Answer:
Step-by-step explanation:
The formula to calculate the future value of an investment with compounded interest is:
Future value = Principal * (1 + rate/compoundings per year)^(number of years * compoundings per year)
In this case, the principal is $10,000, the interest rate is 2.5%, compounded annually, and the number of years is 20. So, the future value can be calculated as follows:
Future value = $10,000 * (1 + 2.5%/1)^(20 * 1)
Future value = $10,000 * (1.025)^20
Future value = $10,000 * 1.62897526
Future value = $16,289.75
Therefore, $10,000 deposited in an account earning 2.5% interest compounded annually would be worth $16,289.75 in 20 years.
the only items in each of containers a, b, and c are 28 disks. in each container, each of the disks is numbered with a different integer from the integers 1 through 28 inclusive. one disk is to be selected at random from each of the 3 containers. what is the probability that at least one of the disks selected has a number greater than 24?
The probability that at least one of the disks selected has a number greater than 24 is 127/343.
To find the probability that at least one of the disks selected has a number greater than 24, we can find the probability that all three disks have numbers less than or equal to 24 and subtract this from 1.
The probability that a disk selected from a container has a number less than or equal to 24
24/28= 6/7
Since,
there are 24 disks with numbers less than or equal to 24 out of a total of 28 disks in each container.
We can assume that the selection of a disk from one container is independent of the selection of a disk from another container, so the probability that all three disks selected have numbers less than or equal to 24 is (6/7)³
since we are making three independent selections.
Therefore,
The probability that at least one of the selected disks has a number greater than 24 is 1 - (6/7)³ ,
which simplifies to 343/343 - 216/343 = 127/343
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an inverted pyramid is being filled with water at a constant rate of 75 cubic centimeters per second. the pyramid, at the top, has the shape of a square with sides of length 2 cm, and the height is 10 cm. find the rate at which the water level is rising when the water level is 2 cm.
The rate at which the water level is rising when the water level is 2 cm is 8 cm.
A pyramid's volume is equal to 1/3 of B, where B is the base's area and h is its height. Given that the base is square, B = s2, where s is a base side The volume is therefore 1/3 s2h.
We are aware that the base's side is 8 cm long and the whole pyramid's height is 11 cm. Also, no matter how high the water is, its surface will always form a square with the same proportion to the water's depth as a side of the pyramid's top has to the pyramid's total height. This indicates that s = 8/11 h regardless of the water depth.
So that means that the formula for the volume of the pyramid formed by the water is V = 1/3 (8/11 h)2 h = 64/363 h3.
Separate this as a function of time to get the rate of change of the volume of water :
V = 64/363 h3
dV/dt = 3 (64/363) h2 dh/dt = 192/363 h2 dh/dt
Nonetheless, we are aware that the volume is shifting at a speed of 65 cc every second. So at any point in time,
65 = 192/363 h2 dh/dt
65 * 363 / 192 = h2 dh/dt
23595 / 192 = h2 dh/dt
(23595 / 192) / h2 = dh/dt
When the level of water (h) is 8, that indicates:
(23595 / 192) / 64 = dh/dt
1.92 = dh/dt
So the water level is rising at the rate of 1.92 cm per second when the water level is 8 cm.
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4 red bricks have a mean weight of 5 kg.
5 blue bricks have a mean weight of 9 kg.
1 green brick has a weight of 6 kg.
Donna says,
"The mean weight of the 10 bricks is less than 7 kg. "
Is Donna correct?
You must show how you get your answer.
Donna is not correct, as the mean is of 7.1 kg, which is greater than 7 kg.
How to obtain the mean of a data-set?The mean of a data-set is obtained as the sum of all observations in the data-set divided by the number of observations.
The sum of the data-set in this problem is given as follows:
4 x 5 + 5 x 9 + 1 x 6 = 71 kg.
The number of observations is given as follows:
10.
Hence the mean is given as follows:
71/10 = 7.1 kg > 7 kg.
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This is the correct answer
Answer: yes
Step-by-step explanation:
write the set b=1/10 1/100 1/1000 in set builder form
The set builder form of the set b = {1/10, 1/00, 1/1000} is b = {x | x = 1/10ⁿ, where n is a positive integer}
In mathematics, set builder notation is a concise way of describing a set using a rule or a formula.
Let's explore how we can use set builder notation to write the set b={1/10, 1/100, 1/1000}.
To begin, we need to identify the common property that these elements share. In this case, we can observe that each element is a rational number with a power of ten as the denominator. So, we can write the set b as follows:
b = {x | x = 1/10ⁿ, where n is a positive integer}
In this notation, the vertical bar represents "such that" and separates the description of the element from the rule that defines the set. The letter x is a variable that represents any element that satisfies the rule. We use the power of ten as a common property to describe the set b.
In this set builder form, we can see that b is a set of elements that can be expressed as 1/10 to the power of a positive integer. We can also use set builder notation to define other sets with different properties, such as sets of even numbers or sets of prime numbers.
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10. Find the measure of each missing angle.
Answer:
see explanation
Step-by-step explanation:
A segment joining the midpoints of two sides of a triangle is
parallel to the third side
∠ 1 and 144° are same- side interior angles and sum to 180° , so
∠ 1 + 144° = 180° ( subtract 144° from both sides )
∠ 1 = 36°
----------------------
∠ 2 and 56° are corresponding angles and are congruent , so
∠ 2 = 56°
-------------------------
∠ 3 and 56° are a linear pair and sum to 180°
∠ 3 + 56° = 180° ( subtract 56° from both sides )
∠ 3 = 124°
--------------------------
the sum of the 3 angles in a triangle = 180° , then
∠ 1 + ∠ 2 + ∠ 4 = 180° , that is
36° + 56° + ∠ 4 = 180°
92° + ∠ 4 = 180° ( subtract 92° from both sides )
∠ 4 = 88°
--------------------------------
∠ 5 and ∠ 1 are corresponding angles and are congruent , so
∠ 5 = 36°
----------------------------------
Answer:
m∠1 = 36° , m∠5 = 36° , m∠4 = 88° , m∠3 = 124° , m∠2= 56°
Step-by-step explanation:
m∠1 and 144° are Co-Interior angles, or the angles which are on the same side of the transveral
m∠1 + 144° = 180°
m∠1 = 36°
angle 5 and 144° are in a linear pair-
144 °+ angle 5 = 180°
m∠5 = 36°
angle 5 + 56° + angle 4 = 180° because addition of angles of a triangle is 180°
36° + 56° + angle 4 = 180°
angle 4 = 180° - 92°
angle 4 = 88°
56° and angle 3 are in a linear pair
56° + angle 3 = 180°
angle 3 = 124°
angle 3 and angle 2 are Co-Interior angles
angle 3 + angle 2 = 180°
124° + angle 2 = 180°
angle 2 = 56°
Hope it helped and you understood it :)
A concert venue wants to make at least $3,750.00 profit for their Saturday night show.
Adult tickets cost $10.00 and children's tickets cost $5.00. The venue can seat up to
500 people. Find three combinations of adult and children's tickets that will make the
profit goal and not be more than 500 total people. Enter your answer as ordered pairs
(A,C) separated by a comma where A is the number of adult tickets sold and C' is
the number of children's tickets sold.
Answer:
(126, 101), (127, 100), (128, 99).
Step-by-step explanation:
The profit from selling one adult ticket is $10.00 and from selling one children's ticket is $5.00.
The total profit from selling A adult tickets and C children's tickets can be represented as 10A + 5C.
The goal is to find combinations of A and C that meet the following conditions:
10A + 5C >= 3750
A + C <= 500
One way to solve this problem is to use a brute force approach and try different values of A and C until we find three combinations that meet the conditions. Another way is to use a more efficient method and find the values of A and C that maximize the number of adult tickets while still meeting the profit and seating limit conditions.
Let's start by finding the maximum number of adult tickets that can be sold while still meeting the profit goal:
10A + 5C >= 3750
10A >= 3750 - 5C
A >= 375 - 0.5C
Since C must be an integer, we can round down the value of A to the nearest integer.
For example, if C = 100, then A >= 125. If we round down A to 125, then the profit from selling 125 adult tickets and 100 children's tickets would be:
10 * 125 + 5 * 100 = 1250 + 500 = 1750
which is less than the profit goal of 3750.
If we increase C by 1, then A would increase by 0.5, and the profit would increase by 5.
So, to reach the profit goal, we need to increase C until the profit is at least 3750.
Let's try C = 101. Then A >= 125.5, which we can round down to 126.
The profit from selling 126 adult tickets and 101 children's tickets would be:
10 * 126 + 5 * 101 = 1260 + 505 = 1765
which is greater than or equal to the profit goal of 3750.
So, the first combination of adult and children's tickets that meets the profit and seating limit conditions is (126, 101).
We can repeat the same process to find the second and third combinations.
For example, the second combination could be (127, 100), and the third combination could be (128, 99).
The final answer is (126, 101), (127, 100), (128, 99).
Answer:
250 $3 tickets and 100 $2 tickets were sold.
Step-by-step explanation:
3(350 – y) + 2y = 950
1050 – 3y + 2y = 950
3y – 2y = 1050 – 950
y = 100
Substitute y = 100 into equation 1
x + 100 = 350
x = 250
The graph of the linear function f(x) = -5x + 6 shows the number of cases of the flu, y, in thousands, x months after a vaccine was administered. What are the rate of change and the initial
value?
A 6,000 cases of the flu per month; initial value: -5,000 cases
B-5 cases of the flu per month; initial value: 6 cases
C 1 case of the flu per month, initial value: 0 cases
D -5,000 cases of the flu per month; initial value: 6,000 cases
Answer:
D
Step-by-step explanation:
The 6 represents the initial value of 6000. The cases are going down 5,000 a month.
What are the zeros of this function?
Which one of the following absolute value equations and inequalities have a solution set that is NOT the empty set?
O |2x-1|-7<-6
O |4x+5| -4=-5
O 3|x+2|-2=-3
O 2|x-5|-4 <-8
Uber charges $5.00 plus $.35/mile to take someone to a destination. Jen needed a
ride to the airport. Her total cost was $17.60. How many miles was she away from the
airport?
Answer:
36
Step-by-step explanation:
First you have to do 17.60 minus the fee ($5) giving you 12.6
after that you want to X the .35 by 36 which will make you reach 12.6
so by that it is 36 miles X the .35 Per mile fee giving you 36 miles (sorry if that made no sense)
Please help :) 10 points (Geometry)
Answer: (2,0)
Step-by-step explanation:
Midpoint formula( [tex]\frac{x1+x2}{2}[/tex],[tex]\frac{y1+y2}{2}[/tex])
P(-4, 6)
Q(8, -6)
Substitute into formula
-4+8/2
4/2
x = 2
6-6/2
0/2
y = 0
Answer (2,0)
Which expression is equivalent to (14x)⁰y-⁷z?
The expression which is equivalent to (14x)⁰y-⁷z as required in the task content is; z / y⁷.
Laws of indicesIt follows from the task content that the expression which is equivalent to the given expression (14x)⁰y-⁷z is to be determined.
Recall from the laws of indices that a⁰ = 1 where a represents any mathematical entity.
Therefore, the resulting expression is;
1 • y -⁷ • z
= z • 1 / y⁷
= z / y⁷.
Ultimately, the resulting expression which is equivalent is; z / y⁷.
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An art teacher is making packages
a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8
b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5
How do we determine the number of packages?In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint
Highest common factor is the highest factor that is common to two or more numbers:
Factors of 24 = 1,2,3,4,6,8,12 and 24
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.
Common factors of 24 and 40 = 1, 2, 4, 8
Therefore, the highest common factor is 8.
The number of paintbrushes in each package:
= Number of brushes / number of package
= 24/8
= 3 brushes
The number of tubes of paint:
= number of tubes of paints / number of package
= 40 / 8
= 5 tubes of paints
Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?".
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A population of a town is 18,000 it decreases at a rate of 8% per year
Approximately it takes 6 years to the population be fewer than 11,000.
What is population growth and population decrease formula?If the constant decrease in population be R% per annum, then the population after n years = P(1-R/100)ⁿ.
Given that, A=11,000, rate of interest=8% and P=18,000.
Here, 11,000=18,000(1-8/100)ⁿ
11/18=(1-0.08)ⁿ
0.611=(0.92)ⁿ
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
n=ln(0.611)/ln(0.92)
Decimal Form: n=5.90847701…
n=6
Therefore, approximately it takes 6 years to the population be fewer than 11,000.
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"Your question is incomplete, probably the complete question/missing part is:"
The population of a town is 18,000. it decreases at a rate of 8% per year. In about how many years will the population be fewer than 11,000?
< A and < B are complementary angles.
< A = 3 x - 2 and < B = 2 x + 12
Find the measure of < A :
Answer: The measure of Angle A is 46 degrees.
Step-by-step explanation:
Complementary angles are angles that when both added together are equal to 90 degrees. So the measure of angle A plus the measure of angle B is equal to 90 or 3x - 2 + 2x + 12 = 90. Add like terms so you get 5x + 10 = 90. Subtract 10 on both sides you get 5x = 80. Divide by 5 on both sides and you get x = 16. To find the measure of angle A, plug in your x value. So M<A = 3(16) - 2. Ange A is equal to 46. I double checked my answer too and plugged my x value into M<B and got 44. So indeed 44 + 46 = 90.
10m+ 4 n 2 10, m, plus, start fraction, n, squared, divided by, 4, end fraction when m=5m=5m, equals, 5 and n=4n=4n, equals, 4.
According to the given question, when m=5 and n=4, the value of the expression 10m + 4n²/4 is 66.
What does a mathematical expression mean?A mathematical expression is a phrase having a minimum of two numbers or variables and at least one mathematical operation. This mathematical operations may be add, subtraction, multiply, or divide. An expression's basic components are as follows: (Math Operator, Number/Variable, Expression)
What are some illustrations of expression?Keep in mind that words can be variables, constants, or coefficients. Therefore, 1+1 is a straightforward example of an expression. This equation has two constant terms and one operation (addition). x³ is another illustration.
To evaluate the expression 10m + 4n²/4 when m=5 and n=4, we substitute these values into the expression and simplify:
10m + 4n²/4
= 10(5) + 4(4^2)/4
= 50 + 4(16)/4
= 50 + 16
= 66
Therefore, when m=5 and n=4, the value of the expression 10m + 4n^2/4 is 66.
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Brian and Mason buy cars at the same time.
The function f(t) = 21,500(0.87)t models the value of Brian’s car t years after purchase.
The function g(t) = 19,200(0.91)t models the value of Mason’s car t years after purchase.
What is the approximate difference between the values of the cars after 4 years?
The approximate difference between the values of the cars after 4 years is $134.82.
What is Function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.
According to question:To find the difference between the values of the cars after 4 years, we can subtract the value of Mason's car from the value of Brian's car at t = 4.
f(4) = 21,500(0.87)^4 ≈ 11,426.91
g(4) = 19,200(0.91)^4 ≈ 11,292.09
Therefore, the approximate difference between the values of the cars after 4 years is:
f(4) - g(4) ≈ 11,426.91 - 11,292.09 ≈ 134.82
So the approximate difference is $134.82.
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ASAP Select the correct answer.
What is the slope of the line that goes through the points (-4,2) and (8,5)?
A.-4
B.-1/4
C.1/4
D.4
What is the measure of ∠w? and What is the measure of ∠y?
Answer:
angle w = 50; angle y = 130
Step-by-step explanation:
because of supp. angles, y + w = 180
12x-2+4x+6=180
16x+4=180
16x=176
x=11
to calculate, sub 11 in
w = 4(11) + 6 = 50
y = 12(11) - 2 = 130
Evaluate the expression if x= -2 and y=7.
(xy)^2 - 2x^5
Thank you.
btw this is Algebra I
Answer:
260
Step-by-step explanation:
Substitute: (-2 · 7)² – 2 x (-2)⁵
Remove parenthesis: (2 · 7)² + 2 · 2⁵
Calculate the first two terms: 14ײ + 2 × 2⁵
Calculate the power: 196 + 2 × 32
Calculate the first two terms: 196 + 64
Calculate the first two terms: 260
Answer: 260
please help i’ll mark brainliest
Answer:
Step-by-step explanation: umm hard the question doesn't sound like a question
This year, Clean Machine used 4,508.8 gallons of soap. That is 16.5% less than last year, How many gallons of soap did the company use last year? (round your answer to the nearest tenth)
The soap used by the machine last year is 5399.76 gallons.
What are percentages?The denominator of a percentage (also known as a ratio or fraction) is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100. In this case, the percentage symbol "%" is read as "percent" or "percentage." This percent symbol can always be changed to a fraction or decimal equivalent by using "divided by 100."
Let the soap used last year = x.
Then, according to the given condition:
4,508.8 = x (1 - 16.5%)
4,508.8 = x (83.5/100)
x = 4,508.8(100) / 83.5
x = 5399.76
Hence, the soap used by the machine last year is 5399.76 gallons.
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In a circle, a 315° sector has area 504π in2. What is the radius of the circle?
Let's call the radius of the circle "r". The formula for the area of a sector of a circle is given by:
(θ/360) * π * r^2,
where θ is the central angle of the sector in degrees.
In this case, we know that the central angle is 315° and the area of the sector is 504π, so we can set up an equation as follows:
(315/360) * π * r^2 = 504π
Solving for r, we can isolate it on one side of the equation:
r^2 = 504 / (π * (315/360))
To simplify the expression on the right-hand side, we can divide both the numerator and denominator by 45 (which is a factor of both 315 and 360):
r^2 = 504 / (π * (7/8))
Finally, taking the square root of both sides gives us:
r = sqrt(504 / (π * (7/8)))
So the radius of the circle is approximately 17.14 inches.
A principal of $900 was invested at 2.5% interest, compounded annually. Let t be the number of years since the start of the investment. Let y be the value of the investment in dollars. Write an exponential function showing the relationship between y and t.
Group of answer choices
Answer: 900 x (2.5 x t) = y
900 hundred dollars originally invested, times the number of years multiplied by the yearly interest rate, equals Y, or the amount of the investment in dollars.
I hope this helps & good luck <3 !!!
A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4 Using this recipe 250g of syrup are needed to make 12 flapjacks find the quantity of oats needed to make 18 of these flapjacks?
A recipe for flapjacks uses only syrup sugar butter and oats in the ratio 1:2:2:4. Using this recipe 250g of syrup are needed to make 12 flapjacks. The quantity of oats needed to make 18 of these flapjacks is 375g.
The recipe for flapjacks has a ratio of syrup to sugar to butter to oats of 1:2:2:4. This means that for every 1 unit of syrup, there are 2 units of sugar, 2 units of butter, and 4 units of oats.
We know that 250g of syrup are needed to make 12 flapjacks. To find out how much oats are needed to make 18 flapjacks, we can set up a proportion:
syrup: sugar: butter: oats = 1:2:2:4
250g:x = 12:18
To solve for x, we can cross-multiply and simplify:
250g * 18 = 12x
4500g = 12x
x = 375g
Therefore, we need 375g of oats to make 18 flapjacks using this recipe.
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Convince Me! Use Patterns and Structure Sue knitted a scarf for her
friend June that was also 4 feet long. After a month, the length of June's
scarf could be represented by the expression 0.5 x 4. How did the length
of June's scarf change? Explain.
The length of June's scarf change using patterns and structure is 4.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that;
The length of friend june scarf= 4 feet
The representation of length of june after a month= 0.5x4
Now,
Sue knitted a scarf for her friend June that was also 4 feet long and, after a month, the length of June's scarf is given by the expression 3/3 x 4, to know how did the length of June's scarf change you must perform the following calculation;
Month; 1 = 4
Month; 2 = 3/3 x 4 = 1 x 4 = 4
Therefore, by algebra the the answer will be 4.
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ABC and QRS are supplementary angles.
If the measure of ABC = 170°, what is the
measure of QRS?
m/QRS =
If the measure of ABC = 170°, the measure of QRS is equal to 10°.
What is a supplementary angle?In Mathematics, a supplementary angle simply refers to two (2) angles or arc whose sum is equal to 180 degrees.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can logically deduce that the sum of angles ABC and QRS are supplementary angles:
m∠ABC + m∠QRS = 180°
Substituting the given parameters into the formula, we have the following;
170° + m∠QRS = 180°
m∠QRS = 180° - 170°
m∠QRS = 10°
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10 point cuz its all i got rn
In the scale drawing, what is the area of the lawn (that is, the area of the whole backyard, except for the deck)?
The area of the lawn in the scale drawing is approximately 996 square feet.
1. Measure the length and width of the lawn in inches on the scale drawing.
Length = 16.5 inches
Width = 15.5 inches
2. Convert the measurements to feet by dividing the inches by 12.
Length = 16.5/12 = 1.375 feet
Width = 15.5/12 = 1.291 feet
3. Calculate the area of the lawn by multiplying the length and width.
Area = 1.375 x 1.291 = 1.75 square feet
4. Multiply the area by the scale factor (in this case, 560) to get the actual area.
Area = 1.75 x 560 = 996 square feet
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slips of paper numbered 1 through 14 are placed in a hat. in how many ways can two numbers be drawn so that the sum of the numbers is 12? assume the random selection is without replacement.
We are assuming that the random selection is without replacement, which means that once a slip is drawn, it is not put back into the hat.
There are 5 possible pairs of numbers that add up to 12 when drawing two slips of paper numbered 1 through 14 without replacement. These pairs are:
1 and 11
2 and 10
3 and 9
4 and 8
5 and 7
Next, we need to find the number of ways to draw each pair. Since the order in which the slips are drawn does not matter, each pair can be drawn in 2 different ways. So, for each of the 5 pairs, there are 2 ways to draw the pair.
Each pair of numbers can be drawn in 2 different order (the order in which the slips are drawn does not matter in this case), so the total number of ways to draw two slips so that the sum of the numbers is 12 is [tex]5 * 2 = 10[/tex].
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