The sector of a circle with a diameter of 8 feet has a central angle measure of 45°. What is the area of the sector?



A. π/2 ft²

B. π ft²

C. 2 π ft²

D. 8 π ft²

The height of Trevor's sandcastle is 3/10 foot taller than his sister's.

Given that, Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall.

Difference in the height of sandcastles = 1/2 - 1/5

= 5/10 - 2/10

= (5-2)/10

= 3/10

So, the difference in heights = 3/10 foot

Therefore, the height of Trevor's sandcastle is 3/10 foot taller than his sister's.

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The missing sides of each geometric system are summarized below:

Case 9: (x, y) = (9, 12)

Case 12: (x, y) = (√51, 7)

Case 15: (x, y) = (8, 15)

In this question we find three cases of geometric systems formed by two right triangles, all missing sides can be found by means of Pythagorean theorem:

r = √(x² + y²)

Where:

Now we proceed to determine all missing sides:

Case 9

y = √(15² - 9²)

y = 12

x = 9

Case 12

x = √(10² - 7²)

x = √51

y = 7

Case 15

y = √(17² - 15²)

y = 8

x = 15

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Answer:

D

Step-by-step explanation:

All the numbers that have fraction are irrational therefore the numbers are real

Answer:

The correct equation to find the total number of bags of glass and plastic Silas will take to the recycling center is C. x - 18 = 6.

In this equation, x represents the total number of bags of glass and plastic Silas will take to the recycling center. The left side of the equation represents the number of bags of glass Silas will take to the recycling center (x - 18), and the right side represents the number of bags of plastic he still needs to take to the recycling center (6).

By setting the two expressions equal to each other (x - 18 = 6), we can solve for x and determine the total number of bags Silas will take to the recycling center. Adding 18 to both sides of the equation gives us x = 24, which means Silas will take a total of 24 bags (18 bags of glass and 6 bags of plastic) to the recycling center.

Answer:

Step-by-step explanation:

First, we need to find the z-scores for q1 and q3.

Q1:

Using the formula for z-score, we get:

z = (x - μ) / σ

where x is the IQ score we want to find the z-score for, μ is the mean IQ of the population, and σ is the standard deviation of the population.

For the first quartile (q1), we want to find the z-score such that 25% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.25 is -0.674.

So we have:

-0.674 = (x - 110) / 16

Solving for x, we get:

x = 99.8

Therefore, q1 is approximately 99.8.

Q3:

Similarly, for the third quartile (q3), we want to find the z-score such that 75% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.75 is 0.674.

So we have:

0.674 = (x - 110) / 16

Solving for x, we get:

x = 120.8

Therefore, q3 is approximately 120.8.

The function that models the population t years after 2000 is P(t) = 14400 * (1.04)^t

The population growth function is of the form:

P(t) = P₀ * (1 + r)^t

Where:

P(t) is the current population after t years

P₀ is the starting population

r is the annual growth rate in percent

Thus, P₀ = 14400 and 4% = 0.04

P(t) = P₀ * (1 + r)^t

P(t) = 14400 * (1 + 0.04)^t

P(t) = 14400 * (1.04)^t

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Complete Question

The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 14400.

a) Find a function that models the population t years after 2000 (t=0 for 2000).

Your answer is P(t) =

Step-by-step explanation:

(a) The lower limit of the 90% confidence interval can be calculated using the formula:

lower limit = sample mean - margin of error

Plugging in the given values, we have:

lower limit = 7.43 - 1.32

lower limit = 6.11 (rounded to 2 decimal places)

Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.

(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.

Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:

500 * 0.9 = 450

So, approximately 450 of these confidence intervals would contain the population mean.

The next 20 octal numbers after 7 are: 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33

In the decimal system, we count from 0 to 9 before moving to the next place value. In the octal system, we count from 0 to 7 before moving to the next place value. Therefore, the next 20 octal numbers after 7 are:

10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33

To understand how this pattern works, consider the decimal number 32. To convert it to octal, we can repeatedly divide it by 8 and record the remainders:

32 ÷ 8 = 4 with remainder 0

4 ÷ 8 = 0 with remainder 4

So the octal representation of 32 is 40. Similarly, we can convert any decimal number to octal by repeatedly dividing by 8 and recording the remainders.

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Answer: ∠DGB or ∠EGA

Step-by-step explanation:

Supplementary: Either of two angles whose sum is 180°.

Starting Angle: ∠DGE

Possible Supplements: ∠DGB or ∠EGA

I hope this helps ^^

The first three terms of the expression (2 · x + 1 / x)¹² are 4096 · x¹², 24576 · x¹⁰ and 67584 · x⁸, respectively.

In this problem we find the case of a expression of the form (a + b)ⁿ, where any term of the expression can be found by binomial theorem:

[tex](a + b)^{n} = \sum\limits_{k = 0}^{n} \frac {n!}{k! \cdot (n - k)!}\cdot a^{n - k}\cdot b^{k}[/tex]

Where:

If we know that a = 2 · x, b = 1 / x and 12, then the first three terms of the power of the binomial are, respectively:

n = 0

[tex]C_{0} = \frac{12!}{0! \cdot (12 - 0)!}\cdot (2\cdot x)^{12 - 0} \cdot (\frac {1}{x})^{0}[/tex]

C₀ = 4096 · x¹²

n = 1

[tex]C_{1} = \frac{12!}{1! \cdot (12 - 1)!}\cdot (2\cdot x)^{12 - 1} \cdot (\frac {1}{x})^{1}[/tex]

C₁ = 12 · (2048 · x¹¹) · (1 / x)

C₁ = 24576 · x¹⁰

n = 2

[tex]C_{2} = \frac{12!}{2! \cdot (12 - 2)!}\cdot (2\cdot x)^{12 - 2} \cdot (\frac {1}{x})^{2}[/tex]

C₂ = 66 · (1024 · x¹⁰) · ( 1 / x²)

C₂ = 67584 · x⁸

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The equation which represents the rule for the variable values is given by option c. y = 2x + 2

The values in the table are,

x  -2   -1    0   1   2

y   -2    0   2   4  6

let us consider two coordinates of the given values in the table .

( x₁ , y₁ ) = ( -2 , -2 )

( x₂ , y₂ ) = ( 0 , 2 )

Using the formula for the slope intercept form of the line we get the equation,

( y - y₁ ) / ( x - x₁ ) = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substitute the values to get the equation of the line we have,

⇒ ( y - ( - 2 ) ) / ( x -  ( -2 ) ) = ( 2 - ( - 2 ) ) / ( 0 - ( - 2 ) )

⇒  ( y + 2 ) / ( x + 2 ) = ( 2 + 2 ) / ( 0 + 2)

⇒  ( y + 2 ) / ( x + 2 ) = 4  / 2

⇒  ( y + 2 ) / ( x + 2 ) = 2

⇒ y + 2 = 2 ( x + 2)

⇒ y + 2 = 2x + 4

⇒ y = 2x + 4 - 2

⇒ y = 2x + 2

Therefore, the equation which represents the rule for the given values of the variable is equal to option c. y = 2x + 2

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Answer:

9. 40 = 2πr

r = 20/π inches = 6.4 inches

d = 40/π inches = 12.7 inches

10. 256 = 2πr

r = 128/π feet = 40.7 feet

d = 256/π feet = 81.5 feet

The probability of rolling a number less than 9 is 1

The probability of rolling a number less than 9 is 1, since all the possible outcomes are 1, 2, 3, 4, 5, 6 and all of them are less than 9.

The set of equally likely outcomes when rolling a 6-sided die is {1, 2, 3, 4, 5, 6}.

There are no outcomes greater than 6 since that is the maximum number on the die.

Therefore, the probability of rolling a number less than 9 is equal to the probability of rolling any number on the die, which is 1, since all outcomes in the sample space are equally likely.

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Answer:

The domain in interval notation is (-infinity, infinity), or all real numbers.

Answer: 4m-24n+3

Step-by-step explanation:

Expand and collect like terms!

[tex](17m-12n-1) + (4-13m-12n)\\= 17m - 12n - 1 + 4 - 13m - 12n\\=4m-24n+3[/tex]

Hope this helps <3

The original selling price of the kayak set, given the discounts, would be $ 520. 63

The kayak is being sold such that a discount was offered of 10 % and then an additional discount was offered for 30 %.

The first step to the original price is:

= 328 / ( 1 - 30 %)

= 328 / 0. 70

= $ 468. 57

Then, the original price, would then account for the original discount of 10 % to become:

= 468. 57 / ( 1 - 10 %)

= 468. 57 / 0. 90

= $ 520. 63

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Answer:

Step-by-step explanation:

a. Variables needed to solve the problem:

Sample size: n = 1,026

Proportion of the sample that responded "Make some major changes": p = 0.39

Confidence level: 95%

b. To determine if a normal distribution can be used to approximate the data, we need to check if the sample size is large enough to meet the requirements for a normal approximation. The sample size should be at least 10 times larger than the number of successes (np) and 10 times larger than the number of failures (n(1-p)). In this case, we have:

np = 1026 x 0.39 = 399.14

n(1-p) = 1026 x 0.61 = 626.86

Both np and n(1-p) are greater than 10, so we can assume that a normal distribution can be used to approximate the data.

c. The standard deviation of the proportion can be calculated using the following formula:

standard deviation = sqrt(p(1-p) / n)

standard deviation = sqrt(0.39 x 0.61 / 1026) = 0.024

d. The point estimate of the proportion of all United States adults who would respond "Make some major changes" is simply the sample proportion, which is p = 0.39. The margin of error can be calculated using the following formula:

margin of error = z* * standard deviation

where z* is the z-score associated with the 95% confidence level. Using a standard normal distribution table or a calculator, we find that the z-score for a 95% confidence level is approximately 1.96. Therefore:

margin of error = 1.96 * 0.024 = 0.047

e. The confidence interval can be calculated using the following formula:

confidence interval = point estimate ± margin of error

confidence interval = 0.39 ± 0.047

confidence interval = (0.343, 0.437)

Therefore, we are 95% confident that the proportion of all United States adults who would respond "Make some major changes" is between 0.343 and 0.437.

(a)The arrow will reach a maximum height of 130 feet.

(b) After around 5 seconds, the arrow will strike the ground.

(c) At 1 second and 4 seconds after launch, the arrow will be 114 feet high.

a) The maximum height of the arrow occurs at the vertex of the parabolic pathway. The x-coordinate of the vertex is given by -b/2a, where a=-16 and b=80. So, t= -b/2a = -80/(2x(-16)) = 2.5 seconds. To find the maximum height, plug in t=2.5 into the equation: h(2.5) = -16(2.5)² + 80(2.5) + 50 = 130 feet.

Therefore, the maximum height of the arrow is 130 feet.

b) To find the time it takes for the arrow to reach the ground, find the value of t when h(t)=0 (since the arrow hits the ground when h=0). We can use the quadratic formula to solve for t:

t = (-V₀ ± √(V₀² - 4ah₀)) / 2a

where a=-16, V₀=80, and h₀=50.

t = (-80 ± √(80² - 4x(-16)50)) / 2(-16) = 5 seconds or -1.5625 seconds

Since time can't be negative, the arrow will hit the ground after about 5 seconds.

c) To find the time it takes for the arrow to be 114 feet high, solve for t when h(t) = 114.

-16t² + 80t + 50 = 114

-16t² + 80t - 64 = 0

Dividing both sides by -16 gives:

t² - 5t + 4 = 0

Factoring gives:

(t-4)(t-1) = 0

So t=4 seconds or t=1 second.

Therefore, the arrow will be 114 feet high at 1 second and 4 seconds after launch.

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Answer:

4. n + 24

5. b - 11

6. d/5

Answer:

Using the logarithmic identity log(a) + log(b) = log(ab), we can simplify the left-hand side of the equation:

log2(x-1) + log2(x+5) = log2((x-1)(x+5))

So the equation becomes:

log2((x-1)(x+5)) = 4

Using the exponential form of logarithms, we can rewrite the equation as:

2^4 = (x-1)(x+5)

Simplifying:

16 = x^2 + 4x - 5

Rearranging:

x^2 + 4x - 21 = 0

Using the quadratic formula:

x = (-4 ± sqrt(4^2 - 4(1)(-21))) / (2(1))

x = (-4 ± sqrt(100)) / 2

x = (-4 ± 10) / 2

So x = -7 or x = 3.

However, we need to check whether these solutions satisfy the original equation. We can see that x = -7 does not work, because both terms inside the logarithms would be negative. Therefore, the only solution is x = 3.

Answer:

Using the properties of logarithms, we can simplify the left-hand side of the equation:

log2(x-1) + log2(x+5) = log2((x-1)(x+5))

Therefore, the equation becomes:

log2((x-1)(x+5)) = 4

Using the definition of logarithms, we can rewrite this equation as:

2^4 = (x-1)(x+5)

16 = x^2 + 4x - 5

Simplifying further:

x^2 + 4x - 21 = 0

We can now use the quadratic formula to solve for x:

x = (-4 ± sqrt(4^2 - 4(1)(-21))) / (2*1)

x = (-4 ± sqrt(100)) / 2

x = (-4 ± 10) / 2

x = -7 or x = 3

However, we need to check if these solutions satisfy the original equation.

When x = -7:

log2(x-1) + log2(x+5) = log2((-7-1)(-7+5)) = log2(16) = 4

So x = -7 is a valid solution.

When x = 3:

log2(x-1) + log2(x+5) = log2((3-1)(3+5)) = log2(16) = 4

So x = 3 is also a valid solution.

Therefore, the solutions to the equation log2(x-1) + log2(x+5) = 4 are x = -7 and x = 3.

Step-by-step explanation:

In a case whereby  stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches the thickness  of one card is 1/320 inches

Based on  the provided information, two hundred eighty cards is placed next to a ruler ten we can set up the expression as

( 7/ 8) / 280

7/ 8 * 1/280

1/320

Therefore, based on the given information, this implies that Each card is 1/320 inches

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The solution is :  the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².

Here, we have,

Use the basic 45-45-90 triangle with side length 1 as the building block here.  If the length of one side is 1, then the perimeter is 1 + 1 + 1 + 1, or 4, and the length of the diagonal is √2.

We are told that the length of the diagonal of the given square is 16 m.

Determine the length of one side of this square, using an equation of proportions:

16        x

------ = -------

√2       1

                                            16

Then (√2)x = 16, and x = -----------

                                            √2

The perimeter of the given square (with diagonal 16 mm)  is 4 times the side length found above, or:

     16                      16

4 ---------- = (2)(2) -----------  =  (2)(√2)(16) = 32√2 (all measurements in mm)

      √2                    √2

This perimeter, rounded to the nearest tenth, is 45.3 mm.

so, area of the  square is:

(16/√2)² = 512mm².

Hence, The solution is :  the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².

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The answer choice that matches the calculated confidence interval is 62.9 to 83.1

In statistics, the mean is a measure of central tendency that represents the average value of a set of numerical data. It is also known as the arithmetic mean, and it is calculated by adding up all the values in the dataset and dividing the sum by the number of values.

The mean is a useful measure of central tendency because it is easy to calculate, and it provides a single value that represents the center of the dataset. It is affected by outliers, which are extreme values that are far from the other values in the dataset, so it may not accurately represent the typical value of the data if there are outliers present.

To construct a 95.44% confidence interval for the mean score, u, of all students taking the test, we can use the formula:

CI = x ± t(alpha/2, n-1) * (s / √(n))

where CI is the confidence interval, x is the sample mean (73), t(alpha/2, n-1) is the t-value for the given alpha level (0.0278) and degrees of freedom (n-1=4) from the t-distribution table, s is the sample standard deviation, and n is the sample size.

The sample standard deviation is not given, so we will assume that it is the same as the population standard deviation, which is 15. Thus, s = 15.

Using the t-distribution table with 4 degrees of freedom and an alpha level of 0.0278, we find that the t-value is approximately 3.747.

Plugging in the values into the formula, we get:

CI = 73 ± 3.747 * (15 / √(5))

Simplifying, we get:

CI = 73 ± 16.27

Therefore, the 95.44% confidence interval for the mean score, u, of all students taking the test is:

CI = (73 - 16.27, 73 + 16.27)

CI = (56.73, 89.27)

Rounding to one decimal place, we get:

CI = (56.7, 89.3)

Therefore, the answer choice that matches the calculated confidence interval is:

62.9 to 83.1

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The complete question is:

The mean score, x on an aptitude test for a random sample of 5 students was 73, assuming that 0 = 15, construct a 95.44% confidence interval for the mean score, u of all students taking the test. answer choices, 43 to 103, 59.6 to 86.4, 62.9 to 83.1, and 67.0 to 79.0.

Answer:

B

Step-by-step explanation:

163 money t for time 2 for 2hours

The probability that exactly 19 men and 7 women are chosen is 0.053107%.

Probability:

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.

[tex]C_n_,_x[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_n_,_x=\frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

19 men, from a set of 21

7 women, from a set of 11

[tex]D= C_2_1_,_1_9[/tex]  × [tex]C_1_1_,_7[/tex] [tex]=\frac{21!}{19!2!}[/tex] ×  [tex]\frac{11!}{7!4!}[/tex][tex]=69,300[/tex]

Total outcomes:

26 people from a set of 21 + 11 = 32.

[tex]T=C_3_2_,_2_6=\frac{32!}{26!6!}[/tex][tex]=13,049,164,800[/tex]

The probability is :

P = [tex]\frac{D}{T}= \frac{69,300}{13,049,164,800} = 5.3107[/tex]

0.053107% probability that exactly 19 men and 7 women are chosen.

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A) (2x+1)⁰ = 96⁰

=> 2x = 96⁰ - 1⁰ = 95⁰

=> x = 95⁰/2 = 47⁰30' (= 47.5⁰)

B) x⁰ = (2x-7)⁰

=> x - 2x = -7

=> -x = -7

=> x = 7⁰

C) mIJ = 45⁰ ; mJK = 57⁰

m✓ IJK = 180⁰- 45⁰ - 57⁰ = 78⁰

=> mIK = 78⁰

Ans: a) 47.5⁰ b) 7⁰ c) mIJ = 45⁰ ; mJK = 57⁰ ; mIK = 78⁰

Ok done. Thank to me >:333

Answer: D

Step-by-step explanation:

When using deduction and starting from a given set of rules and conditions, you can determine what must be true. Therefore, the correct answer is:

D. What must be true