Answer:
The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 9 years is $232.56.
Step-by-step explanation:
Given
Total accrued Amount A = 400.00 (Let say $)Time period t = 9 yearsInterest rate r = 8% = 0.08To determine
Principle P = ?
Using the formula
P = A / (1 + rt)
substituting A = 400.00, t = 9 and r = 0.08 in the formula
P = 400 / ( 1 + (0.08 × 9))
P = $232.56
Therefore, the principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 9 years is $232.56.
Write the fraction as a sum of fractions three different ways.
7/10
Leslie bought 5.2 gallons of gas. There are approximately 3.8 liters in 1 gallon. Which measurement is closest to the number of liters of gasoline Leslie bought?
A 5.72 L
B 1.37 L
B 19.76 L
D 7.1 L
Answer:
C
Step-by-step explanation:
What is the x- coordinate of the ordered pair that satisfies this system of linear equations?
х+5y = 16
x+3y = 10
what does x and y equal
Multiply 154.18 and 5 together. Round to the nearest hundredth when necessary.
Answer:
that will be 725.10 im not sure
Answer:
The answer is 770.9 and cant be rounded to the nearest tenth.
This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 90 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically, 3% of the components are identified as defective, and the components can be assumed to be independent.
Required:
a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
Answer:
a) 0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b) 0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c) 0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it is defective, or it is not. The components can be assumed to be independent. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
3% of the components are identified as defective
This means that [tex]p = 0.03[/tex]
a. If the manufacturer stocks 90 components, what is the probability that the 90 orders can be filled without reordering components?
0 defective in a set of 90, which is [tex]P(X = 0)[/tex] when [tex]n = 90[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{90,0}.(0.03)^{0}.(0.97)^{90} = 0.0645[/tex]
0.0645 = 6.45% probability that the 90 orders can be filled without reordering components.
b. If the manufacturer stocks 102 components, what is the probability that the 100 orders can be filled without reordering components?
At most 102 - 100 = 2 defective in a set of 102, so [tex]P(X \leq 2)[/tex] when [tex]n = 102[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{102,0}.(0.03)^{0}.(0.97)^{102} = 0.0447[/tex]
[tex]P(X = 1) = C_{102,0}.(0.03)^{1}.(0.97)^{101} = 0.1411[/tex]
[tex]P(X = 2) = C_{102,2}.(0.03)^{2}.(0.97)^{100} = 0.2204[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0447 + 0.1411 + 0.2204 = 0.4062[/tex]
0.4062 = 40.62% probability that the 100 orders can be filled without reordering components.
c. If the manufacturer stocks 105 components, what is the probability that the 100 orders can be filled without reordering components?
At most 105 - 100 = 5 defective in a set of 105, so [tex]P(X \leq 5)[/tex] when [tex]n = 105[/tex]
Then
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{105,0}.(0.03)^{0}.(0.97)^{105} = 0.0408[/tex]
[tex]P(X = 1) = C_{105,0}.(0.03)^{1}.(0.97)^{104} = 0.1326[/tex]
[tex]P(X = 2) = C_{105,2}.(0.03)^{2}.(0.97)^{103} = 0.2133[/tex]
[tex]P(X = 3) = C_{105,3}.(0.03)^{3}.(0.97)^{102} = 0.2265[/tex]
[tex]P(X = 4) = C_{105,4}.(0.03)^{4}.(0.97)^{101} = 0.1786[/tex]
[tex]P(X = 5) = C_{105,5}.(0.03)^{5}.(0.97)^{100} = 0.1116[/tex]
[tex]P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0408 + 0.1326 + 0.2133 + 0.2265 + 0.1786 + 0.1116 = 0.9034[/tex]
0.9034 = 90.34% probability that the 100 orders can be filled without reordering components
I NEED THIS RIGHT NOW PLEASE. You have two options for a moon bounce rental company for the school carnival. The first company charges a $50 fee plus $15 per day. The second company charges a $80 fee plus $20 per day. Write and SIMPLIFY an expression that represents how much more the second company charges?
Answer:
The second one charges $35 more then the first one.
The Step-by-step explanation:
The first one 50+15=65
THe next one 80+20=100
100-65=35
I need help ASAP!!!!!
Answer:
3
Step-by-step explanation:
The square root of 9 is 3
Solve the following rational equation for x.
x+5/9 = 11/15
Which one doesn't belong? 100, 25, 36, 30
Answer:
Step-by-step explanation:
100 bro
Express 3 kilograms as a fraction of 1800 grams
Answer:
3000/1800 = 5/3
Step-by-step explanation:
3 kilograms is 3000 grams = 3000/1800 simplified to the smallest is 5/3
sorry if this isn't what you're looking for
Find the y-intercept for the parabola defined by
this equation:
y=x^2 + 8x + 12
Separate the values with a comma.
in the six grade 54% of the are boys. there are 189 boys in the sixth grade. what is the total number of the students in sixth grade
189 boys is 54%x is 46%(100-54)Cross multiply:189*46%=54%*x86.94=0.54xx=161189 boys 161 girls350 altogetherHope this helps plz hit the crown :D
Answer:
the total number of students in 6th grade would be 350
Step-by-step explanation:
I hope this helps! ^^
☁️☁️☁️☁️☁️☁️☁️☁️
The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that your answers are equivalent. 6x^5(x^6-2)dx
Answer:
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C[/tex]
Step-by-step explanation:
To find:
∫[tex]6x^5(x^6-2)\,dx[/tex]
Solution:
Method of substitution:
Let [tex]x^6-2=t[/tex]
Differentiate both sides with respect to [tex]t[/tex]
[tex]6x^5\,dx=dt[/tex]
[use [tex](x^n)'=nx^{n-1}[/tex]]
So,
∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫ [tex]t\,dt[/tex] = [tex]\frac{t^2}{2}+C_1[/tex] where [tex]C_1[/tex] is a variable.
(Use ∫[tex]t^n\,dt=\frac{t^{n+1} }{n+1}[/tex] )
Put [tex]t=x^6-2[/tex]
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1[/tex]
Use [tex](a-b)^2=a^2+b^2-2ab[/tex]
So,
∫[tex]6x^5(x^6-2)\,dx[/tex] = [tex]\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C[/tex]
where [tex]C=2+C_1[/tex]
Without using substitution:
∫[tex]6x^5(x^6-2)\,dx[/tex] = ∫[tex]6x^{11}-12x^5\,dx[/tex] = [tex]\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C[/tex]
So, same answer is obtained in both the cases.
A hotel manager is adding a tile border around the hotel's rectangular pool. let n represent the width of the pool, in feet. the length is 5 more than 2 times the width, as shown. Write two expressions that represent the perimeter of the pool.
Answer:
2(3x+5)
6x+10
Step-by-step explanation:
W= x
L= 2x+5
2(x) + 2(2x+5)
Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. 5, 13
Answer:
Leg= Leg- hypotenuse
Step-by-step explanation:
5 suquared= 25
13 squared= 169
25+169 =194
194 square root is 13.9
How to determine each side of a right triangle
if leg a is the missing side, then transform the equation to the form when a is on one side, and take a square root: a = √(c² - b²)
if leg b is unknown, then. b = √(c² - a²)
for hypotenuse c missing, the formula is. c = √(a² + b²)
Answer:
13.9 (rounded)
Step-by-step explanation:
The pathaegorean theorem is A²+B²= C²
5²=25
13²= 169
169+25=194
√194=13.9
Can someone please help me? I already done the first two just confused on the last part please explain when u answer thx peeps brainliest :)
Answer:
c.
[tex] - 1 < - 0.25 < 0 < 0.5 < 1.5[/tex]
n the figure, j∥k and m∠7 = 65°. What is the m∠6?
Answer:
ΔABC ~ ΔEFD
Step-by-step explanation:
ΔABC ~ ΔEFDc
Answer:
I'm a cat, I'm a kitty cat, and a meow meow meow, and a meow meow meow
Bianca graphs the data in the table and finds that the trend line is s = 2.2 f + 4.7. Based on the information given, a player who makes 22 free throws in a game should score about how many points? 39 44 53 66
Answer:
s = 53
Step-by-step explanation:
Bianca graphs the data in the table and finds that the trend line is :
s = 2.2 f + 4.7
We need to find the score when there are 22 free thrown in a game. Put f = 22 in the above equation.
s = 2.2(22) + 4.7
= 53.1
pr
s = 53
Hence, there is 53 score when f = 22.
Answer:
c
Step-by-step explanation:
i need help on this pls
Answer: 10
Step-by-step explanation:
All you have to do to get the bottom number is add the numbers already there
Answer:
The width is equal to 12 meters
Step-by-step explanation:
The Volume equals length x width x height. In our case, we know the length and the height so we can find the width the following way...
V = (l)(w)(h)
[tex]w = \frac{V}{(l)(h)}[/tex]
[tex]w = \frac{288}{(4)(6)}[/tex]
[tex]w = \frac{288}{24}[/tex]
w = 12 m
-1/2(2x-8) distribution
Answer:
-1x+4
Step-by-step explanation:
-1/2 times 2x equals -1x. -1/2 times -8 equals 4.
Need help with this please also explain
Answer:
430 cm³
Step-by-step explanation:
= 11 × 10 × 2
= 220 cm³
= 10 × 3 × (9-2)
= 210 cm³
= 220 + 210
= 430 cm³
Answer:
430 cubic centimeters
Step-by-step explanation:
Lets start by separating both figures. Start with the one in the back, which is the bigger one.
Given:
Length = 10 cm
Width = 3 cm
Height = 9 cm
This is a rectangle and the volume of a rectangle is L x W x H. Therefore,
Volume = 10 x 3 x 9 = 270 cubic centimeters
Now we move on to the second figure.
Given:
Length = 10 cm (Given from the other rectangle)
Width = 8 cm (We do 11 - 3 since we separated the rectangles)
Height = 2 cm
Using the same formula we get the following.
Volume = 10 x 8 x 2 = 160 cubic centimeters
____
Finally, we add both volumes back since we separated the figures in the beginning.
Volume = 270 + 160 = 430 cubic centimeters
From a sample of 120 batteries, 3 are faulty. Work out the percentage of faulty
batteries.
Answer:
2.5%
Step-by-step explanation:
% = (faulty batteries / total batteries) x 100
= (3/120) x 100
= 0.025 x 100
= 2.5
The length of a rectangle is 8 ft longer than twice the width. If the perimeter is 70 ft, find the length and width of the rectangle.
Answer:
9 ft and 26 ft
we will take as x the width, then
P rect. = 2(A+B)
A = 2x + 8 | 2×x, because there is b twice less, and + 8, because there is at 8 longer
B = x
70 = 2(2x + 8 + x)
70-16 = 4x + 2x
54= 6 x
54/6 = 9 => B = 9; A = 2×9+8 = 26
Please put the Brainlest
A plane is flying to Metro City. The plane started its journey 1275 miles from Metro City.
Write an equation in standard form to represent the situation if the plane travels a hours at 550 mph and b hours at
590 mph.
Which equation is correctly written in standard form to represent this scenario?
0 590a - 550b = 1275
550a +590b = 1275
590a + 550b = 1275
550a - 5906 = 1275
Answer:
550a + 590b = 1275
Step-by-step explanation:
We use the following relation to solve this question:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the speed.
In this question, we find the distance, so we use:
[tex]d = v*t[/tex]
A plane is flying to Metro City. The plane started its journey 1275 miles from Metro City.
This means that [tex]d = 1275[/tex].
Write an equation in standard form to represent the situation if the plane travels a hours at 550 mph and b hours at 590 mph.
This means that [tex]v*t = 550a + 590b[/tex].
Which equation is correctly written in standard form to represent this scenario?
[tex]d = v*t[/tex]
1275 = 550a + 590b
550a + 590b = 1275
What percentage of 10000 is 1847?
the answer is,
541.42%
I think this is the answer.
PLZ HELP ME THIS IS 7TH GRADE MATH
Answer:
x would be 54 degrees
Step-by-step explanation:
Since x lies on a straight line, and it gives you the other angle (126) just subtract 180 and 126.
180 - 126 = 54
Find the surface area of the triangular pyramid. The side lengths of the base are equal.
8.7 cm
6 cm
10 cm
The surface area is
square centimeters.
Answer:
522.0
Step-by-step explanation:
10*6=60
60*8.7=522.0
or you can take out the zero either way that's the answer
Answer:
522.0
Step-by-step explanation:
Step-by-step explanation:
10*6=60
60*8.7=522.0
or you can take out the zero either way that's the answer
6.2÷3/4= ? and Explain how you got your answer.
Answer:
8.26 or 8.3 (If Rounded)
Step-by-step explanation:
When I'm dealing with problems involving fractions. I turn the fractions to decimals. So, on a calculator, just do 3/4, you'll get 0.75.
Then, the problem would be 6.2 ÷ 0.75 = 8.26
321. The lanes on the circular outdoor track are one meter wide. By running in the lane next to the innermost lane, Corey ran extra distance in an eight-lap race. How much