Answer:
C. $452115.44
Step-by-step explanation:
To solve this, we will follow the steps below;
first write down the formula for compound interest
A= P [ 1 + [tex]\frac{r}{n}[/tex]]^nt
where A is the ending amount
P represent the principal
r represent the interest rate
n represent the number of compounding a year
t represent the time {in years)
from he question above
p= $318 000
r = 0.071
n = 4 since is quarterly
t= 5
we can now proceed to insert the values into the formula
A= P [ 1 + [tex]\frac{r}{n}[/tex]]^nt
=318 000 [1+[tex]\frac{0.071}{4}[/tex]] ^4(5)
= $318 000 [1+[tex]\frac{0.071}{4}[/tex]] ^20
=$318 000 [1+0.01775] ^20
= $318 000 [1.01775] ^20
=$318 000× 1.421747
≈$452 115.44
He will have $452 115.44 in the account
Ms Adams shares out 21 pencils between Niamah and Jack in the ratio 2:5 how many pencils does each child get
Answer:
niamah : jack
2 : 5
2×3 : 5×3
6 : 15
niamah gets 6 pencils
jack gets 15 pencils
*6+15 = 21
Answer:
Step-by-step explanation:
If the ratio of Niamah to Jack is 2:5, that means that for every 2 pencils that N gets, J gets 5. If there are a total of 21 pencils, then
2x + 5x = 21 and
7x = 21 so
x = 3.
That means that N gets 2(3) which is 6, and J gets 5(3) which is 15. Notice that 6:15 is the same ratio as 2:5 when it is reduced.
Cancel mom please help me with this I’m stuck and I don’t know how to do this
Answer:
20
Step-by-step explanation:
The triangles are similar so we can use ratios
8 32
--- = -----
8+5 32+x
Using cross products
8(32+x) = 32(13)
Divide each side by 8
(32+x) = 32(13)/8
32+x = 4*13
32+x =52
Subtract 32
x = 20
Judging from past basketball games, the probability that you make a free throw is 4/5. If you get 220 attempts this season, how many free throws can you expect to make?
Answer: 176 free throws
Step-by-step explanation: 4/5 = 80% 80% of 220 = 176
One sheet of paper is 9 x 10 to the power of -3 to cm thick. Mark wants to put 500 sheets of paper into the paper tray of his printer. The paper tray is 4 cm deep. Is the paper tray deep enough for 500 sheets of paper? You must explain your answer. Input note: write down the thickness of the 500 sheets of paper.
Answer:
The paper tray is not deep enough.
Step-by-step explanation:
500 * 9 * 10^-3
= 500 * 0.009
= 4.5 cm which is greater than the depth of the paper tray (4 cm).
The paper tray is not enough for sheets of paper.
The thickness of 500 sheets of paper is 45 cm.
What is multiplication?Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
One sheet of paper is [tex]9[/tex] × [tex]10^{-3}[/tex] to the power of -3 to cm thick.
Mark wants to put 500 sheets of paper into the paper tray of his printer.
The thickness of 500 sheets of paper is
[tex]9[/tex] × [tex]10^{-3}[/tex] × 500 = 45 cm
But the paper tray is 4cm deep
45 cm > 4 cm
So the paper tray is not enough for sheets of paper.
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what is a listed method in mathematics
Answer:
Listing method is a method to list all the elements separating each element by the comma and enclosing
Step-by-step explanation:
Aubrey's parents are signing her up for summer camps. If there are 5 weeklong camps to choose from, in how many orders can they select 3 of the camps to sign her up for?
Answer:
This can be done in a total of 10 ways
Step-by-step explanation:
This is a selection problem.
What we are trying to do is to properly select 3 week long camps from the total 5. we are looking for the number of ways in which we can do this.
Now, since this is a selection problem, the proper mathematical term and approach to use is the COMBINATION
Mathematically, having r items to pick from a total n, the number of ways to do this is nCr ways
which is mathematically equivalent to;
n!/(n-r)!r!
now applying this to the problem at hand, what we have is 5C3
= 5!/(5-3)!3! = 5!/2!3! = (5 *4)/2 = 20/2 = 10 ways
Please answer correctly !!!! Will mark brainliest !!!!!!!!!!!!!!
Answer:
6 seconds
Step-by-step explanation:
- ( 6 - 2)^2 + 16
- (4)^2 + 16
- 16 + 16
= 0
The ball is hits the ground or is at 0 height when x = 6.
solve the question 2 (3x plus 5) Square - 16 = 0 buy completing the square
Answer:
Step-by-step explanation:
Share 35 sweets in the ratio 4:3
number sweet is 35
we divided ratio =4x:3x
total = 4x+3x
7x= 35
= 35/7
x= 5
1 st part will be 4x = 4*5= 20 sweets.
2 nd part will be 3x = 3*5= 15sweets
Evaluate the expression for
m = -3.
-4 |5+m |
Answer: the correct answer is -8
Step-by-step explanation:
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
Substitute the given value of m into the expression:
-4|5 + (-3)|.
Then evaluate using the order of operations:
-4|5 + (-3)|
= -4|2|
= -4(2)
= -8
What is the first step in evaluating an expression?The first step in evaluating an expression is to substitute the given value of a variable into the expression. Then you can finish evaluating the expression using arithmetic.
What is an example of evaluating expressions?A variable is a letter, for example, x, y, or z, that represents an unspecified number. To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.
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How do you put 0.02 in scientific notation
Answer:
2 x 10^-2
Step-by-step explanation:
0.02 equals to 2/100
therefore 0.02= 2/102 (remember this is negative)
= 2x10^-2 (therefore -2)
The solution to the number 0.02 in scientific notation is 2 * 10⁻²
How to express the number 0.02 in scientific notationFrom the question, we have the following parameters that can be used in our computation:
Number = 0.02
Multiply the number by 1
So, we have
Number = 0.02 * 1
Express 1 as 100/100
So, we have the following representation
Number = 0.02 * 100/100
Next, we have
Number = 2 * 1/100
Express 1/100 as 10⁻²
So, we have
Number = 2 * 10⁻²
Hence, the solution is 2 * 10⁻²
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The explicit formula for a particular arithmetic
sequence is an = 8 + (n - 1)3, with n > 1
What are the first three terms?
ai -
11
az
a3 =
Answer:
8, 11, 14
Step-by-step explanation:
The n th term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given
[tex]a_{n}[/tex] = 8 + (n - 1)3 , then
a₁ = 8 and d = 3 , thus
a₂ = 8 + 3 = 11
a₃ = 11 + 3 = 14
The first 3 terms are 8, 11, 14
Answer:
8
11
14
THAT IS THE ANSWER TO THE QUESTION
Which ordered pair is a solution of the equation? 5x+12y=60
(0,5)
2, 25/6
both
or neither
Answer:
both
Step-by-step explanation:
you can solve this problem with substitution:
5(0) + 12(5) = 60
0 + 60 = 60 is true, therefore the first ordered pair is a solution
the second ordered pair is:
2, 25/6
therefore:
5(2) + 12(25/6) = 60
10 + 50 = 60
10 + 50 = 60 is true, therefore the second ordered pair is also a solution.
in conclusion, both of the ordered pairs are solutions.
Which monomial has a degree of 3?
a. 3
b. 3x2
c. 3x
d. -2x3
Answer:
So a degree means the power. So which ever has a power of three. I think you forgot to show to power, its D i think
D is answer
Need help with this
Pls!! Show work
Answer:
a) S_tot 320 cm² (cube), 282.743339 cm² (cylinder) thus the cube is a greater surface area.
b) V = 300 cm³ (cube) V = 314.159265 cm³ (cylinder) thus the cylinder has a greater volume.
Step-by-step explanation:
First solve for the cube:
length l = 10 cm
width w = 10 cm
height h = 3 cm
diagonal d = 14.4568323 cm
total surface area Stot = 320 cm²
lateral surface area S_lat = 120 cm²
top surface area S_top = 100 cm²
bottom surface area S_bot = 100 cm²
volume V = 300 cm³
Agenda: l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
Formulas for a rectangular prism or cube:
Volume of Rectangular Prism:
V = lwh
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
Space Diagonal of Rectangular Prism:
d = √(l² + w² + h²)
_______________________________
Second we solve for the cylinder
radius r = 5 cm d/2 = 10/2 = 5 cm
height h = 4 cm
volume V = 314.159265 cm³
lateral surface area L = 125.663706 cm²
top surface area T = 78.5398163 cm²
base surface area B = 78.5398163 cm²
total surface area A = 282.743339 cm²
In Terms of Pi π
volume V = 100 π cm³
lateral surface area L = 40 π cm²
top surface area T = 25 π cm²
base surface area B = 25 π cm²
total surface area A = 90 π cm³
Agenda:
Agenda: l = length
w = width
h = height
d = diagonal
S_tot = total surface area
S_lat = lateral surface area
S_top = top surface area
S_bot = bottom surface area
V = volume
Cylinder Formulas in terms of r and h:
Calculate volume of a cylinder:
V = πr²h
Calculate the lateral surface area of a cylinder (just the curved outside):
L = 2πrh
Calculate the top and bottom surface area of a cylinder:
T = B = πr²
Total surface area of a closed cylinder is:
A = L + T + B = 2πrh + 2(πr²) = 2πr(h+r)
find the total surface area of this cylinder. Give yor answer to 1 decimal place. Award is brainliest answer
Answer:
2261.95
Step-by-step explanation:
A=2πrh+2πr2
Answer:
2261.9
Step-by-step explanation:
the other users answer was correct, but not with 1 decimal place
- 2.5f + 0.4f - 15 - 4
Answer:
Simplify the f's variables -2.1
Simplify the numbers -19
-2.1f -19 is the answer
-2.1f -19Answer-2.1f-24:
Step-by-step explanation:
factorise 2x^2 -x-21
Answer:
(x + 3) × (2x - 7)
Step-by-step explanation:
2x² - x - 21
Write as a difference
2x² + 6x - 7x - 21
Factor the expressions
2x × (x + 3) - 7 (x + 3)
Factor the expression
(x +3) × (2x - 7)
surface area of a triangular prism
Answer:
54ft squared
Step-by-step explanation:
All faces:
Front: 2*3/2=4.5f squared * 2 (other side)= 9ft squared
Sides: 10*3/2= 15ft squared * 2 (other side)= 30ft squared
Bottom: 3*10/2= 30/2= 15ft squared
=54 ft squared
Surface area of the triangular prism is 96 feet.
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
A triangular prism has 2 triangular bases and 3 rectangular lateral faces.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
There are 2 triangles at the top and bottom.
Here base = 3 feet and height = 2 feet
Total surface area on the top and bottom = 2 × [tex]\frac{1}{2}[/tex] × base × height
= base × height
= 3 × 2
= 6 feet
There are 3 rectangular faces.
Area of the rectangle = Length × width
Here, length = 10 feet and width = 3 feet
Area of the rectangular face = 10 × 3 = 30 feet
Since there are 3 rectangular faces,
Total lateral surface area = 3 × 30 = 90 feet
Total surface area of the triangular prism = 90 + 6 = 96 feet
Hence the total surface area of the given triangular prism is 96 feet.
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I really need help please :(
Answer:
0≤y≤5
Step-by-step explanation:
The range is the values of the output, or in this case the y values
The y values go from 0 to 5
0≤y≤5
The answer is C.
You can see visually that the function's domain lies within range from -5 to 5 on the x axis.
The value x is
Please help I’m stuck
Step-by-step explanation:
EL ÁNGULO DE LA LINEA HORIZONTAL ES 0° EL ÁNGULO DE LA LINEA
VERTICAL ES 90° Y EL ÁNGULO DE LA LINEA DE ENMEDIO ES 3=° CON
RESPECTO A LA VERTICAL. ES DECIR 55° CON RESPECTO A LA
HORIZOANTAL, PERO ESTÁ ESCRITO 5x!, ENTONCES
5x° = 55°
DESPEJA x
x = 55°/5° = 11
The first equation from the previous system of
equations is graphed. Graph the second equation to
find the solution of the system of equations.
y = -2x + 4,
y=-x-1
What is the solution to the system?
Answer: x = 5 and y=-6
Step-by-step explanation:
If we graph both equations, the interception is the point (5,-6). Therefore the solution for x is 5 and for y is -6.
A=-2[[-6,4],[3,7],[12,10]] B=3[[-2,2,8],[8,5,6]]and D=-1[[-12,8],[6,14],[24,20]] are equal matrices ANSWERS a nd b are equal b and c are equal c and d are equal d and a are equal
Answer:
D and A are equalStep-by-step explanation:
Two matrices A and B are said to be equal if both matrices have the same number of rows and columns. Given the following matrices
[tex]A = -2\left[\begin{array}{ccc}-6&4\\3&7\\12&10\end{array}\right] \\multiplying\ the \ matrix\ through\ by\ -2\ will\ give\\A = \left[\begin{array}{ccc}12&-8\\-6&-14\\-24&-20\end{array}\right] \\\\\\B =3 \left[\begin{array}{ccc}-2&2&8\\8&5&6\end{array}\right] \\B = \left[\begin{array}{ccc}-6&6&24\\24&15&18\end{array}\right] \\\\\\D = \left[\begin{array}{ccc}12&-8\\-6&-14\\-24&-20\end{array}\right][/tex]
From the above matrices, it can be seen that matrix A and C both has 3 rows and 2 columns each which matrix b has 2 rows and 3 columns.
Based on the conclusion, it can be seen that matrices A and D are equal since they have the same number of rows and columns
help me with this pls like omg soooo stressful
Answer:
t =1
Step-by-step explanation:
3t - 18 = 4(-3-3/4t)
Distribute
3t - 18 = -12 -3t
Add 3t to each side
3t -18+3t = -12 -3t+3t
6t -18 =-12
Add 18
6t -18+18 = -12+18
6t = 6
Divide by 6
6t/6 = 6/6
t =1
Answer:
t = 1
Step-by-step explanation:
start by distributing the 4 to whats in the parentheses.
4 (-3 - 3/4t)
-12 - 3t
*helpful tip: if you multiply a fraction by its denominator the product is equal to its numerator
now you have:
3t - 18 = -12 - 3t
add 18 to both sides
3t = 6 - 3t
add 3t to both sides
6t = 6
divide both sides by 6
t = 1
Can someone please help me on this????
which expression is equivalent
HELP ME PLEASE
Answer:
the 4th option is correct
Step-by-step explanation:
[tex]xy^{2/9}[/tex] Original expression
[tex]x(y^{2})^{1/9}[/tex] Split up the exponent
[tex]x(\sqrt[9]{y^{2} } )[/tex] The 1/9 of an expression is the same thing is the 9th root of the expression.
The floor of the cage measures 11 yardyard wide by 66 feetfeet long. One bag of shavings covers 55 square feetfeet. How many bags will HarperHarper have to buy to cover the floor of the cage? Explain.
Answer:
3 3/5 bags
Step-by-step explanation:
We have to find the surface area of the floor of the cage first.
The cage measures 1 yard wide by 6 feet long.
1 yard = 3 feet
The floor of the cage is rectangular, so, the surface area of the floor of the cage is therefore:
3 * 6 = 18 square feet
One bag of shavings covers 5 square feet.
To find the number of bags we need to cover the floor, we divide the surface area of the floor by the number of bags per square feet.
The number of bags needed for the floor of the cage is therefore :
18 / 5 = 3 3/5 bags
Solve for x in the diagram below.
3x
75°
T =
Answer:
x=35
Step-by-step explanation:
The 2 angles are on a straight line together. This means they are supplementary. When they are added together, they must equal 180 degrees.
3x+75=180
We want to find out what n is. In order to do this, we have to get n by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.
75 is being added to 3x. The opposite of addition is subtraction. Subtract 75 from both sides.
3x+75-75=180-75
3x=180-75
3x=105
x is being multiplied by 3. The opposite of multiplication is division. Divide both sides by 3.
3x/3=105/3
x=105/3
x=35
x is equal to 35.
Last question! I need help with showing my work! I already have the answer in the attached image below, thanks!
Answer:
see explanation
Step-by-step explanation:
Given
[tex]\sqrt{\frac{4x^2}{3y} }[/tex]
= [tex]\frac{\sqrt{4x^2} }{\sqrt{3y} }[/tex]
= [tex]\frac{2x}{\sqrt{3y} }[/tex]
Rationalise the denominator by multiplying the numerator/ denominator by [tex]\sqrt{3y}[/tex]
Note that [tex]\sqrt{a}[/tex] × [tex]\sqrt{a}[/tex] = a
= [tex]\frac{2x}{\sqrt{3y} }[/tex] × [tex]\frac{\sqrt{3y} }{\sqrt{3y} }[/tex]
= [tex]\frac{2x\sqrt{3y} }{3y}[/tex]
Are you an expert? then answer this.
Answer:
a) n = 3
b) every 9 cm represents 175,000 km
Step-by-step explanation:
a) 20 min : 1 hour
Let's convert it into same units
⇒20 min : 60 min
÷ 20 ÷ 20
⇒ 1 : 3
So n = 3
b) 1 : 25,000
Which means every 1 cm on the map represents 25,000 km
And,
1 cm = 25,000 km
So,
9 cm = 25,000 × 9
9 cm = 175,000 km
So every 9 cm represents 175,000 km
Answer:
a) 3
b) 2.25 km
Step-by-step explanation:
a) 20 min : 1 hour = 1 : n
20 min : 60 min= 1 :3
n=3
b) 1: 25000 scale
1 mm : 25000 mm
9 cm = 90 mm
90 mm : 90*25000 mm
9 cm : 2250000 mm
9 cm : 2.25 km
