The expression for the number of quarters Peter has in terms of the number of dimes is [tex]\( \frac{3}{4}d \)[/tex].
Let's denote the number of dimes Peter has as [tex]\( d \)[/tex]. According to the problem, Peter has three times as many quarters as dimes. Therefore, if we let [tex]\( q \)[/tex] represent the number of quarters, we can write the relationship between the number of quarters and dimes as:
[tex]\[ q = 3d \][/tex]
However, the question asks for an expression that gives the number of quarters in terms of the number of dimes, but using the same variable [tex]\( d \)[/tex] to represent the total value of the dimes in dollars. Since each dime is worth $0.10, the total value of the dimes in dollars is:
[tex]\[ \text{Total value of dimes} = 0.10d \][/tex]
To find the number of quarters in terms of the total value of the dimes in dollars, we need to divide the total value of the dimes by the value of one quarter, which is $0.25, and then multiply by 3 because there are three times as many quarters as dimes:
[tex]\[ q = \frac{0.10d}{0.25} \times 3 \][/tex]
Simplifying the fraction [tex]\( \frac{0.10}{0.25} \)[/tex] gives us [tex]\( \frac{1}{2.5} \)[/tex], which simplifies further to [tex]\( \frac{2}{5} \)[/tex]. Therefore:
[tex]\[ q = \frac{2}{5}d \times 3 \][/tex]
[tex]\[ q = \frac{3}{5} \times 2d \][/tex]
[tex]\[ q = \frac{3}{5} \times 2 \times \frac{d}{1} \][/tex]
[tex]\[ q = \frac{3}{5} \times \frac{2d}{1} \][/tex]
[tex]\[ q = \frac{3}{5} \times d \times 2 \][/tex]
[tex]\[ q = \frac{3}{5} \times d \times \frac{2}{1} \][/tex]
[tex]\[ q = \frac{3}{5} \times \frac{2d}{1} \][/tex]
[tex]\[ q = \frac{3 \times 2d}{5} \][/tex]
[tex]\[ q = \frac{6d}{5} \][/tex]
However, we must remember that the original relationship was [tex]\( q = 3d \)[/tex], not . This means we made a mistake in our calculation. Let's correct it:
[tex]\[ q = 3d \][/tex]
Since each quarter is worth $0.25, the total value of the quarters in dollars is:
[tex]\[ \text{Total value of quarters} = 0.25q \][/tex]
[tex]\[ \text{Total value of quarters} = 0.25 \times 3d \][/tex]
[tex]\[ \text{Total value of quarters} = 0.75d \][/tex]
Now, to express the number of quarters [tex]\( q \)[/tex] in terms of the total value of the dimes in dollars using the same variable [tex]\( d \)[/tex], we need to adjust our equation to account for the value difference between dimes and quarters. Since the value of the dimes is given in dollars as [tex]\( d \)[/tex], and each quarter is worth $0.25, we can express the number of quarters as:
[tex]\[ q = \frac{d}{0.25} \times 3 \][/tex]
[tex]\[ q = \frac{d}{\frac{1}{4}} \times 3 \][/tex]
[tex]\[ q = d \times 4 \times 3 \][/tex]
[tex]\[ q = 4d \times 3 \][/tex]
[tex]\[ q = 12d \][/tex]
But this is not the expression we are looking for, as it gives us the number of quarters in terms of the total value of the dimes in dollars, not in terms of the number of dimes. We need to divide by 10 to convert the total value of the dimes in dollars back to the number of dimes:
[tex]\[ q = \frac{12d}{10} \][/tex]
[tex]\[ q = \frac{3}{4}d \times 4 \][/tex]
[tex]\[ q = 3d \][/tex]
This is the correct expression, as it gives us the number of quarters in terms of the number of dimes, with [tex]\( d \)[/tex] representing the number of dimes, not their value in dollars.
Add.
7 2/15 + 5 2/3 + 9 13/15
20 2/3
21 10/15
21 2/3
22 2/3
Adding together the whole number parts gives us 21. When we add the fractions, we get 25/15, which simplifies to 1 10/15. Adding this to our whole number sum gives us 22 10/15, or 22 2/3.
Explanation:To find the sum of these mixed numbers, you'll want to first add the whole number parts, and then add the fractions. In this case, adding together the whole numbers 7, 5, and 9 gives us 21.
The fractions 2/15, 2/3, and 13/15 can be added together by finding a common denominator. The common denominator for 15 and 3 is 15, therefore 2/3 becomes 10/15 when it is converted.
When we add 2/15, 10/15, and 13/15, we get 25/15, which can be reduced to 1 10/15.
When we add this to our whole number sum, we get 22 10/15,
which simplifies to 22 2/3.
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An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 145 for 5 < x ≤ 6
B. C(t) = 145 for 6 < x ≤ 7
C. C(t) = 170 for 5 < x ≤ 6
D. C(t) = 170 for 6 < x ≤ 7
Find the value of y log4 64=y
Answer:
y=log4 64=2.6665.
Step-by-step explanation:
We are given that logarithmic expression
y=log 464
By using logarithmic rules
Substitute the decimal point after end digit and then put zero after decimal point
We can write as
y=log464.0
To put the decimal point after one digit from left then we move two steps.Therefore ,we write 2 on left side of the decimal point in final result
Now, we see the value of 46 at 4 from log table then we get the value of 46 at 4 is 6665
Therefore , y=log464=2.6665
Hence, the value of y=2.6665
The value of y to the equation log₄(64) = y is y = 3.
The given logarithmic equation is :
y = log₄(64)
This can be written in exponential form as :
4^(y) = 64
It is known that :
4 × 4 × 4 = 64
So,
4³ = 64
Hence the value of y = 3.
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if the quotient of -20 and 4 is decreased by 3 what number results
quotient is divide
-20/4 = -5
-5 -3 = -8
Find f(5) for f (x)=1/4 (2)^x
The correct option is A. 8
Given f (x)=1/4 (2)^x.
[tex]f(x)[/tex] [tex]=\frac{1}{4} 2^{x}[/tex]
We have to calculate F(5), means put x = 5.
So, [tex]f(5)=\frac{1}{4} 2^{5}[/tex]
[tex]f(5)=\frac{1}{4} \times 32[/tex]
[tex]f(5)=8[/tex]
Hence [tex]f(5)=8[/tex] .
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A car manufacturer wants to change the content of a certain automobile to have less steel in order to get better gas mileage. One hundred standard cars and 100 cars of the new content are built and test driven across country to determine the overall gas mileage. This study is an
Answer:
experiment
Step-by-step explanation:
I have a value that is 35% of the total value. I want to know what the total value is and what formula is used to work this out?
The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 455 sofas in 48 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation?
find a linear function h such that h(3)=7 and h(-1)= 14. what is h (1/2)?
If ab= 8 in. and cd= 6 in., how long is a radius?
What is the relationship between the 3s in the number 24,335
A batch of 140 semiconductor chips is inspected by choosing a sample of 5 chips. assume that 10 of the chips do not conform to customer requirements. the number of samples of 5 containing exactly one nonconforming chip is closest to:
Is 3 a good estimate for 3.4x0.09
Time measured in minutes is an example of a(n) _______________ scale.
The answer can be written in statement form as,"Time measured in minutes is an example of a(n) interval scale."
What is an interval scale?A numerical scale known as an interval scale is one in which both the order of the variables and their differences are known. Using the Interval scale, variables with recognizable, consistent, and calculable differences are categorized.
It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.
The value of time is given in minutes.
The given quantity can be measured on interval scale.
Hence, the required scale is known as interval scale.
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Write an equation in point-slope form of the line that passes through the point (−8, −2) and has a slope of m=5
To write the equation in point-slope form, we can use the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Explanation:To write an equation in point-slope form, we can use the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the given point is (-8, -2) and the slope is 5. Plugging in these values into the formula, we get:
y - (-2) = 5(x - (-8))
Simplifying the equation, we get:
y + 2 = 5(x + 8)
Therefore, the equation in point-slope form of the line that passes through the point (-8, -2) with a slope of 5 is y + 2 = 5(x + 8).
What is the area of a banner with 4 2/3 ft and 1 1/2 ft
What Is 22/55 in lowest terms
The function d(x) =3x +2 determine how many donuts need to be purchased for a meeting, where x is the number of people at the meeting. The office manager uses h(d(x)) to find the amount of money to bring for the donuts purchase. The function h(x) = 2x + 7 . Solve for how much money to bring when there are 8 people In the meeting.
A.25
B.26
C.52
D.59
Do I add the lenghs of the sides of a figure and multiply them by the height to get the area?
Chelsea has four hours of free time on Saturday. She would like to spend no more than 2/3 of an hour on each activity. How many activities can she do during her time?
How can knowing the multiplication properties help you multiply 5x(2x6)?
Use the result from part c to find the two solutions to the equation 2x2−3x−5=0. enter the two solutions separated by a comma. (the order is not important.)
The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.
Explanation:To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:
x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
Simplifying further, we have:
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.
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p=21+2w (solve for w)
The average weight of a mature human brain is approximately 1400 grams. What is the equivalent weight in pounds? Use the conversion equivalency 1 kilograms (kg) = 1000 grams (g) and 2.20 pounds (lb) = 1 kg.
Lines are drawn through the point (2, 8) and the points given below. Select two points that correspond with lines with negative slopes.
(-2, -6)
(0, 9) (
1, -3)
(5, 6)
(10, 11)
To find two points with negative slopes, we can calculate the slopes of the lines passing through the point (2, 8) and each of the given points. The pairs of points with negative slopes are (-2, -6) and (1, -3).
Explanation:A line has a negative slope when it goes down from left to right. To find two points with negative slopes, we can calculate the slopes of the lines passing through the point (2, 8) and each of the given points.
Using the slope formula, slope = ∆y / ∆x, we can calculate the slopes:
-2, -6: slope = (-6 - 8) / (-2 - 2) = -14 / -4 = 3.5
1, -3: slope = (-3 - 8) / (1 - 2) = -11 / -1 = 11
Therefore, the pairs of points with negative slopes are (-2, -6) and (1, -3).
Drag the blue labels onto the table to identify the data that is relevant to each hypothesis. then use the pink labels to indicate whether each hypothesis is supported or not supported by the data answers
Hypothesis 1 supported (potentially adapted wings), 2 needs more data, 3 and 4 not supported (scavengers and traffic constant).
Here's how to proceed:
1. Match Data to Hypotheses:
Hypothesis 1:
Relevant Data: "The wing shapes of swallows killed on roads differ from those of the general population."
Hypothesis 2:
Relevant Data: Not directly provided in the given options. More information is needed about the actual population size of cliff swallows living near roads over time.
Hypothesis 3:
Relevant Data: "Avian scavengers did not increase during this time, and terrestrial scavengers probably did not increase."
Hypothesis 4:
Relevant Data: "Car traffic stayed the same or increased during this time."
2. Evaluate Hypothesis Support:
Hypothesis 1:
Supported (additional data may be needed). The wing shape difference suggests potential adaptation, but more evidence would strengthen the conclusion.
Hypothesis 2:
Cannot be determined without direct data on population size changes.
Hypothesis 3:
Not supported (probably not a factor). The data indicates scavenger populations haven't increased, suggesting they aren't significantly affecting the number of road-killed swallows found.
Hypothesis 4:
Not supported (probably not a factor). The data shows car traffic has remained steady or increased, making it less likely to be the cause of a decrease in observed road-killed swallows.
Complete Question:
The function f(x) = 68(1.3)x represents the possible squirrel population in a park x years from now. Each year, the expected number of squirrels is ____ the number the year before.
Answer:
1.3 times
Step-by-step explanation:
What is 48,371 rounded to the nearest thousand?
5+10x+5.15=60.15 what's the value of x?
837,164 and 4,508 the value of 8