The future value of $82,100 invested at a 4.3% annual interest rate compounded continuously for 2 years using the formula V = Pe^{rt}, will be approximately $90,137.30.
Explanation:Your question involves the calculation of the future value of an investment using the formula for continuous compound interest, in this case $82,100 invested at an annual rate of 4.3%, over 2 years. This scenario relies on the mathematical concept of compound interest, which means the interest earned on the initial investment is added to the principal, and this combined amount earns interest as well.
Using the formula V = Pe^{rt}. where:
P = principal amount (initial investment) = $82,100,
r = annual nominal interest rate (decimal) = 4.3/100 = .043,
t = time the money is invested for = 2 years,
e = Euler's number (approx. 2.71828).
The calculation then becomes: V = $82,100 * e^(0.043 * 2) = $82,100 * e^(0.086). Using a calculator to do the exponentiation and the multiplication, the balance in the account after 2 years would approximately be $90,137.30.
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A closet is in the shape of a right rectangular prism. It measures 414 feet long, 314 feet wide, and 6 feet tall.
What is the volume of the closet?
Answer:
82.875
Step-by-step explanation:
4 1/4x 3 1/4x 6= 82.875
Answer:
82 7/8 I belive, thats what i got. Hope this helps
Step-by-step explanation:
which equation represents the graph?
The equation of the graph which shows a hyperbola passing through the point (0, 8) is,
⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]
Given that,
The graph of the equation of the hyperbola is shown.
Now, Take a point on the graph of the hyperbola.
Let the point is, (0, 8), which lies on the graph.
Since the point must satisfy the equation of the graph.
Hence, we can check all the options,
A. Equation of graph is,
⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]
Substitute x = 0, y = 8;
⇒ [tex]\frac{(8 - 1)^2}{49} - \frac{0^2}{81} =1[/tex]
⇒ [tex]\frac{(7)^2}{49} - 0 =1[/tex]
⇒ [tex]\frac{49}{49} = 1[/tex]
⇒ 1 = 1
Which is true.
Therefore, the equation of the hyperbola is,
⇒ [tex]\frac{(y - 1)^2}{49} - \frac{x^2}{81} =1[/tex]
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Use polynomial identities and number properties to calculate 25^3
Answer:
15625
Step-by-step explanation:
25^3
The base is 25 and the power is 3
That means we multiply 25 together 3 times
= 25*25*25 =15625
Answer:
15,625
Step-by-step explanation:
(a + b)³ = a³ + 3a²b + 3ab² + b³
(20+5)³
20³ + 3(20²)(5) + 3(20)(5²) + 5³
8000 + 6000 + 1500 + 125
15625
Felicia makes \frac{1}{2}
2
1
gallon of fruit punch. She pours an equal amount into 8 glasses.
What fraction of a gallon fruit punch is in each glass?
Question:
Felicia makes ½ gallon of fruit punch. She pours an equal amount into 8 glasses.
What fraction of a gallon fruit punch is in each glass?
Answer:
The fraction of a gallon fruit punch is in each glass is 1/16
Step-by-step explanation:
Given
Size of fruit punch = ½ gallon
Number of glass = 8
Required
Fraction of a gallon fruit punch is in each glass?
To solve this question, the following assumption has to be made.
- The 8 glass cups are of equal sizes.
Having said that;
The interpretation of the question is that, the fruit is evenly distributed into the 8 glass cups.
Mathematically, the size of the fruit punch will be divided by the number of glass cups.
So, we have
Fraction = ½ ÷ 8 (convert ÷ to *)
Fraction = ½ * ⅛
Fraction = 1/16
Hence, the fraction of a gallon fruit punch is in each glass is 1/16
Final answer:
To find the fraction of a gallon of fruit punch in each glass, divide 1/2 gallon by 8. This results in each glass containing 1/16 of a gallon of fruit punch.
Explanation:
The student asked how to find the fraction of a gallon of fruit punch in each glass if Felicia makes ½ gallon of fruit punch and pours an equal amount into 8 glasses. To answer this question, you need to perform a division of the total amount by the number of glasses. Given that Felicia has ½ gallon, which is the same as 2/4, we can divide this by 8 to find the amount in each glass.
Step-by-step solution:
Start with the fraction of a gallon Felicia has: ½ gallon.
Convert ½ to fourths to make the division easier: ½ = 2/4 gallons.
Since there are 8 glasses, divide 2/4 by 8. This is done by multiplying the denominator by 8:
(2/4) × (1/8) = 2/32.
Simplify the fraction by dividing numerator and denominator by the common factor of 2: 2/32 = 1/16.
Therefore, each glass contains 1/16 of a gallon of fruit punch.
hey i need help!!!!!!!
Answer:
A) h = 40
Step-by-step explanation:
Because 40/2 = 20
Which is greater than 16 and makes the equation true
What shapes can be cross sections of the rectangular pyramid?
A slice parallel to the base will take the shape of a .
A slice perpendicular to the base and through the top vertex will take the shape of a .
A slice perpendicular to the base and not through the top vertex will take the shape of a .
Answer:
What shapes can be cross sections of the rectangular pyramid?
A slice parallel to the base will take the shape of a
✔ rectangle
.
A slice perpendicular to the base and through the top vertex will take the shape of a
✔ triangle
.
A slice perpendicular to the base and not through the top vertex will take the shape of a
✔ trapezoid
.
A slice parallel to the base will take the shape of the rectangle. A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".
A slice perpendicular to the base and through the top vertex will take the shape of a .
A slice perpendicular to the base and not through the top vertex will take the shape of a .
Take a rectangle and the base. Now take four triangles such that each of them is connected to one-one side of the base rectangle and when they are taken together, they form a closed object.
That shape is called a rectangular pyramid.
A slice parallel to the base will take the shape of a "rectangle"
A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".
A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".
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Chayton read a report that said the probability that a randomly selected American is left-handed is 14%.
He was curious how many left-handed students to expect in a class of 20 students.
He simulated 25 classes of 20 students where each student selected had a 0.14 probability of being left-
handed.
Chayton counted how many left-handed students were in each simulated class. Here are his results:
Answer:
P(2 or fewer left-handed) = 9/25 = 0.36
Step-by-step explanation:
From Chayton simulations, we can see that in 9 simulations there are 2 or fewer left-handed students in a class of 20 students. He simulated 25 classes of 20 students, then the probability to find 2 or fewer left-handed is: 9/25 = 0.36
A right triangle has side lengths 7, 24, and 25 as shown below.
Use these lengths to find cos A, tan A, and sinA.
cosA =
0
tan A =
0
co
B
sinA =
Answer: Cos A = 0.96, Tan A = 0.29 and Sin A = 0.28
Step-by-step explanation: The right angled triangle can be solved by applying the trigonometric ratios given a follows;
Sin A = opposite/hypotenuse
Cos A = adjacent/hypotenuse
Tan A = opposite/adjacent
In the triangle ABC, the side AB (25) is the hypotenuse [facing the right angle], the side CB (7) is the opposite [facing the reference angle A°] while the side AC (24) is the adjacent [line between the reference angle and the right angle].
Therefore, using angle A as the reference angle;
(a) Cos A = adjacent/hypotenuse
Cos A = AC/AB
Cos A = 24/25
Cos A = 0.96
(b) Tan A = opposite/adjacent
Tan A= CB/AC
Tan A = 7/24
Tan A = 0.29
(c) Sin A = opposite/hypotenuse
Sin A = CB/AB
Sin A = 7/25
Sin A = 0.28
In a sequence, the first term is 8 and the common difference is -5. The fifth term in this sequence is
Answer:
5th term is -12
Step-by-step explanation:
First term is 8, which means 0th term is 13.
You can use the equation to find the nth term: y = -5(x) + 13
y = -5(5) + 13
y = -25 +13
y= -12
The fifth term in the sequence is -12.
What is an arithmetic sequence?It is a sequence where the difference between each consecutive term is the same.
We have,
First term = 8
Common difference = -5
We can consider the sequence to be an arithmetic sequence.
Now,
a = 8
Second term.
= a + (n - 1)d
= 8 + (2 - 1)(-5)
= 8 - 5
= 3
Third term.
= 8 + (3 - 1) (-5)
= 8 + 2 x -5
= 8 - 10
= -2
Fourth term.
= 8 + (4 - 1) x -5
= 8 + 3 x -5
= 8 - 15
= -7
Fifth term.
= 8 + (5 - 1) x -5
= 8 + 4 x -5
= 8 - 20
= -12
Thus,
The fifth term of the sequence is -12.
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Which geometric series converges?
0.02+0.02+0.02+0.02+...
4+0.08 +0.0016+0.000032+
4+80+ 1.600+ 32,000+.
0.02+0.04+0.08+0.16+.
Answer:
4+0.08 +0.0016+0.000032+ ....
Step-by-step explanation:
a+ar+ar²+ar³+ar⁴+…
the geometric series converges if |r| < 1
The geometric series converges:
4+0.08 +0.0016+0.000032+ ....
0.08=4*0.02
0.0016=4*(0.02)²
0.000032=4*(0.02)³
r=0.02<1
The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.
What is the geometric series?A geometric series is one where each pair of subsequent terms' ratios is a fixed function of the accumulation index. The ratio is a rational function of the accumulation index in a more comprehensive sense. creates what is known as a hypergeometric sequence.
If the common ratio is the same throughout the series, then the series is known as geometric series.
If the common ratio is less than one, then the series is known as convergence.
Let's check all the options, then we have
A. 0.02+0.02+0.02+0.02+...
Then the common ratio is given as,
r = 0.02 / 2 = 0.02 / 0.02
r = 1 = 1
B. 4+0.08 +0.0016+0.000032+....
Then the common ratio is given as,
r = 0.08 / 4 = 0.0016 / 0.08
r = 0.02 = 0.02
C. 4+80+ 1,600+ 32,000+.....
Then the common ratio is given as,
r = 80 / 4 = 1600 / 80
r = 20 = 20
D. 0.02+0.04+0.08+0.16+......
Then the common ratio is given as,
r = 0.04 / 0.02 = 0.08 / 0.04
r = 2 = 2
The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.
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Solve the equation. First estimate using the perfect square closest to 45. Then use a calculator. n2=45
Answer:22.5
Step-by-step explanation: just saying that is no the actual answer you still have to estimate it
The equation n² =45 is solved step by step. The nearest perfect squares, 36 and 49, are identified. Using a calculator, the square root of 45 is found to be approximately 6.708, satisfying the equation.
let's go through the steps to solve n² = 45 in detail:
Step 1: Find the Perfect Squares
The closest perfect squares to 45 are 6² = 36 and
7² = 49.
Since 45 is between 6² and 7², we'll use these values as reference.
Calculate the Square Root
We'll use a calculator to find the square root of 45.
√45 ≈ 6.708203932499369
So, the square root of 45 is approximately 6.708203932499369.
Step 3: Solve for n
Since we're looking for n² = 45, we have √n = 45.
Plugging in the calculated square root:
√n = 45
n ≈ 6.708203932499369
Thus, the approximate value of n that satisfies the equation n² = 45 is n ≈ 6.708.
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someone please help i just need help with this one question please and thank you :)
Answer:
Thanks for asking!
Step-by-step explanation:
For ABD x equals 18 and for DBC equals 54.
Answer:
ABD = 36
DBC = 54
Step-by-step explanation:
The three angles form a straight line so they add to 180
2x + 3x +90 = 180
Combine like terms
5x+90 =180
Subtract 90 from each side
5x+90-90=180-90
5x= 90
divide each side by 5
5x/5 = 90/5
x =18
ABD = 2x = 2*18 = 36
DBC = 3x = 3*18 =54
What is the vertex of the quadratic function?
х) = (х – 8)(х – 4)
А. (-6,4)
В. (6-4)
с. (-4,8)
D. (4,8)
Answer:
The vertex is (6, -4)
Step-by-step explanation:
f(x) =(х – 8)(х – 4)
First find the zeros
0 = (х – 8)(х – 4)
0 = x-8 0 =x-4
x=8 x=4
The zeros are x=8 and x=4
The vertex is 1/2 way between the zeros
(8+4)/2 = 12/2 =6
To find the y value, substitute 6 into the function
f(6) = (6-8) (6-4)
= -2 (2) = -4
The vertex is (6, -4)
Find the area of the section of the basketball court that is showh.
Round to the nearest tenth.
Answer:
Area is Base multipled by your height, so fro that particular section, it's quite a simple equation! :D
Step-by-step explanation:
Let's identify our sides. 39ft6in is our HEIGHT, and 5ft3in is our BASE.
- 39ft and 6in is a total of: 472 inches. 472 inches is 39.3ft
- 5ft and 3in is a total of: 63 inches. 63 inches is 5.3ft
Now that we know this, we can plug it in depending on the unit you need to find! Let's assume it's feet?
The Equation Completed: 5.3 × 39.3 = 208.29, which rounds to 208.3!
FINAL ANSWER: 208.3ft
Which of the following is the best approximation of the area of a circle whose diameter is 14 feet?
88 square feet
44 square feet
616 square feet
154 square feet
Algebraic Expression: The length of a rectangle is five inches less than triple the width. If the width is w inches, how long is the length of the rectangle?
Answer:
l=(3w-5) Inches
Step-by-step explanation:
Let the width of the rectangle =w inches
The length of a rectangle is five inches less than triple the width.
Let us break the statement down into parts.
Triple the width=3wFive inches less than triple the width =3w-5Therefore, the length of the rectangle, l= (3w-5) Inches
A triangle has side lengths 2.83 m, 4 m, and 2.24 m. The angles measures are 45°, 63°, and 72°.
What type of triangle is this triangle?
acute isosceles
obtuse isosceles
obtuse scalene
acute scalene
The given triangle is an acute scalene triangle.
What is a triangle?A triangle is a closed polygon with three sides and angles.
Obtuse triangle - the triangle with angle greater than 90°;
Acute triangle - the triangle with all interior angles under 90°;
Isosceles triangle - the triangle with a pair of equal sides;
Scalene triangle - the triangle with all three sides (or angles) of different measure.
We have,
All sides are different and all angles are under 90°.
Hence the given triangle is an acute scalene triangle.
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A rectangular block of material is on your dad’s desk that acts as a paperweight. The measurements are 3 cm times 4 cm times 6 cm and has a mass of 184.32 g. Determine what the paperweight is made off?
Someone help me please TvT
Answer: Marble
Step-by-step explanation:
Multiply 3x4x6 and you should get 72. Divide 184.32 by 72 and you should get 2.56 which is marble.
what is the circumference of a circle with a diameter of 36 ft?
Answer:
36x3.14=113.04
Step-by-step explanation:
Answer:
Approximately 113.1
Step-by-step explanation:
C = π d = π · 36 ≈ 113.09734
Simplify.
3a + 2b - 8a + b
11a+ 3b
5a+3b
-5a+3b
-11a + 2b
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION
Answer:
The value of DC is 66.34.
Step-by-step explanation:
The triangles ABC and DCA are right angled triangles.
The straight line AC is a bisector for angles C and A.
The measure of ∠C is 30°.
Then the measure of angles BCA and ACD will be 15° each.
The measure of angle DAB is 150°.
Then the measure of angles DAC and BAC will be 75° each.
Now consider the right angled triangle ABC.
The measure of side AC is:
[tex]AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}[/tex]
Consider the right angled triangle DCA.
The angle DAC measure 75°.
Using the trigonometric identities compute the value of Perpendicular DC as follows:
[tex]tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34[/tex]
Thus, the value of DC is 66.34.
I really don’t get this how do I do this:(?
Answer:
You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line, square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.
Step-by-step explanation:
what is the mean of the value set 13,19,22,20,31,16,25,30
Answer:
the mean is the midle one
we can get this by getting the average
add all of it and divide by how many it is
How does multiplying the variable of an absolute value function by a positive constant, k, affect the vertex of the function?
The vertex shifts up k units.
The vertex shifts to the right k units.
The vertex of the function doesn't change.
The vertex of the function changes from a minimum to a maximum or vice versa.
Answer:
C. The vertex of the function doesn't change.
Is this relation a function? Justify your answer.
No, the relation isn't a function. Though positive and balanced, one input has two outputs, violating the "one input, one output" rule.
No, the relation depicted in the image is not a function. While the relation does have the same number of x values as y values, and all the values are positive, a key characteristic of a function is missing.
For a relation to be a function, each input (represented by the x -value) must correspond to exactly one output (represented by the y -value).
In the image, we see that the input value 1 has two corresponding output values, 7 and 11. Since an input value cannot have multiple outputs, this relation is not a function.
So the answer is D. No, because two points with the same x -value have different y values.
A block of cheese has a volume of 187 cm3 and a mass of 140 g.
What is the density of the cheese in g/cm3 rounded to 2 decimal places?
Answer:
0.75 g/cm^3 to 2 decimal places.
Step-by-step explanation:
Density = mass / volume
= 140 / 182
= 0.7487 g/cm^3.
The density of the cheese is 0.75 [tex]g/cm^3[/tex].
The student has asked to calculate the density of a block of cheese with a given volume and mass. Density is defined as mass per unit volume and is calculated using the formula:
Density = Mass / Volume
To find the density of cheese:
Use the given mass of the cheese, which is 140 grams.
Divide the mass by the given volume of the cheese, which is 187 [tex]g/cm^3[/tex].
Perform the division to get the density in grams per cubic centimeter ( [tex]g/cm^3[/tex].)
The calculation is as follows:
Density = 140 g / 187 [tex]g/cm^3[/tex]= 0.7487 [tex]g/cm^3[/tex].
After rounding to two decimal places, the density of the cheese is 0.75 [tex]g/cm^3[/tex].
At Shower and Body Works, there are different sizes of lotion dispensers. Two of the versions are shown below.
Bottle X
$9.96
Bottle Y
$14.40 4 .
3 .
6 .
1 .
1.5 .
2 .
Part A: How many times more lotion is in Bottle Y than in Bottle X?
Part B: Which bottle is the better buy?
Part C: If a third bottle is on sale for $. has a height of three inches and a base area of six square inches, then determine which bottle is a better buy, Bottle Y or the third bottle. Justify your answer.
AlgebraNation.
Answer:
Right now I only have the time to give the answer's.
Part A Answer:There is 1.5 times more lotion in Bottle Y than in Bottle X. 6/4=1.5
Part B Answer: Bottle X is better because it is cheaper and there is not much of a difference.
Part C Answer:It would be better to buy the third bottle because it has the same amount as Bottle Y but at a cheaper price.
Step-by-step explanation:
Your welcome.
Martin is using unit cubes to build a tower in the shape of a rectangular prism. A decripion of the tower is listed the bottom layer is made of 16 unit cubes. the bottom layer shape is in the shape of a square prism. 9 more equal layers of unit cubes are added on the top of the bottom layer. what is the total volume in cubic units of the completed tower
Answer:
Volume of the completes tower = 160 units³
Step-by-step explanation:
Martin is using unit cubes to build a tower in the shape of rectangular prism.
Bottom layer of the prism is in the square shape.
Since number of unit cubes used in the bottom layer = 16
So, one side of the square base will measure = √16 = 4 units
Therefore, Length = width = 4 units
On this base, additional layers added on the top = 9
Therefore, height of the tower = (9 + 1) = 10 units (each layer having 16 cubes)
Volume of the tower = Volume of the rectangular prism
= Length × width × height
= 4×4×10
= 160 cubic units.
Volume of the completed tower will be 160 cubic units.
The total volume in cubic units of the completed tower is 160 units³.
Calculation of the total volume;Since number of unit cubes used in the bottom layer = 16
So, one side of the square base should be
= √16 = 4 units
Now
Length = width = 4 units
The additional layers added on the top = 9
So, height of the tower = (9 + 1)
= 10 units
Now
Volume of the tower = Volume of the rectangular prism
= Length × width × height
= 4×4×10
= 160 cubic units.
hence, The total volume in cubic units of the completed tower is 160 units³.
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Josh bought a pizza with eight slices of pizza for $12. What is the cost of a slice of pizza? $12 $3 $1 $1.50
Answer:
$1.50
Step-by-step explanation:
12÷8=3/2 or 1.50
Answer: the answer would be 1$ and 50 cents
Step-by-step explanation:
What is the median of the data shown below?
Answer:
72
Step-by-step explanation:
You need to add the two middle numbers then divide them by two.
Hope this helps.
Answer: 72
Step-by-step explanation: The median is the middle number in the data set when the data set is written from least to greatest.
Notice that our data set is already written from least to greatest so all we have to do now is find the number that appears in the middle.
Notice however that there are two numbers in the middle.
When this happens, take the sum of the two numbers in the middle or add them together and then divide the sum of the numbers by 2.
So if we add 71 + 73, we get 144.
Now just divide 144 by 2 to get 72.
So the median of the data set shown here is 72.