how can you use absolute value to represent a negative number in a real world situation
The sum of three consecutive integers is −261−261. Find the three integers.
You need to fill a football with air to play with it. You know that your pump expels air at speed of 8.2 ft/s. The needle of your pump has a radius of 4.5 millimeters. What is the volume flow rate of the air being pumped into the football?
Answer:
The volume flow rate of the air being pumped into the football is approximately [tex]\( 5.261 \times 10^{-7} \)[/tex] cubic feet per second.
Explanation:
To find the volume flow rate of the air being pumped into the football, we first need to calculate the cross-sectional area of the needle of the pump.
Given:
- The radius of the needle, [tex]\( r = 4.5 \)[/tex] millimeters.
The cross-sectional area, [tex]\( A \)[/tex], of the needle can be calculated using the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
Converting the radius from millimeters to feet:
[tex]\[ r = \frac{4.5}{1000} \text{ feet} \][/tex]
Now, let's calculate the cross-sectional area:
[tex]\[ A = \pi \left( \frac{4.5}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \left( \frac{0.0045}{1000} \right)^2 \][/tex]
[tex]\[ A \approx \pi \times 2.025 \times 10^{-8} \text{ square feet} \][/tex]
Now, we can find the volume flow rate, [tex]\( Q \)[/tex], of the air being pumped into the football. The volume flow rate is the product of the cross-sectional area of the needle and the speed of the air:
[tex]\[ Q = A \times \text{Speed} \][/tex]
Given:
- Speed of the air, [tex]\( \text{Speed} = 8.2 \)[/tex] ft/s
Now, let's calculate the volume flow rate:
[tex]\[ Q = \pi \times 2.025 \times 10^{-8} \text{ square feet} \times 8.2 \text{ ft/s} \][/tex]
[tex]\[ Q \approx 5.261 \times 10^{-7} \text{ cubic feet/s} \][/tex]
Juan's baseball card collection was worth 800$. Over the last 5 years,thw collection decreased $300 in value. What integer representa the average decrease in value each year.
Final answer:
The average yearly decrease in the value of Juan's baseball card collection, which decreased by $300 over 5 years, is $60. This integer represents the yearly reduction in value.
Explanation:
Juan's baseball card collection was worth $800. Over the last 5 years, the collection decreased by $300 in value. To find the average decrease in value each year, we can use the formula: Average decrease per year = Total decrease / Number of years.
Given that the total decrease is $300 and the time period is 5 years, the calculation would be:
Average decrease per year = $300 / 5 = $60.
Therefore, the integer that represents the average decrease in value each year for Juan's baseball card collection is $60.
if f(x)=4-x^2 and g(x)=6x, which expression is equivalent to (g-f)(3)?
Write 24.652 as a mixed number.
Write forty and eight tenths as a decimal
Find the exact circumference of a circle with the given radius. 36 inches C = 72 in. 36 in. 18 in. IN PIE TERMS PLEASE!!!!!:)
Answer:
The circumference of a circle is [tex]72\pi [/tex] .
Step-by-step explanation:
Forrmula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of the circle .
As given in the question
The radius of the circle is 36 inches .
Put all the values in the formula
[tex]Circumference\ of\ a\ circle = 2\times 36\pi [/tex]
[tex]Circumference\ of\ a\ circle = 72\pi [/tex]
Therefore the circumference of a circle is [tex]72\pi [/tex] .
a 26 inch piece of Steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is 2 in more than three times the length of the first piece find the links of the pieces
In the parabola y = (x + 1)2 + 2, what is the vertex?
The vertex form of a quadratic equation is expressed as y = a(x - h)^2 + k. The vertex of the parabola is (-1, 2)
Vertex form of an equationThe vertex form of a quadratic equation is expressed as:
y = a(x - h)^2 + k
where (h, k) is the vertex of the equation
Given the equation of the parabola as y = (x - 1)^2 + 2, On comparing;
h = -1
k =2
Hence the vertex of the parabola is (-1, 2)
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The Sears tower in Chicago is 1,454 feet tall. Write the height as an integer
Jonathan can jog 3 2/5 miles in 7/8 hour.Find his average speed in miles per hour
Write the quadratic equation whose roots are -2 and 3, and whose leading coefficient is 3
Solve your formula from problem 12 for m. Then find the taxi driver’s hourly rate of his pickup rate is $2 and he charges $19.50 for a 7 - mile trip
Answer: Cost per mile m = $4.78.
Step-by-step explanation:
Since we have given that
Pick up rate = $2
Charges for a 7 mile trip = $19.50
Charges for a mile trip would be
[tex]\dfrac{19.50}{7}\\\\=2.78[/tex]
So, amount of taxi's drivers is given by
[tex]\$2.78+\$2\\\\=\$4.78[/tex]
Hence, cost per mile m = $4.78.
A sample of n = 8 scores has ss = 50. if these same scores were a population, then the ss value for the population would be ____.
Answer:
5.69999
Step-by-step explanation:
What is the expression for the calculation double 5 and then multiply by 3?
Explain why you add to find the sum of two integers, but subtract to find the sum of a positive and negative integer
evaluate the expression 4(2x + 3) + 2(x + 1)-7
Express the side length of a square as a function of the length d of the square’s diagonal. then express the area as a function of the diagonal length.
The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation 20,000e^0.15t=28,000 represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
A. 2 years
B.9 years
C. 17 years
D. 22 years
The correct option is: A. 2 years
Explanation
The given growth equation is: [tex]20000e^0^.^1^5^t = 28000[/tex], where [tex]t[/tex] is the number of years the population has been growing.
For finding the number of years, we will solve the above equation for [tex]t[/tex].
First, dividing both sides by 20000, we will get........
[tex]\frac{20000e^0^.^1^5^t}{20000}=\frac{28000}{20000}\\ \\ e^0^.^1^5^t = 1.4[/tex]
Now taking 'natural log' on both sides, we will get........
[tex]ln(e^0^.^1^5^t)=ln(1.4)\\ \\ 0.15t*ln(e)= ln(1.4)\\ \\ 0.15t*1=ln(1.4)\\ \\ t=\frac{ln(1.4)}{0.15}=2.243..... \approx 2[/tex]
So, the population of the town has been growing about 2 years.
The town has been growing for 17 years
Exponential functionsGiven the exponential function
Given the expressions 20,000e^0.15t=28,000
We are to find the value of "t" which is the time.
e^0.15t = 28000/20000
e^0.15t = 7/5
e^0.15t = 1.4
Take the ln of both sides
lne^0.15t = ln 1.4
0.15t = 2.639
t = 2.639/0.15
t = 17years
Hence the town has been growing for 17 years
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Let f = {(–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5)}. Let g = {(–3, 3), (–1, 1), (0, –3), (1, –4), (3, –6)}. What is g(f(2))? -5 -1 2 The composition is undefined.
The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month? 0.2158 0.8750 0.0362 0.1151
Answer:
0.1151
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 75[/tex].
What is the probability that a family spends less than $410 per month?
This probability is the pvalue of Z when X = 410. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{410 - 500}{75}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a pvalue of 0.1151. This is the answer.
The cost of a new house can be represented by the regression equation c = 120f + 90,000, where $120 is the cost per square foot and $90,000 is the cost of the lot. A new house on a lot costs $438,000. How many square feet does it have?
Answer: 2900 Square Feet
Step-by-step explanation: i took the test
Joe practiced his trumpet 3/4 hour on Monday and 7/12 hour on Tuesday. How long did he practice altogether
What number is 2 hundred 15 tens and 6 one
Which of the various ways of orienting the definitional triangle must be used to resolve n⃗ into components in the tilted coordinate system shown? (in the figures, the hypotenuse is blue (long dashes), the side adjacent to θ is red (short dashes), and the side opposite is yellow (solid).)?
what is length of DE
Each U.S. penny weighs 2.5 grams. How many pennies,x is how many pennies it an equation, are on scale if their total weight is 37.5 grams:A. 2.5+x=37.5 x=12,B. 2.5x=37.5 x=15, C. x-2.5=37.5 x=40,D. 2.5x=37.5 x=18???? please answer quick.
What is the fourth term in the arithmetic sequence 13,10,7
The fourth term in the arithmetic sequence 13, 10, 7 is 4.
Explanation:The arithmetic sequence 13, 10, 7 has a common difference of -3. To find the fourth term, we can start with the first term and keep subtracting the common difference. So, 13 - 3 = 10, 10 - 3 = 7, and 7 - 3 = 4. Therefore, the fourth term in the arithmetic sequence 13, 10, 7 is 4.
Three consecutive integers whose sum is 36