To find the number of adults needed for 48 children at a daycare with an adult to child ratio of 3:16, we set up a proportion and solve for the unknown number of adults. We cross-multiply and divide to find that 9 adults are required.
The question asks us to calculate how many adults are needed for 48 children in a daycare center given an adult to child ratio of 3:16. To solve this, we need to set up a proportion based on the ratio and solve for the number of adults needed.
We have the ratio of adults to children as 3:16, which means for every 3 adults, there are 16 children. To find out how many adults are needed for 48 children, we set up the proportion:
3 adults / 16 children = x adults / 48 children
Now we cross-multiply and solve for x:
(3 adults) / (48 children) = (16 children)
144 = 16x
x = 144 / 16
x = 9
Therefore, 9 adults are needed to take care of 48 children at the daycare center.
Each canvas bag will hold exactly 5 pounds of kings tomatoes. How many bags will be necessary to hold 5 kg worth of these same tomatoes? (1 kg = 2.25 pounds)
1 kg = 2.25 pounds
5*2.25 = 11.25 pounds
11.25/5 = 2.25 bags
so you would need 3 bags
for f(x) = x^3-7X^2+8x+16 find f(10) using synthetic division
Explain why we need more than one digit to express certain quantities
Susan invests
2
times as much money at
8%
as she does at
4%
. If her total interest after
1
year is
$800
, how much does she have invested at each rate?
Final answer:
To find how much Susan has invested at each rate when she invests 2 times as much money at 8% as she does at 4%, create and solve an equation based on the total interest earned.
Explanation:
Susan has invested $x at 4% interest rate and $2x at 8% interest rate.
Given that the total interest after 1 year is $800, we can create the equation: $x(0.04) + $2x(0.08) = $800.
Solving the equation, we find that Susan has $3,000 invested at 4% and $6,000 invested at 8%.
Hello, I'm working on a project and I've been stumped.
How would I find the central ark of a ferris wheel? I'm using the London Eye ferris wheel for my project, and so far I know it has a diameter of 120 meters and 32 cars. It has a circumference of 377m and an area of 11,310m.
How can that information help me? Please include all steps and a clear explanation, and give the answer in degrees. Thank you.
a circle has 360 degrees
the ferris wheel has 32 cars so the circle is broken up into 32 sections
the central angle would be the angle between 2 of the cars
so divide 360 by 32
360/32 = 11.25 degrees
Compare the value of the
4 in 40 and 400
let A and B be nxn matrices such that AB is singular prove that either A or Bis singular
53 ℃ below zero degrees
Write an equation of a line that is perpendicular to the given line and that passes through the given point.
-x + 5y= 14; (-5, -2)
A. Y=-5x-27
B.y=-1/5x-27
C. Y=-1/5x-15
D. Y=5x-27
find the equation of a line containing the given point and slope (10,5); m=9/20
What is the integral of 1/x?
Final answer:
The integral of 1/x is the natural logarithm of the absolute value of x, plus an integration constant C. This expression is central to calculations in many areas of science and mathematics.
Explanation:
The integral of 1/x is known as the natural logarithm of the absolute value of x, plus a constant of integration, commonly referred to as C. In mathematical terms, this is expressed as:
[tex]\( \int \frac{1}{x} dx = \ln(|x|) + C \)[/tex]
The natural logarithm arises due to the fundamental properties of the integral, and it's significant as it appears frequently across various fields of science and mathematics. While the basic form of integration of 1/x involves the natural logarithm, in applied examples like the cases mentioned above, where one works with additional functions or domain restrictions, the integral may lead to more complex expressions or even vanish under certain symmetry conditions.
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
Consider a line l with positive x- and y- intercepts. Suppose l makes an angle of with the positive x- axis. What is the slope of l in terms of theta?
What if the atom has no charge
If m and n are positive integers such that the greatest common factor of [tex] m^{2} n^{2}[/tex] and [tex] m n^{3}[/tex] is 45, then which of the following could n equal?
(A) 3
(B) 5
(C) 9
(D) 15
(E) 45
What is after 100,99,07,94,90
Curt is installing a picket fence around his garden which is 45.45 ft by 14.63 ft. When he gets to the hardware store he finds that each picket fence slat is two feet wide. If Curt does not want any spaces between each slat, use estimation to determine how many slats of fencing he should buy.
what is the value of x in the equation 5(4x-10)+10x=4(2x-3)+2(x-4) ?
-7/4
-1/4
3/20
3/2
Answer:
[tex]\frac{3}{2}[/tex]
Step-by-step explanation:
Here, the given expression is,
[tex]5(4x-10)+10x=4(2x-3)+2(x-4)[/tex]
By distributive property,
[tex]20x - 50 + 10x = 8x - 12 + 2x - 8[/tex]
By combining like terms,
[tex]30x -50=10x-20[/tex]
Adding 50 on both sides,
[tex]30x=10x-20+50[/tex]
[tex]30x = 10x + 30[/tex]
Subtracting 10x on both sides,
[tex]20x = 30[/tex]
Divide both sides by 20,.
[tex]x=\frac{3}{2}[/tex]
Hence, LAST option is correct.
If f(x)=2x^2sqrt(x-2), complete the following statement f(6)
The value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
How to determine the function value?The function is given as:
[tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex]
Substitute 6 for x
[tex]f(6)=2 * 6^2 + 5\sqrt{6-2}[/tex]
Evaluate the difference
[tex]f(6)=2 * 6^2 + 5\sqrt{4}[/tex]
Evaluate the exponents
f(6)=2 * 36 + 5 * 2
Evaluate the sum of products
f(6) = 82
Hence, the value of f(6) in the function [tex]f(x)=2x^2 + 5\sqrt{x-2}[/tex] is 82
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A motorboat takes 3 hours to travel 108 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
What is 4.76 hours converted to min and sec
If 12 bumper stickers cost $8.64, then how much do 18 cost
The proportion is solved and the cost of 18 bumper stickers is $ 12.96.
Given data:
To find out how much 18 bumper stickers cost, use a proportion since the cost of bumper stickers is directly proportional to the number of stickers.
Cost of 12 bumper stickers / Number of 12 bumper stickers = Cost of 18 bumper stickers / Number of 18 bumper stickers
On simplifying the proportion:
$8.64 / 12 = x / 18
Now, solve for x (the cost of 18 bumper stickers):
x = ($8.64 / 12) * 18
x = $12.96
Hence, 18 bumper stickers cost $12.96.
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A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents the original price of the jacket, which expression represents the final price of the jacket during this sale? 0.2x – 3 0.8x – 12 0.8x – 15 0.2x – 15
0.8x – 12
Explanation:The sale price is (x-15). After the 20% discount, the final price is 0.80 times the sale price, so is ...
... final price = 0.80×(x -15) = 0.80x -12
Answer:
The correct option is B.
Step-by-step explanation:
Let the original price of the jacket be x.
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases.
The price of jacket after $15 off is [tex]x-15[/tex].
Then 20% discount is applied, so the final price of the jacket is
[tex]P=(x-15)(1-\frac{20}{100})[/tex]
[tex]P=(x-15)(1-0.2)[/tex]
[tex]P=(x-15)(0.8)[/tex]
[tex]P=0.8x-12[/tex]
The final price of the jacket during this sale is 0.8x-12. Therefore the correct option is B.
The Greasy Grab Bag claims that customers can make 20 different meal combinations from the menu items. If the Greasy Grab Bag has 4 sandwiches, 3 sides, and 2 drinks, which of the following is correct?
The correct number of different meal combinations that customers can make from the menu items at the Greasy Grab Bag is 24.
To determine the number of different meal combinations, we need to consider that each meal consists of one sandwich, one side, and one drink. Given that there are 4 sandwiches, 3 sides, and 2 drinks to choose from, we can calculate the total number of combinations by multiplying the number of choices for each category together.
The number of sandwich choices is 4, the number of side choices is 3, and the number of drink choices is 2. Therefore, the total number of meal combinations is calculated as follows:
Total combinations = Number of sandwich choices — Number of side choices — Number of drink choices
Total combinations = [tex]$4 \times 3 \times 2$[/tex]
Now, let's calculate the total number of combinations:
Total combinations =[tex]$4 \times 3 \times 2 = 12 \times 2 = 24$[/tex]
Thus, there are 24 different meal combinations that customers can make, which means the Greasy Grab Bag's claim of 20 different meal combinations is incorrect. The correct number is 24.
Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?
Answer: The expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Step-by-step explanation:
Since we have given that
Distance covered by mountaineer = 1000 feet
Speed at which he climbed = x feet per hour
Time taken by him would be
[tex]\dfrac{1000}{x}[/tex]
Additional distance covered by him = 5000 feet
Speed at which he climbed this time = 2x-10
So, Time taken is given by
[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]
Hence, the expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Angle BCA is congruent to angle DAC, and angle BAC is congruent to angle DCA by:
the vertical angle theorem.
the alternate interior angles theorem.
the reflexive property.
None of the choices are correct.
Angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
here,
The pro[perty of parallel lines states that when two parallel lines intersect by the same transversal line the alternate interior angle will be equal as also the alternate exterior angles.
So,
Line BC and AB are parallel lines and AC is a transversal line,
So,
Angle BAC = angle DCA
Thus, angle BAC is congruent to angle DCA by the alternate interior angles theorem. Option B is correct.
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Convert the measurement as indicated.
26ft= _ yd _ ft
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
Tank 1 initially contains 50 gals of water with 10 oz of salt in it, while tank 2 initially contains 20 gals of water with 15 oz of salt in it. water containing 2 oz/gal of salt flows into tank 1 at a rate of 5 gal/min and the well-stirred mixture flows from tank 1 into tank 2 at the same rate of 5 gal/min. the solution in tank 2 flows out to the ground at a rate of 5 gal/min. if x1(t) and x2(t) represent the number of ounces of salt in tank 1 and tank 2, respectively, set up but do not solve an initial value problem describing this system.
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056