Find side BC for the triangle shown (round to the nearest tenth).

The 90% confidence interval estimate for the difference between the two population means is given as follows:

(-18.24, 10.24).

The difference between the sample means is given as follows:

42 - 46 = -4.

The standard error for each sample is given as follows:

The standard error for the distribution of differences is then given as follows:

\(s = \sqrt{2.4^2 + 2.6^2}\)

s = 8.36.

The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 14 + 15 - 2 = 27 df, is t = 1.7033.

The lower bound of the interval is given as follows:

-4 - 1.7033 x 8.36 = -18.24.

The upper bound of the interval is given as follows:

-4 + 1.7033 x 8.36 = 10.24.

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A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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There are n x (n-1) number of ways for the speaker and vice speaker to be selected in the demonstrator's party, where n is the number of members in the party.

For the demonstrator's party, the first position of the speaker can be filled by any of the n members. After the speaker is chosen, there are n-1 members left to select from for the position of vice speaker. Therefore, the total number of ways the speaker and vice speaker can be selected is n x (n-1).

For example, if the demonstrator's party has 4 members, there are 4 choices for the speaker position. After the speaker is chosen, there are 3 choices left for the position of vice speaker. So, the total number of ways to select a speaker and vice speaker in the party is 4 x 3 = 12.

This formula can be applied to any size of the party to determine the total number of possible ways to select a speaker and vice speaker.

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Answer:

30 dollars and 23 cents

Step-by-step explanation:

hope this helps your welcome

Answer:

It would be 23,000.

Answer:

23,000

Step-by-step explanation:

I did rounding.

Brainlest pls.

Answer:

14.5, 14.8, 15, 15.3, 15.8

Step-by-step explanation:

9514 1404 393

Answer:

  see attachment

Step-by-step explanation:

The "experimental probability" is the ratio of actual outcomes of interest to the number of trials. It is based on actually performing the selection over and over some number of times. The "theoretical probability" will be the fraction that is the outcomes of interest divided by the total number of possible outcomes.

We note that Mel's purse contains a total of 6 +8 +4 +7 = 25 coins. The theoretical probability of selecting any given coin is then 1/25.

__

Orange

A. The experimental probability of selecting a dime is ...

  number of dime outcomes / number of trials = 30/150 = 1/5

B. The theoretical probability of selecting a dime is ...

  (4 dimes)/(25 coins) = 4/25

C. The assumption in probability experiments is that randomly selected outcomes will always approach the theoretical probability in their frequency of occurrence.

See the attachment for the appropriate answer choices.

__

Purple

A. The experimental probability of selecting a penny is ...

  number of penny outcomes / number of trials = 45/200 = 9/40

B. The theoretical probability of selecting a penny is ...

  (6 pennies)/(25 coins) = 6/25

C. The difference between these values is ...

  6/25 -9/40 = 48/200 -45/200 = 3/200

See the attachment for the appropriate answer choices.

The angle that satisfies the necessary requirements is  1041° - 2(360°) = 321°. Coterminal angles are those with the same terminal point in the standard position.

To understand, follow the 2 basic steps:

Step 1: Find the specified angle.

Step 2: Finding a coterminal angle.

Tally up or tally down a multiple of 360.

θ = 1041°

Every multiple of 360 degrees added or subtracted results in an angle that is coterminal with the provided angle.

Hence, 1041° - 2(360°) = 321° is an angle that satisfies the necessary requirements.

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Answer:

36.45

Step-by-step explanation:

40.50* 0.10 =4.05

40.5-4.05=36.45

Answer: We need to add 40 ounces of water to the 100 oz of concentrated juice and water to obtain a new mixture that is 20% concentrated juice.

Step-by-step explanation:

We can begin by setting up an equation based on the given information.

Let's say we need to add x ounces of water to the 100 oz of concentrated juice and water to obtain the new 20% mixture.

The amount of pure juice in the original 100 oz mixture is 28% of 100 oz, which is 0.28(100) = 28 oz.

After x ounces of water are added, the total volume of the mixture becomes 100 + x oz. The amount of pure juice remains the same at 28 oz. We want to find the amount of water that needs to be added to reach a concentration of 20%.

Setting up the equation:

0.20(100 + x) = 28

Expanding and simplifying:

20 + 0.20x = 28

0.20x = 8

x = 40

Answer:

143

Step-by-step explanation:

100 oz is 28 % of the drink

So total volume of the drink = 357 oz.

A drink that of 100 oz juice and is 20% juice has a volume of 500 oz.

So, we need to add 500 - 357

= 143 oz water.

Answer:

Step-by-step explanation:

The diagonals of the rhombus divide it into 4 congruent right triangles.

So we can use Pythagorean theorem to calculate side of a rhombus.

\((\frac e2)^2+(\frac f2)^2=s^2\\\\e=30\,cm\quad\implies\quad\frac e2=15\,cm\\\\f=16\,cm\quad\implies\quad\frac f2=8\,cm\\\\15^2+8^2=s^2\\\\s^2=225+64\\\\s^2=289\\\\s=17\)

Perimeter:

P = 4s = 4•17 = 68 cm

the correct answer is C. 71,224,900.To compare the numbers, we need to write them in scientific notation.

A. 5,678,889 can be written as 5.678889 × 10^6
B. 9.897752 × 10 can be written as 9.897752 × 10^1
C. 71,224,900 can be written as 7.12249 × 10^7
D. 2.468 × 10 can be written as 2.468 × 10^0

Now, let's compare the exponents of 10.

The given number is 3.14159 × 10^0.

Comparing the exponents:

A. 10^6
B. 10^1
C. 10^7
D. 10^0

Since 10^7 is the largest exponent among the options, it means that 7.12249 × 10^7 (Option C) is the number that is greater than 3.14159 × 10.

Therefore, the correct answer is C. 71,224,900.

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Answer:

The answer is 1.52.

Step-by-step explanation:

I don't know why it's not 1.52 no matter how I calculate it's 1.52

Answer:

5 : 2

Step-by-step explanation:

Given that:

Number of gumdrops = 420

Number of chocolate bars = 280

Total Number of candies = 700

To find:

The ratio of candies to chocolate bars = ?

Solution:

First of all, let us discuss the method to find the ratio of any two quantities.

Suppose, we need to find the ratio of two numbers \(p\) and \(q\).

Then to find the ratio \(p:q\) , we need to divide p by q and represent it in the simplest form \(\frac{a}{b}\) such that a and b can not be divided further.

Here, to find the ratio of candies to chocolate bar:

\(Ratio = \dfrac{\text{Number of candies}}{\text{Number of chocolate bars}}\\\Rightarrow \dfrac{700}{280}\)

Here, we can simplify the fraction by dividing the numerator and denominator by 10 first:

\(\dfrac{70}{28}\)

Now, let us divide the numerator and denominator by 14:

\(\dfrac{5}{2}\)

So, the ratio is 5 : 2

The result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

To subtract the expression 7x - 9 from 2x² - 11, we need to distribute the negative sign to every term within the expression 7x - 9, and then combine like terms.

First, let's distribute the negative sign:

2x² - 11 - (7x - 9)

Now, distribute the negative sign to each term within the parentheses:

2x² - 11 - 7x + 9

Next, let's combine like terms:

2x² - 7x - 2

Therefore, the result of subtracting 7x - 9 from 2x² - 11 is 2x² - 7x - 2.

In this expression, the highest power of x is 2, which means it is a quadratic expression. The coefficient of x² is 2, and the coefficient of x is -7. The constant term is -2.

This quadratic expression can be further simplified or factored if needed, but the subtraction process is complete with the result 2x² - 7x - 2.

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The sketch of the polynomial function f(x) = x^3 + x^2 - 9x - 9 has a left-hand behavior that starts up and a right-hand behavior that ends down. It has a y-intercept of (0, -9), and its real zeros are x = -3, -1, and 3, each with a multiplicity of 1. The value of y at x = 22 is 10847.

Here is the four-step process to sketch the polynomial function f(x) = x^3 + x^2 - 9x - 9:

Step 1: Find the end behavior of the function

As x approaches negative infinity, f(x) approaches negative infinity because the leading term x^3 dominates. As x approaches positive infinity, f(x) approaches positive infinity because the leading term x^3 still dominates.

Step 2: Find the y-intercept

To find the y-intercept, we set x = 0 and evaluate f(0) = (0)^3 + (0)^2 - 9(0) - 9 = -9. Therefore, the y-intercept is (0, -9).

Step 3: Find the real zeros of the polynomial

We can use synthetic division or factor theorem to find the zeros of the polynomial:

Using synthetic division with x = -3, we get (x+3)(x^2 - 2x - 3), indicating that x = -3 is a zero of multiplicity 1.

Factoring x^2 - 2x - 3, we get (x-3)(x+1), indicating that x = -1 and x = 3 are also zeros of multiplicity 1.

Therefore, the real zeros of the polynomial are x = -3, -1, and 3.

Step 4: Determine the multiplicity of each zero

The zero located farthest left on the x-axis is x = -3, which has a multiplicity of 1.

The zero located between the leftmost and rightmost zeros is x = -1, which also has a multiplicity of 1.

The zero located farthest right on the x-axis is x = 3, which has a multiplicity of 1.

To evaluate a test point, we can choose any value of x and evaluate f(x). Let's choose x = 22. Then, f(22) = (22)^3 + (22)^2 - 9(22) - 9 = 10847.

Therefore, the sketch of the polynomial function f(x) = x^3 + x^2 - 9x - 9 has a left-hand behavior that starts up and a right-hand behavior that ends down. It has a y-intercept of (0, -9), and its real zeros are x = -3, -1, and 3, each with a multiplicity of 1. The value of y at x = 22 is 10847.

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Answer:

100

Step-by-step explanation:

if you are doing this you need to do 50x2 which in this case equals = 100

Answer:

Step-by-step explanation:

A parallelogram also has the following properties:

Opposite angles are congruent;

Opposite sides are congruent;

Adjacent angles are supplementary;

The diagonals bisect each other.

Question 3: True

Question 4: False

Question 5: True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c.

This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

Question 3: If f'(c) < 0 then f(x) is decreasing and the graph of f(x) is concave down when x = c.

True

When the derivative of a function, f'(x), is negative at a point c, it indicates that the function is decreasing at that point. Additionally, if the second derivative, f''(x), exists and is negative at x = c, it implies that the graph of f(x) is concave down at that point.

Question 4: A local extreme point of a polynomial function f(x) can only occur when f'(x) = 0.

False

A local extreme point of a polynomial function can occur when f'(x) = 0, but it is not the only condition. A local extreme point can also occur when f'(x) does not exist (such as at a sharp corner or cusp) or when f'(x) is undefined. Therefore, f'(x) being equal to zero is not the sole requirement for a local extreme point to exist.

Question 5: If f'(x) > 0 when x < c and f'(x) < 0 when x > c, then f(x) has a maximum value when x = c.

True

If the derivative of a function, f'(x), is positive for values of x less than c and negative for values of x greater than c, then it indicates a change in the slope of the function. This change from positive slope to negative slope suggests that the function has a maximum value at x = c. This is because the function is increasing before x = c and decreasing after x = c, indicating a peak or maximum at x = c.

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Answer:

19,188

Step-by-step explanation:

hope this helps ;)

Answer:

8.3

Step-by-step explanation:

just move the decimal in 83 over one digit since your already just dividing by 10

Answer:

  C.  142°

Step-by-step explanation:

You want the angle between vectors u=3i+√3j and v=-2i-5j.

There are a number of ways the angle between the vectors can be found. For example, the dot-product relation can give you the cosine of the angle:

  u•v = |u|·|v|·cos(θ) . . . . . . where θ is the angle of interest

You can find the angles of the vectors individually, and subtract those:

  u = |u|∠α

  v = |v|∠β

  θ = α - β

When the vectors are expressed as complex numbers, the angle between them is the angle of their quotient:

  \(\dfrac{\vec{u}}{\vec{v}}=\dfrac{|\vec{u}|\angle\alpha}{|\vec{v}|\angle\beta}=\dfrac{|\vec{u}|}{|\vec{v}|}\angle(\alpha-\beta)=\dfrac{|\vec{u}|}{|\vec{v}|}\angle\theta\)

This method is used in the calculation shown in the first attachment. The angle between u and v is about 142°.

A graphing program can draw the vectors and measure the angle between them. This is shown in the second attachment.

__

Additional comment

The approach using the quotient of the vectors written as complex numbers is simply computed using a calculator with appropriate complex number functions. There doesn't seem to be any 3D equivalent.

The dot-product relation will work with 3D vectors as well as 2D vectors.

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Answer:

Leah has 80 less paychecks than the weekly person.

Step-by-step explanation:

Leah is getting 24 paychecks in 2 years, Weekly person gets 104 paychecks in 2 years, 104 - 24 = 80 paychecks.

Answer:

6

Step-by-step explanation:

The prime factorization of 12x is 3*2*2x. The prime factorization of 18 is 2*3*3. The same thing that appears in both prime factorizations is 3*2, or 6.

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Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

The side length of each piece of quilt is approximately 24.06 inches.

In the given scenario, quilt square is cut on the diagonal to form triangular quilt pieces. The hypotenuse of the resulting triangles is 34 inches long. We have to determine the side length of each piece.

In a right triangle, according to the Pythagorean theorem, the sum of the squares of the legs is equal to the square of the hypotenuse.

So, we can use the Pythagorean theorem to find the length of the sides of the triangular quilt pieces.

The theorem states that a² + b² = c². In this case, c = 34 inches.

Let's assume that each quilt square has sides of length x inches.

When the square is cut diagonally, it is divided into two triangles with legs of length x inches.

According to the Pythagorean theorem, the length of the hypotenuse (34 inches) of each triangle is given by:

x² + x² = 34²2x² = 1156x² = 578x = √578 ≈ 24.06 inches

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Volume represents the capacity of the barrel. It tells us the quantity of a substance that it can hold.

When trying to determine the amount of paint needed to completely cover the outside of a wooden barrel, we need to find the surface area of the barrel. Thus, the answer is

False

According to the information given in the exercise, Xavier drank 20% of the 36 ounce cup with water.

You can write 20% as a decimal number by dividing it by 100:

Let be "x" the amount of water