A collection of nickels, dimes, and quarters consist of
11
coins with a total of
$1.70
. If the number of dimes is equal to the number of nickels, find the number of each type of coins.

The value of CD is 9.92 cm

Given:

Find: CD

Triangle ABC is an isosceles triangle with base AB, because AC = BC. In isosceles triangle angles adjacent to the base are congruent. So,

m<A = <mB = 72°

The sum of the measures of all interior angles is 180°, thus

m<C =  180° -72° - 72° = 36°

The area of the triangle ABC is

AABC= 1/2AC.BC.sin<C

If we expand,

AC = 10.43cm

Consider right triangle ACD. In this triangle,

sin <A = CD/AC

sin 72° = CD/10.43

therefore,

CD = 9.92 cm.

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Given: ∆ABC, CD ⊥ AB, AC = BC, Area of ABC = 32 cm2, m∠A = 72°

Find: CD

Answer:

18°, 162°

Step-by-step explanation:

Angles that form a linear pair are supplementary, so their measures add to 180°.

Let the measure of the smaller angle = x.

The larger angle measures 9x.

9x + x = 180

10x = 180

x = 18

9x = 9(18) = 162

Answer: 18°, 162°

Answer:8.64

Step-by-step explanation:

Answer:

8,64

Step-by-step explanation:

[tex]\frac{18}{100}[/tex]*48=8,64

a) The rate in this problem is 23 miles.

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel 276 miles.

Unit rate is the ratio of two different units, with denominator as 1.

Given:

A certain car gets 23 miles to the galloon open highway.

a) The rate in this problem is 23 miles

b) The unit fraction is associated with this rate is 23/1.

c) In 12 gallons the car will travel

23/ 1 = x/ 12

x= 23 . 12

x= 276 miles

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Answer:

a. The number of ounces of oat flakes in the box is 15 ounces - a ounces, or 15 - a ounces.

b. The cost of the almonds (in cents) is 30 cents * a ounces, or 30a cents.

c. The cost of the oat flakes (in cents) is 15 cents * (15 - a) ounces, or 15 * (15 - a) cents.

d. The total cost of a box of Almond Oats (in cents) is the cost of the almonds plus the cost of the oat flakes, or 30a + 15 * (15 - a) cents.

The ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.

To discover the unknown values in a mathematical equation, we cross multiply the numbers in the equation. The method of cross multiplication is frequently employed to identify the missing variable in an equation. We multiply both the numerator and denominator of the provided expression or fractions.

Given that the ant can travel at a constant speed of 980 inches every 5 minutes.

Thus,

5 minutes = 980 inches

1 minute = x inches

Using cross multiplication method or Butterfly method of multiplication we have:

x = 980/5

x = 196 inches.

In 7 minutes the ant can travel:

(7)(196) = 1372 inches.

Hence, the ant can travel 196 inches in 1 minute and 1372 inches in 7 minutes.

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Answer:

Step-by-step explanation:

Straight line= 180 degrees

|_= 90 degrees

180-90=90

3s-2=52

2s+2=38

52+38=90

s=18

Answer: 4

Step-by-step explanation: 15-11=4

The required solution of the given expression δ = 0.0002. as of the given conditions

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

Here,
Given |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.

Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,

|5x - 15| = |5(3 + δ) - 15|
            = |15 + 5δ- 15|
                = |5δ|

Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,

|5δ|/5 < 0.001/5

|δ| < 0.001/5

Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.

Similarly, if x = 3 - delta, we have:

|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|

|-5δ|/5 < 0.001/5

|δ| < 0.001/5

So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.

Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.

So, δ= 0.001/5 = 0.0002.

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The zeros of the polynomial function f(x) are:

x = -1, -3/2, -2 + i/2, -2 - i/2

To find the complex zeros of the given polynomial function f(x), we can use the fact that every polynomial with complex coefficients has at least one complex zero.

First, we can use the Rational Zeros Theorem to find any rational zeros. The possible rational zeros are of the form p/q, where p is a factor of the constant term 45 and q is a factor of the leading coefficient 2. Therefore, the possible rational zeros are ±1, ±3/2, ±5, ±9/2, ±15, and ±45/2. We can test each of these values using synthetic division or long division to see if they are actually zeros of the polynomial.

Using long division, we find that x=−1 and x=−3/2 are zeros of the polynomial. Therefore, we can factor out (x+1) and (x+3/2) from the polynomial to get:

f(x) = (x+1)(x+3/2)(2x^3+8x^2+14x+30)

Next, we can use the quadratic formula to find the zeros of the cubic factor 2x^3+8x^2+14x+30. The quadratic formula gives:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = 8, and c = 15. Plugging in these values, we get:

x = (-8 ± sqrt(8^2 - 4(2)(15))) / 4

= (-8 ± 2i) / 4

= -2 ± i/2

These are the exact values of the complex zeros of the polynomial function.

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Using a system of equations, the number of points given for an arrow in target B is 7.

A system of equations means two or more equations solved at the same time or concurrently.

A system of equations is also described as simultaneous equations since they are solved simultaneously.

                              Target A    Target B   Total Score

Rence shots                3                1                  19

Sunil shots                  2                2                22

Let the points for an arrow into target A = x

Let the points for an arrow into target B = y

3x + y = 19 ... Equation 1

2x + 2y = 22 ... Equation 2

Multiply Equation 1 by 2:

6x + 2y = 38 ... Equation 3

Subtract Equation 2 from Equation 3:

6x + 2y = 38

-

2x + 2y = 22

4x = 16

x = 4

From Equation 1, substitute x = 4:

3x + y = 19

3(4) + y = 19

12 + y = 19

y = 19 -12

y = 7

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Answer:

Step-by-step explanation:

heyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

113.097 is the area (i used 3.14) pls comment for explanation :)

The values 6, 4 and 12 are the measures of PR, PQ and RI respectively.

The given diagram is a triangle and the expression to be used based on the theorem is expressed as:

TP/TQ = PR+3/15

3/5 =  PR+3/15

5(PR +3)= 3(15)
5(PR + 3) = 45

PR + 3 = 9

PR = 9 - 3

PR = 6

For the measure of PQ

PQ^2 = 5^2 - 3^2

PQ^2 = 25 - 9

PQ = 4

Determine the measure of RI

3/PQ = TR/RI
3/4 = 9/RI

1/4 = 3/RI
RI = 12

Hence the measure of PR, PQ and RI are 6, 4, and 12 respectively

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Answer:

C

Step-by-step explanation:

The area formula of a circle is A=[tex]\pi r^{2}[/tex], where r (or radius) is equal 1/2 times diameter (or d/2). So pi times (10/2)^2= 78.54 and  pi times (16/2)^2=201.06.   201.06-78.54 = about 122.52, which is closest to 122.46, or C.

The number of text messages all of the teenagers in the United States send each month is 17600 million.

In mathematics, an integer is a grouping comprising both positive and negative numbers. Integers are similar to whole numbers in that they do not include the fractional portion. Integers are thus numbers that can be positive, negative, or zero but not fractions. All mathematical operations, including addition, subtraction, multiplication, and division, can be carried out on integers.

Given that,

Number of teenagers = 22 million

Text sent on average = 800

Total messages sent = (22)(800) = 17600 million

Hence, the number of text messages all of the teenagers in the United States send each month is 17600 million.

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Answer:

563

Step-by-step explanation:

The required, Ask each regular customer which flavor they would like to see in his shop, would be the best method. Option C is correct.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Asking each regular customer which flavor they would like to see in the shop would be the best method because the customers are the ones who will be buying and consuming the ice cream, so their preferences are the most important. By directly asking the customers for their opinions, the owner can get a better understanding of what flavors people are interested in, and it can also help to build a relationship with the customers by showing that their input is valued.

Option A, determining the current best-selling flavor, would only provide information about the current sales and not necessarily reflect customers' interests in new flavors. Option B, visiting other ice cream shops, could provide some ideas, but it would not necessarily reflect the local market and the preferences of the shop's specific customer base. Option D, randomly generating customers to survey, may not be representative of the actual customer base and may not provide a reliable indication of which new flavor to sell.

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Answer:

C = 235

Step-by-step explanation:

given the graph passes through (10, 1 ) then the coordinates of the point make the equation true.

substitute x = 10, y = 1 into the equation and solve for C

10² + 1² + 12(10) + 14(1) - C = 0

100 + 1 + 120 + 14 - C = 0

235 - C = 0 ( subtract 235 from both sides )

- C = - 235 ( multiply both sides by - 1 )

C = 235

Answer: god

Step-by-step explanation: god god god god god god god god

The mean and the standard deviation are  144 and 4.3200

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

Proportion, p = 64%

Sample size, n = 225

The mean is calculated as

Mean = np

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

Mean = 64% * 225

Mean = 144

The standard deviation is calculated as

SD = √Mean * (1 - p)

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

SD = √144 * (1 - 64%)

Evaluate

SD = 4.3200

Hence, the mean is 144

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Complete question

Coffee: The National Coffee Association reported that 64% of U.S. adults drink coffee daily. A random sample of 225 U.S. adults is selected. Round your answers to at least four decimal places as needed.

(a) Find the mean

(b) Find the standard deviation

To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

(a) The yearly percent rate of growth of the world population is 1.0103%.

(b) The world population in 2020 was 7.68 billion people. The model predicts that the world population in 2026 will be 8.336 billion people.

(c) The projected average rate of change of the world population between 2020 and 2026 is 0.556 million people per year.

(a) The yearly percent rate of growth of the world population can be found by taking the exponential rate of change of the equation. The rate of change is 1.0103%.

(b) To find the world population in 2020, we can plug in t=0 into the equation. This gives us P=7.68 billion people. To find the world population in 2026, we can plug in t=6 into the equation. This gives us P=8.336 billion people.

(c) To find the projected average rate of change of the world population between 2020 and 2026, we can take the difference in population between 2020 and 2026 and divide it by the number of years (6). This gives us 0.556 million people per year.

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The following statements are true:

A:The car makes a complete revolution in 10 seconds

B:The maximum height of the Ferris wheel is 65 feet

A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.

A. The car makes a complete revolution in 10 seconds:

This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.

B. The maximum height of the Ferris wheel is 65 feet:

This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.

C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.

It is not possible to determine the radius of the Ferris wheel based on the given information alone.

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The statement that is true is: B. A piece of copy paper is approximately four times thicker than a human hair.

Scientific notation is a system of expressing extremely large figures in a standard form.

Considering the figures given in the question,

Thickness of copy paper = 4 × 10^-3 in

Thickness of human hair = 1 × 10^-3 in

So that;

Thickness of copy paper/ Thickness of human hair = 4 × 10^-3/ 1 × 10^-3

                                                    = 4 × 10^-3 * 10^3

                                                    = 4

Thus it can be concluded that the copy paper is approximately four times thicker than a human hair. Thus option B.

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Vertex A: (90°, 3) and Vertex B: (90°, -1) of the sine function.

The vertex A of the curve y = sin x + 2 is obtained by shifting the vertex of y = sin x upward by 2 units. Since the vertex of y = sin x is (90°, 1), the vertex of y = sin x + 2 will be:

A = (90°, 1 + 2) = (90°, 3)

Therefore, the coordinates of the vertex A of the curve y = sin x + 2 are (90°, 3).

b) The curve y = -sin x is obtained by reflecting the curve y = sin x about the x-axis. Since the vertex of y = sin x is (90°, 1), the vertex of y = -sin x will be:

A = (90°, -1)

Therefore, the coordinates of the vertex A of the curve y = -sin x are

(90°, -1).

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The value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

A relation is a function if it has only One y-value for each x-value.

The given function is f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 such that x=5

We need to find the value of f(5)

Plug x=5 in the above function

f(x) = x⁴ - 7x³ + 2x² + 40x

f(5) = 5⁴ - 7(5)³ + 2(5)² + 40(5)

=625-875+50+200

=0

Hence, the value of f(5) is 0 in the function f(x) = x⁴ - 7x³ + 2x² + 40x

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Complete question is below

f(x) = x⁴ - 7x³ + 2x² + 40x and given x-5 find value of f(5)

A valid inference about the data of Video Games Play Time among students is A). 50% of students spend 2- or 3 hours playing video games.

An inference is an evidence-based conclusion.

Inferences are reached when the necessary facts are available, and the researcher has done some calculations and reasoning using the facts.

Video Games Play Time

Hours Played     Number of Students

0                                        2

1                                         4

2                                        6

3                                        8

4                                        5

5 or more hours               3

Total number of students 28

Number of students = 14 (6 + 8)

14/28 - 50%

50% = 50%

Number of students = 8 (5 + 3)

8/28 = 28.6%

28.6% > 10%

Number of students = 10 (4 + 6)

10/28 = 35.7%

35.7% > 10%

Number of students = 13 (8 + 5)

13/28 = 46.3%

46.3% ≠ 50%

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Video Games Play Time

Hours Played     Number of Students

0                                        2

1                                         4

2                                        6

3                                        8

4                                        5

5 or more hours               3

Total number of students 28

A). 50% of students spend 2- or 3 hours playing video games.

B). Less than 10% of the students spend 4 or more hours playing video games.

C). Less than 10% of the students spend 1- or 2 hours playing video games.

D). More than 50% of the students spend 3- or 4 hours playing video games.

Answer:

(2,4)

Step-by-step explanation:

Answer:

x=10.

Step-by-step explanation:

4x = 3x + 10

4x - 3x = 10

x = 10

Answer:

Step-by-step explanation:

The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.

Let's first calculate the total revenue:

Number of tickets sold = 200

Price per ticket = $4

Total revenue = 200 * $4 = $800

Next, let's calculate the cost of the tickets:

Number of tickets sold = 200

Price per ticket = $4

Total cost = 200 * $4 = $800

Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:

Profit = Total revenue - Total cost

Profit = $800 - $800 = $0

So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.