Dave Bowers collects U.S. gold coins. He has a collection of 43 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $640. how many of each denomination does he have?

Answer:

71.62

Step-by-step explanation:

[tex]A = \frac{C^2}{4 \times \pi }\\A = \frac{30^2}{4 \times 3.14 }\\A = 71.62[/tex]

Answer: i hope this answers your question

Step-by-step explanation:

the function is negative over the interval (-3,5)

the function is positive over the interval (-..-5)

the function is positive over the interval (3,..)

Answer:here

Step-by-step explanation:

the function is negative over the interval (-3,5)

the function is positive over the interval (-..-5)

the function is positive over the interval (3,..)

Answer:

Q1: Plane

Q2: Point

Q3: line

                                  I hope this helps!

Using linear function concepts, it is found that this doubling property does not hold for every linear relationship.

A linear function is modeled by:

y = mx + b

In which:

One example of function is:

y = 4x + 3.

When x = 1:

y = 4 + 3 = 7.

When x = 2:

y = 8 + 3 = 11.

The input did not double, meaning that this doubling property does not hold for every linear relationship, it doubles only for a linear function with a slope of 2 and intercept of 0.

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It means that if you rotated the figure 60 degrees (clockwise or counterclockwise) about its center, then the figure does not change.

The "before" and "after" are identical. In other words, the preimage and image are the same.

2x - 3y = -9  is equation of line which passes through slope 2/3.

Describe slope using an example?

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

put x₁ = 3 , x₂ = -3 , y₁ = 3 and y₂ = -1

m = [tex]\frac{-1 - 3}{-3 - 3}[/tex]

m = [tex]\frac{-4}{-6}[/tex]

m = 2/3

The line that passes through (3, 5) =

                    ⇒   y - y₁ = m( x - x₁)

                    ⇒ y - 5 = 2/3 ( x - 3)

                    ⇒ 3( y - 5 ) = 2 ( x - 3 )

                     ⇒ 3y - 15 = 2x - 6

                      ⇒ 2x - 3y = -15 + 6

                     ⇒ 2x - 3y = -9

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Answer:

4 Square units

Step-by-step explanation:

The height is incorect

It is meant to be the vertical height which is the distance from A to AB (3 - 1 = 2)

[tex] \frac{1}{2} bh = \frac{1}{2} \times 4 \times 2 \\ = 4 \: square \: units[/tex]

The equation that states the sum of the tickets sold is -

30x + 45y = 60900.

We have concert promoter.

We have to write an equation that states that the total amount received from the sale, which is 60,900 dollars.

The equation modelling is a process of writing a mathematical equation from a mathematical statement involving variables, constants etc.

According to the question -

Money earned from $30 tickets = $30x

Money earned from $45 tickets = $45y

Total money from 1780 tickets = $60,900

Therefore -

30x + 45y = 60900

Hence, the equation that states the sum of the tickets sold is -

30x + 45y = 60900.

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[ The given question is incomplete, the complete question is

A concert promoter needs to make $60,900 from the sale of 1780 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. Write an equation that states that the total amount received from the sale is 60900 dollars.]

The amount taken from Jim's check for FICA taxes is $75.51.

FICA (Federal Insurance Contributions Act) taxes are of two types: Social Security tax and Medicare tax.

FICA taxes simply mean United States federal payroll (or employment) taxes imposed on both employees and employers.  The purpose of FICA taxes is to fund Social Security and Medicare.

These two federal programs benefit retirees, the disabled, and the children of deceased workers.

The rate for the Social Security tax is 6.2% of the taxpayer's gross pay.

The rate for the Medicare tax is 1.45% of the income earner's gross pay.

The FICA taxes rate is 7.65%.

Gross pay for the week = $987

FICA taxes = 7.65%

FICA taxes in dollars = $75.51 ($987 x 7.65%)

Thus, the amount Jim paid in FICA taxes is $75.51.

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The required value of the standard deviation is 0.04.

Given that,

1 mile ≈ 1.6 kilometers, what is the standard deviation in kilometers is to be determined. Where s = 5

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
1 miles = 1.60934 Km
Given
1 mile = 1.6
Standard deviation = 1.60934 - 1.6000
                                = 0.00934
S = 5
Standard deviation = 5 * 0.00934
                                = 0.04670

Thus, the required value of the standard deviation is 0.04.

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The set of numbers is S = { x ∈ N ; x > 22 }.

We have the statement:

Set of natural numbers greater than 22.

We need to make the set from it.

A set is a collection of different things objects or elements that are used to represent a situation or a function in a concise form.

For example a set of real numbers can be denoted by x ∈ R.

There can be finite or infinite sets. In finite sets, the number of elements are limited whereas in infinite sets it is not limited.

Here, the set that will be formed can be written as:

S = { x ∈ N ; x > 22 }

Therefore, the set of numbers is S = { x ∈ N ; x > 22 }.

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[tex] \sqrt{15} \approx3.873\\ \\ \sqrt{15} < 3.9[/tex]

Answer: B. 60.96

Step-by-step explanation:

27% of 48 is 12.96

12.96+48=60.96

Explanation:

So, looking at the ruler, we;re going to take the whole number of the measurment from the whole bars of inches it overlaps (1-3) since we know it goes past there we will have a fraction beside it (because it does not go all the way to 4) If you see the longest lines in between the 3 and 4, there are 3 bars (which means each is 1/4.) Now, we know that it covers 3/4 of the last inch. To convert to /8, we multiply the numerator and denominator by 2 so we have 6/8. The CLOSEST (but not completely correct) (in 1/8 inches) would be D. (but ONLY if A is incorrect because that is simplified and the accurate answer.

Answer: The answer is play on words, or a pun - a row of large animals separating two yards is called an elefence.

Step-by-step explanation: The first part of the word, ele-, obviously refers to elephants, which are large animals. The second part is a fence, which separates two yards. So this is intended to have a humorous effect (I got this from go.ogle....)

Answer: $63

Step-by-step explanation:

so you put 6 where the w is to find out the answer

45+3(6)=45+18=63

Step-by-step explanation:

medium =9

range = 12-7=5

mode=7

The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of Orchestra, y represent the main seat and z represent the balcony seat.

A Broadway theater has 510 ​seats, Hence:

x + y + z = 510    (1)

Also:

140x + 135y + 100z = 62700    (2)

And:

135y + 100z + (1/2)(140)x = 55700    (3)

From the three equations:

x = 100, y = 220, z = 190

The Broadway theater had 100 Orchestra, 220 main seat and 190 balcony seats.

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Answer: 6

Step-by-step explanation:

7+2+5+10= 24
24 divided by 4 equals 6

Answer:

Step-by-step explanation:

90 - 65 = 25

x = 25 degrees

90 - 25 = 65

y = 65 degrees

Reason:

32 = 8*4

56 = 8*7

We see that 8 is the largest common factor, aka GCF, of 32 and 56

So this is the greatest number of guests possible.

Each guest will get 32/8 = 4 cookies and 56/8 = 7 slices of pizza.

Answer:

1 in 6

Step-by-step explanation:

The probability of getting the original green is 1 in 7 (1 green pencil and 7 total)

If you take it out, there will be 6 pencils left

The thermometer show the temperature at 73°F when there is a percentage error.

From the information, the thermometer has a percent error of 3% and the actual temperature is 75°F.

Therefore, the temperature down on the thermometer will be:

= 75 - (3% ×75)

= 75 - 2.25

= 72.75

= 73 approximately.

Therefore, the thermometer show the temperature at 73°F when there is a percentage error.

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The statements which are true about parallel lines are;

Parallel lines in their simplest description are lines which would never meet or cross each other under any circumstance.

Also, It follows from line geometry that such lines have the same slope and are coplanar, exist in the same plane.

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Answer:

circumference=44cm

44cn

Area=154cm

200cm

Answer:

a. = 1

b. = 0

c. = 2

d. = 7

Hopefully this helps

Carl calculates the z-score corresponding to the weight 255oz= -1.5.

Now, Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.

Given that,

In an orchard, apple weights are typically distributed. Fred the farmer concludes from a sample that the average weight of a box of apples is 270 ounces, with a standard deviation of 10 ounces.

He is interested in knowing what proportion of the apple boxes he has gathered for sale will weigh less than 255 oz.

Mean is 270

Standard deviation is 10

x = 255

Formula for z-score,

z = (x - mean)/SD

z = (255 - 270) / 10

=> z = -15 / 10

=> z = -1.5

Hence, by using z-table,

-1.5 equates to 0.0668, which suggests that 0.07

Therefore, 7% of Apple boxes weigh less than 255 oz.

The ratio of boxes is between 255 oz and 270 oz,

Calculating the proportion

Now,

50% - 7% = 43%.

Therefore, Carl calculates the z-score corresponding to the weight 255oz= -1.5.

Carl decides to find the percent associated with boxes less then 255 oz, so he rounds to hundred and substract 50% - 7% = 43%.

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x = 40 is the value of vertical angles .

What is vertical opposite angles?

Angles that are vertically opposed to one another at a certain vertex are formed by two straight lines intersecting. Angles that are vertically opposed to one another are equal.

The total of the two vertical angle pairs, or four angles, is always 360 degrees. Angles that come from each pair of vertical angles are supplementary and are referred to as neighboring angles (the angles sum up to 180 degrees).

(3x + 2)° and (5x-78)° are equal .

because of they are  vertical opposite angles.

3x + 2 = 5x - 78

5x - 3x = 78 + 2

2x = 80

x = 40

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Use the change-of-base identity and the exponent property for logarithms.

[tex]\log_b(a) = \dfrac{\log_c(a)}{\log_c(b)} \implies \log_b(a) = \dfrac1{\log_a(b)}[/tex]

[tex]\log_c(a^b) = b \log_c(a)[/tex]

This lets us rewrite

[tex]\log_{(k+1)^{2k-1}} (k+2)^{2k} = \dfrac{2k}{\log_{k+2}(k+1)^{2k-1}} = \dfrac{2k}{(2k-1) \log_{k+2}(k+1)}[/tex]

[tex]\log_{(k+2)^{2k-1}} (k+1)^{k^2} = \dfrac{k^2}{\log_{k+1} (k+2)^{2k-1}} = \dfrac{k^2}{(2k-1) \log_{k+1}(k+2)}[/tex]

It follows that

[tex]a_k = \dfrac2k \dfrac{\log_{k+2}(k+1)}{\log_{k+1}(k+2)} = \dfrac2k \left(\ln^2(k+1)}{\ln^2(k+2)}[/tex]

so that the product of [tex]a_k[/tex] telescopes:

[tex]\displaystyle \prod_{k=1}^{n-1} a_k = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(2)}{\ln^2(3)}\cdot\frac{\ln^2(3)}{\ln^2(4)}\cdot\frac{\ln^2(4)}{\ln^2(5)} \cdots \frac{\ln^2(n-1)}{\ln^2(n)} \cdot \frac{\ln^2(n)}{\ln^2(n+1)} \\\\ ~~~~~~~~ = \frac{2^{n-1}}{(n-1)!} \frac{\ln^2(n+1)}{\ln^2(2)}[/tex]

We can similar reduce the coefficient of [tex]P_n[/tex] to write

[tex]\log_{(n+1)^{2n-1}}(2^{2n}) = \dfrac{2n}{(2n-1) \log_2(n+1)}[/tex]

[tex]\log_{2^{2n-1}}(n+1)^{n^2} = \dfrac{n^2}{(2n-1)\log_{n+1}(2)}[/tex]

[tex]\implies \dfrac{\log_{(n+1)^{2n-1}}(2^{2n})}{\log_{2^{2n-1}}(n+1)^{n^2}} = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)}[/tex]

Then the expression for [tex]P_n[/tex] reduces significantly to

[tex]P_n = \dfrac2n \dfrac{\ln^2(2)}{\ln^2(n+1)} \cdot \dfrac{2^{n-1}}{(n-1)!} \dfrac{\ln^2(n+1)}{\ln^2(2)} = \dfrac{2^n}{n!}[/tex]

and we ultimately find

[tex]\displaystyle \sum_{n=2}^\infty P_n = \sum_{n=0}^\infty \frac{2^n}{n!} - \frac{2^1}{1!} - \frac{2^0}{0!} = \boxed{e^2 - 3}[/tex]

where we recall the power series

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]