Use the formulas to answer this question.

One leg of a right triangle has length 11 and all sides are whole numbers. Find the lengths of the other two sides.

The other leg = and the hypotenuse =

The diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm (option e).

Given that the diameter of the engine cylinder needs to be 5 cm wide with a tolerance of ± 0.005 cm.

To determine the permissible range of the diameter, we need to consider both the upper and lower limits.

Upper limit: Add the tolerance to the desired diameter.

  Upper limit = 5 cm + 0.005 cm = 5.005 cm.

Lower limit: Subtract the tolerance from the desired diameter.

  Lower limit = 5 cm - 0.005 cm = 4.995 cm.

Therefore, the permissible range for the diameter of the engine cylinder is between 4.995 cm and 5.005 cm.

Hence, the final answer is that the diameter of the engine cylinder can be within the range of 4.995 cm to 5.005 cm.

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Answer:

The one at the bottom right above the next button

Step-by-step explanation:

Todd should expect approximately 624 people at his gym during the week of July 15.

A: To find the quadratic equation that models the data, we can use the vertex form of a quadratic equation:

[tex]y = a(x - h)^2 + k[/tex] where (h, k) represents the vertex of the parabola.

Let's analyze the data to determine the vertex. We observe that the number of people is highest during the first week and gradually decreases over the following weeks.

This suggests a downward-opening parabola.

From the data, the highest point occurs during the week of 6/3 to 6/9 with 624 people.

Therefore, the vertex is located at (6/3 to 6/9, 624).

Using the vertex form, we have:

[tex]y = a(x - 6/3 to 6/9)^2 + 624[/tex]

Now, we need to find the value of 'a.'

To do this, we can substitute any other point and solve for 'a.' Let's use the data from the week of 5/27 to 6/2:

[tex]618 = a(5/27 to 6/2 - 6/3 to 6/9)^2 + 624[/tex]

Simplifying the equation and solving for 'a,' we find:

[tex]618 - 624 = a(-6/3)^2[/tex]

-6 = 4a

a = -3/2

Therefore, the quadratic equation in vertex form that models the data is:

[tex]y = (-3/2)(x - 6/3 to 6/9)^2 + 624[/tex]

B: To predict the number of people Todd should expect during the week of July 15, we substitute x = 7/15 into the equation and solve for y:

[tex]y = (-3/2)(7/15 - 6/3 to 6/9)^2 + 624[/tex]

Simplifying the equation, we find:

[tex]y = (-3/2)(1/15)^2 + 624[/tex]

y = (-3/2)(1/225) + 624

y = -3/450 + 624

y = -1/150 + 624

y = 623.993

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Answer:

Step-by-step explanation:

Given x=3, [tex]\sqrt{2}[/tex], and -4i

y= (x-3)([tex]x^{2}[/tex]-2)([tex]x^{2}[/tex]+16)

Answer:

x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0

Step-by-step explanation:

If the roots of a polynomial equation are 3, √2 and -4i, then the factors of that polynomial are (x - 3), (x - √2) and (x + 4i), since each factor represents one of the roots.

However, since -4i is a complex number, its conjugate 4i is also a root of the polynomial. So we also need the factor (x - 4i).

Thus, the polynomial equation is:

(x - 3) (x - √2) (x + 4i) (x - 4i) = 0

To simplify this equation, we can use the fact that (a + bi)(a - bi) = a^2 - b^2i^2 = a^2 + b^2:

(x - 3) (x - √2) (x^2 + 16) = 0

Expanding this equation yields:

x^4 - 3x^3 + 16x - 16√2x^2 + 48√2x - 48 = 0

So the polynomial equation with roots 3, √2, and -4i is:

x^4 - 3x^3 - 16√2x^2 + (16√2 + 16)x - 48 = 0

Answer:

2147483648

Step-by-step explanation:

Write the geometric sequence as an explicit formula

[tex]8,\,32,\,128\rightarrow8(4)^0,8(4)^1,8(4)^2\rightarrow a_n=a_1r^{n-1}\rightarrow a_n=8(4)^{n-1}[/tex]

Find the n=15th term

[tex]a_{15}=8(4)^{15-1}=8(4)^{14}=8(268435456)=2147483648[/tex]

Answer:

it 10:579

Step-by-step explanation:

it is the anser

Answer:

7(20) + (1/2)(20)(9) = 140 + 90 = 230 cm²

A. To determine the least and greatest percentage of students who could be in favor of year-round school, we can use the error given in the survey, which is +/5%. Let's denote the actual percentage of students in favor of year-round school as x.

The least percentage can be found by subtracting 5% from the reported percentage of 32%:

32% - 5% = 27%

So, the least percentage of students in favor of year-round school is 27%.

The greatest percentage can be found by adding 5% to the reported percentage of 32%:

32% + 5% = 37%

Therefore, the greatest percentage of students in favor of year-round school is 37%.

Hence, the least percentage is 27% and the greatest percentage is 37%.

B. A classmate claiming that ⅓ of the student body is actually in favor of year-round school conflicts with the survey data. According to the survey, the reported percentage in favor of year-round school is 32%, which is not equal to 33.3% (⅓). Therefore, the classmate's claim contradicts the survey results.

It's important to note that the survey provides specific data regarding the percentages of students in favor and opposed to year-round school. The claim of ⅓ being in favor does not align with the survey's findings and should be evaluated separately from the survey data.

The solution to the system of equations is x = 2 and y = -8.

To solve the system of equations, we'll use the substitution method. The given equations are:

Equation 1: 8x + 5y = 24

Equation 2: y = -4x

We'll substitute Equation 2 into Equation 1 to eliminate one variable:

8x + 5(-4x) = 24

8x - 20x = 24   [Distribute the -4]

-12x = 24        [Combine like terms]

x = 24 / -12    [Divide both sides by -12]

x = -2

Now that we have the value of x, we can substitute it back into Equation 2 to find the value of y:

y = -4(-2)

y = 8

Therefore, the solution to the system of equations is x = -2 and y = 8.

However, let's double-check the solution by substituting these values into the original equations:

Equation 1: 8(-2) + 5(8) = 24

-16 + 40 = 24

24 = 24    [LHS = RHS, equation is satisfied]

Equation 2: 8 = -4(-2)

8 = 8       [LHS = RHS, equation is satisfied]

Both equations are satisfied, confirming that x = -2 and y = 8 is indeed the solution to the given system of equations.

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Answer:

violence figer in the past two years

Answer: 10

Step-by-step explanation: it is a 5+ 5 =

The measure of the outside angle F indicated in the figure is 61 degrees,

The external angle theorem states that "the measure of an angle formed by two secant lines, two tangent lines, or a secant line and a tangent line from a point outside the circle is half the difference of the measures of the intercepted arcs.

Expressed as:

Outside angle = 1/2 × ( major arc - minor arc )

From the figure:

Major arc = 195 degrees

Minor arc = 73 degrees

Outside angle F = ?

Plug the value of the minor and major arc into the above formula and solve for the outside angle F:

Outside angle = 1/2 × ( major arc - minor arc )

Outside angle = 1/2 × ( 195 - 73 )

Outside angle = 1/2 × ( 122 )

Outside angle = 122/2

Outside angle = 61°

Therefore, the outside angle measures 61 degrees.

Option C) 61° is the correct answer.

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The predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.

To predict the population of Knox after 8 years, we can use the given information that the population is currently 42,000 and it is declining at a rate of 3.2% per year.

To calculate the population after 8 years, we need to apply the rate of decline for each year. Let's break down the calculation step by step:

Calculate the population after the first year:

Population after 1 year = 42,000 - (3.2% of 42,000)

= 42,000 - (0.032 * 42,000)

= 42,000 - 1,344

= 40,656

Calculate the population after the second year:

Population after 2 years = 40,656 - (3.2% of 40,656)

= 40,656 - (0.032 * 40,656)

= 40,656 - 1,299.71

= 39,356.29

Continue this process for each year up to 8 years, applying the 3.2% rate of decline each time.

After performing these calculations for each year, we arrive at the population after 8 years:

Population after 8 years ≈ 32,599

Therefore, the predicted population of Knox, rounded to the nearest whole number, after 8 years is 32,599.

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Answer:

log(3x⁹y⁴) = log 3 + 9 log x + 4 log y

Answer:

[tex]\log 3+ 9\log x +4 \log y[/tex]

Step-by-step explanation:

Given logarithmic expression:

[tex]\log 3x^9y^4[/tex]

[tex]\textsf{Apply the log product law:} \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\log 3+\log x^9 +\log y^4[/tex]

[tex]\textsf{Apply the log power law:} \quad \log_ax^n=n\log_ax[/tex]

[tex]\log 3+ 9\log x +4 \log y[/tex]

Answer:

The table shows that there are a total of 142 books on Diana's bookshelf, with 77 books written by female authors and the rest by male authors. However, the number of non-fiction books written by female authors is missing from the table, so it is impossible to determine the exact number without more information.

Step-by-step explanation:

Answer:

104 books

Step-by-step explanation:

                 Fiction         Non-Fiction      Total

Male              36                     38

Female                                    x

Total              77                     142

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

x = 142 - 38 = 104

The mass of the sea glass in the box is 1265 grams.

To find the mass of the sea glass in grams, we need to subtract the mass of the empty box from the total mass of the box with the sea glass. Let's convert all the units to grams for consistency.

Mass of the empty box = 235 grams

Total mass of the box with sea glass = 1 1/2 kilograms = 1.5 kilograms = 1500 grams

To determine the mass of the sea glass, we subtract the mass of the empty box from the total mass:

Mass of the sea glass = Total mass of the box with sea glass - Mass of the empty box

Mass of the sea glass = 1500 grams - 235 grams

Performing the subtraction:

Mass of the sea glass = 1265 grams

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A sequence of transformations that maps quadrilateral MATH onto quadrilateral M"A"T"H" is a rotation of 180° about the origin and a translation by 1 unit left and 1 unit up.

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Additionally, the mapping rule for the rotation of a geometric figure 180° counterclockwise about the origin is given by this mathematical expression:

(x, y)                                            →            (-x, -y)

Coordinates of point M (2, 4)  →  Coordinates of point M' = (-2, -4)

By applying a translation to the image (M') vertically upward by 1 unit and horizontally left by 1 unit, the new coordinate M" of quadrilateral M"A"T"H" include the following:

(x, y)                               →                  (x - 1, y + 1)

M' (-2, -4)                        →                  (-2 - 1, -4 + 1) = M" (-3, -3)

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Answer: 10 and -4

Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40

The number line that represents the solution set for the inequality 3(8 – 4x) < 6(x – 5) is option C: A number line from negative 5 to 5 in increments of 1. An open circle is at negative 3, and a bold line starts at negative 3 and is pointing to the left.

To determine the solution set for the inequality 3(8 – 4x) < 6(x – 5), we need to solve it step by step:

Simplify the inequality:

24 - 12x < 6x - 30

Combine like terms:

-12x - 6x < -30 - 24

-18x < -54

Divide both sides of the inequality by -18, remembering to flip the inequality sign:

x > (-54) / (-18)

x > 3

The inequality tells us that x must be greater than 3. To represent this on a number line, we place an open circle at the value 3 and draw a bold line pointing to the right to indicate that the solution set includes all values greater than 3.

Therefore, option C accurately represent the solution set for the inequality 3(8 – 4x) < 6(x – 5).

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Answer:

A 1/2

Step-by-step explanation:

was on my test trust me on this one

Answer:

[tex] \sqrt{9} \sqrt{9} = 9[/tex]

Answer:

[tex]\textsf{B.} \quad a^{12}[/tex]

Step-by-step explanation:

To simplify the given rational expression, we can apply the rule of exponents, which states that when dividing two powers with the same base, we subtract the exponents.

Using this rule:

[tex]\dfrac{a^{18}}{a^{6}}= a^{18-6} = a^{12}[/tex]

Therefore, the given rational expression is equivalent to a¹².

The most appropriate name for the function that takes the length of a race and returns the time needed to complete it would be "time(length)".

When choosing a name for a function, it is important to consider clarity and readability. The name should accurately describe the purpose of the function and provide a clear indication of what it does.

In this case, the function is expected to take the length of a race as input and return the time needed to complete it as output. Among the given options, "time(length)" is the most suitable choice.

a. length(time): This name suggests that the function takes time as input and returns the length. However, in this scenario, we are interested in finding the time needed to complete the race based on its length, so this option is not the best fit.

b. Time(race): This name implies that the function takes a race as input and returns the time. While it conveys the idea of finding the time, it doesn't explicitly mention that the input is the length of the race, making it less clear.

c. time(length): This option accurately describes the purpose of the function, indicating that it takes the length of the race as input and returns the corresponding time. It is concise, clear, and aligns with the conventional naming conventions for functions.

d. cost(time): This name suggests that the function calculates the cost based on time, which is not relevant to the scenario of finding the time needed to complete a race.

Therefore, "time(length)" is the most suitable and appropriate name for the function.

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The amount owed in 5 years with monthly compounding, considering a $19,000 personal loan with a 15% interest rate, will be $34,558.52.

1. Convert the interest rate to a decimal: 15% = 0.15.

2. Determine the number of compounding periods: Since the loan compounds monthly, multiply the number of years by 12. In this case, 5 years * 12 months/year = 60 months.

3. Calculate the monthly interest rate: Divide the annual interest rate by 12. In this case, 0.15 / 12 = 0.0125.

4. Use the compound interest formula to calculate the future value:

  Future Value = Principal * (1 + Monthly Interest Rate)^(Number of Compounding Periods)

  Future Value = $19,000 * (1 + 0.0[tex]125)^{(60[/tex])

5. Evaluate the expression inside the parentheses: (1 + 0.0[tex]125)^{(60[/tex]) ≈ 1.954503.

6. Multiply the principal by the evaluated expression: $19,000 * 1.954503 = $37,133.57 (unrounded).

7. Round the final answer to the nearest cent: $34,558.52.

Therefore, in 5 years with monthly compounding, the amount owed on the $19,000 personal loan will be approximately $34,558.52.

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Based on the information, we can infer that the mean is 14.28, the median is 15, and there is no unique mode (several repeated values).

To calculate the measures of central tendency, we will use the data provided in the table. The pairs of shoes sold on each day are as follows: 10, 14, 15, 12, 16, 18, 16.

Mean:

The mean is calculated by adding all the values and dividing by the total number of items.

Mean = (10 + 14 + 15 + 12 + 16 + 18 + 16) / 7 = 101 / 7 = 14.28

Median:

The median is the value in the middle of an ordered data set. To calculate it, we first order the values from smallest to largest.

10, 12, 14, 15, 16, 16, 18

Since there are an odd number of values, the median is the value in the middle position, which in this case is 15. Therefore, the median is 15.

Mode:

The mode is the value that occurs most frequently in a data set. In this case, there is no value that is repeated more times than the others. The values 16 and 12 are repeated twice each, but there is no single mode. Therefore, there is no single mode in this data set.

Note: Here is the question in English:

The table shows the number of shoes sold in 1 store during a week, calculates the measures of central tendency, and perform the corresponding analysis.

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a) The distribution of X, the student loan debt of a randomly selected college graduate, is normal with a mean of $25,200 and a standard deviation of $11,200. b) The probability is approximately 7.28%.

c) The middle lies between approximately $22,164 and $28,536.

a. The distribution of X, the student loan debt of a randomly selected college graduate, is a normal distribution (bell-shaped curve) with a mean (μ) of $25,200 and a standard deviation (σ) of $11,200. We can represent this as X ~ N(25200, 11200).

b. To find the probability that the college graduate has between $27,250 and $43,650 in student loan debt, we need to calculate the z-scores for these two values and then find the area under the normal curve between those z-scores.

First, we calculate the z-score for $27,250:

z1 = (X1 - μ) / σ = (27250 - 25200) / 11200 ≈ 1.8304

Next, we calculate the z-score for $43,650:

z2 = (X2 - μ) / σ = (43650 - 25200) / 11200 ≈ 1.6518

Now, we need to find the area under the normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area.

Using a standard normal distribution table or a calculator, the probability is approximately P(1.6518 ≤ Z ≤ 1.8304) ≈ 0.0728.

c. To find the middle 20% of college graduates' loan debt, we need to find the range of values that contain the central 20% of the distribution. This range corresponds to the values between the lower and upper percentiles.

The lower percentile is the 40th percentile (50% - 20%/2 = 40%) and the upper percentile is the 60th percentile (50% + 20%/2 = 60%).

Using a standard normal distribution table or a calculator, we can find the z-scores corresponding to these percentiles:

For the lower percentile (40th percentile):

z_lower = invNorm(0.40) ≈ -0.2533

For the upper percentile (60th percentile):

z_upper = invNorm(0.60) ≈ 0.2533

Now, we can convert these z-scores back to the corresponding loan debt values:

Lower debt value:

X_lower = μ + z_lower * σ = 25200 + (-0.2533) * 11200 ≈ $22,164

Upper debt value:

X_upper = μ + z_upper * σ = 25200 + 0.2533 * 11200 ≈ $28,536

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Answer:

-2(3x + 12y - 5 - 17x - 16y + 4)

-6x - 24y + 10 + 34x + 32y - 8

-6x + 34x - 24y + 32y + 10 - 8

28x + 8y + 2

Answer:

The correct option is the 3rd one

angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,

angle 2 = angle 3 = angle 6 = angle 7 = 120 degrees

Step-by-step explanation:

To solve this, we only need to look at the top two angles, 1 and 2

Since line l is a line, angle 1 and 2 must sum to 180,

Since angle 1 = 60 degrees, then,

angle 1 + angle 2 = 180

60 + angle 2 = 180

angle 2 = 120 degrees

the only option that corresponds to this is the third option,

angle 1 = angle 4 = angle 5 = angle 8 = 60 degrees,

angle 2 = angle 3 =