What is the diameter of a hemisphere
with a volume of 8052 m°, to the nearest
tenth of a meter?

The factored form of x² - 3x - 10 is (x-5)(x+2).

The given quadratic expression: x² - 3x - 10.

Step 1: Identify the terms in the expression
- Quadratic term: x²
- Linear term: -3x
- Constant term: -10

Step 2: Find two numbers that multiply to the constant term (-10) and add up to the linear term's coefficient (-3)
- Factors of -10: (-1, 10), (1, -10), (-2, 5), (2, -5)
- The pair (2, -5) adds up to -3

Step 3: Rewrite the expression using the factors found in Step 2
- x² - 3x - 10 = x² + 2x - 5x - 10

Step 4: Factor by grouping
- Group the terms: (x² + 2x) + (-5x - 10)
- Factor out the greatest common factor (GCF) from each group:
 - x(x + 2) - 5(x + 2)

Step 5: Factor out the common binomial
- (x + 2)(x - 5)

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The sum of 4/7 and -5/7 is -1/7, which represents a negative part of a whole, and is less than one-seventh of the total.

To add the fractions 4/7 and -5/7, we need to find a common denominator. Since the denominators are the same, we can simply add the numerators and put the result over the common denominator.

So, 4/7 + (-5/7) = (4 - 5)/7 = -1/7.

Therefore, the sum of 4/7 and -5/7 is -1/7. This means that if we have a group of objects that we divide into 7 equal parts, we would have 4 of those parts in one group, and then we would take away 5 of those parts, leaving us with a negative part, or -1/7 of the whole group.

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The 98% confidence interval of 93 course evaluation the estimation of the population standard deviation is (0.454, 0.681). For 93 professor evaluations, it is (0.318, 0.457). The course evaluations have a wider interval, indicating more variability compared to professor evaluations.

The construction of 98% confidence interval from which the 93 course evaluations were obtained, by using the formula

Confidence interval = (√((n-1)*s²)/√(chi-square upper)-√((n-1)*s²)/√(chi-square lower)),

where n is the sample size, s is the sample standard deviation, and chi-square upper and chi-square lower are the values from the chi-square distribution table with degrees of freedom (df) equal to n-1 and a cumulative probability of 0.99/2 = 0.495.

Using the given data, we have n = 93 and s = 0.56. From the chi-square distribution table with df = 92 and cumulative probability of 0.495, we obtain chi-square upper and chi-square lower as 67.339 and 49.645, respectively.

putting the values in the formula, we get

Confidence interval = (√((93-1)*0.56²)/√(67.339)-√((93-1)*0.56²)/√(49.645))

Confidence interval = (0.454, 0.681)

Therefore, we are 98% confident that the standard deviation of the population from which the 93 course evaluations were obtained falls within the interval (0.454, 0.681).

To construct a 98% confidence interval estimate of the standard deviation of the population from which the 93 professor evaluations were obtained, we can use the same formula as in above part, but with n = 93 and s = 0.41 (the sample standard deviation for professor evaluations).

From the chi-square distribution table with df = 92 and cumulative probability of 0.495, we obtain chi-square upper and chi-square lower as 67.339 and 49.645, respectively.

putting the values in the formula, we get

Confidence interval = (√((93-1)*0.41²)/√(67.339)-√((93-1)*0.41²)/√(49.645))

Confidence interval = (0.318, 0.457)

Therefore, we are 98% confident that the standard deviation of the population from which the 93 professor evaluations were obtained falls within the interval (0.318, 0.457).

Comparing the results from other parts, we can see that the confidence interval for the standard deviation of the population from which the course evaluations were obtained is wider than that for the population from which the professor evaluations were obtained. This suggests that there is more variability in the course evaluations than in the professor evaluations.

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Answer:

70 people out of 108 prefer pizza

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 1200}}{\left( \cfrac{30}{100} \right)1200}\implies 360~\hfill \underset{\textit{Jacob's apartment} }{\stackrel{1200~~ - ~~360 }{\text{\LARGE 840}}}[/tex]

Answer:

Step-by-step explanation:

The discount on each beach umbrella is $20 - $18 = $2.

The discount percentage can be found by dividing the discount by the original price and then multiplying by 100:

$2/$20 x 100% = 10%

Therefore, the discount percentage is 10%.

Answer:

y = 1/2x + 2

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (0,2) (2,3)

We see the y increase by 1 and the x increase by 2, so the slope is

m = 1/2

Y-intercept is located at (0,2)

So, the equation of the line is y = 1/2x + 2

The shares that has the highest price today is shares B. The Option D is correct.

Share price means the value of a company's stock. The total value of a public company is market capitalization which is arrived at by adding up the value of all of the stock outstanding.

Let the initial unit price of each share be $1.

After the first year, the prices become:

$1 * (1 - 10%), $1 * (1-20%), $1 * (1-30%)

A=$0.9, B=$0.8, C=$0.7.

After the second year, the prices become:

$0.9 (1 - 30%), $0.8*(1-20%), $1 * (1-10%)

A = $0.63, B = $0.64, C = $0.49.

Therefore, the Share B has the highest price today which is $0.64.

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Answer:

AOC=

130 degrees

Step-by-step explanation:

(circle)3x + (square)94 + (circle)x + square)18 + (circle)2x (square)-4 = 180

circles = 3x + x + 2x = 6x

squares = 94 + 18 + (-4) = 108

6x + 108 = 180

- 108 -108

6x = 72

6x/6 = 72/6

x= 12

angle AOC =

3x + 94

3 times 12 + 94

36+94 = 130 degrees

The probability of not rolling a 2 or 3 is 2/3

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes

Since Paris is not interested in rolling a 2 or 3, the number of favorable outcomes will be ?

Number of favorable outcomes = 6 - 2 = 4

Total number of outcomes = 6

The probability of not rolling 2 or 3 = 4 / 6 = 2/3

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There are 66 possible combinations of two committee members that can be chosen from the 12 applicants.

To determine the number of combinations possible for choosing two committee members out of twelve applicants, we can use the formula for combinations, which is:

[tex]nCk = n! / (k!(n-k)!)[/tex]

Where n is the total number of applicants (12), and k is the number of committee members to be chosen (2).

Plugging in the values, we get:

[tex]12C2 = 12! / (2!(12-2)!)[/tex]

12C2 = 66

The formula for combinations takes into account the number of ways to choose k items from a total of n items, without regard to order. This is why we use the combination formula instead of the permutation formula, which would take into account the order of the items chosen.

In this case, we want to choose two committee members out of 12 applicants, so we use the combination formula with n=12 and k=2 to get the answer of 66 possible combinations.

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The value of x for the given attached triangle satisfies the proportion of similar triangles is equal to 10.

From the attached figure,

In triangle ΔNMO and ΔTUV we have,

NM = 7,

MO = 9

TU = 3x - 9,

UV = 27

The corresponding sides of similar triangles are proportional,

Set up the proportion we get,

ΔNMO ~ ΔTUV

⇒ NM/TU = MO/UV

Substituting the given values, we get,

⇒ 7/(3x - 9) = 9/27

Simplifying, we get,

⇒ 7/(3x - 9) = 1/3

Cross-multiplying, we get,

⇒ 21 = 3x -9

Adding 9 to both sides, we get,

⇒ 3x = 30

Dividing both sides by 3, we get,

⇒ x = 30/3

⇒ x = 10

Therefore, the value of x that satisfies the proportion is x = 10.

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The above question is incomplete, the complete question is:

Solve for x. Set up the proportion.

In triangle ΔNMO ~ ΔTUV.

NM = 7, MO = 9

TU = 3x - 9, UV = 27

Attached figure.

Answer:To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 3:5.

The scaled base will be:

16 feet x (3/5) = 9.6 feet

The scaled height will be:

9 feet x (3/5) = 5.4 feet

Therefore, the dimensions of the new deck will be 9.6 feet for the base and 5.4 feet for the height.

Step-by-step explanation:

Answer:

Part A:

The ratio of the sides of the new deck to the original deck is 2:5. Therefore, the base and height of the new deck can be found by multiplying the base and height of the original deck by the scale factor, which is 2/5.

Base of new deck = 15 * (2/5) = 6 feet

Height of new deck = 9 * (2/5) = 3.6 feet

Therefore, the dimensions of the new deck are 6 feet for the base and 3.6 feet for the height.

Part B:

The area of a triangle can be found by multiplying the base and height and dividing by 2.

Area of original deck = (15 * 9) / 2 = 67.5 square feet

Area of new deck = (6 * 3.6) / 2 = 10.8 square feet

Therefore, the area of the original deck is 67.5 square feet and the area of the new deck is 10.8 square feet.

Part C:

The ratio of the areas of the new deck to the original deck is:

Area of new deck / Area of original deck = 10.8 / 67.5 = 0.16

The scale factor is 2:5, or 0.4 as a decimal. The ratio of the areas is smaller than the scale factor. This means that the new deck is smaller than what it would be if it were built to scale.

The requried complete statement is a system of equations consisting of two equations with two variables in each, x and y.

A system of equations is a set of two or more equations that contain multiple variables. The variables in the system are usually represented by the same letters in each equation, and the goal is to find a set of values for the variables that satisfy all of the equations simultaneously.

Thus, the requried complete statement is a system of equations consisting of two equations with two variables in each, x and y.

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The proportional segment lengths that verify that QS || MN is 9/1.5 = 12/2

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

The triangles

The triangles are similar triangles

So, we have

RM/MQ = RN/NS

substitute the known values in the above equation, so, we have the following representation

9/1.5 = 12/2

Hence, the proportion is 9/1.5 = 12/2

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The factored form of the equation f(x) = 2x² – 9x – 18 is  (2x-3)(x+6)

The given equation is 2x² – 9x – 18

We have to factor out the expression

Let us take a=2, b=-9 and c =-18

To factor the equation, we need to find two numbers that add to -9 (which is the b variable in the equation) and multiply to -36

2x²+12x-3x – 18

2x(x+6)-3(x+6)

(2x-3)(x+6)

Hence, the factored form of the equation f(x) = 2x² – 9x – 18 is  (2x-3)(x+6)

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Step-by-step explanation:

To determine which team had the best overall record for the season, we need to compare the total points earned by each team across all the games they played. We can calculate the total points for each team by adding up the points earned in each game.

For the Eagles:

Total points = 3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55

= 310

For the Falcons:

Total points = 24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14

= 300

Based on these calculations, the Eagles earned a total of 310 points while the Falcons earned a total of 300 points, making the Eagles the team with the best overall record for the season.

To determine the best measure of center to compare, we need to consider whether the data is skewed or not. A skewed dataset has a long tail on one side, which can affect the mean value. In this case, we can calculate both the mean and the median to compare the central tendency of the data.

For the Eagles, the mean is:

Mean = (3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55) / 15

= 20.67

For the Falcons, the mean is:

Mean = (24 + 24 + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14) / 15

= 20.00

The median for the Eagles is 21, which is higher than the median for the Falcons, which is 24. Therefore, the best measure of center to compare is the median. This suggests that the Eagles were more consistent in their point-scoring throughout the season, with fewer extreme values that might have skewed the mean.

Answer:

L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Step-by-step explanation:

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 225 sq.ft. Therefore, we have:

L x W = 225

The perimeter of the rectangle is given by:

2L + 2W

We need to find the dimensions of the rectangle that will give the smallest possible perimeter. To do this, we need to minimize the expression for the perimeter subject to the constraint that the area is 225 sq.ft. We can use the method of Lagrange multipliers to solve this problem.

Let f(L, W) = 2L + 2W be the expression for the perimeter and g(L, W) = L x W - 225 be the expression for the area. We want to minimize f(L, W) subject to the constraint g(L, W) = 0.

The Lagrange function is given by:

L(L, W, λ) = f(L, W) - λg(L, W)

= 2L + 2W - λ(LW - 225)

Taking partial derivatives and setting them equal to zero, we get:

∂L/∂λ = W = 0

∂W/∂λ = L = 0

∂L/∂λ = -λW = 0

∂W/∂λ = -λL = 0

∂L/∂λ = 2 - Wλ = 0

∂W/∂λ = 2 - Lλ = 0

Solving these equations, we get:

λ = 2/L = 2/W

Substituting λ in the expression for the area, we get:

L^2 = 225

Therefore, L = 15 and W = 15. Hence, the dimensions of the rectangle with the smallest perimeter and area of 225 sq.ft. are 15 ft x 15 ft (i.e. a square).

Answer:

width = 15 ft

length = 15 ft

Step-by-step explanation:

Let x = length and y = width.

area = length × width

A = xy

perimeter = 2(length + width)

P = 2(x + y)

P = 2x + 2y

A = 225

xy = 225

y = 225/x

P = 2x + 2(225/y)

P = 2x + 450/x

P = 2x + 450x^-1

dP/dx = 2 + 450(-1)(x^-2)

dP/dx = 2 - 450/x²

2 - 450/x² = 0

2x² - 450 = 0

x² - 225 = 0

x = ±√225

x = ±15

Discard x = -15.

width = 15 ft

length = 15 ft

The width of the rectangle is 0.9 cm to 1 d.p.

A triangle is a three-sided polygon or a three-dimensional object composed of three flat surfaces that intersect at three vertices. Triangles can be classified based on their sides and angles. Equilateral triangles have all three sides equal, isosceles triangles have two sides equal, and scalene triangles have all three sides of different lengths. Triangles can also be classified based on their angles. Right triangles have one 90-degree angle, obtuse triangles have one angle greater than 90-degrees, and acute triangles have all angles less than 90-degrees.

The circumference of the shaded face can be calculated using the formula for circumference of a circle, C = 2πr, where r is the radius of the circle. The radius of the shaded face can be found by subtracting the height of the net (h) from the radius of the cylinder (R). Therefore, the circumference of the shaded face can be calculated as follows:

C = 2π(R-h)
= 2π(2-1)
= 2π
= 6.28

The circumference of the shaded face is 6.28 cm to 1 d.p.

b) To calculate the width, w, of the rectangle, we can use the formula for area of a rectangle, A = lw, where l is the length of the rectangle. The area of the rectangle can be found by adding the area of the two semicircles (πr2) and subtracting the area of the triangular part (½bh). Therefore, the width of the rectangle can be calculated as follows:

A = lw
w = A/l
w = (2πr2+2πr2-½bh)/2(2πr)
w = (4πr2-½bh)/(4πr)
w = (8-1)/(8)
w = 7/8

The width of the rectangle is 0.9 cm to 1 d.p.

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The width of the rectangle is 0.9 cm to 1 d.p.

What is triangle?

A triangle is a three-sided polygon or a three-dimensional object composed of three flat surfaces that intersect at three vertices. Triangles can be classified based on their sides and angles. Equilateral triangles have all three sides equal, isosceles triangles have two sides equal, and scalene triangles have all three sides of different lengths. Triangles can also be classified based on their angles. Right triangles have one 90-degree angle, obtuse triangles have one angle greater than 90-degrees, and acute triangles have all angles less than 90-degrees.

The circumference of the shaded face can be calculated using the formula for circumference of a circle, C= 2nr, where r is the radius of the circle. The radius of the shaded face can be found by subtracting the height of the net (h) from the radius of the cylinder (R). Therefore, the circumference of the shaded face can be calculated as follows:

С = 2π(R-h)

= 2m(2-1)

= 2π

= 6.28

The circumference of the shaded face is 6.28 cm to 1 d.p.

b) To calculate the width, w, of the rectangle, we can use the formula for area of a rectangle, A = lw, where I is the length of the rectangle. The area of the rectangle can be found by adding the area of the two semicircles (mr²) and subtracting the area of the triangular part (½bh). Therefore, the width of the rectangle can be calculated as follows:

A = Iw

w = A/I

w = (2πг²+2πг²-2bh)/2(2πг)

w = (4πr²-2bh)/(4πг)

w = (8-1)/(8)

W = 7/8

The width of the rectangle is 0.9 cm to 1 d.p.

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A fence of 15 m with the start of the fence at coordinates (8,5), the coordinates of the other end of the fence is equals to the (5.75, 2).

Grady's father wants to build a 15-meter fence with the start point of the fence at coordinates (8,5). Midpoint of fence at coordinates (3.5,-1). We have to determine the coordinates of the other end of the fence. The midpoint is defined as the centre point of a line segment. It is at equal distance from both endpoints,

Let the cordinate of other side point be (x,y). Using the mid point formula, [tex](x,y) = (\frac{x_1 + x_2 }{2}, \frac{y_1 + y_2 {2}[/tex]), where

For x-coordinate, 2x = 3.5 + 8

=> 2x = 11.5

=> x = 5.75

for y-coordinate, 2y = 5 - 1 = 4

=> y= 2

Hence, required value is (5.75, 2).

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The probability that it is snowing in Greenland when glaciers are growing is approximately 0.7165.

To solve this problem, we can use Bayes' theorem, which states that the probability of an event A given that event B has occurred is equal to the probability of event B given that event A has occurred, multiplied by the probability of event A, divided by the probability of event B.

Let A be the event that it is snowing in Greenland, and let B be the event that glaciers are growing. We want to find P(A|B), the probability that it is snowing in Greenland given that glaciers are growing.

We are given that the probability of glaciers growing when it snows in Greenland is 0.21, and the probability of glaciers growing when it does not snow is 0.03. We are also given that it snows in Greenland once every 24 days, so the probability of it snowing is 1/24 = 0.0417.

Using Bayes' theorem, we can calculate P(A|B) as follows:

P(A|B) = P(B|A) * P(A) / P(B)

P(B|A) is the probability of glaciers growing given that it is snowing, which is 0.21.

P(A) is the probability of it snowing, which is 0.0417.

P(B) is the overall probability of glaciers growing, which is the weighted average of the probabilities of glaciers growing when it snows and when it does not snow:

P(B) = 0.21 * 0.0417 + 0.03 * (1 - 0.0417) = 0.0342

Substituting these values into Bayes' theorem, we get:

P(A|B) = 0.21 * 0.0417 / 0.0342 = 0.2558

Therefore, the probability that it is snowing in Greenland when glaciers are growing is approximately 0.7165 (rounded to four decimal places).

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Answer:

$120

EXPLANATION

since the total cost is $8880

and his parents are giving $6000

so left money he need to save is $2880

now he has time of 2 years which means 24 months

so using unitary method

24 months = $2880

1 month= $2880/24

1 month = $116.66

which is nearly $120

The square root of a negative number is undefined in the real number system because any real number squared will always yield a non-negative result.

In the complex number system, the square root of -x can be expressed as √-x = i√x, where i is the imaginary unit (√-1). This means that the square root of a negative number is a purely imaginary number.

For the function f(x) = √-x, the domain must be restricted to non-negative real numbers (x ≥ 0) to ensure that the argument of the square root is always non-negative. The range of the function includes all purely imaginary numbers (yi) where y is a real number.

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The correct question is:

The square root of a negative number, such as √-144, is undefined. Explain why the square root of –x,√-x , is not necessarily undefined and what this means about the domain and range of f(x) = .√-x

A digit that makes the number 6,197,34_ divisible by 6 is given as follows:

0.

(6 is another possible answer).

A number is said to be divisible by six when it is:

A number is divisible by 2 when it is an even number, meaning that it finishes in either 0, 2, 4, 6 or 8.

A number is divisible by 3 when the sum of the digits is a multiple of 3.

The sum of the digits is given as follows:

6 + 1 + 9 + 7 + 3 + 4 + x = 30 + x.

Hence with a final digit of zero or six, the number is divisible by six.

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Answer:

ddd

Step-by-step explanation:

Therefore, Mario's winnings of 177 dollars is approximately 2.92 standard deviations below the mean.

We can calculate the number of standard deviations that Mario's winnings of 177 dollars is from the mean using the formula:

z = (x - μ) / σ

where x is the value we want to convert to standard deviations, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

In this case, Mario's winnings of 177 dollars is the value we want to convert to standard deviations, the mean is μ = 323 dollars, and the standard deviation is σ = 50 dollars. Substituting these values into the formula, we get:

z = (177 - 323) / 50

= -2.92

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If the length of a rectangle is 4 units less than its width w+10, the area of the rectangle is expressed in terms of w as w² + 6w.

Let's assume that the width of the rectangle is w. As given, the length of the rectangle is 4 units less than its width plus 10, which means the length is (w + 10) - 4 = w + 6.

So, the width of the rectangle is w units and the length is (w + 6) units.

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the rectangle is:

Area = length x width

Area = (w + 6) x w

Area = w² + 6w

If we are given the value of w, we can find the area by substituting the value of w in the equation. If the value of w is not given, then the area of the rectangle cannot be calculated.

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Complete question is:

The length of a rectangle is 4 units less than its width w+10. Find expression for area of rectangle.

The factor of expression is,

⇒ (x + 4)

Given that;

Equation is,

⇒ 6x³ - 12x² - 48x

Now, We can factored the expression as;

⇒ 6x³ - 12x² - 48x

⇒ 6x (x² - 2x - 8)

⇒ 6x (x² - 4x + 2x- 8)

⇒ 6x (x (x - 4) + 2 (x - 4))

⇒ 6x (x - 4) (x + 2)

Thus, The factor of expression is,

⇒ (x + 4)

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