Another weird looking question. Someone help please

Another Weird Looking Question. Someone Help Please

Answers

Answer 1

The measure of the angle m∠CBD between points CD is equal to 495°°

How to evaluate for the angle m∠CBD

From the question, we observe that the larger angle between AD consists of the two angles between m∠ABC and m∠CBD, so we shall sum the two small angles and equate the result to the larger angle m∠ABD to solve for the value of x as follows:

7x - 9 + 6x + 27 = 96

x + 18 = 96

x = 96 - 18 {collect like terms}

x = 78

put the value of x in m∠CBD;

m∠CBD = 6(78) + 27

m∠CBD = 495

In conclusion, the measure of the angle m∠CBD between points CD is equal to 495°

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Related Questions

Rectangle ABCD has consecutive vertices
A(3, 1), B(3, 7). C(6, 7), and D(6, 1). (Lesson 4)
A. What are the lengths of the sides of the
rectangle?
B. What is the perimeter of the rectangle?

Answers

The side lengths are 6 units by 3 units and the perimeter is 18 units

What are the lengths of the sides of the rectangle?

From the question, we have the following parameters that can be used in our computation:

Rectangle ABCD has consecutive vertices

A(3, 1), B(3, 7). C(6, 7), and D(6, 1).

The lengths of the rectangles are

AB, BC. CD and DA

Since the vertices share the same x or y coordinate, then we have

AB = 7 - 1 = 6

BC = 6 - 3 = 3

So, the side lengths are 6 units by 3 units

What is the perimeter of the rectangle?

This is calculated as

P = sum of the side lengyhs

So, we have

P =2 * (6 + 3)

Evaluate

P = 18

Hence, the perimeter is 18 units

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Which best describes the conditions on integer coefficients a, b, m, and n for the sum of ax^2+b and mx^2+nx to be linear?

Answers

In summary, for the sum of ax^2 + b and mx^2 + nx to be linear, either both x^2 terms should be zero or equal, or both x terms should be zero or equal.

For the sum of ax^2 + b and mx^2 + nx to be linear, the conditions on the integer coefficients a, b, m, and n are:

The coefficients of x^2 terms (a and m) must be zero or equal to each other.

If a = 0 and m = 0, both terms become constant terms (b and n), resulting in a linear expression.

If a = m, the x^2 terms cancel out, leaving only the linear term.

The coefficients of the x terms (b and n) must be zero or equal to each other.

If b = 0 and n = 0, both terms become x^2 terms (ax^2 and mx^2), resulting in a quadratic expression.

If b = n, the x terms cancel out, leaving only the x^2 terms.

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Write an equivalent fraction for
2/6
that has a numerator of 3.

Answers

Answer:

3/9

Step-by-step explanation:

2/6 divided by 2 = 1/3

So, 2/6 times 2 = 2/9

PLS MARK BRAINLIEST...thx

According to a survey conducted by the "Internet & Life Project" (May, 2010), 20% of Internet users go online at home using a wireless network. In a random sample of 200 Internet users, let x be the number who go online at home using a wireless network.
a) Explain why x is a binomial random variable. b) Find the probability that her age will be less than 35 years. c) Find the probability that her age will exceed 40 years. d) Find the approximate probability that the number of Internet users who go online at home using a wireless network in a sample of 200 is less than or equal to 50.

Answers

The probability that the number of Internet users who go online at home using a wireless network in a sample of 200 is less than or equal to 50 is approximately 0.9616.


a) x is a binomial random variable because it meets the following criteria:
1. There are a fixed number of trials (n = 200 Internet users in this case).
2. There are only two possible outcomes for each trial (either a user goes online at home using a wireless network or they do not).
3. The probability of success (p = 0.20) remains constant for each trial.
4. The trials are independent, meaning the outcome of one trial does not affect the outcome of any other trial.

b) The question about age seems unrelated to the provided information about Internet users and wireless networks. Please provide more context or information about the age distribution to answer this part.

c) Similar to part (b), we need more information about the age distribution to answer this part.

d) To find the approximate probability that the number of Internet users who go online at home using a wireless network in a sample of 200 is less than or equal to 50, we can use the binomial formula or the normal approximation:

Binomial formula: P(X ≤ 50) = Σ [C(n, k) * p^k * (1-p)^(n-k)] for k = 0 to 50, where n = 200, p = 0.20, and C(n, k) is the number of combinations of n items taken k at a time.

Normal approximation:
1. Calculate the mean (μ) and standard deviation (σ) of the binomial distribution:
  μ = n * p = 200 * 0.20 = 40
  σ = √(n * p * (1-p)) = √(200 * 0.20 * 0.80) ≈ 5.6568
2. Convert the given value (50) to a z-score:
  z = (X - μ) / σ = (50 - 40) / 5.6568 ≈ 1.7678
3. Use a standard normal table or calculator to find the area to the left of the z-score:
  P(Z ≤ 1.7678) ≈ 0.9616

Using the normal approximation, the probability that the number of Internet users who go online at home using a wireless network in a sample of 200 is less than or equal to 50 is approximately 0.9616. Note that this is an approximation, and the exact value can be calculated using the binomial formula.

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It takes Carrie 585858 minutes to get home. If Carrie leaves for home at 1{:}321:321, colon, 32, what time will she arrive?

Answers

Carrie will arrive at home at 4:02 PM on the same day she leaves.

To determine the time Carrie will arrive, we need to add the number of minutes it takes her to get home to her departure time.

Carrie leaves for home at 1:32 PM. To convert this time to minutes, we multiply the hours (1) by 60 and add the minutes (32). This gives us a total of 92 minutes.

Next, we add the 58,858 minutes it takes Carrie to get home to the departure time of 92 minutes:

92 minutes + 58,858 minutes = 58,950 minutes.

Now, we need to convert the total minutes back to hours and minutes. Since there are 60 minutes in an hour, we divide 58,950 by 60:

58,950 minutes ÷ 60 = 982.5 hours.

The decimal part represents the remaining minutes. To convert this decimal to minutes, we multiply it by 60:

0.5 (decimal part) × 60 = 30 minutes.

Therefore, Carrie will arrive at 982 hours and 30 minutes after her departure time.

To convert this back to a 12-hour clock format, we divide 982 by 12, which gives us a quotient of 81 with a remainder of 2. This means Carrie will arrive 81 days after her departure time, with an additional 2 hours and 30 minutes.

As for the exact time she will arrive on the day she leaves, we need to add the 2 hours and 30 minutes to her departure time:

1:32 PM + 2 hours and 30 minutes = 3:62 PM.

However, since we are using a 12-hour clock format, we need to adjust the time to the correct format:

3:62 PM can be rewritten as 4:02 PM.

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write (-5⁵)² as a single power

Answers

Answer:

-5¹⁰

Step-by-step explanation:

(-5⁵)² = -5⁵ˣ² = -5¹⁰ = 9,765,625

What is the value of the expression 2344+835

Answers

The expression 2344 + 835 has a value of 3179 when evaluated because it is the result of adding the numbers

Evaluating the expression 2344+835

From the question, we have the following parameters that can be used in our computation:

2344 + 835

The above statement is a summation expression that adds the values of 2344 and 835

Also, there is a need to check if there are like terms in the expression or not

This is because we are adding the terms

So, we have

2344 + 835 = 3179

This means that the value of the expression is 3179 i.e the result of adding the numbers

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Complete the table below to prove the solution to the given equation. (* Complexity Level 3)
(4x + 12) = 6(x + 7)
Statement
(4x + 12) = 6(x + 7)
6 = 4x + 42
m = -9
Justification of Steps
Given
Distributive Property
Division Property of Equality

Answers

The complete table to prove the solution to the given equation is shown below.

Given that;

Expression is,

1/2 (4x + 12) = 6 (x + 7)

Now, We can simplify as;

1/2 (4x + 12) = 6 (x + 7)

(Given)

2x + 6 = 6x + 42

(By distribution property)

6 = 6x - 2x + 42

6 = 4x + 42

(Subtract 2x both side)

6 - 42 = 4x

4x = - 36

x = - 9

(By division property of equality)

Thus, The complete table to prove the solution to the given equation is shown

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Suppose A and B are sets. Describe the conditions under which the following statement would be true. AUB = A

Answers

The statement AUB = A is true if and only if set B is a subset of set A.

Describe the conditions for AUB = A.

To see why this is the case, we can use the definition of set union. Recall that AUB is the set of all elements that belong to either A or B (or both). So, if AUB = A, every element in B must also be in A (since all elements in AUB are also in A). Therefore, B is a subset of A.

In summary, AUB = A is true if and only if every element in B is also in A, which means that B is a subset of A.

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27. Find the distance between the pair of points. Round to the nearest tenth is necessary. (-13, -8) and (6, 17)

Answers

The distance between the given points is 31.4 units.

Given are two points (-13, -8) and (6, 17) we need to find the distance between them,

We know that the distance between two points is given by =

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here,

(x₁, y₁) and (x₂, y₂) are (-13, -8) and (6, 17),

So,

[tex]D = \sqrt{(6+13)^2+(17+8)^2}\\\\D = \sqrt{19^2+25^2}\\\\D = \sqrt{986}[/tex]

D = 31.4

Hence the distance between the given points is 31.4 units.

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PLEASE HELP ME I WILL GIVE 36 POINTS PLEASE RIGHT ANSWER FIRST RIGHT ANSWER GETS THE 36 POINTS AND BRAINLIESET!

Answers

Answer

[tex]592in^{2}[/tex]

Step-by-step explanation:

A=2(wl+hl+hw)

2·(10·8+12·8+12·10)

=592

Answer: 592

Step-by-step explanation:

so A = 2 (wl+hl+hw)

Then what we will do next is do 2·(10·8+12·8+12·10)

which will give us 592 and that is our answer.

I hope this helps!

| x | < 4 and x is an integer. Find the smallest possible value of x

Answers

The lowest integer value of x that fulfills the given inequality is -3.

If |x| < 4, then we know that x must be between -4 and 4, but not including -4 and 4.

Since x is also an integer, the smallest possible value of x that satisfies this condition is -3.

To see why, consider that the next smallest integer after -3 is -4, which is not allowed since it violates the inequality |x| < 4. Similarly, the next smallest integer before -3 is -5, which is also not allowed.

Therefore,  -3 is the smallest possible value of x that satisfies the given inequality and is an integer.

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What is 4 1/2 minus 2 2/6?

Answers

Answer:[tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

It is 2 1/6

2+1/6
= 2 1/6

A teacher selects two different numbers, pand q, and states that p+q=0.
Which statement could be true about these two numbers?
a. Both numbers are positive.
b. Both numbers are negative.
One number is zero and the other number is positive.
d. One number is positive and the other number is negative.

Answers

Answer: D

Step-by-step explanation:


-10
ious Activity
Type har
-5
10+y
O
-10
-20
5
Select the quadratic inequality that represen
graph.
Ov²(x+3)²-24
vs-(x-3)²+24
v2 - (x-3)2+24
Oys (x+3)²-24
O

Answers

The quadratic inequality defined on the graph is given as follows:

y ≥ 2/3(x + 3)² - 24.

How to define the quadratic inequality?

The coordinates of the vertex of the quadratic function are given as follows:

(-3, -24).

Hence the quadratic function is given as follows:

y = a(x + 3)² - 24.

In which a is the leading coefficient.

When x = 3, y = 0, hence the leading coefficient a is obtained as follows:

0 = a(3 + 3)² - 24

36a = 24

a = 24/36

a = 2/3.

Hence:

y = 2/3(x + 3)² - 24.

The quadratic function has a solid curve, and the values above it are pained, hence the inequality is given as follows:

y ≥ 2/3(x + 3)² - 24.

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The focus of a parabola is (3, −7) and the directrix is y=−4.

What is an equation of the parabola?

Responses

(x−3)2=−3(y+10)
open parenthesis x minus 3 close parenthesis squared equals negative 3 open parenthesis y plus 10 close parenthesis

(x−3)2=−1.5(y+5.5)
open parenthesis x minus 3 close parenthesis squared equals negative 1.5 open parenthesis y plus 5.5 close parenthesis

(x−3)2=−12(y+10)
open parenthesis x minus 3 close parenthesis squared equals negative 12 open parenthesis y plus 10 close parenthesis

(x−3)2=−6(y+5.5)

Answers

The equation of the parabola is (x-3)² = -4(y+4)

Given data ,

Let the equation of the parabola be represented as A

Now , the value of A is

The focus of the parabola is F ( 3 , -7 )

Let the directrix is y = -3

And , y = a ( x - h )² + k

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

(x-3)² = -4y - 16

Multiplying both sides by -1/4, we get:

-(1/4)(x-3)² = y + 4

Subtracting 4 from both sides, we get:

-(1/4)(x-3)² - 4 = y

So the equation of the parabola with focus (3,-7) and directrix y=-4 is:

y = -(1/4)(x-3)² - 4, which is equivalent to (x-3)² = -4(y+4)

Hence , the equation is (x-3)² = -4(y+4)

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the only calculated fields you can create in access are those involving addition and subtraction. True or false?

Answers

Answer:

false

Step-by-step explanation:

False.

Access supports a wide range of built-in functions and operators that can be used to create calculated fields. These functions and operators include mathematical functions (such as multiplication, division, exponentiation), string functions (such as concatenation, trimming, and formatting), date and time functions, aggregate functions (such as sum, average, count), and more.

In addition, Access also allows you to create user-defined functions using VBA (Visual Basic for Applications), which can be used to perform custom calculations on your data.

Therefore, the statement "the only calculated fields you can create in Access are those involving addition and subtraction" is false.

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Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of ....

Answers

Using the multiplication rule, the joint probability of event A and event B is computed by multiplying the conditional probability of event A given event B by the probability of event B.

Mathematically, it can be represented as P(A and B) = P(A|B) × P(B), where P(A|B) is the conditional probability of A given B, and P(B) is the probability of B.

In other words, the multiplication rule is used to compute the probability of two events occurring together, given the probability of one event occurring and the probability of the other event occurring given the first has occurred. This rule is widely used in probability and statistics to calculate the probability of complex events, especially in cases where events are not mutually exclusive.

For example, consider a scenario where we want to calculate the probability of getting two heads when flipping two coins. Using the multiplication rule, we can calculate this probability as follows: P(Two heads) = P(Head on first flip) × P(Head on second flip given the first flip was a head) = (1/2) × (1/2) = 1/4.

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For which distribution shape is it usually appropriate to use the median when summarizing the data?

Answers

The median is usually appropriate to use when summarizing data for distributions with skewed or asymmetric shapes.

The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median.

These distributions include the positively skewed (right-skewed) distribution and the negatively skewed (left-skewed) distribution. In such cases, the median provides a more robust measure of central tendency than the mean, which may be influenced by extreme values in the tails of the distribution.

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When blenders are sold for p dollars apiece, local consumers will buy D(p)= 7225/(3p+13) blenders. It is estimated t months from now, the unit price of the blenders will be p(t)=1/12*t^1.5+6 dollars. What is the rate of change of the monthly demand for blenders with respect to time 3 years from now.

Answers

Answer:

the rate of change of the monthly demand for blenders with respect to time 3 years from now is approximately -0.0429 blenders per month.

Step-by-step explanation:

To find the rate of change of the monthly demand for blenders with respect to time 3 years from now, we will first need to find an expression for D(p(t)), which represents the demand for blenders as a function of time.

Given the unit price of the blenders, p(t) = 1/12 * t^1.5 + 6, we need to substitute this expression into the demand function D(p):

D(p(t)) = 7225 / (3 * (1/12 * t^1.5 + 6) + 13)

Now, we want to find the rate of change of the demand with respect to time, which is the derivative of D(p(t)) with respect to t. Let's denote this as dD/dt:

dD/dt = d(D(p(t)))/dt

To find the derivative, we can use the chain rule, which states that if we have a function of a function, like D(p(t)), then the derivative is the derivative of the outer function times the derivative of the inner function. In this case, the outer function is D(p) and the inner function is p(t).

Let's first find the derivative of the inner function, p(t), with respect to t:

dp/dt = d(1/12 * t^1.5 + 6)/dt = (1/12) * d(t^1.5)/dt = (1/12) * 1.5 * t^0.5

Now, we need to find the derivative of the outer function, D(p), with respect to p:

dD/dp = d(7225 / (3p + 13))/dp

To find this derivative, we can use the quotient rule, which states that if we have a function in the form of f(x) = u(x) / v(x), then the derivative of f(x) with respect to x is:

df/dx = (v * du/dx - u * dv/dx) / v^2

Applying the quotient rule to D(p):

u(p) = 7225

v(p) = 3p + 13

du/dp = 0 (since 7225 is a constant)

dv/dp = 3

Using the quotient rule:

dD/dp = ((3p + 13) * 0 - 7225 * 3) / (3p + 13)^2 = -21675 / (3p + 13)^2

Now, we can find dD/dt using the chain rule:

dD/dt = dD/dp * dp/dt = (-21675 / (3p + 13)^2) * (1.5 * t^0.5 / 12)

We are asked to find the rate of change of the monthly demand for blenders with respect to time 3 years from now. Since there are 12 months in a year, 3 years is equal to 3 * 12 = 36 months. Therefore, we want to find dD/dt when t = 36:

dD/dt(36) = (-21675 / (3 * (1/12 * 36^1.5 + 6) + 13)^2) * (1.5 * 36^0.5 / 12)

To find the numerical value, use a calculator:

dD/dt(36) ≈ -0.0429

So, the rate of change of the monthly demand for blenders with respect to time 3 years from now is approximately -0.0429 blenders per month.

Tiffany is buying a $165,000 house. What is the closing cost range?

A) 2% of the purchase price? B) 7% of the purchase price?

Answers

If the closing cost is 7% of the purchase price, then the cost for Tiffany's $165,000 house would be approximately $11,550.

To find the closing cost range for Tiffany's $165,000 house, we can use the given percentages of the purchase price.

A) If the closing cost is 2% of the purchase price, then we can find it as:

Closing cost = 2% of $165,000

Closing cost = 0.02 x $165,000

Closing cost = $3,300

Therefore, if the closing cost is 2% of the purchase price, then the cost for Tiffany's $165,000 house would be approximately $3,300.

B) If the closing cost is 7% of the purchase price, then we can find it as:

Closing cost = 7% of $165,000

Closing cost = 0.07 x $165,000

Closing cost = $11,550

Therefore, if the closing cost is 7% of the purchase price, then the cost for Tiffany's $165,000 house would be approximately $11,550.

So, the closing cost range for Tiffany's $165,000 house is between approximately $3,300 (if the closing cost is 2% of the purchase price) and $11,550 (if the closing cost is 7% of the purchase price).

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Peter sent out a total of 150 envelopes. Some required a 44-cent stamp. the rest required 61-cents postage. If his total package cost was $74.50, determine how many envelopes were sent at each postage rate.

Answers

Answer:

Let's start by assigning variables to the unknowns in the problem. Let x be the number of envelopes that required a 44-cent stamp and y be the number of envelopes that required a 61-cent stamp. We know that the total number of envelopes is 150, so we can write an equation:

x + y = 150

We also know the cost of each type of envelope. If we multiply the number of envelopes by the cost per envelope, we should get the total cost of postage. Using this logic, we can write another equation:

0.44x + 0.61y = 74.50

Now we have two equations with two unknowns. We can solve this system of equations using substitution or elimination. Let's use substitution. Solve the first equation for x:

x = 150 - y

Now substitute this expression for x in the second equation:

0.44(150 - y) + 0.61y = 74.50

Simplify and solve for y:

66 - 0.44y + 0.61y = 74.50

0.17y = 8.50

y = 50

Now that we know y, we can substitute it back into either of the original equations to find x:

x + 50 = 150

x = 100

Therefore, Peter sent 100 envelopes that required a 44-cent stamp and 50 envelopes that required a 61-cent stamp.

Step-by-step explanation:

Let's call the number of envelopes that required a 44-cent stamp "x". Then the number of envelopes that required 61-cents postage is "150 - x".

The total cost of the 44-cent envelopes would be 0.44x, and the total cost of the 61-cent envelopes would be 0.61(150 - x).

We know that the total package cost was $74.50, so we can set up the equation:

0.44x + 0.61(150 - x) = 74.50

Simplifying and solving for x:

0.44x + 91.5 - 0.61x = 74.50
-0.17x = -17
x = 100

So Peter sent out 100 envelopes that required a 44-cent stamp, and 150 - 100 = 50 envelopes that required 61-cents postage.

Choose the symbol that makes the statement true. 1,217 ___ 700 + 417

Answers

The symbol ">" would make the statement true:

1,217 > 700 + 417

The statement "1,217 ___ 700 + 417" is asking us to choose a symbol that represents the relationship between the two values: 1,217 and 700 + 417.

The expression 700 + 417 represents the sum of two numbers: 700 and 417. Evaluating this expression gives us 1,117. So, the statement is essentially asking us to compare the value 1,217 to 1,117 using a symbol that represents the relationship between them.

In this case, we need to choose a symbol that represents "greater than", because 1,217 is greater than 1,117. The symbol ">" is commonly used to represent "greater than", so we can write:

1,217 > 700 + 417

This statement is true because 1,217 is indeed greater than 1,117.

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PLEASE HELP ITS DUE SOON!! For babysitting, nicole charges a flat fee of $10, plus $7 per hour. Write an equation that represents the amount of money nicole makes each time she babysits. How much money will she make if she babysits for 6 hours?

Answers

Answer:

[tex]t = 10 + 7x[/tex]

t = total

x = hours

t = 10 + 7(6)

t = 10 + 42

t = 52

If Nicole babysits for 6 hours, she will earn 52 dollars.

Find the solution(s) to the system of equations. Select all that apply.

A. (0,-3)

B. (-1,0)

C. (3,0)

D. (4,5)

Answers

Answer:

A

Step-by-step explanation:

it should be A


XYZ Corp. has filled 100,000 purchase orders during its existence. 1,100 of the purchase orders have had errors. Using an empirical probability, the probability of the next purchase order having an error is __________ (round your answer to three decimal places and enter as a probability not a percentage)"

Answers

Using an empirical probability, the probability of the next purchase order having an error is 0.011, or 1.1%

To find the empirical probability of the next purchase order having an error at XYZ Corp.,
- Determine the total number of purchase orders: 100,000
-Identify the number of purchase orders with errors: 1,100
-Calculate the probability by dividing the number of errors by the total number of purchase orders.

-So, the probability of the next purchase order having an error is:
[tex]\frac{1100}{100000} = 0.011[/tex]
-Rounding to three decimal places, the empirical probability is 0.011, or 1.1% as a percentage.

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Can someone help me with the picture?

Answers

The terms on quartiles, when matched with their definition would be:

the middle value when data values are listed in order - medianthe middle value of the lower half of the data when data values are listed in order - lower quartilethe middle value of the upper half of the data when data values are listed in order upper quartile

What are the quartiles ?

The division of a dataset into two precisely even halves can be achieved through the use of the median, which essentially serves as a separator accompanied by an equal number of values on either side: below and above.

The first quartile (Q1), also recognized as the lower quartile, is situated in the middle position of the submedian half of the data; it divides that specific section equally as well. Correspondingly, the uppermost mid-positioned value located within the other discriminate half of the given data is fittingly titled the third quartile, or Q3.

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The spirit club buys shirts in bulk for $8 each. They mark up the shirt 75% to sell in the school store. At the end of the year, they sell the shirts for 25% off. How much profit does the spirit club make on each shirt sold at the end of the year?

Answers

The cost price of each shirt is; $8.

They mark up the shirts 25%, that means they increase the price by (25/100) $8 = $2.

So, the selling price of each shirt;

$8 + $2 = $10.

At the end of the year, they sell the shirts for 25% off, that means they reduce the price by (25/100) $10 = $2.50.

Therefore, the selling price of each shirt after the discount, $10 - $2.50 = $7.50.

The profit made on each shirt sold at the end of the year is the difference between the selling price and the cost price, is;

$7.50 - $8 = -$0.50.

Since the profit is negative, it means that the Spirit Club is making a loss of $0.50 on each shirt sold at the end of the year.

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Given the size of pizzas in a pizza restaurant is normally distributed. The average size is 9 inches, and standard deviation is 0.8 inches. What is the probability that 4 randomly selected pizza is smaller than 9.5 inches

Answers

The probability that 4 randomly selected pizzas are all smaller than 9.5 inches is approximately 0.284, or 28.4%.

To solve this problem, we first need to standardize the variable using the formula:
z = (x - μ) / σ
where:
x = 9.5 inches (the cutoff for being considered "smaller")
μ = 9 inches (the mean)
σ = 0.8 inches (the standard deviation)
z = (9.5 - 9) / 0.8 = 0.625
Next, we need to find the probability that a randomly selected pizza is smaller than 9.5 inches using a standard normal distribution table or calculator.

This probability can be denoted as P(Z < 0.625), where Z is a standard normal random variable.
The probability that all 4 randomly selected pizzas are smaller than 9.5 inches, we will raise the probability to the power of 4:

Probability = 0.734 ≈ 0.291 So, the probability that 4 randomly selected pizzas are smaller than 9.5 inches is approximately 0.291 or 29.1%.
Using a standard normal distribution table or calculator, we can find that P(Z < 0.625) is approximately 0.734.

This means that the probability of a randomly selected pizza being smaller than 9.5 inches is 0.734.
To find the probability that 4 randomly selected pizzas are all smaller than 9.5 inches, we need to multiply this probability by itself four times, since the selection of each pizza is independent of the others.

This gives:
P(4 pizzas smaller than 9.5 inches) = 0.734 = 0.284
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The probability that 4 randomly selected pizzas are all smaller than 9.5 inches is approximately 0.284, or 28.4%.

To solve this problem, we first need to standardize the variable using the formula:

z = (x - μ) / σ

where:

x = 9.5 inches (the cutoff for being considered "smaller")

μ = 9 inches (the mean)

σ = 0.8 inches (the standard deviation)

z = (9.5 - 9) / 0.8 = 0.625

Next, we need to find the probability that a randomly selected pizza is smaller than 9.5 inches using a standard normal distribution table or calculator.

This probability can be denoted as P(Z < 0.625), where Z is a standard normal random variable.

The probability that all 4 randomly selected pizzas are smaller than 9.5 inches, we will raise the probability to the power of 4:

Probability = 0.734 ≈ 0.291

So, the probability that 4 randomly selected pizzas are smaller than 9.5 inches is approximately 0.291 or 29.1%.

Using a standard normal distribution table or calculator, we can find that P(Z < 0.625) is approximately 0.734.

This means that the probability of a randomly selected pizza being smaller than 9.5 inches is 0.734.

To find the probability that 4 randomly selected pizzas are all smaller than 9.5 inches, we need to multiply this probability by itself four times, since the selection of each pizza is independent of the others.

This gives:

P(4 pizzas smaller than 9.5 inches) = 0.734 = 0.284

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Denise is scuba diving off the coast of Hawaii. When she is ready to come back to the surface, she rises at a safe speed of 1 foot every 2 seconds. If her dive was 40 yards deep, how many minutes will it take her to resurface? Write your answer as a whole number, decimal, or simplified fraction. Do not round. Minutes

Answers

It will take Denise 4 minutes to resurface.

To determine the time it takes for Denise to resurface, we need to convert the depth from yards to feet and then calculate the time.

Given that 1 yard is equal to 3 feet, the depth of the dive in feet is:

40 yards * 3 feet/yard = 120 feet

Denise rises at a rate of 1 foot every 2 seconds. To find the time in seconds it takes for her to resurface, we divide the depth by the rising speed:

Time in seconds = 120 feet / 1 foot/2 seconds = 240 seconds

Finally, to convert seconds to minutes, we divide by 60:

Time in minutes = 240 seconds / 60 = 4 minutes

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