Answer:
2.5 m/s
Step-by-step explanation:
we have given that Matty jogs 9 km/hr
we have to convert 9 km/hr to m/s
we know, 1 km= 1000 m
and 1 hr= 60 minutes and 1 minute= 60 seconds
which implies that 1 hr=60 x 60 = 3600 seconds
now, to convert km/hr into minute/second we have to multiply it by 1000/3600 or 5/18
i.e. 9×1000/3600= 5/2=2.5 m/s
simplify each expression -(5p+3)
Answer:
-5p-3
Step-by-step explanation:
use the distributive property
Given the function h(x) = 4x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.
Part A: Find the average rate of change of each section. (4 points)
Part B: How many times greater is the average rate of change of Section B than Section A? Explain why one rate of change is greater than the other. (6 points)
Answer:
The rate of change of section A is 3 and rate of change of section B is 48.
Step-by-step explanation:
The given function is
[tex]h(x)=4^x[/tex]
Formula for average rate:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
Section A is from x = 0 to x = 1, the average rate of change of section A is
[tex]m_1=\frac{h(1)-h(0)}{1-0}=\frac{4-1}{1}=3[/tex]
Section B is from x = 2 to x = 3, the average rate of change of section B is
[tex]m_2=\frac{h(3)-h(2)}{3-2}=\frac{64-16}{1}=48[/tex]
Therefore rate of change of section A is 3 and rate of change of section B is 48.
[tex]m_1\times k=m_2[/tex]
[tex]3\times k=48[/tex]
[tex]k=12[/tex]
Therefore average rate of change of Section B is 12 times of Section A.
The given function is an exponential function and rate of change is not constant.
Adding Rational Expressions
you can buy 5 cans of green beans at the Village Market for $2.20 you can buy at 10 of the same cans of beans at Sam's Club for $5.10 Which places is the better buy
The temperature in mariah’s town was at 5.2 f midnight. the temperature decreased at a steady rate of 1.1 per hour until 7:00 a.m. at 7:00 a.m. the temperature increased by a total of 4.9until noon. what was the temperature at noon?
The temperature at noon was 2.4 degrees Fahrenheit.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
To determine the temperature at noon, we need to first calculate the temperature decrease between midnight and 7:00 a.m. and then add the temperature increase from 7:00 a.m. to noon.
The temperature decreased at a rate of 1.1 degrees Fahrenheit per hour, and it took 7 hours from midnight to 7:00 a.m., so the temperature decreased by a total of 7 hours x 1.1 degrees per hour = 7.7 degrees.
The temperature at 7:00 a.m. would therefore be 5.2 degrees - 7.7 degrees = -2.5 degrees Fahrenheit.
At noon, the temperature increased by a total of 4.9 degrees, so the temperature at noon would be -2.5 degrees + 4.9 degrees = 2.4 degrees Fahrenheit.
Thus, the temperature at noon was 2.4 degrees Fahrenheit.
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Using polar coordinates, evaluate the integral ∫∫rsin(x2+y2)da where r is the region 16≤x2+y2≤81.
The value of the integral is: πcos(16)- πcos (81)
What are polar coordinates?The polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a from a reference point and an angle from a reference direction.
Given:
∫∫ r sin(x²+y²)dA and 16≤x²+y²≤81.
Now,
x =rcosϕ
y=rsinϕ
I=r
Find the integration limits:
ϕ∈[0,2π]
16≤x²+y²≤81
16≤r² cos² Ф + r²sin² Ф≤81
16≤r²≤81
4≤r≤9
So, r∈[4,9]
Now,
∫∫ r sin(x²+y²)dA=
= [tex]\int\limits^9_4 {dr} \int\limits^{2\pi}_0 {rsin \;(r^{2}) } \, d\phi[/tex]
=2π [tex]\int\limits^9_4 {rsin \;(r^{2}) } \, dr[/tex]
Let r² = u
2rdr=du
Also, limit will change from 16 to 25.
5→25
4→16
So,
= π[tex]\int\limits^{81}_{16} {sin \;(u) } \, du[/tex]
=−π|cos (u)∣[tex]^{81}_{16}[/tex]
= πcos(16)- πcos (81)
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What is the quotient? −4 1/2 ÷ (−2 2/3) Enter your answer as a mixed number, in simplified form, in the box. Will Mark Brainliest
The quotient of −4 1/2 ÷ (−2 2/3) would be equal to 1 1/16 as a mixed number, in simplified form.
What are the Quotients?Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.
Thus,
[tex]\dfrac{a}{\frac{b}{c}} = a \times \dfrac{1}{\frac{b}{c} } = a \times \dfrac{c}{b} = \dfrac{a \times c}{b}[/tex]
We have been given that [tex]-4 \dfrac{1}{2}[/tex] ÷ (-[tex]2 \dfrac{2}{3}[/tex])
But first convert the mixed fraction into simple fraction
[tex]-4 \dfrac{1}{2}[/tex] = -9/2
(-[tex]2 \dfrac{2}{3}[/tex]) = -8/3
Thus, we have to divide the terms;
[tex]-4 \dfrac{1}{2}[/tex] ÷ (-[tex]2 \dfrac{2}{3}[/tex])
-9/2 ÷ -8/3
-9/2 x -3/8
27/ 16
In a mixed fraction; [tex]1\dfrac{1}{16}[/tex]
Hence, the quotient of −4 1/2 ÷ (−2 2/3) would be equal to 1 1/16 as a mixed number, in simplified form.
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Kimmy bought a 5kg mg can of peanuts for $4.50 what is the unit price
When Kaitlin divided a fraction by 1/2, the result was a mixed number. Was the original fraction less than or greater than 1/2? Explain your reasoning
Use the regression line for the data in the scatter plot to answer the question. On average, how many more goals will a player score for every additional hour of practice?
A. )1/2 of a goal
B. )3/4of a goal
C.) 1 goal
D.) 4/3 goals
Answer:
Step-by-step explanation:
Given is a scatter plot and the regression line using least squares.
We are required to find out how many more goals a player will score for every additional hour of practice.
In other words, we are to find the slope of the regression line.
By taking two points on the line we can find slope of the line.
(1.5,2) and (6.5,6) are points on the line
Find slope using two point formula
Slope = [tex]\frac{y2-y1}{x2-x1} =\frac{6-2}{6.5-1.5} \\=\frac{4}{5}[/tex]
near slope is 3/4
Hence answer is option b.
On average, the goals a player scores for every additional hour of practice will be 3/4.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
We need to find out how many more goals a player will score for every additional hour of practice.
In other words, we have to find the slope of the regression line.
By taking two points on the line we can find the slope of the line.
Lets (1.5,2) and (6.5,6) are points on the line
So, the slope will be
Slope = y-y₁ / (x-x₁)
= 6- 2 / 6.5 - 1.5
= 4/5
Thus, the near slope is 3/4. Option B is correct.
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The perimeter of a rectangle is 99 inches. It’s width is 11 inches. What is the length of the rectangle? Solve algebraically and arithmetically.
What is the most appropriate way to report the distance driven using the cars odometer
simplify (9/4)^-3/2 x (125/27)^-2/3 x (3/5)^-2
a rectangle is 9ft long and 40 in wide what is its area in square feet?
Gerard bought 9 hamburgers and 3 orders of fries for 24.75. Chris bought 6 hamburgers and 4 orders of fries for 19.50. Each hamburger cost the same amount. Each Order of fries cost the same amount. Wrote a system of equations that can be used to find how much one hamburger and one Order of fries cost.
Complete the inequality statement. 2/7___5/14
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>
=
Which best describes the formula for the perimeter of a rectangle? A. It’s twice the length plus the width. B. P = 2l + 2w is the perimeter of a shape. C. Double the length and width to get the perimeter. D. The formula for the perimeter of a rectangle is P = 2l + 2w.
You are ordering a hamburger and can get up to 77 toppings, but each topping can only be used once. you tell the cashier to surprise you with the toppings you get. what is the probability that you get 00 toppings? express your answer as a fraction or a decimal number rounded to four decimal places.
A boat is traveling at a velocity represented by : 2x^3-10x^2+72x3−10x2+7. At the same time, current is pushing the boat in the same direction with a velocity given by : 5x^3+19x^2+4x5x3+19x2+4x. What is the total traveling velocity of the boat?
7x^3 +9x^2 +4x +7
Step-by-step explanation:The total velocity is represented by the sum of the two polynomials:
(2x^3-10x^2+7) + (5x^3+19x^2+4x) = x^3·(2+5) +x^2·(-10+19) +4x +7
... = 7x^3 +9x^2 +4x +7
Find the probability that your friend is at least 20 minutes late
If the graph has 1/3 length…
At least 20 minutes late: this would mean 20 minutes late or more.
20 or more minutes goes from 20 to 30. So that is a difference of 30 – 20 = 10. The distance of your rectangle is 10.
Length * width = (1/30) * 10 = 1/3 or 0.3333. The probability the friend is at least 20 minutes late is 0.3333.
If an investment of $3000 grows to $4432.37 in eight years with interest compounded annually , what is the interest rate?
Tomas plans to work in his garden on a day when it is least likely to rain.
He checks the weather forecast for the following week
probability of rain
Monday 18%
Tuesday 12%
Wednesday 73%
Thursday 61%
Friday 20%
Tomas plans to work in his garden on Tuesday.
What is the probability that it will not rain on Tuesday?
8/10 divided by 1/3 Help Needed
Find the area of the surface. the part of the paraboloid z=4-x^2-y^2 that lies above the xy-plane
Ray should consume 2,000 calories every day. He consumes 1,735 calories to get essential nutrients. What is Ray's discretionary calorie allowance? 115 calories 265 calories 1,735 calories 2,000 calories
Answer: 265 calories
Step-by-step explanation:
The discretionary calorie allowance is the balance of a person can take after achieving the number of calories need to get essential nutrients.
Given : Every day Energy allowance for Ray = 2,000 calories
Energy level required to get essential nutrients =1,735 calories
Then Ray's discretionary calorie allowance =
Energy allowance - Calories required to get essential nutrients
=2000-1735=265 calories
Hence, Ray's discretionary calorie allowance will be 265 calories.
You are building a rectangular garden and would like the area to be 32 square feet and the length twice the size as the width. What should the dimensions of your garden be?
Resolva o sistema a seguir:
2x - 4y = 8
x . y = 6
The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 325 miles above the earth's surface?
what is 260% as a fraction in simplest form
Evaluate (x + y)0 for x = -3 and y = 5.
A. -1/2
B. 0
C. 1
D. 2