[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$16000\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semi-annually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &5 \end{cases} \\\\\\ A=16000\left(1+\frac{0.05}{2}\right)^{2\cdot 5}\implies A=16000(1.025)^{10}\implies A\approx 20481.35[/tex]
$16000 for five years at 5% APR compounded semiannually gives an interest of 4481 dollars.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest compounded semiannually is,
A = P[1 + (r/2)/100]²ⁿ.
Where, A = amount, P = principle, r = rate and n = time in years.
Given, $16,000 is deposited for five years at 5 % compounded semiannually.
A = 16000[1 + (5/2)/100]²ˣ⁵.
A = 16000[1 + 0.025]¹⁰.
A = 16000[1.025]¹⁰.
A = 16000×1.28.
A = 20481.
So, the interest earned is (20481 - 16000) = 4481 dollars.
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11. Write an equation of the line with x-intercept (-7,0) and y-intercept (0,5).
Answer:
5x-7y+35=0.
Step-by-step explanation:
1) according to the condition it is possible to make up the required equation:
[tex]\frac{x}{-7} =\frac{y}{5} =1;[/tex]
note, the numbers -7 and 5 are from the given coordinates;
2) if to re-write the equation into common form, then
5x-7y+35=0.
Question Nine 8 coins are tossed what is the probability of getting at least one Head showing on any of the coins?
The probability of at least one of the coins showing heads is 4
|x|=x^2+x-15 solve absolute value equation and show steps please
Answer:
x=√15 or x = -5 or x=3
Step-by-step explanation:
Possibility one:
x=x^2+x-15
x-x^2=x^2+x-15-x^2 (subtract x^2 from both sides)
-x^2+x=x-15
-x^2+x-x=x-15-x (subtract x from both sides)
-x^2=-15
-x^2/-1=-15/-1 (divide both sides by -1)
x^2=15
square root both sides
x=√15 or x=-√15
Possibility two:
x=(-x^2+x-15)
x=-x^2-x+15 (simplify)
x-(-x^2-x+15)=-x^2-x+15-(-x^2-x+15) (subtract both sides by -x^2-x+15)
x^2+2x-15=0
(x-3)(x+5)=0 (factor left side of equation)
x-3=0 or x+5=0 (set factors equal to 0)
x=3 or x=-5
a shape is shown on the centimetre grid below work out the area of the shape after it has been enlarged by scale factor 2 state the units of your answer
Answer:
20 cm²
Step-by-step explanation:
If the given shape has been enlarged by scale factor 2, then each of the side lengths will be increased from 1 cm to 2 cm, as 1 × 2 = 2
Area of the given shape is 5 cm².
As we are working with area, we cannot simply multiply the area of the given shape by the scale factor. Area is measured in square units, therefore we need to multiply the area of the given shape by the square of the scale factor.
⇒ area of the enlarged shape = area of given shape × sf²
= 5 cm² × 2²
= 5 cm² × 4
= 20 cm²
(see attached image for proof)
Any one able to help me out with this one?
Answer:
54 yards²
Step-by-step explanation:
First, we can find the area of the figure as a whole.
6 x 11 = 66
Now we have to find the area of the smaller rectangle
3 x 4 = 12
Finally, we subtract the whole and the smaller rectangle
66 - 12 = 54
At a football game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 455 people attending the game supported the home team, what was the total number of people attending the game?
Answer:
1300 ppl
Step-by-step explanation:
35% = .35 in decimal
.35 x =455
x = 455/.35 = 1300 ppl
Find the indicated side of the
triangle.
Answer:
[tex]\huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]
Step-by-step explanation:
[tex]a = 12 \sin 30 \degree \\ \\ \implies \: a = 12 \times \frac{1}{2} \\ \\ \implies \: \huge \red{ a = 6} \\ \\ b = 12 \cos 30 \degree \\ \\ \implies \: b = 12 \times \frac{ \sqrt{3} }{2} \\ \\ \implies \: b = 6 \times \sqrt{3} \\ \\ \implies \: \huge \orange{b = \boxed{ 6} \sqrt{ \boxed{3}} }[/tex]
Aiden earned $334.40 at his job when he worked for 16 hours. How much money did he earn each hour?
Answer:
$20.90
Step-by-step explanation:
If we want to find Aiden's hourly rate, and we know how long he worked, and how much money he made, then we can simply divide his profit by how long he worked. This will give us the precise amount of money he made per hour.
So,
$334.40 / 16 hours = 20.9
This means Aiden earned approximately $20.90 per hour.
Hope this helped!
do a and b have the same value in the equations 2(a-1.1)=5.8 and 5/2b-2 3/4=7 1/4
Answer:
YesStep-by-step explanation:
Solve each equation and compare the solutions
1.
2(a - 1.1) = 5.8a - 1.1 = 5.8/2a - 1.1 = 2.9a = 2.9 + 1.1a = 42.
(5/2)b - 2 3/4 = 7 1/42.5b = 7 1/4 + 2 3/42.5b = 10b = 10/2.5b = 4Both a and b have same value
Answer:
Yes, a and b have the same value in the given equations.
Step-by-step explanation:
Equation 1
[tex]2(a-1.1)=5.8[/tex]
[tex]\implies 2a-2.2=5.8[/tex]
[tex]\implies 2a-2.2+2.2=5.8+2.2[/tex]
[tex]\implies 2a=8[/tex]
[tex]\implies \dfrac{2a}{2}=\dfrac{8}{2}[/tex]
[tex]\implies a=4[/tex]
Equation 2
[tex]\dfrac{5}{2}b-2\frac{3}{4}=7 \frac{1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{2 \times 4+3}{4}=\dfrac{7 \times 4+1}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}=\dfrac{29}{4}[/tex]
[tex]\implies \dfrac{5}{2}b-\dfrac{11}{4}+\dfrac{11}{4}=\dfrac{29}{4}+\dfrac{11}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=\dfrac{40}{4}[/tex]
[tex]\implies \dfrac{5}{2}b=10[/tex]
[tex]\implies 2 \cdot \dfrac{5}{2}b=2 \cdot 10[/tex]
[tex]\implies 5b=20[/tex]
[tex]\implies \dfrac{5b}{5}=\dfrac{20}{5}[/tex]
[tex]\implies b=4[/tex]
Conclusion
As a = 4 and b = 4, the two variables have the same value in the given equations.
The area of triangle ABC is 50 square units. What is the length of CD?
If two samples are drawn randomly from the same population and sample A has n=350 and sample B has n=500, which sample will have a larger standard error of the mean?
Group of answer choices
Sample B
Sample A
The standard errors will be the same
Reason:
The standard error of the mean has the formula [tex]\frac{\sigma}{\sqrt{n}}[/tex] where [tex]\sigma[/tex] (greek letter sigma) is the standard deviation and n is the sample size.
As n gets bigger, the standard error [tex]\frac{\sigma}{\sqrt{n}}[/tex] gets smaller, and vice versa. This assumes sigma is fixed. A larger sample indicates the error goes down to narrow in better on the population mean.
Based on what I mentioned, this tells us that sample A has the larger standard error since n = 350 is smaller than n = 500 for sample B.
how many solutions does the following equation have? explain
5x- 3x + 5 = 8x +5
Answer:
Plug into desmos, the exact equation, and put in what point comes out.
Step-by-step explanation:
Answer:
Once fully solved, x is equal to 0, so it means that there is only one solution
Step-by-step explanation:
When you combine like terms (without adding variables to either side), the equation is equal to:
2x + 5 = 8x + 5
Then, the next step is:
5 = 8x + 5 - 2x
Finally, the last one is:
0 = 6x, which is x = 0.
hey can anyone help find the missing measurement pls
Answer:
? ≈ 6.5 yd
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here A = 13.3 and h = 4.1 , then
[tex]\frac{1}{2}[/tex] × 4.1b = 13.3 ( multiply both sides by 2 to clear the fraction )
4.1b = 26.6 ( divide both sides by 4.1 )
b = ? ≈ 6.5 yd ( to the nearest tenth )
What is the sum of all the angles that are labeled?
Answer:
61 + 142 + 44 = 247˚
Step-by-step explanation:
Just add haha
the person above is right
Write 2.19 as the ratio of two integers in fraction form
Answer: [tex]\frac{219}{100}[/tex]
======================================================
Explanation:
Think of [tex]2.19[/tex] as [tex]\frac{2.19}{1}[/tex] or [tex]\frac{2.19}{1.00}[/tex]
This works because dividing anything over 1 does not change the original number.
Then we can move the decimal point two spots to the right for each number
2.19 becomes 2191.00 becomes 100Therefore, [tex]2.19 = \frac{219}{100}[/tex]
a. What is the volume, in cubic feet, of the box in the diagram?
b. How many of these boxes can fit in the cargo hold of the truck?
Volume is a three-dimensional scalar quantity. The number of boxes that can fit in the cargo hold of the truck is 54.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of the box = Volume of the cube = a³ = (2.50)³ = 15.625 ft³
The volume of cargo hold = 7.50 × 7.50 × 15 = 843.75 ft³
Now, the number of boxes that can fit in the cargo hold of the truck will be,
Number of boxes = (Volume of truck container)/(Volume of box)
= 843.75/15.625
= 54
Hence, the number of boxes that can fit in the cargo hold of the truck is 54.
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What is volume of the box in diagram (in cubic ft.)
a = 2.5ft.Volume of cube = a³
putting the value of a
Volume = (2.5ft.)³
Volume = 15.625 ft³
To find how many such boxes can be fit into the truck , we need to first find the volume of cargo hold of the truck and then divide it by the volume of 1 box
Volume of Cargo hold of truck =
= 15ft. × 7.5ft. × 7.5ft
= 843.75 ft³
No. of boxes that can be fit into the truck =
Volume of truck/ Volume of one box
= 843.75ft.3³/15.625ft.³
= 54 boxes
A jogger on the beach at Cape Hatteras covered 8 miles at a constant speed. Given that distance run varies directly as time, what is the constant of variation in miles per hour if it took the jogger 45 minutes to cover the 8 miles?
The velocity of the jogger will be 0.18 miles per minute.
What is velocity?Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that:-
It took the jogger 45 minutes to cover the 8 milesThe velocity will be calculated as:-
V = Distance ÷ Time
V = 8 ÷ 45
V = 0.18 miles per minute
Therefore the velocity of the jogger will be 0.18 miles per minute.
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150 inches equals how many feet and inches?
Answer:
12 feet and 6inches ..................
Answer:
12 feet and 6 inches
Step-by-step explanation:
What is the product of 709 and 68?
Answer:
[tex]709*68=48212[/tex]
ans = 48212
whats the volume formula?
Jaxon is flying a kite, holding his hands a distance of 3.25 feet above
the ground and letting all the kite's string play out. He measures the
angle of elevation from his hand to the kite to be 24°. If the string from
the kite to his hand is 105 feet long, how many feet is the kite above the
ground? Round your answer to the nearest tenth of a foot if necessary.
Using the slope concept, it is found that the kite is 46.50 feet above the ground.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The angle is of 24º.The vertical change is of 3.5 + x.The horizontal change is of 105.Hence:
tan(24º) = (3.5 + x)/105.
3.5 + x = 105tan(24º)
x = 105tan(24º) - 3.5
x = 43.25 ft.
Hence, the height of the kite is:
43.25 ft + 3.25 ft = 46.50 feet.
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Answer:
Step-by-step explanation:
�
105
105
x
sin
24
1
=
1
sin 24
=
�
105
105
x
105
sin
24
=
105 sin 24=
�
x
Cross multiply.
�
=
42.707347...
x=42.707347...
Type into calculator.
Add 3.25, the distance from the ground to his hand:
Add 3.25, the distance from the ground to his hand:
42.707347...
+
3.25
=
42.707347...+3.25=
45.957347...
45.957347...
≈
≈
46
46
Round to the nearest tenth.
The kite is 46 feet above the ground.
The kite is 46 feet above the ground.
Which expression is equivalent to the expression shown?
7
71 7²
2
16
7
1'
712
7¹⁴÷7²
= 7¹⁴-²
=7¹²
hope this helps:)
is 3 divisible by 811
ans = 0.00369913687
hope it helps...!!!!
762/164,391
Need full work
Answer:
254/54797
Step-by-step explanation:
image attached
I need help finding the answer to this
Answer:
Step-by-step explanation:
Remark
If the figures are similar then this is a proportion question. A proportion is 2 equation ratios. The ratios can have at most 1 unknown.
Givens
DC = 7
ML = 4.9
AB = 4
JK = x
Equation
DC/ML = AB/x Substitute values into equation and solve
Solution
7/4.9 = 4/x Cross Multiply
7x = 4 * 4.9 Combine the right.
7x = 19.6 Divide by 7
7x/7 = 19.6/7
x = 2.8
Answer
x = 2.8
The GCF of 12 and 28 is _____.
Answer:
The GCF of 12 and 28 is 4
hope it helpsss
Answer: is 4 thats the answer
Step-by-step explanation: i have none im not good at explaining math welp have a good day
(BRAINLIEST) What is the slope of the line shown in the graph?
2
−1
−fraction 1 over 2
fraction 1 over 2
Answer: the slope is y=-1/2
Step-by-step explanation:
because the line is moving from left to right, it is a negative slope
<~~• ¥ Pls HELP me!! ¥ • ~~>
Pls help me figure out the 3 boxes left pls help me
Step-by-step explanation:
divide equation by 2
subtract 6
-x
Round your answer to the nearest hundredth.
calculate the height of a cuboid with the following dimension a length is equal to 10 cm, height is equal to 5.5 cm, volume is equal to 385cm³
Volume is a three-dimensional scalar quantity. The height of the cuboid is 7 cm.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the volume of the cuboid is 385cm³, the length of the cuboid is 10cm, while the width of the cuboid is 5.5 cm, therefore, the height of the cuboid is,
385cm³ = 10cm × 5.5cm × H
H = 385cm³/(10cm×5.5cm)
H = 7cm
Hence, the height of the cuboid is 7 cm.
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