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
What is the relationship between the 3s in the number 24,335
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:
5+10x+5.15=60.15 what's the value of x?
what is the exponent used in cubing a number
Which of the following gives an example of a set that is closed under multiplication? CHOOSE ALL THAT APPLY !!!! 15 PTS
A. The product of an even number and an even number
B. The product of 0 and 0
C. The product of a negative number and a negative number
D. The product of a perfect square and a perfect square
What is 48,371 rounded to the nearest thousand?
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).
Peter has only quarters and dimes in his coin collection. If he has three times as many quarters as dimes, which is an expression for the number of quarters he has in terms of the number of dimes?
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.
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 77.0 divided by 200
How can knowing the multiplication properties help you multiply 5x(2x6)?
what is 150% as a fraction
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?
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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What is the area of a banner with 4 2/3 ft and 1 1/2 ft
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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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:
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 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
wes has six errands to run (picking up the dry cleaning, going to the grocery store, getting gas, going to the bank, going to the library, and going to the video store). he only haves time to run 3 errands this afternoon. how many different combinations of three errands could he choose to run?
Answer: 120 different combinations .
Step-by-step explanation:
The combination of n things taking m things at a time is given by :-
[tex]C(n,m)=\dfrac{n!}{m!(n-m)!}[/tex]
Given : The total numbers of errands = 6
Now, the combination of 6 errands taking 3 at a time is given by :-
[tex]C(6,3)=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]
Hence, he could choose to run 120 different combinations of three errands .
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?
What Is 22/55 in lowest terms
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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A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?
A. 8 hours
B. 12 hours
C. 24 hours
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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find a linear function h such that h(3)=7 and h(-1)= 14. what is h (1/2)?
p=21+2w (solve for w)