*
Which pins must be knocked over to score exactly 100 points? Check as
many as you need to get 100.
13 8
57
48
39
47
24

Answer:

The answer is 3x^2-13x-10

Step-by-step explanation:

Answer:

3x^2-13x-10

Step-by-step explanation:

(3x+2)(x-5)

3x^2-15x+2x-10

3x^2-13x-10

The number that is ten thousand greater than 585,501 is 595,501.

A greater number is a number that when compared with another has a higher numerical value than the former.

To show that a number is greater than another, more values can be determined to account for their differences using basic mathematical operations like addition, subtraction, multiplication, and division.

The population of Wyoming in 2020 = 585,501

Additional population to Wyoming = 10,000

New population of Wyoming = 595,501 (585,501 + 10,000)

Thus, the number that is ten thousand greater than 585,501 is 595,501.

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Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

Answer: 166.72 \(ft^{2}\)

Step-by-step explanation: math

Step-by-step explanation:

All you have to do here is use the surface area, or SA, equation.

Sa=2lw+2lh+2hw
sa=2(8.5)(3.2)+2(8.5)(4.8)+2(4.8)(3.2)

Sa=54.4+81.6+30.72

Sa=166.72

Hope this helped!

The real GDP in 1984 and 2005 were both $5,000.

A. The GDP price index for 1984, using 2005 as the base year, can be calculated as follows:
- First, we need to find the nominal GDP for 1984 and 2005. Nominal GDP is the total output of an economy multiplied by the price of the output.
- In 1984, nominal GDP = 10,000 buckets of chicken x $10 = $100,000
- In 2005, nominal GDP = 25,000 buckets of chicken x $20 = $500,000
- Next, we need to calculate the GDP price index for 1984, using 2005 as the base year. The formula for the GDP price index is: (nominal GDP / real GDP) x 100
- Since we are using 2005 as the base year, the real GDP for 2005 is the same as the nominal GDP for 2005, which is $500,000.
- Therefore, the GDP price index for 1984 = ($100,000 / $500,000) x 100 = 20

B. To find the percentage increase in the price level between 1984 and 2005, we can use the formula: [(GDP price index in 2005 - GDP price index in 1984) / GDP price index in 1984] x 100
- The GDP price index in 2005 is 100, since we are using 2005 as the base year.
- The GDP price index in 1984 is 20, as calculated in part A.
- Therefore, the percentage increase in the price level between 1984 and 2005 = [(100 - 20) / 20] x 100 = 400%

C. To find the real GDP for 1984 and 2005, we can use the formula: real GDP = nominal GDP / GDP price index
- In 1984, nominal GDP = $100,000 and GDP price index = 20, so real GDP = $100,000 / 20 = $5,000
- In 2005, nominal GDP = $500,000 and GDP price index = 100, so real GDP = $500,000 / 100 = $5,000
- Therefore, the real GDP in 1984 and 2005 were both $5,000.

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There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

3x + 6 =27

Step-by-step explanation:

A. The solution is 7! First I Subtracted 6 from both sides of the equation, Then I Divided both sides of the equation by the same term. Then I got "7" from doing the following.

B. The solution is the x in the answer which is the amount of juice he poured.

"Diego has 27 ounces of juice. He pours equal amounts for each of his 3 friends and has 6 ounces left for himself"

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

work is shown and pictured

The triangle given is a scalene acute triangle

A triangle can be classified based on the measures of its angles and the lengths of its sides.

In this case, the angle measures of the triangle are 82, 75, and 23 degrees. Since the sum of the angles in a triangle is always 180 degrees, we can verify that these angles satisfy this condition: 82 + 75 + 23 = 180.

The triangle is not an equilateral triangle because all the sides are not of equal length.

The triangle also doesn't have one right angle so it can't be right triangle.

Now, as per the angle measures, none of the angles are right angles, but one angle is greater than 90 degree, so this triangle is not acute triangle.

So, this triangle is not an Obtuse triangle since it has no angle greater than 90 degrees.

As the triangle has no sides of equal length, it is also a Scalene triangle.

Therefore, the triangle would be classified as a Scalene acute triangle (c).

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Answer:

38° because the other two are cm? also you haven't linked a photo so I can't work out angle A

Answer:

Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.

Answer:

25 degrees

Step-by-step explanation:

Angles on a line add up to 180

180-50=130

angles in a triangle add up to 180

An isosceles triangle has two equal angles

180-130=50

50/2=25

25 degrees

By setting up the equation and solving for the unknown variable, we find that the number in question is -15. The answer provides a step-by-step method for solving an equation that represents a word problem.

Let's start by translating the given problem into an equation.

"The product of a number and -6" can be written as "-6x", where "x" is the unknown number. "Five times the sum of that number and 33" can be written as "5(x+33)".

Putting these together, we get:

-6x = 5(x+33)

Now we can solve for "x":

-6x = 5x + 165

-11x = 165

x = -15

Therefore, the number we're looking for is -15.

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The surface area of a cylinder is given by:

And the volume by:

Where:

r = radius = 4in

h = height = 6in

so:

Answer:

502.5pi or 1578.1415

Step-by-step explanation:

find area of one triangle (BH divided by 2), then multiply it by two since there are two, then find area of circle(pir^2),  divide in half because it is a semi-circle, add the areas together

Answer:)Angle FIH and GIE after keeping angle EIH at 140° is 40° while ∠FIG will is the opposite angle of ∠EIH so it will remain the same as 140°.

Step-by-step explanation:We need to intersect both lines and make ∠EIH > 135°

So,Let's keep ∠EIH = 140°

Then,∠FIG = 140° (opposite angle)∠FIH = ∠GIE = x (opposite angle)

Now,The Sum of all angles around I will be 360 degrees.

So,140 + x + 140 +  x = 360 ,2x + 280 = 360, 2x = 80 ⇒ x = 40°.

The new dimension of the rectangular field are 45 ft by 120ft.

If the field has originally dimensions length L and width W, and we apply a scale factor K, then the new dimensions of the rectangle are:

lenght = K*L

width = K*W

In this case the original dimensions are:

L = 30ft

W = 80ft

And the scale factor is K = 1.5, then the new dimensions are:

L' = 1.5*30ft = 45ft

W' = 1.5*80ft = 120ft

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Answer:

Not rounded:

1.62 increased by 8% of the value = 1.7496

The actual change:

1.7496 - 1.62 = 0.1296

Rounded off to max. 2 decimal places:

1.62 increased by 8% of the value ≈ 1.75

The actual change:

1.75 - 1.62 ≈ 0.13

Step-by-step explanation:

'Percent (%)' means 'out of one hundred':

8% = 8 'out of one hundred',

p% is read p 'percent',

p% = p/100 = p ÷ 100

8% = 8/100 = 8 ÷ 100 = 0.08

100% = 100/100 = 100 ÷ 100 = 1

The value of the percentage increase = 8% × 1.62

The new value = 1.62 + The value of the percentage increase

The new value =

1.62 + The value of the percentage increase =

1.62 + (8% × 1.62) =

1.62 + 8% × 1.62 =

(1 + 8%) × 1.62 =

(100% + 8%) × 1.62 =

108% × 1.62 =

108 ÷ 100 × 1.62 =

108 × 1.62 ÷ 100 =

174.96 ÷ 100 =

1.7496 ≈

1.75

The actual change =

The new value - 1.62 =

1.7496 - 1.62 =

0.1296 ≈

0.13

The value of the percentage increase =

8% × 1.62 =

8 ÷ 100 × 1.62 =

8 × 1.62 ÷ 100 =

12.96 ÷ 100 =

0.1296 ≈

0.13

From the pie-chart given, the best estimate for central angle for the leading cause which is "Human Error" is: B. 165 degrees.

The leading cause of train derailment will be the cause on the pie-chart that has the largest sector.

From the pie-chart given, the largest sector in the diagram is the sector for "Human Error."

This means that the leading cause is definitely "Human Error."

The central angle of the sector for "Human Error." is between 90 degrees and 180 degrees. That's less than half a full circle and less of a quarter circle. The best estimate from the given options is 165 degrees.

Therefore, from the pie-chart given, the best estimate for central angle for the leading cause which is "Human Error" is: B. 165 degrees.

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Answer:

B 165

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = area of triangle + area of rectangle 1 +  area of rectangle 2 + area of rectangle 3

= (1/2)*10*20 + 9 * 14 + 21* 3 + 5*7

= 100 + 126 + 63 + 35

= 324 sq.in

Answer:

Option D

Step-by-step explanation:

A matched pairs t-test is appropriate for this experiment. It compares two means that are from the same individual; the before drug administration and the after drug administration. It compares the before-and-after observations on the same subjects.

The best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

The test is one of the kinds of inferential statistics. It is deployed in decision making. As such, it involves the test to see if there is significant difference between the means of two groups, which may be related.

Hence, in this study, the best and convincing statistical evidence of a change, on average, in blood pressure is the t test.

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Answer:

2, 1/2

Step-by-step explanation:

Arithmetic mean of two numbers is given as

\(n=\frac{a+b}{2}\)

Here a=x and b=1/x

\(n=\frac{x+1/x}{2}\)

\(\frac{5}{4} =\frac{x^{2}+1}{2x}\)

\(\frac{5}{2}x=x^{2} +1\\ x^{2}-\frac{5}{2}x+1=0\)

\(x=2, \frac{1}{2}\)

Hence the numbers are 1/2 and 2.

If x is any real number, then the reciprocal of this number will be 1/x. For example, the reciprocal of 5 is 1 divided by 8, i.e. 1/5.

Given, one number is reciprocal to another.

So if we choose the first number to be x , the the other number becomes its reciprocal i.e. 1/x.

Now, it is given that the arithmetic mean of these two numbers is 5/4.

So using formula for arithmetic mean ,

Mean = Sum of Observations / No. of observations

\(\frac{5}{4} =\frac{x+\frac{1}{x}}{2} \\\frac{5*2}{4}= \frac{x^{2} +1}{x} \\\frac{5}{2} =\frac{x^{2}+1}{x} \\\)

On cross Multiplication and Factorization, we get:

\(5x=2x^{2}+2\\2x^{2} -5x+2=0\\2x^{2} -4x-x+2=0\\2x(x-2)-1(x-2)=0\\(2x-1)(x-2)=0\\2x-1=0 , x=1/2\\x-2=0 , x=2\)

So , when x=1/2 , then 1/x=2

and when x=1/2 , then x=2

Hence,  the numbers are 2 and 1/2 .

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The given system of equations have only one solution, y = -7/5.

Given,

The system of equations;

y = 1/3x - 1

y = 2x + 1

We have to find the number of solutions for this system of equations;

For that, lets check the slope of the equations.

y = 1/3x - 1. Slope, m = 1/3

y = 2x + 1. Slope, m = 2

Here the equations have different slope. Then it will not be on the same line. Also it has only one solution.

Lets check.

Equate the equations and find x.

That is,

1/3x - 1 = 2x + 1

1/3x - 2x = 1 + 1

1/3x - 6/3x = 2

-5/3x = 2

-5x = 6

x = -6/5

Now find y using x as -6/5.

y = 1/3x - 1

y = 1/3 x -6/5 - 1

y = -6/15 - 1

y = -2/5 - 1

y = -2 -5 / 5

y = -7/5

Now solve for next equation. Will get the same solution.

y = 2x + 1

y = 2 x -6/5 + 1

y = -12 /5 + 1

y = -12 + 5 / 1

y = -7/5

That is, the given system of equations have only one solution, y = -7/5.

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To estimate the population proportion to within plus or minus 2% with 95% confidence, a sample size of at least 804 is needed.

This can be calculated using the formula for determining sample size for estimating a population proportion:

n = (Z^2 * p * (1-p)) / (E^2)

Where n is the sample size, Z is the z-score corresponding to the desired level of confidence (1.96 for 95% confidence), p is the estimated proportion of the population with the characteristic of interest (assumed to be 0.5 for this calculation), and E is the maximum margin of error desired (2% in this case). Plugging these values into the formula, we get:

n = (1.96^2 * 0.5 * (1-0.5)) / (0.02^2) = 803.84

Since this is a sample size estimate, we should round up to the next whole number, resulting in a sample size of 804.

Therefore, the correct answer is as given above

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Answer:

X < 3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

2x - 2 < 4

      +2   +2

2x = 6

/2      /2

x = 3

Answer:

no

Step-by-step explanation:

Answer:  (11) Julius asks Rachel if she would like to sell her boat. Rachel privately has no interest in selling her boat and believes that Julius can't afford her boat anyway. Rachel says, "I'd sell my boat to you for $20,000." To Rachel's surprise, Julius responds "Ok, it's a deal." Rachel does not want to sell the boat to Julius for any price. Julius and Rachel have:

The inequality expression that corresponds to the solution of the inequality graph is x² + 3x - 3 < 0.

option B.

The inequality expression that corresponds to the solution of the inequality graph is determined by simplifying the equations as follows;

The solution of the graph,

x > -4 and x < 1

The first equation with "≥" is ruled out because the graph doesn't have a thick dot.

Let's simplify the second expression;

x² + 3x - 3 < 0

solve using quadratic formula;

x > -3.79 or x < 0.79

The third expression is ruled out since its solution will be complex.

For the last expression;

x² + 3x - 3 > 0

x < -3.79 or x > 0.79

Thus, the correct inequality expression is x² + 3x - 3 < 0.

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