SHOW WORK A snowboarder stands at the edge of a 4.50 m high half-pipe. The mass of the snowboarder is 55.0 kg. What is the gravitational potential energy of the snowboarder thanks

Answer:

The value of a is 4. This can be determined by multiplying both sides of the equation by 10, which yields 5√10 = 4√10 + 6√10. Subtracting 4√10 from both sides yields a√10 = 6√10, and dividing both sides by 6 yields a = 4.

The answer to this question after completing the recursively-defined function to describe this sequence the next term would be 10206.

The sequence described in the problem is generated by a recursively-defined function, where each term is calculated based on the previous term. The first term of the sequence is given as f(1) = 14000. The next terms are then calculated by applying the function f(n) = f(n-1) x 0.9, where n is the position of the term in the sequence, starting from 1.So, in this sequence, the second term is given by f(2) = f(1) x 0.9 = 14000 x 0.9 = 12600. The third term is then given by f(3) = f(2) x 0.9 = 12600 x 0.9 = 11340. This pattern continues, with each term being calculated as the previous term multiplied by 0.9.Given this information, the next term in the sequence can be calculated as f(n) = f(n-1) x 0.9, where f(n-1) = 11340. Hence, the next term in the sequence is f(n) = 11340 x 0.9 = 10206.Therefore, the answer to the question is 10206.

f(1)=14000; f(n)= f(n-1) x 0.9

14000,12600,11340…

12600=14000=0.9;11340/12600=0.9

f(1)=14000

f(2)=12600=1400x0.9=f( 1).0.9

f(3)=11340=12600x0.9=f(2).0.9……..

f(n)=f(n-1).0.9

Therefore the next sequence is 11340x0.9

=10206

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Answer:

(-3, -1/2)

Step-by-step explanation:

[tex]y=\frac{1}{2}x+1[/tex]

[tex]y=\frac{3}{2}x+4[/tex]

Move all the variables to one side and the numbers to the other

[tex]\frac{1}{2}x-y=-1[/tex]

[tex]\frac{3}{2}x-y=-4[/tex]

Multiply the first equation by -1 to solve by elimination

[tex]-\frac{1}{2}x+y=1[/tex]

[tex]\frac{3}{2}x-y=-4[/tex]

Subtract

[tex]x=-3[/tex]

Use substitution

[tex]y=\frac{(-3)}{2} +1[/tex]

[tex]y=-1.5+1[/tex]

[tex]y=-0.5=\frac{-1}{2}[/tex]

a. The mean of the sampling distribution of ô is 8%.

b. The standard deviation of the sampling distribution is 0.0115

c. The sampling distribution of p is approximately Normal

d. Probability that the random sample of 1000 adults will give a result within 2 would be -17.39 and 17.39.

e. No, finding that 10% of a sample of 1000 adults have never had a cavity does not provide convincing evidence that the American Dental Association needs to update their statistics and there is more than 8% of adults who have never had a cavity.

What is Standard deviation, Probability?

Standard deviation: Standard deviation is a measure of how evenly distributed numbers are. It is the square root of the Variance, which is the average of the squared deviations from the Mean.

Probability: Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true.

a. The mean of the sampling distribution of ô is 8%. This is the proportion of adults in the population who have never had a cavity, as stated by the American Dental Association.

b. The standard deviation of the sampling distribution of p is given by the formula:

[tex]$\sigma_{\hat{p}}\\ = \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\= \sqrt{\frac{0.08(1-0.08)}{1000}} \\= 0.0115$[/tex]

The standard deviation measures how much the sample proportions are likely to vary from the true population proportion.

In this case, the standard deviation of the sampling distribution is 0.0115, which means that the sample proportions are likely to vary by approximately 0.0115 from the true population proportion.

c. The sampling distribution of p is approximately Normal because the Large Counts condition is met. The Large Counts condition states that the sample size is large enough such that the sample proportions are approximately normally distributed, even if the population is not normally distributed. In this case, with a sample size of 1000, the sample proportions are likely to be approximately normally distributed.

d. To find the probability that the random sample of 1000 adults will give a result within 2 percentage points of the true value (6%-10%), we need to find the area under the normal curve that corresponds to this interval.

First, we need to standardize the interval by using the standard deviation of the sampling distribution:

[tex]$z_1 = \frac{6 - 8}{0.0115} = -17.39$[/tex]

[tex]$z_2 = \frac{10 - 8}{0.0115} = 17.39$[/tex]

Using a standard normal table or a normal calculator, we find that the area under the normal curve to the left of -17.39 is approximately 0 and the area under the normal curve to the right of 17.39 is approximately 0. Hence, the area under the normal curve between -17.39 and 17.39 is approximately 1, which means that the probability of getting a result within 2 percentage points of the true value is 100%.

e. No, finding that 10% of a sample of 1000 adults have never had a cavity does not provide convincing evidence that the American Dental Association needs to update their statistics and there is more than 8% of adults who have never had a cavity. The result of 10% is within the range of values that can be expected based on random sampling error. It is possible that the sample proportion of 10% is due to random chance, rather than a true change in the population proportion. To determine if the true population proportion has changed, more data and statistical analysis are needed.

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Answer:

Step-by-step explanation:

Sorry if the dots confuse you, it's where the dots are graphed for people to see where I place them and to see if it matches. (Blue marks are 5 intervals.)

The two-columns method can be used to prove that the triangles ΔABC and ΔADC are congruent (ΔABC ≅ ΔADC), by completing the included table as follows;

Step [tex]{}[/tex]                          Statement                  [tex]{}[/tex]              Reason

1  [tex]{}[/tex]                              [tex]\overline{AD}[/tex] ≅ [tex]\overline{AB}[/tex]   [tex]{}[/tex]                            

 [tex]{}[/tex]                                [tex]\overline{AB}[/tex] ⊥ [tex]\overline{BC}[/tex]          [tex]{}[/tex]                        Given

[tex]{}[/tex]                                  [tex]\overline{AD}[/tex] ⊥ [tex]\overline{DC}[/tex]                                

2. [tex]{}[/tex]                ΔABC and ΔADC are right Δs              Definition

3. [tex]{}[/tex]       [tex]\overline{AC}[/tex] is the hypotenuse side of the right Δs   Definition

4.     [tex]{}[/tex]                         [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                                   Reflexive property

5. [tex]{}[/tex]                          ΔABC ≅ ΔADC                            HL congruency rule

Congruent triangles are triangles in which the lengths of the three sides of each triangle are the same measure with the lengths of the three sides of the triangle with which they are congruent.

The details of the reasons used to prove the congruency of the triangles ΔABC and ΔADC, are presented as follows;

Definition of right triangles

A right triangle is a triangle that has an interior angle of 90°. The angle formed between two perpendicular lines is 90°.

The sides [tex]\overline{AB}[/tex] and [tex]\overline{BC}[/tex] of the triangle ΔABC are perpendicular, thereforte, the angle ∠B is 90°

Similarly, the sides [tex]\overline{AD}[/tex] and [tex]\overline{DC}[/tex] are perpendicular, therefore, the measure of the angle D, m∠D is 90°

Therefore, the triangles ΔABC and ΔADC are right triangles

Hypotenuse side of a right triangle

The hypotenuse side of a right triangle is the side linking the perpendicular sides and facing the 90° angle

HL congruency rule

The Hypotenuse-Leg (HL) congruency rule states that if the hypotenuse side and a leg of a right triangle are congruent to a hypotenuse side and a leg of a right triangle, the two right triangles are congruent.

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The scale factor of the dilation from △ABC to △A"B"C" is 416.

What is scale factor?

A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller)

The scale factor of a dilation is equal to the ratio of the lengths of corresponding sides of the preimage and the image.

In this case, the dilation from △ABC to △A'B'C' has a scale factor of D(13), and the dilation from △A'B'C' to △A"B"C" has a scale factor of D(32). To find the scale factor of the dilation from △ABC to △A"B"C", we need to multiply these two scale factors:

D(△ABC to △A"B"C") = D(13) * D(32)

D(△ABC to △A"B"C") = 13 * 32

D(△ABC to △A"B"C") = 416

So, the scale factor of the dilation from △ABC to △A"B"C" is 416.

This means that the lengths of corresponding sides of △ABC and △A"B"C" are related by a factor of 416.

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Answer:

108

Step-by-step explanation:

480÷30= 6 [no. of groups in 30]

18×6= 108

Answer:

288

Step-by-step explanation:

To estimate the number of 7th graders attending the dance, we need to extrapolate the sample proportion to the total population.

The sample proportion of 7th graders who are going to the dance is 18/30 = 0.6.

So, the estimated number of 7th graders who will attend the dance is:

0.6 * 480 = 288.

Answer:

4e-4=e-4

subtract 4 from both sides

4e=e

subtract e from both sides

4e-e=0

4e-e equals 3e

3e= 0

divide by 3 both sides

3/3=0/3

e=0

Answer:

e = 0

Step-by-step explanation:

4e - 4 = e - 4 ( subtract e from both sides )

3e - 4 = - 4 ( add 4 to both sides )

3e = 0 ( divide both sides by 3 )

e = 0 ÷ 3 = 0

The function f(x) = (x² - 4)/x is increasing over it's entire domain as the derivative is always positive.

The function for this problem is defined as follows:

f(x) = (x² - 4)/x.

Applying the quotient rule, the derivative of the function is given as follows:

f'(x) = [2x(x) - (x² - 4)]/x²;

f'(x) = [2x² - x² + 4]/x²;

f'(x) = (x² + 4)/x²;

We have a quotient in which both terms are always positive(x² is always positive, and so is x² + 4), hence the derivative is always positive and the function is increasing over it's entire domain.

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The measure of angle 5 of the transverse lines is; C.) 105°

The line transversal theorem states that If two parallel lines are cut by a transversal, then it means that corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.

Now, we are given that the measure of 2 is 75°. It is clearly seen that angle 5 is a corresponding angle to angle 1 and angle 1 forms a straight line with angle 2. Sum of angles on a straight line is 180 degrees. Thus;

angle 5 = 180 - 75

angle 5 = 105°

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Answer:

1st table: -2/1   2nd table: 3/-4

Step-by-step explanation:

Slope=m=[tex]\frac{rise}{run}[/tex]

1st table:

rise -2

run 1

2nd table:

rise 3

run -4

A. The rate of change for function A is, 3

B. The rate of change for function B is, 2

C. The function which has greater rate of change is, Function A

Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.

So formula for the rate is,

m = change in one quantity/change in another quantity = Δy/Δx

Given that,

Two functions,

A.   y = 3x - 4

B.   x     -7    -5   -3    -1    1

     y      -10  -6  -2    2   6

Rate of change in both  =?

In simple words, rate of change is known as slope of the line,

Function A is already given in standard form of line, y = mx + c

So, by comparing it

m = 3

Rate of change in function A, 3

For function B, it is required to form equation of line,

By taking two values of x & y,

(-1, 2) & (1, 6)

Two points form of equation is,

y-y₁ =  y₂-y₁/x₂-x₁(x-x₁)

By putting values we get the equation,

y - 2 = (6-2)/(1-(-1))*(x - (-1))

y-2 = 4/2(x + 1)

y   =  2x + 4

By comparing it with, y = mx+ c

m = 2

Rate of change in function B = 2

And, it clearly visible, Rate of change in A is greater than In B

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The length and the width are 12 yards and 16 yards

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter =2( l + w)

Given that the parameter are;

Length = 4 + w

Substitute the values into the formula

52 = 2( 4 + w + w)

collect like terms

52 = 2(4 + 2w)

expand the bracket

52 = 8 + 4w

collect like terms

4w = 52 - 8

subtract the values

4w = 48

Make 'x' the subject of formula

w = 12 yards

L = 16 yards

Hence, the values are 12 yards and 16 yards

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Answer:

183.25

Step-by-step explanation:

5.56 × 32.958

= 183.24648

Estimated to 2 Decimal Places:

183.25

The ratio of candidates for President to total candidates is given as follows:

Number of candidates for President : Total number of candidates.

The ratio between two amounts a and b is obtained applying a proportion, as it is the division of the amount a by the amount b, as follows:

r = a : b.

The amounts for this problem are given as follows:

Hence the ratio is given as follows:

Number of candidates for President : Total number of candidates.

The problem is incomplete, hence the general procedure to obtain the ratio was presented.

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The decimal numbers of given statements assuming that all other place values not mentioned are zeroes are:

1) = 50.06208

2) = 0.08088

3) = 10.02406

4) = 5.00439

5) = 0.06824

Decimal numbers are a type of real number representation that uses a base-10 system. Decimal numbers are made up of digits, with each digit representing a different place value. The place value of each digit in a decimal number is determined by its position in the number, with the rightmost digit representing the units place, the second digit from the right representing the tenths place, the third digit from the right representing the hundredths place, and so on. The decimal point is used to separate the integer part of the number from the fractional part. For example, in the decimal number 3.14, the integer part is 3 and the fractional part is 0.14.

Tens place reffers to the two digit first number while tenths place refers to the two digits and number from the decimal point

For example

Tens place = 198.879

While Tenths place = 198.879

And the same works for hundreds and hundredths and thousands and the thousandths.

Now, with information,

Put the values at their places as prescribed in  the question:

1)

5 in the tens place

6 in the tenths place

2 in the hundredths place

8 in the ten thousandths place

= 50.06208

2)

8 in the ten thousandths

place

8 in the thousandths place

8 in the tenths place

= 0.08088

3)

4 in the hundredths place

1 in the tens place

2 in the tenths place

6 in the ten thousandths place

= 10.02406

4)

3 in the thousandths place

4 in the hundredths place

5 in the ones place

9 in the ten thousandths place

= 5.00439

5)

8 in the hundredths place

6 in the tenths place

4 in the ten thousandths place

2 in the thousandths place​

0.06824

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Answer:

in this case, the polynomial function has a degree of 5 which means that is has at most 5 complex zeros. however, it doesn't necessarily mean it will have 5 zeros, it could have fewer or none at all.

Answer:

$10800

Step-by-step explanation:

The price of the car is $9000.

The interest is 20% of the price of the car, so the interest is 20% of $9000.

20% of $9000 = 0.2 × $9000 = $1800

She paid $1800 in interest.

The total she paid was the price of the car plus $1800 in interest.

$9000 + $1800 = $10800

Answer:

Step-by-step explanation:

aerospace and aviation industry.

Answer:

aerospace and aviation

Step-by-step explanation:

no explanation sorry :)

To find a percentage of a whole, you first need to know exactly what you're measuring. For instance, if 38 people in your community have library cards, and you wish to work out the percentage of library card holders in the population, you'll first need to know the total size of your community.

A percentage of a total is equal to the subset of a total divided by the total, then multiplied by 100. If your community has 230 people in it, you can calculate the percentage of people with a library card. First, you divide 38 by 230, then multiply that total by 100.

38/230 = .165 .165 x 100 = 16.5

Therefore 16.5 percent of the people in your community have a library card.

A fraction has two parts, a numerator on the top and a denominator on the bottom. Any percentage can be expressed as a fraction with the percentage value as the numerator and 100 as the denominator. So 80 percent is also 80/100. You can use this to convert a fraction into a percentage as well.

For example, to turn the fraction 4/25 into a percent, you'll need a fraction with 100 as the denominator. So you'll need to multiply the denominator by 4 since this will produce 100. You then need to also multiply the numerator by the same amount.

4/25 = (4 x 4)/(25 x 4) = 16/100

You now have a fraction of 100, so you can convert it to a percentage quite easily: 16/100 is equal to 16 percent. Here's another example:

3/5 = (3 x 20)/(5 x 20) = 60/100 = 60%

If you have access to a calculator, you could also divide the numerator by the denominator and turn the fraction into a decimal. Decimals are simple to convert into percent notation.

Decimals are even easier to convert into percentages. To convert a decimal into a percentage, multiply the decimal by 100 and add the percent sign. To multiply a decimal by 100, move the decimal point two digits to the right:

0.8= 0.8 x 100 = 80% 0.53: 0.53 x 100 = 53% 0.173: 0.173 x 100 = 17.3%

You can also use this method to convert decimal numbers that are larger than 1. Say you know there are 1.34 times as many books in your library this year than last year, and you want to know what percentage the number of books you have this year is of the books you had last year. As before, you would multiply 1.34 by 100 and add the percent sign:

1.34 x 100 = 134%

Your number exceeds 100 percent because you're comparing this year's book total to the total books from last year, a number represented by 100 percent. Since there are more books this year, that percentage is larger than 100.

You can convert percentages to decimals using the opposite operation. Instead of multiplying the decimal by 100, divide the percent by 100. If 56 percent of people eat roast beef sandwiches you could also say that for every 100 people, 56 eat roast beef. Divide 56 by 100. Because you're dividing by 100, you'll move the decimal point two places to the left:

56/100 = 0.56

Other conversion examples are: 5%: 5/100 = 0.05, 79%: 79/100 = 0.79, 295%: 295/100 = 2.95

Greetings!

Let's find the domain of the function.

We were given: f(x) = 9 - 5/(x^4)

The domain of a function is a group of values that are valid within the function. The domain could range from (-∞, ∞)

However, since we have a fraction, there will be a limit to the range of values.

In this case, we will have to find what value the variable "x" can't be.

Since we are analyzing the "5/(x^4)" part of the function, we know that fractions can't have a denominator of 0. This means that the denominator can't equal zero.

x^4 ≠ 0

Solve for "x" by taking the root of both sides of the equations.

x ≠ 0 Therefore x can't equal 0.

This means that the value of "0" will not be in our domain, making our domain from:

(-∞, 0)∪(0, ∞)

The above means that we are including all the values (due to the use of infinity), except for the value 0.

Answer:

(-∞, 0)∪(0, ∞)

The discounted cost per person is, $24.50

And, The total cost for 20 people at the discounted price is, $2,205.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A group of 20 people wants to go on the Caribbean cruise.

And, The cruise ship offers a discount of 10%, or 0.1 times the cost, for groups of more than 10 people.

Hence, The discounted cost per person is,

⇒ 1% of $2450

⇒ 1/100 × $2450

⇒ $24.50

And, The total cost for 20 people at the discounted price is,

⇒ $2450 - 10% of 2450

⇒ $2450 - 10/100 × 2450

⇒ $2450 - $245

⇒ $2,205

Thus, The discounted cost per person is, $24.50

And, The total cost for 20 people at the discounted price is, $2,205.

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The equation does not represent a direct proportion

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

2.5=q-1.6

The above equation is a linear equation

When the equation is solved, we have"

q = 2.5 + 1.6

Evaluate the like terms

q = 4.1

The equation q = 4.1 is not a direct proportion

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The length of time will the two marathon runners will be one - half of a mile apart is 15 minutes.

The first marathon runner is going at 10 miles per hour while the second runner is going at 8 miles per hour.

This means that in one hour, the first runner would have covered 10 miles while the second would have covered 8 miles. They would be 2 miles apart.

If they would be 2 miles apart in one hour, the time till they are half a mile apart would be:

= 0. 5 / 2 x 60 minutes in an hour

= 15 minutes

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Answer:

Step-by-step explanation:

[tex]2a^{2} +6a=20\\2a^{2} +6a-20=0\\a^{2} +3a-10=0\\a^{2} +5a-2a-10=0\\a(a+5)-2(a+5)=0\\(a+5)(a-2)=0\\a=2,-5[/tex]

On solving the linear equations - 9x - 3y = -21 and 9x + 9y = -9 the value of x is x = 4 and y is y = -5.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

The linear equations are -

- 9x - 3y = -21 .... (1)

9x + 9y = -9 .... (2)

Add the equations (1) and (2) -

- 9x - 3y + 9x + 9y = -21 - 9

6y = -30

y = -5

Substitute the value of y in equation (1) -

- 9x - 3(-5) = -21

- 9x + 15 = -21

- 9x = -36

-x = -4

x = 4

Therefore, the values of x and y is 4 and -5.

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The average condition that must be imposed on k1 and k2 so that is also an unbiased estimator of is that k1 + k2 must equal 1.

In order for to be an unbiased estimator of the same parameter that and are estimating, the constants k1 and k2 that are multiplied by and must be carefully chosen. This is because in order for an estimator to be unbiased, its expected value must be equal to the parameter it is estimating. In other words, the sum of k1 and k2 multiplied by the parameter must equal the parameter itself. Therefore, for and to be unbiased estimators of the same parameter, the condition that must be imposed on k1 and k2 is that the sum of the two constants must be equal to 1. In other words, k1 + k2 = 1. This condition ensures that the expected value of is equal to the parameter, and thus is also an unbiased estimator of the same parameter.

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Answer:

Below

Step-by-step explanation:

Veritcal lines are   x= ....

  so    x = 8

Horizontal lines are   y = ....

   so   y = -1