answers to be dragged in red box are 30 units², 105.5 units² and 36.1 units² respectively and the answers to be dragged in orange box are 190 units³, 2170 units³ and 386.1 units³ respectively.

Step-by-step explanation:

The area of base of prism is literally the area of the base part of the prism. In this case, its a triangular prism so its base is a Triangle. You can find base area of 1st figure by using 1/2 ×perpendicular×base of right angled triangle whereas on 2nd and 3rd figure you can use 1/2 ×height×base of Triangle.

The volume of Prism is given by base area ×height of the prism, so you can easily find it.

Hope it was helpful and i apologize for my English because I am not a native speaker of English.

The tank will be filled in 6 minutes with the new pipes.

Let the capacity of the tank be C.

Then the rate at which the first pipe can fill the tank is C/12 per minute, and the rate at which the second pipe can fill the tank is C/15 per minute.

If the first pipe is changed with a pipe having twice of its radius, then the rate at which the new pipe can fill the tank is (2C)/12 = C/6 per minute.

If the second pipe is changed with a pipe having half of second’s radius, then the rate at which the new pipe can fill the tank is (1/2)C/15 = C/30 per minute.

Let t be the number of minutes it takes to fill the tank with the new pipes. Then we have:

(C/6 + C/30)t = C

Simplifying this equation, we get:

5Ct/30 = C

Multiplying both sides by 30/5C, we get:

t = 6 minutes

Therefore, the tank will be filled in 6 minutes with the new pipes.

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Answer:

b ≈ 25.7, C ≈ 24.2, A ≈ 119.8

Step-by-step explanation:

b² = a² + c² - 2ac·cos(B)

b² = 38² + 18² -2·38·18·cos(36°) ≈ 661.26475

b ≈ 25.715

sin(C)/c = sin(B)/b

C = arcsin(c/b·sin(B)) ≈ 24.29515°

∠A can be found as 180° - ∠B - ∠C

A = arcsin(a/b·sin(B)) ≈ 119.70485°

True, a researcher wants to compare performance scores for men versus women on a motor skills task. it would not be possible to use a repeated measures design for this study.

What is a performance comparison?

They are frequently used while benchmarking, which is the practice of evaluating an organization's performance versus that of the best-performing businesses.

                 The measures are employed in productivity improvement projects to monitor changes in productivity over time.

Why is performance measurement important?

Comparing is one of the most important growth drivers. Only when we contrast our development with that of our rivals or our current performance with our former performance do we get motivated to advance and accomplish greater feats.

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Answer:

\(m^{21}\)

Step-by-step explanation:

\((\frac{m^{13} }{m^{20}})^{-3} = (\frac{1}{m^7})^{-3}=(m^{-7})^{-3}=m^{(-7)*(-3)}=m^{21}\)

Answer:

( x + 4)^2

Step-by-step explanation:

x^2 + 8x + 7 + 9

x^2 + 8x + 16

(x + 4)( x + 4) = ( x + 4)^2

The coordinates of the point q on the segment with endpoints a (2, −1) and c (4, 2) which partitions the segment in a 4:1 ratio. are (2, 7/5).

We can solve this question by using the section formula, which states that if we have a line segment with endpoints (x1, y1) and (x2, y2) and we want to find a point on the segment that divides it in the ratio of m:n, then the coordinates of the point can be found using the following formula:

q(x,y) = ((mx2 + nx1) / (m + n), (my2 + ny1) / (m + n))

In our case,

m=4, n=1

x1=2, x2=4

y1=-1 ,y2=2

By using the given values in the formula mentioned above, we get the coordinates of q as:

q(x,y)=( [4*4+1*2]/5 ,[4*2+1*-1]/5 )

q(x,y)=( 18/5), (7/5)

So the x coordinate of q is: 18/5

the y coordinate of q is: 7/5

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