You are scheduled to receive $16,500 in three years. when you receive it, you will invest it for nine more years at 9.5 percent per year. how much will you have in twelve years?
The total amount you will have in twelve years is calculated by multiplying your initial amount of $16,500 with (1 + 0.095) raised to the power of 9 (years of investment). This is a demonstration of the future value concept in finance.
Explanation:This question is about the concept of future value in finance. First, you receive $16,500 after three years. Following this, you invest this amount at an interest rate of 9.5% for nine more years. To calculate the future value of an investment, you can use the formula: Future Value = Present Value * (1 + Interest rate)^numbers of years. In this case, it would be $16,500 * (1 + 0.095)^9. This calculation will give you the total amount you will have in twelve years after the investment.
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A 12 lb shankless ham contains 16 servings. What is the rate in servings per pound?
Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
Answer: 52
Step-by-step explanation:
To find the 30th number sequence with the given values of: -6,-4,-2,0.
Multiply 30 by 2 because we add 2 to the sequence every time we go up.
30*2 gives us 60, then we subtract however many 2's were in the given sequence.
From -6 to -4 to -2 to 0, we get 8.
60-8 = 52.
Thank you and I hope this helps. Even if my math is wrong somewhere, I got the answer right on my assignment so this is 100% correct.
7/8m +9/10-2m-3/5 how to do this question
4.1 Find the Least Common Multiple
The left denominator is : 8
The right denominator is : 10
Least Common Multiple:
40
4.2 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 5
Right_M = L.C.M / R_Deno = 4
4.3 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
4.4 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 40 as the denominator :
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
5.2 Adding up the two equivalent fractions
7.1 Pull out like factors :
36 - 45m = -9 • (5m - 4)
7.2 Find the Least Common Multiple
The left denominator is : 40
The right denominator is : 5
Least Common Multiple:
40
7.3 Calculate multipliers for the two fractions
Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno
Left_M = L.C.M / L_Deno = 1
Right_M = L.C.M / R_Deno = 8
7.4 Rewrite the two fractions into equivalent fractions
7.5 Adding up the two equivalent fractions
8.1 Pull out like factors :
12 - 45m = -3 • (15m - 4)
Reteach to build to understand 10-4
What is the range of arcsinx
Final answer:
The range of the inverse sine function, or arcsin(x), is the set of angles from -π/2 to π/2 radians, which is the same as -90° to 90° degrees. This defines the possible output values of the function for all real numbers in the interval [-1, 1].
Explanation:
The question "What is the range of arcsinx" concerns itself with the inverse trigonometric function, specifically the inverse of the sine function. The range of a function is the set of all possible output values it can produce. For the inverse sine function, or arcsin(x), the range is the set of angles that can produce all possible sine values, which are within the closed interval [-1, 1].
The sine function itself has a range from -1 to 1, so the arcsine function, being its inverse, takes on values that are angles that correspond to these sine values. In terms of angles, the range of the arcsin function is [-π/2, π/2] or [-90°, 90°] in degrees. This means that for any input value x within [-1, 1], the output of arcsin(x) will always be an angle measured in radians (or degrees) that falls within this range.
Joel has 210 baseball and football cards. He has 50 more baseball cards than football cards. How many of each does he have?
Need to explain this to a 3 rd grade without dividing?
Draw cubes to show the number. Write the number different ways. Love has seven ones Nick has 5 ones they put all their once together what number did they make
Benjamin solved the equation 3 + x over 2 = 10 and justified each step as shown.
Identify Benjamin’s error and fix his mistake
Step:
3 + x/2 = 10
X/2 = 7
X= 14
Justification:
Given
Multiplication Property of Equality
Subtraction Property of Equality
Answer:
The equation itself is fine but the justification looks wrong step2 is subtraction property of equality and step3 is Multiplecation property of equaliity
I could be wrong but im 95% sure
Good luck!
a baseball team plays 83 games in a season. if the team won 17 more than twice as many as they lost how many times did the did lose?
Final answer:
By creating an equation based on the information provided and solving for L, which represents the number of games lost, it was determined that the baseball team lost 22 games during the season.
Explanation:
To determine how many games the baseball team lost during the season, let us denote the number of lost games as L. The problem states that the baseball team won 17 more than twice the number of games they lost, which can be expressed as 2L + 17. Since the team played a total of 83 games in the season, we have the following equation to represent the total number of games played:
L + (2L + 17) = 83.
Combining like terms, we get:
3L + 17 = 83.
Now, subtract 17 from both sides of the equation:
3L = 66.
Then, we divide both sides of the equation by 3:
L = 22.
So, the baseball team lost 22 games during the season.
To find the number of times the team lost, set up an equation using the given information. The team won 17 more than twice the number of times they lost. The team lost 22 times.
Explanation:To find the number of times the team lost, we can set up an equation using the given information.
Let's assume the number of times the team lost is x.
According to the given information, the team won 17 more than twice the number of times they lost. So, the number of times the team won is 2x + 17.
The total number of games played is 83, which is the sum of the number of games won and lost.
So we have the equation 83 = x + (2x + 17).
Simplifying this equation, we get 83 = 3x + 17.
Subtracting 17 from both sides, we have 66 = 3x.
Dividing both sides by 3, we get x = 22.
Therefore, the team lost 22 times.
Which sentence explains the correct first step in the solution of this equation?
2(x−4)=12
A. Subtract 12 from both sides.
B. Add 4 to both sides.
C. Apply the distributive property to get 2x - 8 = 12
D. Apply the distributive property to get 2x - 4 = 12
Answer: like 5 years late but wtv
Step-by-step explanation:
Suppose that factory a produces 12 tables and 6 chairs an hour while factory b produces 8 tables and 4 chairs and hour. how many hours should each factory work to produce 48 tables and 24 chairs? how many different solutions are there to this problem?
Factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
The rates of both factories are given as:
Factory A = 12 tables and 6 chairs in an hour
Factory B = 8 tables and 4 chairs in an hour
To produce 48 tables and 24 chairs, we make use of the following equation
[tex]h = \frac{Produce}{Rate}[/tex]
Where h represents time (in hours)
So, we have:
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{12\ tables, 6\ chairs}[/tex]
[tex]h = 4[/tex]
Factory A
[tex]h = \frac{48\ tables, 24\ chairs}{8\ tables, 4\ chairs}[/tex]
[tex]h = 6[/tex]
Hence, factory A should work for 4 hours, while factory B should work for 6 hours to produce 48 tables and 24 chairs
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Factory A should work for 0 hours and Factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Explanation:To find out how many hours each factory should work to produce 48 tables and 24 chairs, we can set up a system of equations. Let's say that factory A works for x hours and factory B works for y hours. From the information given, we can write the following equations:
12x + 8y = 48 (equation 1, for tables)
6x + 4y = 24 (equation 2, for chairs)
We can solve this system of equations using substitution or elimination method. Let's solve it using the substitution method:
From equation 1, we can isolate x by subtracting 8y from both sides:
12x = 48 - 8y
x = (48 - 8y) / 12
Substituting this value of x in equation 2:
6((48 - 8y) / 12) + 4y = 24
Simplifying the equation:
3(48 - 8y) + 4y = 24
144 - 24y + 4y = 24
-20y = -120
y = (-120) / (-20)
y = 6
Substituting the value of y in equation 1:
12x + 8(6) = 48
12x + 48 = 48
12x = 0
x = 0
Therefore, factory A should work for 0 hours and factory B should work for 6 hours to produce 48 tables and 24 chairs. There is only one solution to this problem.
Find the dimensions of a rectangle with perimeter 100m area of 336
A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. if 67.36% of his students received grades of c or above, what is the minimum score of those students receiving a grade of at least a c?
Using the properties of normal distribution and the Z-score related to the given percentile, it can be inferred that the minimum grade for a 'C' in this college statistics class is approximately 72.
Explanation:In this scenario, the professor's grades reflect a normal distribution, therefore, we can utilize the properties of normal distribution to answer your question. The probability given, 67.36%, corresponds to a Z-score of -0.45 (you can find this in standard statistical tables).
We'll utilize the formula Z = (X - μ) / σ, Z is the Z-score, X is the data point, μ is the mean, and σ is the standard deviation. Therefore, if we rearrange the formula to find X (the data point,or in this case, the lowest grades for students receiving a C or above), it will be X = Z * σ + μ. Substituting the given values in the equation gives X = -0.45 * 9 + 76.5. This results in a minimum score approximately equal to 72.45, or 72 if we consider only whole marks. Hence, our conclusion that the minimum grade for a 'C' is 72.
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The minimum score required to receive at least a grade of C in this normally distributed class is approximately 72.54.
To determine the minimum score that students need to receive at least a grade of C in a class where grades are normally distributed, we analyze the problem with a mean [tex](\mu)[/tex] of 76.5 and a standard deviation [tex](\sigma)[/tex] of 9.
We know that 67.36% of the students received a grade of C or above.
This corresponds to the top 67.36% of the distribution.
The bottom 32.64% of the distribution received less than a C.
The z-score associated with the 32.64th percentile can be found using z-tables or a standard normal distribution calculator:
z = -0.44
Next, we convert this z-score to the actual score using the formula:
[tex]X = \mu + z\cdot \sigma[/tex]
Substituting the given values:
X = 76.5 + (-0.44 * 9) = 76.5 - 3.96 = 72.54
Thus, the minimum score required for a grade of at least C is approximately 72.54.
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In right triangle ABC, AB = 10, AC = 6 and BC = 8 units. What is the distance from C to the midpoint of segment AB?
What happened to the glass blower who inhaled
Answer: he got pane in his stomach
Step-by-step explanation:
because he ate glass
A recipe for krispy rice treats calls for 6 cups of rice cereal and 40 large marshmallows. You want to make a larger batch of goodies and have 9 cups of rice cereal. How many large marshmallows do you need? However, you only have the miniature marshmallows at your house. You find a list of substitution quantities on the internet that suggests 10 large marshmallows are equivalent to 1 cup miniatures. How many cups of miniatures do you need?
what is 5879 rounded to the nearest hundredth
Estimate the area of the irregular shape. Explain your method and show your work. Can someone explain this to me?
Answer:
Approximate area: 27.5 square units
Step-by-step explanation:
The irregular shape is very similar to a trapezium with coordinates (-3,3), (2, 2), (2, -2) and (-3, -4).
Area of a trapezium: [(a+ b)/2]*h
where a and b refer to the two parallel sides and h is the distance between them. From the above coordinates: a = 7 length units, b = 4 length units and h = 5 length units. Therefore, approximate area = [(7+ 4)/2]*5 = 27.5 square units
Becky bought 4 pounds of grapes for $8.24.How much did the grapes cost per pound?
One number is twice another number and their sum is 36. which system of equations represents the word problem? 2x y = 36 and x y = 36 x y = 36 and y = 2x y = 2x and 2x y = 36
Let
y------>one number
x------> another number
we know that
[tex]y=2x[/tex] ------> equation A
[tex]x+y=36[/tex] ------> equation B
substitute equation A in equation B
[tex]x+2x=36[/tex]
[tex]3x=36[/tex]
[tex]x=12[/tex]
Find the value of y
[tex]y=2x[/tex]
[tex]y=2*12=24[/tex]
the numbers are [tex]24[/tex] and [tex]12[/tex]
therefore
the answer is
The system of equations are
[tex]x+y=36[/tex] and [tex]y=2x[/tex]
A store discounts the price of a beanbag chair by 20%. The price of the beanbag chair is marked as $16. What was the original price of the beanbag chair?
original price of the beanbag chair was $20 before the 20% discount was applied.
To find the original price of the beanbag chair that has been discounted by 20%, we set up an equation. Let's denote the original price as P. A 20% discount on the original price means the chair is being sold for 80% (100% - 20%) of P. This is represented by the equation 0.80P = $16.
To find P, we simply divide both sides of the equation by 0.80:
P = $16 / 0.80
This gives us:
P = $20
Therefore, the original price of the beanbag chair was $20 before the 20% discount was applied.
F=9/5C+32 What Does C And F represent
Write a situation in which positive and negative numbers are used to describe values that have the opposite meaning.
Divide then check using multiplcation
1056÷37=
A right triangle has sides 5.0 m, 12 m, and 13 m. the smallest angle of this triangle is nearest:
Final answer:
To find the smallest angle in a right triangle with side lengths of 5.0 m, 12 m, and 13 m, we use the inverse tangent function with the shortest leg over the adjacent leg, yielding an angle of approximately 22.6 degrees.
Explanation:
The subject of the question is mathematics, and it pertains to high school level geometry. The question is asking to determine the smallest angle in a right triangle with sides measuring 5.0 m, 12 m, and 13 m. To find the smallest angle, we can use trigonometry, specifically the inverse tangent function.
Step-by-Step Explanation
Identify the sides of the triangle. In this case, we know that the sides are 5.0 m, 12 m (which could be interpreted as legs), and 13 m (the hypotenuse).
Because we are looking for the smallest angle, we will use the smallest leg, which is 5.0 m, and the next largest leg, which is 12 m.
Use the tangent function, which relates the opposite side to the adjacent side in a right triangle. The smallest angle, which we will call θ, will have the opposite side of 5.0 m and an adjacent side of 12 m.
Calculate θ using the inverse tangent function (also known as arctangent). θ = tan-1(5.0/12).
Perform the calculation using a calculator to find the nearest degree. θ = tan-1(5.0/12) ≈ 22.6°.
Therefore, the smallest angle in the triangle is approximately 22.6 degrees.
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long. How wide is the box?
The width of the rectangular prism will be 4.5 centimeters.
What is the volume of the rectangular prism?A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.
Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
The volume of a box of soup broth is 972 cubic centimeters. The box is 20 centimeters high and 10.8 centimeters long.
Then the width of the rectangular prism is calculated as,
972 = 20 x W x 10.8
Simplify the equation, then we have
972 = 20 x W x 10.8
972 = 216W
W = 4.5 centimeters
The width of the rectangular prism will be 4.5 centimeters.
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540 less than the product of 54 and a number is 918
Find the volume v of the described solid s. the base of s is the triangular region with vertices (0, 0), (5, 0), and (0, 5). cross-sections perpendicular to the y-axis are equilateral triangles.
Final answer:
To find the volume of the solid with a triangular base and equilateral triangular cross-sections, we integrate the area of the cross-sections along the y-axis from 0 to 5 based on the changing side length, which is a linear function of y.
Explanation:
The problem requires finding the volume of a solid with a triangular base and equilateral triangular cross-sections perpendicular to the y-axis. The base of the solid, S, is a right triangle with vertices at (0, 0), (5, 0), and (0, 5). The height of each equilateral triangular cross-section at any point y is the distance from the point (y, 0) to the hypotenuse of the triangular base, which is linear and can be described by the equation x + y = 5. Because cross-sections are equilateral triangles, each side of a cross-section is twice the length of the height. Therefore, the area of a cross-section is ½∙height²∙√3.
As we move along the y-axis from 0 to 5, the length of a side of each cross-section decreases linearly from 5 to 0. We can integrate the area of these cross-sections from y = 0 to y = 5 to find the total volume of the solid. The integral for the calculation of volume is:
∫ (2∙(5-y))² × √3/4 dy from y=0 to y=5
Upon integrating, this gives us the volume of the solid S.