Answer:
Using a system of equations, however, allows me to use two different variables for the two different unknowns.
number of adults: a
number of children: c
With these variables, I can create equations for the totals they've given me:
total number: a + c = 2200
total income: 4a + 1.5c = 5050
Now I can solve the system for the number of adults and the number of children. I will solve the first equation for one of the variables, and then substitute the result into the other equation:
a = 2200 – c
4(2200 – c) + 1.5c = 5050
8800 – 4c + 1.5c = 5050
8800 – 2.5c = 5050
–2.5c = –3750
c = 1500
Now I can back-solve for the value of the other variable:
a = 2200 – (1500) = 700
I have values for my two variables. I can look back at my definitions for the variables to interpret these values. To answer the original question, there were:
1500 children and 700 adults.
Final answer:
A word problem involving two people and their apples, where Alice has twice as many apples as Bob. The variables are defined, the equation is written, and the solution is found.
Explanation:
Word Problem:
Alice has twice as many apples as Bob. Together, they have 15 apples. Define the variable 'x' as the number of apples Bob has.
Equation:
Alice's apples: 2x
Bob's apples: x
2x + x = 15
Solution:
Combining like terms: 3x = 15
Dividing both sides by 3: x = 5
Sentence Explanation:
We defined the variable 'x' as the number of apples Bob has. Since Alice has twice as many apples, we expressed her number of apples as 2x. The total number of apples they have together is 15, so we created an equation by summing up both Alice's and Bob's apples. By solving for 'x', we found that Bob has 5 apples.
1. Find the common difference of the sequence: 31, 26, 21, 16, ...
Answer:
it is subtract 5
Step-by-step explanation:
Find the percent of change from the original price of $184 to the sale price of $138.
Answer: 25%
Step-by-step explanation:
184-138= 46
184*.25=46
(x-4) (x - 4) =
x^2 -8x - 16
Ox^2+8x +16
Ox^2-8x+ 16
Ox^2-8x-16
A bag contains 18 small red, 19 small black, 13 large black, and 15 large red T-shirts, and nothing else. What is the least number of T-shirts Alpa must take out of the bag (without looking at them) to be absolutely sure of having at least two T-shirts among them that differ only by size or only by color?
Alpa must take out five T-shirts in order to be absolutely sure of having at least two T-shirts that differ only by size or by color.
Explanation:The subject of this question is a probability problem, which falls under the domain of Mathematics, more specifically combinatorics. In scenarios such as this, we want to ensure we have at least two T-shirts that only differ by size or color. To guarantee this, Alpa must select one T-shirt of each color and size first. That means she must take out four T-shirts: a red small, a red large, a black small, and a black large. For the fifth T-shirt that she takes out, it will either be the same color as one she already has but different in size or it will be the same size as one she already has but a different color. So, the least number of T-shirts Alpa must take out of the bag in order to be absolutely sure of having at least two T-shirts among them that differ only by size or color is five.
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find the perimeter of the figure to the nearest hundredth.
Answer:
I think it's 640 i may be wrong or its 40.
Step-by-step explanation:
when finding the perimeter you just add up the outsides of the shape.
Answer:
90.24 mm
Step-by-step explanation:
Perimeter of the figure
[tex] =(20 + 20 ) + \frac{1}{2} \times 2\pi \: r \\ = (40 ) + 3.14 \times 16 \\ = 40 + 50.24 \\ = 90.24 \: mm[/tex]
60.2 rounded to the nearest hundredth
To round 60.2 to the nearest hundredth, we need to look at the digit in the thousandth place, which is the second digit after the decimal point. If this digit is 5 or greater, we'll round up, and if it's less than 5, we'll round down. In this case, the digit in the thousandth place is 2, which is less than 5. So, when rounding 60.2 to the nearest hundredth, we round down to 60.20.
Explanation:To round 60.2 to the nearest hundredth, we need to look at the digit in the thousandth place, which is the second digit after the decimal point. If this digit is 5 or greater, we'll round up, and if it's less than 5, we'll round down.
In this case, the digit in the thousandth place is 2, which is less than 5. So, when rounding 60.2 to the nearest hundredth, we round down to 60.20.
Answer: 60.20
A person places $5540 in an investment account earning an annual rate of 2.5%,
compounded continuously. Using the formula V = Pent, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and ris the rate of interest, determine the amount of money, to the
nearest cent, in the account after 20 years.
Answer:
$9,133.92
Step-by-step explanation:
V = P*e^(rt)
V = $5540 * e ^ (0.025*20)
V = 5540 * e^(0.5)
V = 5540 * 1.648721
V = $9,133.9158
about $9,133.92
Final answer:
The amount of money in the account after 20 years with continuous compounding at an annual rate of 2.5% is approximately $9138.13.
Explanation:
To calculate the amount of money in an investment account after 20 years with continuous compounding, we use the formula V = Pe^rt, where:
P is the principal amount ($5540),
e is the base of the natural logarithms (approximately 2.71828),
r is the annual interest rate (2.5% or 0.025 as a decimal), and
t is the number of years the money is invested (20 years).
Plugging these values into the formula, we get:
V = $5540 × e^(0.025 × 20)
Using a calculator with the capability to compute e raised to a power, we find:
V ≈ $5540 × 2.71828^0.5
V ≈ $5540 × 1.64872
V ≈ $9138.13
Hence, the value of the investment after 20 years, to the nearest cent, is approximately $9138.13.
Which fraction is equal to 0.54 ?
A. 27/50
B. 49/90
C. 6/11
D. 5/4
Answer: A if you want exact not rounded
Step-by-step explanation: 27/50 = .54
49/90 = .544444444444444444444444444444.....repeating
6/11 = .5454545454545454545454545454545...... repeating
5/4= 1.25 which is wrong
please help me out here! I’ll give you brainliest if you give me the correct answer! :)
Answer:
0.31
0.36
A
Step-by-step explanation:
Answer:
0.31 and 0.36 (A) is the answer
Find angles b,c and d
Answer:
B = 73°, c = 107°, d= 107°
Step-by-step explanation:
[tex]b + 107 \degree = 180 \degree..(straight \: line \: \angle s) \\ b = 180 \degree - 107 \degree \\ \huge \red{ \boxed{b = 73 \degree}} \\ \\ \huge \purple{ \boxed{c = 107 \degree }}\\..(vertical \: \angle s) \\ \\ \huge \orange{ \boxed{d = 107 \degree }}\\..(corresponding \: \angle s) \\ \\ [/tex]
Clint wants to wrap a present. He placed the gift in a rectangular box measuring 12 in x 3 in x 6 in. How much wrapping paper did he use?
Answer:
she use 216 ft of wrapping paper i think
32 slices from 4 cakes = slices from 5 cakes
If 4 cakes make 32 slices, one cake will make [tex]\frac{32}{4}[/tex] = 8 slices. Therefore, 5 cakes will make (8 x 5) = 40 slices.
Answer:
You can get 40 slices from 5 cakes because each cake has 8 slices in it.
Step-by-step explanation:
The scatter plot shows a regression line of advertising dollars spent and sales. What amount has the greatest error term?
A) $5,650
B) $5,850
C) $6,000
D) $6,750
Answer:
6750
Step-by-step explanation:
please help on this problem
Answer:
n+2n = 150
n = 50
Step-by-step explanation:
n = smaller angle
The other angle is 2n
Add them together to get 150
n+2n = 150
Combine like terms
3n = 150
Divide by 3
3n/3 =150.3
n = 50
The regular price of a calculator is $12.30. Warren paid 75¢ less than the regular price for the calculator. He also paid $1.48 for a pad of paper. What is the total amount Warren paid for these two items?
Answer:
The total amount Warren paid for these two items is $13.03
Step-by-step explanation:
Warren paid:
75¢ less than $12.30 is $12.30 - $0.75 = $11.55 on the calculator.
$1.48 for the pad of paid.
What is the total amount Warren paid for these two items?
$11.55 + $1.48 = $13.03
The total amount Warren paid for these two items is $13.03
Compare the subtraction problems (6 8 − 5 8 = 1 8 ) and (6 9 − 7 9 = −1 9 ). Why is the answer to the first problem positive and the answer to the second problem negative? Check all that apply. In the second problem, the first fraction is less than the second fraction. The answer to the first problem is positive because the denominator is even. The answer to the second problem is negative because the denominator is odd. If you subtract a lesser number from a greater number, the answer is positive. If you subtract a greater number from a lesser number, the answer is negative.
Answer:
A D E
Step-by-step explanation:
A. In the second problem, the first fraction is less than the second fraction.
D. If you subtract a lesser number from a greater number, the answer is positive.
E. If you subtract a greater number from a lesser number, the answer is negative.
The correct options are given below:-
A. In the second problem, the first fraction is less than the second fraction.
D. If you subtract a lesser number from a greater number, the answer is positive.
E. If you subtract a greater number from a lesser number, the answer is negative.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.
The expressions are as follows:-
(6/ 8 − 5/8 = 1 8 ) and (6/ 9 − 7 / 9 = −1 / 9 )
In the second problem, the first fraction is less than the second fraction. If you subtract a lesser number from a greater number, the answer is positive. If you subtract a greater number from a lesser number, the answer is negative. All the statements are correct for the given expressions.
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Can someone please help this is due today
Answer:
3.2
Step-by-step explanation:
First, you have to arrange them in proper numerical order (least to greatest).
84, 88,90,92,96
Next, find the mean by adding them all up and dividing them by 5.
84 + 88 + 90 + 92 + 96 = 450
450 divide by 5 equals 90.
Now, that we have our mean, we have to subtract it from each of the numbers in the data set. Remember this is absolute so there is no negatives.
84 - 90 = 6
88 - 90 = 2
90 - 90 = 0
92 - 90 =2
96 - 90 = 6
Next, line them up again.
2,2,6,6
Find the mean of them:
2 + 2 + 6 + 6 = 16
16 divided by 4 is 4.
Therefore, our answer would be the MAD is 4.0
On Monday, 218 students went on a trip to the zoo. All 5 buses were filled and 8 students
had to travel in cars. How many students were in each bus?
Answer:
Their were 42 kids on each bus.
Step-by-step explanation:
You have to divide the number of kids(210) by the number of buses.
Answer:
42
Step-by-step explanation:
if you take the total of kids and subtract the 8 that went into the cars the you do 210 divided by the total of buses and you get 42
George and Cameron went on a bicycle trip they took a bus to the starting point they bought the rest they traveled 350 km in total and they bite 80 km more than they were biased how many kilometers are they travel by bike
Answer:
215
Step-by-step explanation:
We assume that the "starting point" is the starting point for the entire trip, including bus travel.
If B is distance traveled by Bus, and "b" is distance traveled by bike, then we seem to have ...
B + b = 350
b -B = 80
Adding these two equations gives ...
2b = 430
b = 215
They traveled 215 km by bike.
A lab technician made a 14 cm diameter hole through the middle of a cylinder that has a diameter of 20 cm and a height of 28 cm. What is the approximate volume of the finished cylinder, to the nearest tenth of a centimeter
Answer:
The volume of the finished cylinder is [tex]4486.2 m^3[/tex]
Step-by-step explanation:
To find the volume of the finished cylinder, we have to first find the volume of the hole (with 14 cm diameter and a height of 28 cm) and subtract it from the volume of the original cylinder (with diameter of 20 cm and a height of 28 cm).
Note: The hole is also cylindrical in shape.
The volume of a cylinder is given as:
[tex]V = \pi r^2h[/tex]
where r = radius, h = height
VOLUME OF THE HOLE
The diameter of the hole is 14 cm, hence, its radius is 7 cm (14 / 2 = 7)
Its volume is:
[tex]V = \pi *7^2 * 28\\V = 4310.3 m^3[/tex]
VOLUME OF THE ORIGINAL CYLINDER
The diameter of the cylinder is 20 cm, hence, its radius is 10 cm (20 / 2 = 10)
Its volume is:
[tex]V = \pi *10^2 * 28\\V = 8796.5 m^3[/tex]
Hence, the volume of the finished cylinder will be:
[tex]8796.5 - 4310.3 = 4486.2 m^3[/tex]
The volume of the finished cylinder is [tex]4486.2 m^3[/tex]
A geometric sequence follows________
A.an exponential pattern
B.a linear pattern
C.a quadratic pattern
D.no pattern
A geometric sequence follows an exponential pattern, where each term is found by multiplying the previous term by a constant called the common ratio. Therefore, the answer is A. An Exponential Pattern.
A geometric sequence follows an exponential pattern. This means that each term in the sequence is found by multiplying the previous term by a constant called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3. Here, each term is obtained by multiplying the previous term by 3.
To clarify, when we say a sequence follows an exponential pattern, it means the terms grow at a rate that involves doubling, tripling, or multiplying by any fixed number, rather than adding or subtracting a fixed amount as in linear patterns or changing according to a square as in quadratic patterns. This type of pattern can be represented by the formula:
a, ar, ar², ar³,...
where a is the first term and r is the common ratio. Understanding that geometric sequences follow an exponential growth pattern helps in solving various mathematical problems related to population growth, finance, and more.
What is the distance from the origin to point A graphed on the complex plane below? On a coordinate plane, Point A is at (negative 3, negative 2). StartRoot 5 EndRoot StartRoot 13 EndRoot 9 13
Answer:
b on edge
Step-by-step explanation:
The distance between the origin and point A is √13.
How to find the distance?
We know that the distance between two points (a, b) and (c, d) is:
[tex]D = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
Here we want to find the distance between the origin, (0, 0), and the point A, which has coordinates (-3, -2).
Using the above formula we will get:
[tex]D = \sqrt{(-2 - 0)^2 + (-3 - 0)^2} = \sqrt{4 + 9} = \sqrt{13}[/tex]
The distance between the origin and point A is √13.
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A birthday candle costs $0.84. How much do 6 birthday candles cost?
Answer:
$5.04
Step-by-step explanation:
Take the cost of one candle and multiply the number of candles desired
6 *.84 =5.04
Answer: $5.04
Step-by-step explanation:
If one candle costs 0.84, and you need 6 then you multiply 0.84 x 6=5.04.
what is the value of 8 plus (27 divided by 9) power of two
Answer:
8+ (27/9)2 = 17
What is 20 times 20 plus 10
Answer:
410
Step-by-step explanation:
20 x 20 = 400 + 10 = 410
Have a great day :)
Answer:
410
Step-by-step explanation:
20 x 20 = 400
400+ 10 = 410
Melissa spent 5 quarters on ice cream. The next day, she spent 13 nickels on candy bar. How much money did Melissa spend?
Answer:
Melissa spent $1.90
Step-by-step explanation:
Each quarter is 25 cents. If you have 5 quarters, that would be 25 times 5. And each nickel is 5 cents, so if you have 13 nickels, then you would multiply 5 by 13. Then to get the total amount spent you would have to add the quarters and nickels. which would be 125 and 65. Every 100 is a dollar. so it would be 190, or $1.90.
Answer:
1.90
Step-by-step explanation:
Trip uses 3.175 liters of water to make
slime. How many milliliters of water does he
use to make the slime?
Answer:
3,175 milliliters
Step-by-step explanation:
There are 1,000 milliliters in a liter, therefore you must use the equation
3.175(1,000), which gives you 3,175 milliliters of water
Answer:
I think 3,175 milliliters in volume if that's what u are looking for
Step-by-step explanation: I converted 3.175 liters to milliliters.
Work out the value of 58 x 5-2 54 Total marks: 2
Answer:
2(29x5−127)
Step-by-step explanation:
Factor 58x5−254
58x5−254
=2(29x5−127)
Answer:
36
Step-by-step explanation:
going by BODMAS,
multiplication is first, 58 * 5 = 290
now, subtraction, 290 -254 = 36
The data set is a list of the heights of 6th grade basketball players: 60, 62, 66, 70, 66, 68, 67, 64, 64, 63. Find the mean of the set.
Answer:
65
Step-by-step explanation:
The mean is 65 because
Step one- Add up 60, 62, 66, 70, 66, 68, 67, 64, 64, 63 together to get 650.Step two- Next you need to divide. since there are 10 numbers that we added up we have to take 650 and divide it by 10. so 650/10=65Finally your answer is 65Hope this helped :)Fencing is sold for $1.50 per foot at the garden store. Shawn needs 24 feet of fence for his new puppy's yard. How much will the fence cost?Immersive Reader
Answer:
$36
Step-by-step explanation:
1.5 × 24 = 36
Hope this helps!
-MoCKEry