Annie paid a total of $2.6 for 1.2 pounds of strawberries
How to determine the amount paid?In this question, we have the following parameters:
Unit cost per pound = $2.13 per pound
Number of pounds = 1.2 pounds
The amount paid for the number of pounds is represented by the equation
Amount paid = Unit cost per pound x Number of pounds
Substitute the known values in the above equation So, we have the following equation
Amount paid = 2.13 * 1.2
Evaluate the products
Amount paid = 2.556
Approximate
Amount paid = 2.6
Hence, the amount is $2.6
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Answer:
2.56
Step-by-step explanation:
Write an equation for the line in the slope-intercept form.
slope= 8/9, y-intercept=-4
A) f(x) = 9/8x +9/2
B) f(x) = -8/9x - 4
C) f(x) = 8/9x - 4
D) f(x) = -8/9x + 4
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
f(x) = mx + c ( m is the slope and c the y- intercept )
here m = [tex]\frac{8}{9}[/tex] and c = - 4 , then
f(x) = [tex]\frac{8}{9}[/tex] x - 4 ← equation of line
a conical tank has height 3 m and radius 2 m at the base. water flows in at a rate of 2 m3/min. cone with bottom radius 2 meters and height 3 meters. how fast is the water level rising when the level is 1 m and when the level is 1.8 m? (use decimal notation. give your answers to four decimal places.)
The speed at which conical tank water will rise is 9/8[tex]\pi[/tex] m/min.
What is cone?
A cone could be a three-dimensional geometric type with a flat base and a sleek tapering apex or vertex.
Main body:
The quick way of solving this is simply to consider the horizontal cross sectional area of the tank at the 2m water depth. This is 2/3 of the way up a tank having radius increasing linearly with depth, and so the radius is 2/3 of the 2m at the top, i.e: 4/3 m. So the area is:
πr²=π(4/3)2=16/9π
Now water having this cross section filling at 2 m³ per minute would fill a cylinder having this volume and cross section each minute. A cylinder has volume equal to cross section times length, so the cylinder would have a height of:
2/(16/9π)=9/8π metres
Therefore the water at this depth is rising at a rate of 9/8π meters per minute.
The longer way around is to calculate the water volume for a given depth and differentiate. We know that the volume of a cone is a third that of a cylinder with the same dimensions, ie: 1/3πr²h . So if our tank has radius R and height H, then the radius of the surface of the water at depth h is (R/H)h , and so the water volume having this depth is:
v=1/3π(R/H)h)²h=[tex]\frac{\pi r^{2} }{3H^3} h^2[/tex]
We’re interested in rate of change with respect to time, so let’s try differentiating this formula with respect to time, remembering that h is changing with time and so we need to use the chain rule:
[tex]\frac{dv}{dt}[/tex]=[tex]\frac{\pi r^{2} }{3H^2} 3h^2[/tex][tex]\frac{dh}{dt}[/tex]=[tex]\frac{\pi r^{2} }{H^2} h^2[/tex][tex]\frac{dh}{dt}[/tex]
Notice that we can solve this for [tex]\frac{dh}{dt}[/tex] , which is the rate of water height change, i.e: the value that we want:
[tex]\frac{dh}{dt}[/tex]= [tex]\frac{H^2 }{\pi r^{2}} h^2[/tex][tex]\frac{dh}{dt}[/tex]
The rate of change of water volume dv/dt is just the rate that water flows in, so now all we need to do is slot the given numbers into the equation:
dh/dt=2(3²/π2²2²)=9/8π meters per minute
Hence the answer is 9/8[tex]\pi[/tex] m/min.
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A swimming pool is being filled with a hose. The hose fills the pool at a constant rate. The pool’s water level rises 30 inches in 15 hours.
What was the rate per hour of the water level change?
How long will it take for the water level to rise 4 feet?
Answer:
1. 2 inches per hr
2. 24 hrs
Step-by-step explanation:
30/15=2/1
4ft=48in
48/2=24
hope it helps
for a random sample of 65 overweight men, the mean of the number of pounds that they were overweight was 29. the standard deviation of the population is 4.3 pounds.
The best point estimate of the mean is 29 pounds.
Sample size n =65; sample means (X) =29; population std (s) =4.3
Since the sample size is more than 30 we can use the central limit theorem. Hence population means estimate is equal to the sample mean which is 29.
At 90% confidence z value = 1.645
Lower limit = X -z * s/[tex]n^{0.5}[/tex]= 29 -1.645 * 4.3/[tex]65^{0.5}[/tex] = 28.1
Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.645 * 4.3/[tex]65^{0.5}[/tex] = 29.9
At 95% confidence z = 1.96
Lower limit = X -z * s/[tex]n^{0.5}[/tex] = 29 -1.96 * 4.3/[tex]65^{0.5}[/tex] = 27.9
Upper limit = X -z * s/[tex]n^{0.5}[/tex] = 29 +1.96 * 4.3/[tex]65^{0.5}[/tex]= 30.1
95% confidence interval is larger. It has a wider range of values than 90% confidence. This is because we are covering more area on a normal curve with a higher confidence interval. So mean value is more likely to fall in the 95% range than the 90% range.
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A flagpole casts a shadow 18m long when the athlete of the sun is 54°. What is the height of the flagpole.
If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
In the question ,
it is given that ,
the length of the shadow of the flag pole = 18m
the angle of "elevation" of the sun = 54°
let the height of the flagpole be = "x" ,
The flagpole and the shadow form a right triangle ,
So , tan(54°) = (height of flag pole)/(shadow of flagpole)
Substituting the values from above ,
we get ,
tan(54°) = x/18
on cross multiplication ,
x = 18 × tan(54°)
x = 18 × 1.3763
x = 24.7734
x ≈ 24.8
Therefore , If flagpole casts a shadow 18m long when the angle of elevation of the sun is 54° then the height of the flagpole will be 24.8 m .
The given question is incomplete , the complete question is
A flagpole casts a shadow 18m long when the angle of elevation of the sun is 54°. What is the height of the flagpole ?
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What is the independent variable
Answer:
Your answer is correct.
Step-by-step explanation:
Answer:
p
Step-by-step explanation:
when p changes, it causes the equation to change
In a two-digit number, the units digit is 5 more than the tens digit. The number itself is three times the sum of its digits. What is this number?
Answer:
The number is 27.
Step-by-step explanation:
Since the units digit has to be 5 more than the tens digit, there are only four possible two-digit numbers which satisfy this condition. They are 16, 27, 38, and 49.
Next, the digits can be added and multiplied by three to check that the answer is the same two-digit number.
3 (1 + 6) = 21 does not work because 16 isn't the same as 21.
3 (2 + 7) = 27 does work because 3 * 9 is 27.
3 (3 + 8) = 33
3 (4 + 9) = 39
Cross multiply the numbers
Answer:
2m/4m = 9m/xm
2m(xm) = 4m(9m)
2xm = 36m
Fourteen more than the product of x and y
Answer:
14+(x*y)
Step-by-step explanation:
Puja Limbu did 8 out of 10 math problem and Raju Lama did 11 out of 15 imilar math problem. Expre the number of problem olved by each of them in fraction and identify who did better performance.
The person that has a better performance is Puja Limbu.
How to illustrate the information?From the information, Puja Limbu did 8 out of 10 math problem. This can be converted to percentage as:
= 8/10 × 100
= 80%
Raju Lama did 11 out of 15 similar math problem. This will be:
= 11/15 × 100
= 73%
Therefore, Puja has a better performance.
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One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
According to the Pythagoras theorem, the value of the other leg is, 15.7 cm
Pythagoras theorem:
Pythagoras theorem defines that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Given,
One of the legs of a right triangle measures 3 cm and its hypotenuse measures 16 cm.
Here we need to find the measure of the other leg and round off it to nearest tenth.
Though the given question, we know that the value of
Hypotenuse = 16 cm
one leg = 3cm,
Then let us consider the length of the other leg as x.
So, according to the Pythagoras theorem,
It can be calculated as,
=> hypotenuse² = one leg² + other leg²
=> 16² = 3² + x²
=> 256 = 9 + x²
Here we need the value of x, so it can be rewritten as,
=> 247 = x²
=> x = √247
When we take square root for 247, then we get the value of x as,
=> x = 15.716
When we round off it to the nearest tenth then we get the value of another leg as 15.7 cm.
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what is 1/3 plus 4.1 in simplest form written as a mixed number
POPULATION The projected population in thousands for a city over the next several years can be estimated by the
function P(x)=x³ + 2x² - 8x + 520, where x is the number of years since 2005. Use synthetic substitution to estimate
the population for 2015.
O 1,640,000
O 1,320,000
O 590,000
O 36,240,000
The population for 2015 is 1,640,000 ,so option A is correct.
Given:
The projected population in thousands for a city over the next several years can be estimated by the function P(x)=x³ + 2x² - 8x + 520.
where x is the number of years since 2005.
x = 2015 - 2005
x = 10
P(x) = x³ + 2x² - 8x + 520.
= [tex]10^{3} +2(10^{2} )-8*10+520[/tex]
= 1000 + 2*100 - 80 + 520
= 1520 + 200 - 80
= 1720 - 80
= 1640.
Given the projected population in thousands so = 1640 * 1000
= 1640000.
Therefore The population for 2015 is 1,640,000 ,so option A is correct.
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College freshmen were asked if they were currently enrolled in Composition I. The results are shown in the table.
How many females are currently enrolled in Composition I?
A) 46
B) 73
C) 75
D) 119
There are 73 females currently involved in the competition.
What is arithmetical operation?The four basic arithmetic operations in Maths, for all real numbers, are: Addition (Finding the Sum; '+') Subtraction (Finding the difference; '-') Multiplication (Finding the product; '×') Division (Finding the quotient; '÷')
Given that, there is a table of male and female involved and not involved in a competition,
Female column total = 103
103-57 = 46
Female row total = 119
119-46 = 73
Hence, There are 73 females currently involved in the competition.
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You work a basic week of 40 hours and your basic rate is $19.50 per hour. What is your basic wage for the week and showing working for this question.
If you work $19.50 per hour and you work 40 hours a week, you need to multiply 19.50 by 40 to get your answer
19.50 x 40 = $ 780 a week.
I hope this helps!
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1. Find the
radius of the circle to the nearest 10th.
The radius of the circle to the nearest 10th is 2.0537.
Given:
In a circle, an angle measuring 9.3 radians intercepts an arc of length 19.1.
we know that,
radians = arc / radius
radius = arc/radians
= 19.1/9.3
= 191/10/93/10
= 191/93
≈ 2.0537
Therefore the radius of the circle to the nearest 10th is 2.0537.
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I Need help for this one is about linear equations
Answer:
not sure what the question is but if you look for the equation
it's
1/4 * x + 1
or in decimal
0.25x + 1
Leah makes $3.25 per hour. Lois makes $8.64 per hour. How much more does Lois make per hour than Leah
Answer:
$11.89 is the answer
Step-by-step explanation:
because $3.25 + $8.64 is $11.89
Hope this helps
Kyle has 80 potatoes he multiples them by 1900 than adds 100000 then he divides them by 53727282 then subtracts 1.5. How many potatoes does Kyle have?
Answer:
-1.49530965
Step-by-step explanation:
Vickie Ewing deposits her savings of $2800 in an investment paying 6% ompounded quarterly and she leaves it there for 5 years. Find (a) the compound amount nd (b) the interest.
The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $2800
Rate of interest = 6% = 0.06
Compound quarterly n = 4
Time period T = 5 yeras
a)
Total amount = P(1 + R/n)^(nT)
Total amount = 2800(1 + 0.06/4)^(4 x 5)
Total amount = 2800(1.015)^20
Total amount = $3771.19
b)
Let's say the equivalent annual interest rate is r.
n = 1
3771.19 = 2800(1 + r/1)^(1 x 5)
3771.19 = 2800(1 + r)^5
1.061 = 1 + r
r = 0.06136 = 6.136%
Hence"The compound amount with the compound quarterly will be $3771.19 and the equivalent annual interest rate will be 6.1363%".
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Evaluate. Write your anwer a a whole number or a a implified fraction.
5 –1
·
8 –2
=
Answer:
Step-by-step explanation:
so basically 2+2=3
QUESTION 10/10 HELP ASAPP
!WILL GIVE BRAINLIEST TO WHOEVER ANSWERS THE OTHER 9 TOO.!
Answer: tyhe image / screenshot
Step-by-step explanation:
The circumference of a circle is 47 cm. Find its radius, in centimeters.
Answer:
The radius (in centimeters) is 18.9999, or roughly 19 centimeters.
Step-by-step explanation:
If you need a step-by-step explanation, please let me know and I will help you. Thanks!
i have no clue what this is can someone help me
Step-by-step explanation:
you have to transform the equations, so that in the end you have only x on one side, and everything else on the other.
and that is the solution.
remember, when doing such transformations, we have to do every change to both sides at the same time.
a)
x/5 = 3 | multiply both sides by 5
x = 3×5 = 15
b)
x/2 = 8.5 | multiply both sides by 2
x = 8.5×2 = 17
Answer:
a=15 b=17
Step-by-step explanation:
since we know x divided by something is 3 we do the inverse method so it's going to b 15. The same thing happened with b.
I hope this helps!!
What is the sum?
- 1 1/8 + (-1/2) = -1 1/8 + ( - 4/8) = ?
Answer:
[tex]-1\frac{5}{8}[/tex]
Step-by-step explanation:
-1 1/8 - 1/2 =- 1 1/8 -4/8
= -9/8-4/8
=-13/8
=-1 5/8
Hopes this helps please mark brainliest
HELP! PLEASE! I WILL NAME YOU THE BRAINLIEST!
Solve the system by graphing.
y = 1/3x - 1
x - 3y = 3
(6, 1)
(0, −1)
This system has no solutions.
This system has infinitely many solutions.
Answer:
This system has infinitely many solutions.
Step-by-step explanation:
The graphic in both functions is the same line, which means the system has many solutions
Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm and
circle B has a diameter of 16 cm.
How much wider was the pair of
compasses when Alex drew circle A than
when he drew circle B?
Answer:
Circle B and 3.14 cm
Step-by-step explanation:
Not 100% sure but good luck :)
The length 1 cm wider was the pair of compasses when Alex drew circle A than when he drew circle B.
What is a diameter?A straight line that runs through the sideways of a body or figure, particularly a circle or sphere, is called as a diameter of a circle or sphere.
Given:
Alex has drawn two circles, A and B.
Circle A has a diameter of 18 cm.
So, the radius is 18/2 = 9 cm.
And circle B has a diameter of 16 cm.
So, the radius is 16/2 = 8 cm.
To find how much wider was the pair of compasses when Alex drew circle A than when he drew circle B:
The difference in the radius,
= 9-8
= 1 cm
Therefore, when Alex drew circle A than when he drew circle B, the compass was wider 1 cm.
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0.75(8+e)=2−1.25e slove for E
The value of 'E' in the algebraic equation is -2
What is algebraic equation?Algebraic equation is a mathematical statement in which two expressions are set equal to each other.
Therefore, let solve for 'E' in the equation 0.75(8+e)=2−1.25e
Use 0.75 to open the bracket
6 + 0.75e = 2 -1.25e
Collect the like terms
0.75e+1.25e = 2-6
2e = -4
Divide both sides by 2
2e/ 2 = -4/2
e =-2
Therefore, the value of 'E' in the equation is -2
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What is -4 (3-1) +2 simplified?
Answer: [tex]-4(3-1)+2=-4(2)+2=-8+2=-6[/tex]
Please help!!!!! ASAP, thank you :)) I’ll give the right answers brainliest
Answer:
Step-by-step explanation:
ok