solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
Suppose a supermarket ordered 13 cases of organic vegetable soup with a list price of $18.90 per case and 4 cases of organic baked beans with a list price of $33.50 per case. The wholesaler offered the supermarket a 39% trade discount. (Round your answers to the nearest cent.)
What is the total net amount (in $) the supermarket owes the wholesaler for the order?
$
So, the total net amount the supermarket owes the wholesaler for the order is $231.61.
To find the total net amount that the supermarket owes the wholesaler for the order, we need to first calculate the cost of each item after the trade discount is applied, and then add up the costs of all the items.
For the 13 cases of organic vegetable soup, the list price per case is $18.90, and the trade discount is 39%. So, the discount amount per case is:
Discount amount = 39% x $18.90 = $7.37
The cost per case after the discount is:
Cost per case = $18.90 - $7.37 = $11.53
So, the total cost of 13 cases of organic vegetable soup is:
Total cost of vegetable soup = 13 x $11.53 = $149.89
Similarly, for the 4 cases of organic baked beans, the list price per case is $33.50, and the trade discount is 39%. So, the discount amount per case is:
Discount amount = 39% x $33.50 = $13.07
The cost per case after the discount is:
Cost per case = $33.50 - $13.07 = $20.43
So the total cost of 4 cases of organic baked beans is:
Total cost of baked beans = 4 x $20.43 = $81.72
Therefore, the total net amount the supermarket owes the wholesaler for the order is:
Total net amount = Total cost of vegetable soup + Total cost of baked beans
= $149.89 + $81.72
= $231.61
So, the total net amount the supermarket owes the wholesaler for the order is $231.61.
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Solve the inequality for x.
-10≤2x-4
Simplify your answer as much as possible.
Answer:
x ≥ -3
Step-by-step explanation:
-10 ≤ 2x - 4
-6 ≤ 2x
x ≥ -3
We can't simplify any more, so the answer is x ≥ -3
Determine the interval(s) on which the function Is constant.
Write your answer as an interval or list of intervals.
When writing a list of Intervals, make sure to separate each interval with a comma and to use as few intervals as possible.
Click on "None* if applicable.
The list of intervals on which the function is constant is:
A(-4,-3) and B(3,6).
What is a constant function?A constant function is a function that returns the same value regardless of the input. In other words, for every value of x, the output of the function is the same constant value. For example, the function f(x) = 2 is a constant function because no matter what value of x is plugged into the function, the output will always be 2. Constant functions are often represented by horizontal lines on a graph.
What does a list of intervals mean in the graph?A list of intervals in a graph typically indicates the range of values or intervals on a given axis. For example, on the x-axis of a graph, a list of intervals might represent the range of values from a lower bound to an upper bound, with each interval indicating a range of values that falls between two specific points on the axis. On the y-axis, the intervals might represent the range of possible values for the dependent variable or data being plotted. In general, the intervals on a graph provide a visual representation of the range of values being considered or plotted.
According to the given informationThe given function in the graph on intervals A(-4,-3) and B(3.6) is a horizontal line which means there is no change in output. So the function is constant.
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Find each value or measure.
x =
(40 points) will give brainiest for effort
Answer:
x = 5
Step-by-step explanation:
given FH is a diameter , then
arc FH = 180°, that is
FG + GH = 180°
103° + GH = 180° ( subtract 103° from both sides )
GH = 77°
the central angle HIG is equal to the arc that subtends it GH , so
∠ HIG = 77°
∠ EIF and ∠ HIG are vertically opposite angles and are congruent , then
∠ EIF = 77°
the arc EF subtends the central angle EIF , so
EF = 77°
the sum of the 3 arcs = 180° , that is
HD + DE + EF = 180
15 + 18x - 2 + 77 = 180
18x + 90 = 180 ( subtract 90 from both sides )
18x = 90 ( divide both sides by 18 )
x = 5
then arc DE = 18x - 2 = 18(5) - 2 = 90 - 2 = 88°
find the solution -b2+2b=0
The solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), which are connected by an equals sign (=). The expressions on each side of the equals sign can be made up of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation can be solved to find the value of the variable(s) that makes both sides of the equation equal.
To find the solution of -b²+ 2b = 0, we can use algebraic manipulation as follows:
-b² + 2b = 0
Factor out -b:
-b(b - 2) = 0
From this equation, we see that either -b = 0 or b - 2 = 0:
-b = 0 or b - 2 = 0
Solving for b in each case, we get:
-b = 0 --> b = 0
b - 2 = 0 --> b = 2
Therefore, the solutions to the equation -b² + 2b = 0 are b = 0 and b = 2.
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The length of a rectangle is 2 units more than the width. The area of the rectangle is
24 square units. What is the width, in units, of the rectangle?
The width of the rectangle is 4 units.
What is rectangle?
Rectangle is a four sided polygon or specifically a particular type of parallelogram having two opposite sides are equal and one angle is right angle that is 90°. It has four vertices and two diagonals intersect each other.
Given that,
The length of a rectangle is 2 units more than the width.
Let, the width of the rectangle is w units.
Then the length of the rectangle is w+2 units.
Area of any rectangle is length × width
= (w+2)×w square units
Given that,
The area of the rectangle is 24 square units.
Equating both the values we get,
w(w+2)= 24
We have to solve the equation for w.
Multiplying the bracket term with w we get,
w²+ 2w = 24
⇒ w² + 2w- 24=0
⇒ (w+6)(w-4)=0
so either w= -6 or w=4
As width cannot be negative so w= 4.
Hence, the width of the rectangle is 4 units.
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How many different possible outcomes are there if you roll two fair six-sided dice in the shape of a cube?
Answer: 36
Step-by-step explanation:
What is the height of the cylinder?
5m diameter
13 m
Cylinder
10.5 m
12 m
13.9 m
9 m
As a result, the cylinder's height is roughly 1.65 metres as In the second line, we failed to deduct 39.27 from both sides.
what is cylinder ?A cylinder is really a muti geometric shape made up of two circular bases that are congruent and parallel to one another, as well as a curving lateral surface that links the bases. It can be envisioned as a reasonable shape that is created by extending a circle perpendicular to the plane of the circle. Several advantageous characteristics of the cylinder, such as a constant bridge area over its whole length, make it suitable for a wide range of practical applications. For instance, a lot of different kinds of containers, such pipes and tubes, have cylindrical shapes. The following formula can be used to figure out the size of a cylinder:[tex]V = \pi r^2h[/tex] where V is the capacity, r is the circumference of the spherical base, and h is the cylinder's height.
given
We must apply the formula for a cylinder's surface area, which is: to determine the cylinder's height.
[tex]SA = 2\pi r^2 + 2\pi rh[/tex]
where SA stands for surface area, r for base radius, and h for cylinder height.
The cylinder has a radius of 2.5 m and a diameter of 5 m.
[tex]13 = 2\pi (2.5)^2 + 2\pi (2.5)h[/tex]
13 = 39.27 + 15.71h
-26.27 = 15.71h
h = -26.27/15.71 ≈ -1.67
In the second line, we failed to deduct 39.27 from both sides. When we do this, the height is given a positive value:
h = (13 - 39.27) / 15.71 ≈ 1.65
As a result, the cylinder's height is roughly 1.65 metres as In the second line, we failed to deduct 39.27 from both sides.
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Answer: 12m
Step-by-step explanation:
What’s 95 divided by 3
Simplify 6^2/6 x 6^12/6^8
Step-by-step explanation:
6^2 / 6^1 x 6^12 / 6^8 =
6^(2-1) x 6^(12-8) =
6^1 x 6^4 =
6^(1+4) = 6^5 or = 7776
The thickness of a one-dollar bill is 1.1 × 10-4 meters. Each measurement below is the thickness of a stack of one-dollar bills. Drag each measurement to the correct dollar amount.
Thickness of 10 dollar bill is 1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill is 1.375×10⁻¹meters
Thickness of 137 dollar bill is1.507 ×10⁻²meters
Define thicknessThickness is the measure of the distance between opposite surfaces of an object. In other words, it is the distance between two parallel planes that bound an object or material. Thickness is often used to describe the dimension of a flat or sheet-like object, such as paper, fabric, or metal, as well as the distance between the front and back surfaces of a three-dimensional object, such as a book or a wall. Thickness can be measured in units such as millimeters, inches, or micrometers.
The thickness of a one-dollar bill is 1.1 × 10⁻⁴ meters
Thickness of 10 dollar bill=10×1.1 × 10⁻⁴
=1.1×10⁻³meters
Thickness of 1.25 × 10³ dollar bill=1.25 × 10³ ×1.1 × 10⁻⁴
=1.375×10⁻¹meters
Thickness of 137 dollar bill=137 ×1.1 × 10⁻⁴
=1.507 ×10⁻²meters
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What are the answer and how do you do it? im confuse on how this works
a): 1.19
b): 0.76 or 0.8
Solve the equation using suntraction. Show all your work. X-6y=11 and 2x-5y=1
Answer:
To solve the system of equations using subtraction, you need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate x by multiplying the first equation by 2 and subtracting it from the second equation:
2x - 5y = 1
- (2(x - 6y) = 2x - 12y = 22)
------------------------
-17y = -21
Now we can solve for y:
-17y = -21
y = (-21) / (-17)
y = 1.2353
Substitute y into one of the original equations to solve for x:
x - 6y = 11
x - 6(1.2353) = 11
x - 7.4118 = 11
x = 18.4118
Therefore, x = 18.4118 and y = 1.2353.
I hope this helps!
6. Two out of every five Canadians read at least 10 books a year. What percent of Canadians read at least 10 books a year?
Answer:
40%
Step-by-step explanation:
2/5=x/100
cross multiply and you get 5x=200
by isolation the variable you will get x=40
therefore, 40% of Canadians read at least 10 books a year
Camille opened a savings account and deposited $8,063.00 as principal. The account earns 14.69% interest, compounded quarterly. What is the balance after 10 years?
Use the formula A=P1+
r
n
nt, where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
Save answer
Answer:$26,141.13.
Step-by-step explanation:
Using the formula A = P * (1 + r/n)^(n*t), where A is the balance, P is the principal, r is the interest rate, n is the number of times per year that the interest is compounded, and t is the time in years, we can calculate the balance in the savings account after 10 years:
A = 8,063.00 * (1 + 0.1469/4)^(4*10)
A ≈ 26,141.13
Therefore, the balance in the savings account after 10 years, rounded to the nearest cent, is $26,141.13.
9.68 x 9.83 Estimated product > or < Exact Product
Will mark brainliest if answer is correct
The x⁶y³ term in the expansion will be: 35 x⁶y³.
The x⁸y² term in the expansion will be: 21x⁸y².
What is the binomial expansion?The binomial expansion of (x + y)ⁿ is given by the binomial theorem, which states:
(x + y)ⁿ = C(n, 0) * xⁿ * y⁰ + C(n, 1) * xⁿ⁻¹ * y¹ + C(n, 2) * xⁿ⁻² * y² + ... + C(n, k) * xⁿ⁻ᵏ * yᵏ + ... + C(n, n) * x⁰ * yⁿ
where;
C(n, k) is the binomial coefficient, defined as C(n, k) = n! / (k! * (n - k)!), and n! represents the factorial of n.Given that the term 210x⁴y⁶ appears in the expansion, we can infer that it corresponds to C(n, k) * x⁴ * y⁶, where k is the number of times y appears in the term, and (n - k) is the number of times x appears in the term.
Comparing this with the given term, we can deduce the values of n, k, and x in the following way:
C(n, k) = 210
x⁴ = x⁴
y⁶ = y³ * y³
Comparing the exponents on x and y, we can set up the following equations:
n - k = 4 (1)
k = 3 (2)
Solving equation (2) for k, we get:
k = 3
Substituting this value of k into equation (1), we can solve for n:
n - 3 = 4
n = 7
So, the value of n is 7.
Now, we can use the binomial coefficient formula to calculate C(n, k):
C(n, k) = C(7, 3) = 7! / (3! * (7 - 3)!) = 35
Finally, substituting the values of n, k, and C(n, k) into the general term of the expansion, we can find the specific terms:
The x⁶y³ term in the expansion will be:
C(7, 3) * x⁶ * y³ = 35 * x⁶ * y³
The x⁸y² term in the expansion will be:
C(7, 2) * x⁸ * y² = 21 * x⁸ * y²
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Please help please and thank u :)
Help pleaseee
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
1. The initial mass of the sample was 32 mg. 2. The mass of the sample 7 weeks after the start is approximately 0.162 mg.
What is radioactive decay?An unstable atomic nucleus releases particles or electromagnetic radiation as it undergoes radioactive decay, changing into a different nucleus. Since this process is unpredictable and spontaneous, the decay's timing cannot be anticipated. The radioactive substance's half-life, or the amount of time it takes for half of its radioactive atoms to decay, is used to calculate the rate of decay. Radiometric dating, nuclear energy production, and medical imaging all employ radioactive decay, which can cause the emission of alpha particles, beta particles, or gamma rays. Understanding the behaviour of matter at the atomic and subatomic level requires knowledge of radioactive decay.
1. The radioactive decay is given by the formula:
[tex]N(t) = N_0 * (1/2)^{(t/T)}[/tex]
Now, for half-life of Palladium-100 is 4 days and t = 16 and N(t) = 2 we have:
[tex]2 = N_0 * (1/2)^{(16/4)}\\2 = N_0 * (1/2)^4\\2 = N_0* 1/16\\N_0 = 2 * 16\\N_0 = 32 mg[/tex]
2. Foe 7 weeks:
7 weeks = 7 * 7 days = 49 days.
[tex]N(49) = N_0 * (1/2)^{(49/4)}\\N(49) = 32 * (1/2)^{(49/4)}\\N(49) = 0.162 mg[/tex]
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The number of parts produced by three different machines are shown in the table only one of the machine produces pods at a constant rate which equation represents why the number of parts produce the next minute for a one machine that produces pods at a constant rate
The equation that represents the number of parts produced by Machine C after t minutes is f(t) = 3t
The equation represents why the number of parts produceTo determine which machine produces parts at a constant rate, we can calculate the ratios of the number of parts produced for each machine:
For Machine A:
The ratio of parts produced from 5 to 10 minutes is: 32/8 = 4The ratio of parts produced from 10 to 20 minutes is: 40/32 = 1.25Since the ratios are not constant, Machine A does not produce parts at a constant rate.
For Machine B:
The ratio of parts produced from 5 to 10 minutes is: 80/40 = 2The ratio of parts produced from 10 to 20 minutes is: 120/80 = 1.5Since the ratios are not constant, Machine B does not produce parts at a constant rate.
For Machine C:
The ratio of parts produced from 5 to 10 minutes is: 30/15 = 2The ratio of parts produced from 10 to 20 minutes is: 60/30 = 2Since the ratios are constant, Machine C produces parts at a constant rate.
To find an equation that represents the number of parts produced by Machine C at any given minute, we can use the ratio of parts produced from 5 to 10 minutes:
The constant rate of production is 30/10 = 3 parts per minute.
Therefore, the equation that represents the number of parts produced by Machine C after t minutes is f(t) = 3t
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Complete question
The number of parts produced by three different machines are shown in the table only one of the machine produces pods at a constant rate which equation represents why the number of parts produce the next minute for a one machine that produces pods at a constant rate
Minutes Machine A
5 8
10 32
20 40
Minutes Machine B
5 40
10 80
20 120
Minutes Machine C
5 15
10 30
20 60
Please help with this math question!
Answer:
[tex]2000 {(1 + \frac{.07}{12}) }^{5 \times 12} = 2835.25[/tex]
Identify the values of a, b, and c in the following quadratic equation: 2x^2 −3x−5
On the Y axis we have the profit from the trucking company and on the X axis we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Therefore, the correct answer is A. Y intercept will be less and X will be less.
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. Graphs are commonly used to display information in a way that is easy to interpret and analyze. They are often used in fields such as science, mathematics, economics, and engineering to help illustrate and explain complex data.
Here,
The introduction of a cost of 0.25 cents per mile for the driver would be an additional expense for the trucking company, and would affect their profit. This means that the profit values (on the y-axis) would decrease for each point on the graph. However, the miles traveled (on the x-axis) would remain the same as the cost of the driver is proportional to the distance traveled.
Therefore, the y-intercept of the graph (the profit when the truck has traveled zero miles) would be less than it was before, because the trucking company has a new cost that reduces their overall profit. However, the x-intercept (the point where the profit is zero) would remain the same, as this point is determined solely by the revenue and cost of the trucking company.
The slope of the graph would also be affected, as the profit now decreases at a faster rate as the miles traveled increase. The new slope would depend on the specific values of the revenue, costs, and driver expenses for the trucking company, but in general, it would be steeper than before.
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A rhombus has a base of 8 cm and a height of 4.2 cm what is the area
The area of the rhombus who has a base of 8 cm and a height of 4.2 cm is 33.6 centimeters².
What is an area?The measurement of the size of a two-dimensional shape or surface is referred to as an area.
It is the area contained within the perimeter of a flat or two-dimensional object and is expressed in square units like square centimetres, square metres, square feet, etc.
For instance, to find the area of a rectangle, multiply its length by width, and to find the area of a circle, multiply pi () by the radius square.
area of rhombus can be found as-
Area = (base x height) / 2
In this case, the base is 8 cm and the height is 4.2 cm, so we can substitute these values into the formula:
Area = (8 cm x 4.2 cm) / 2
Area = 33.6 cm²
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the perimeter of rectangle is 76m if one side is 16m what is the other side?
Answer: 22
Step-by-step explanation:
The formula for perimeter of a rectangle is side 1 + side 1 + side 2 + side 2. Side one is 16. This means that 16x2 is 32. Then, you realize there are 44 meters remaining. 44/2=22. The other side is 22.
Test the following hypotheses by using the given sample information and α = .01. Assume the populations are normally distributed.
H0 : σ2 =σ2 Ha:σ2 >σ2 1212
n1 =10, n2 =11, s2 =562, s2 =1013 12
Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis.
What is null hypothesis?A null hypothesis is a statement that establishes the equality of two expressions and frequently includes variables, constants, and mathematical operations.
The equal sign (=) is used to denote the space between the two sides, which are referred to as the left-hand side (LHS) and the right-hand side (RHS).
To test the given hypothesis, we will use the F-test for two variances.
The null and alternative hypotheses are:
H0: σ1² = σ2² (no difference in population variances)
Ha: σ1² > σ2² (population variance of first group is greater than that of second group)
The test statistic is calculated as:
F = s1² / s2²
Where s1² and s2² are the sample variances of the two groups.
The degrees of freedom for the F-distribution are df1 = n1 - 1 and df2 = n2 - 1.
Using the given sample information, we have:
n1 = 10, n2 = 11
s1² = 562, s2² = 1013
Therefore, the test statistic is:
F = s1² / s2² = 562 / 1013 = 0.555
The degrees of freedom are df1 = 9 and df2 = 10.
Using a significance level of α = 0.01 and the F-distribution tables or a calculator, the critical value for the right-tailed test with df1 = 9 and df2 = 10 is 4.025.
Since the calculated F-value of 0.555 is less than the critical value of 4.025, we fail to reject the null hypothesis. There is not enough evidence to conclude that the population variance of the first group is greater than that of the second group at a significance level of α = 0.01.
We can conclude that there is not enough evidence to support the claim that σ1² > σ2².
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simplify the expression ^4√16x^12y^16
(show explanation please).
Answer: 2x^3y^4
Step-by-step explanation:
The expression ^4√16x^12y^16 can be simplified as follows:
^4√16 = 2, since 2^4 = 16
x^12 can be written as (x^3)^4, and ^4√(x^3)^4 = x^3
y^16 can be written as (y^4)^4, and ^4√(y^4)^4 = y^4
Therefore, ^4√16x^12y^16 simplifies to:
2x^3y^4
How how much water can this container hold? Use 3.14 to approximate high battery to the nearest 100
A spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.
To solve the question :
The volume of a sphere = 4/3 πr³
Where,
π = mathematical constant pi and
r = radius of the sphere.
Given,
radius (r) = 8 cm and
π = 3.14,
Substituting the values of π and r to the volume equation
V = (4/3) x 3.14 x 8³
V = (4/3) x 3.14 x 512
V = 2688.53 cm³ (rounding off to the nearest hundredth)
Hence, a spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.
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The owner of a stereo store wants to advertise that she has many different sound systems in stock. The store carries 5 different CD players, 8 different receivers, and 10 different speakers. A sound system consists of one of each item. How many different sound systems can the store owner advertise?
The owner can advertise 400 different sound systems. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be explained using the four fundamental operations, generally known as "arithmetic operations." In mathematics, operations like quotient, product, sum, and difference occur after operations like division, multiplication, addition, and subtraction.
We are given that the owner of a stereo store carries 5 different CD players, 8 different receivers, and 10 different speakers and each sound system consists of one of each item.
So, the different sound systems that the owner can advertise is obtained by using the multiplication operation, which gives:
⇒ Different sound systems = 5 * 8 * 10
⇒ Different sound systems = 400
Hence, the owner can advertise 400 different sound systems.
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