Answer:
(1165, 1235) (hours)
Step-by-step explanation:
The "middle 68%" of a set of normally distributed data is that data that lies within ONE standard deviation of the mean:
(1200 - 35, 1200 + 35), or
(1165, 1235) (hours)
This is an application of the Empirical Rule.
The interval of hours represents the lifespan of the middle 68% of light bulbs is (1165, 1235) (hours).
What is the standard deviation?It is a measurement of statistical data dispersion. The degree to which the value varies is known as dispersion.
With a mean of 1200 hours and a standard variation of 35 hours, the length of time a certain brand of light bulb lasts is typically distributed.
The data that is within one standard deviation of the mean is referred to as the "middle 68 percent" of a collection of normally distributed data:
The interval of hours represents the lifespan of the middle 68% of light bulbs is found as;
(1200 - 35)=1165
( 1200 + 35)=1235
(1165, 1235) (hours)
Hence,the interval of hours represents the lifespan of the middle 68% of light bulbs is (1165, 1235) (hours).
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Please help with scale factor!!!!!!!! I will mark brainliest if right! Two rectangular prisms have a side scale factor of 1/4. If the smaller prism has a surface area of 45cm square, what is the surface area of the larger prism? Find the scale factor and area.
Answer:
1/16720 cm²Step-by-step explanation:
Area is the product of two dimensions.
If the scale factor is 1/4, the ratio of the areas will be:
(1/4)² = 1/16The smaller prism has a surface are of 45 cm².
The larger prism has a surface area:
45*16 = 720 cm²A line graph titled Video Rental Stores has year on the x-axis and stores (thousands) on the y-axis. In 2009, there were 4,000 stores.
The line graph shows the number of video rental stores for the years 2005 through 2012.
There were stores in 2009.
Answer:
its 4,000
Step-by-step explanation:
The results of a survey asking 500 people about their favorite ice cream flavor are shown in the table.
Find the experimental probability of each outcome in the sample space. Enter your answers in the boxes.
Flavor Number of People
Chocolate 90
Vanilla 125
Strawberry 60
Mint Chip 50
Other 175
P(chocolate) =
%
P(vanilla) =
%
P(strawberry) =
%
P(mint chip) =
%
P(other) =
%
Chocolate = 18%
Vanilla = 25%
Strawberry = 12%
Mint Chip = 10%
Other = 35%
The explanation for me getting these exact percentages is because of the formulas given for calculating the percentages from specific numbers and real world problems like this. When you are trying to find the calculation precentages of these types of questions, you divide the number by the total surveyed and multiple by 100.
Example:
125 / 500 = 0.25
0.25 x 100 = 25%
So, this is also how I got the other numbers, just change the "125" to the other numbers.
The experimental probability of each outcome in the sample space are:
P(chocolate) = 18%, P(strawberry) = 12%, P(vanilla ) = 25%, P(mint chip) = 10% and P(other) = 35%
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Flavor Number of people
chocolate 90
strawberry 60
vanilla 125
mint chip 50
other 175
So, the Experimental probability are:
P(chocolate)= 90/ 500 x 100 = 18%
P(strawberry) = 60/ 500 x 100 = 12%
P(vanilla ) = 125/ 500 x 100 = 25%
P(mint chip) = 50/ 500 x 100 = 10%
P(other) = 175/ 500 x 100 = 35%
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In circle o,find the value of x, rounded to the nearest tenth.
Answer:
[tex]\huge\boxed{x \approx 5.4}[/tex]
Step-by-step explanation:
We can break down this problem by first realizing different parts of the circle.
The line which is 8 units long is a chord of the circle.The line that is 3.6 is almost the radius of the circleThe line that x sits on is the radius.With this, we can find out if we find the radius of the circle, we have our answer.
We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.
What we need is a way to find the radius of the circle. This will get us x. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.
If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).
We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:
[tex]\displaystyle a^2 + b^2 = c^2[/tex]Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!
[tex]3.6^2 + 4^2 = c^2[/tex] [tex]12.96+16=c^2[/tex] [tex]28.96=c^2[/tex] [tex]\sqrt{28.96} = c[/tex] [tex]5.4 \approx c[/tex]Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.
The line X does just that. Therefore, the value of x is also 5.4.
Hope this helped!
Imagine that you would like to purchase a $275,000 home. Using 20% as
a down payment (or $55,000), determine the monthly mortgage payment
for your dream home using the loan terms below. Hint: Read the Loan
Calculator tip at right for a tool that will help you make the calculations.
A. 15-year mortgage term with a 3% interest rate
Total Amount Paid Over Loan Term
Minimum Monthly Payment:
B. 20-year mortgage term with a 6% interest rate
Total Amount Paid Over Loan Term:
Minimum Monthly Payment:
C. 30-year mortgage term with a 5% interest rate
Total Amount Paid Over Loan Term:
Minimum Monthly Payment:
Which mortgage would you choose and why?
Answer:
The mortgage chosen is option A;
15-year mortgage term with a 3% interest rate because it has the lowest total amount paid over the loan term of $270,470
Step-by-step explanation:
The details of the home purchase are;
The price of the home = $275,000
The mode of purchase of the home = Mortgage
The percentage of the loan amount payed as down payment = 20%
The amount used as down payment for the loan = $55,000
The principal of the mortgage borrowed, P = The price of the house - The down payment
∴ P = $275,000 - 20/100 × $275,000 = $275,000 - $55,000 = $220,000
The principal of the mortgage, P = $220,000
The formula for the total amount paid which is the cost of the loan is given as follows;
[tex]Outstanding \ Loan \ Balance = \dfrac{P \cdot \left[\left(1+\dfrac{r}{12} \right)^n - \left(1+\dfrac{r}{12} \right)^m \right] }{1 - \left(1+\dfrac{r}{12} \right)^n }[/tex]
The formula for monthly payment on a mortgage, 'M', is given as follows;
[tex]M = \dfrac{P \cdot \left(\dfrac{r}{12} \right) \cdot \left(1+\dfrac{r}{12} \right)^n }{\left(1+\dfrac{r}{12} \right)^n - 1}[/tex]
A. When the mortgage term, t = 15-years,
The interest rate, r = 3%
The number of months over which the loan is payed, n = 12·t
∴ n = 12 months/year × 15 years = 180 months
n = 180 months
The monthly payment, 'M', is given as follows;
M =
The total amount paid over the loan term = Cost of the mortgage
Therefore, we have;
220,000*0.05/12*((1 + 0.05/12)^360/( (1 + 0.05/12)^(360) - 1)
[tex]M = \dfrac{220,000 \cdot \left(\dfrac{0.03}{12} \right) \cdot \left(1+\dfrac{0.03}{12} \right)^{180} }{\left(1+\dfrac{0.03}{12} \right)^{180} - 1} \approx 1,519.28[/tex]
The minimum monthly payment for the loan, M ≈ $1,519.28
The total amount paid over loan term, A = n × M
∴ A ≈ 180 × $1,519.28 = $273,470
The total amount paid over loan term, A ≈ $270,470
B. When t = 20 year and r = 6%, we have;
n = 12 × 20 = 240
[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.06}{12} \right) \cdot \left(1+\dfrac{0.06}{12} \right)^{240} }{\left(1+\dfrac{0.06}{12} \right)^{240} - 1} \approx 1,576.15[/tex]
The total amount paid over loan term, A = 240 × $1,576.15 ≈ $378.276
The monthly payment, M = $1,576.15
C. When t = 30 year and r = 5%, we have;
n = 12 × 30 = 360
[tex]\therefore M = \dfrac{220,000 \cdot \left(\dfrac{0.05}{12} \right) \cdot \left(1+\dfrac{0.05}{12} \right)^{360} }{\left(1+\dfrac{0.05}{12} \right)^{360} - 1} \approx 1,181.01[/tex]
The total amount paid over loan term, A = 360 × $1,181.01 ≈ $425,163
The monthly payment, M ≈ $1,181.01
The mortgage to be chosen is the mortgage with the least total amount paid over the loan term so as to reduce the liability
Therefore;
The mortgage chosen is option A which is a 15-year mortgage term with a 3% interest rate;
The total amount paid over the loan term = $270,470
Type the correct answer in each box. Use numerals instead of words.
Consider the quadratic equation x² + 10x + 27 = 0.
Completing the square leads to the equivalent equation (x + ___)² = ___.
.
Answer:
(x + 5)² = 2 ==> x² + 10x + 27 = 0
Completing the square of the given quadratic equation leads to the equivalent equation (x + 5)² = -2.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
Given quadratic equation is,
x² + 10x + 27 = 0
We have the algebraic identity that,
(a + b)² = a² + 2ab + b²
The given quadratic equation is in the form of a² + 2ab + b², where a = x.
So, 2xb = 10x
⇒ b = 5
Now, b² = 25.
So, the given can be written as,
(x² + 10x + 25) + 2 = 0
(x + 5)² = -2
Hence the equivalent form is (x + 5)² = -2.
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find the missing side lengths of the triangle 20 units 21 units
Answer:
29
Step-by-step explanation:
In a triangle, a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
Given this formula, we knoe c^2 is the product of 21^2 + 20^2.
This gives you 841. Now you just find the square root of 841 which is 29.
Hope this helps :)
Someone please help with this khan assignment
Answer:
slopes is 1/4
y intercept is 3 i think the inequality would be y=mx+b so it would be y=1/4x+3
Step-by-step explanation:
What is the simplest form of the fraction below?
24/36
Answer:
2/3
Step-by-step explanation:
Four students ran for the position of school president. Use the following results to figure out who won. Jenna received 22% of the votes. Jordan received of the votes. Kelsey received 6 out of every 20 votes. Nathan received of the votes. The winner was A Jenna B Jordan C Kelsey D Nathan
Answer:
A Jenna
Step-by-step explanation:
Because if Jenna received 22% votes and Jordan, Kelsey, Nathan received less 20 percentage that means Jenna won for school president.
4. Before tax, you make $575 every paycheck. If 8% is deducted for taxes, how much tax is taken from your
check?
A) $46 B) $529 C) $621 D) $460
Answer:
A . $46
Step-by-step explanation:
because 575 - 8% = 529
529 + 49 = 575
Which one is the answer? Please be honest this is for my friend.
Answer:
A 0.4kg object rolling at 2 m/s that's d right answer
Answer:
A 0.4 kg object moving at 4 m.
Step-by-step explanation:
The heavier the object is, the faster it goes. Also the faster is goes and the heavier it is, the more momentum it has.
PLS HELP!!
In the following diagram, L || M. (i think that's an L, i dont know)
Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.
Answer:
Un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas. Un
sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal. Una solución de un sistema es una asignación de valores para las incógnitas que hace
verdadera cada una de las ecuaciones. Resolver un sistema signifi ca hallar todas las soluciones del sistema.
Step-by-step explanation:
The radius of a circle is 7 miles. What is the circle's area?
Use 3.14 for .
Answer:
A≈153.94mi²
Step-by-step explanation:
A = πr2 = π · 72 ≈ 153.93804mi²
Need help What is 6/10 in simplest form
Answer:
3/5
Step-by-step explanation:
35.
Step-by-step explanation:
The simplest form of 610 is 35.
Choose the equation where b= 6 11-b=6 b+4=9 8xb=48 63/3=9
Convert 5 1/6 to a decimal through long division.
Answer:5.83
Step-by-step explanation:
Gross profit of Inner Spark's company amounted to Php275,000. Net Sales is Php400,000 compute for cost of goods sold?
Answer:Cost of goods sold =Php125,000
Step-by-step explanation:
Profit = Cost Price-Selling Price
Also we know that
Gross Profit = Net Sales– Cost of Goods Sold
Php275,000=Php400,000– Cost of Goods Sold
Cost of Goods Sold=Php400,000-Php275,000=Php125,000
A water pipe has a flow of 2 gallons per minute how many 2 qt could fill it in 1/2 hour?
Answer:
60 Gallons in 1/2 hour. So we can convert that to 240 quarts. it says 2 so we divide that by two. 240/2=120
Step-by-step explanation:
Hope this helps!
PLEASE HELP AND EXPLAIN HOW TO DO THIS
Find Sn for the given geometric series.
1=0.11, 5=895.956875, =9.5
Answer:
1001.35
Step-by-step explanation:
Assuming
n
=
5
for which sum to be found.
We know sum of geometric series up to
n
th term is
S
n
=
a
1
⋅
r
n
−
1
r
−
1
Here
a
1
=
0.11
,
r
=
9.5
,
n
=
5
∴
S
5
=
a
1
⋅
r
5
−
1
r
−
1
=
0.11
⋅
9.5
5
−
1
9.5
−
1
≈
1001.35
[Ans]
Puteti sa ma ajutati va rog
Answer:
I read the title wrong, please remove my answer
Step-by-step explanation:
What variable in the equation y=mx+b represents the rate of change?
A) y
B) m
C) x
D) b
Answer:
D) b
Step-by-step explanation:
Rise Over Run = Rate of change.
What is the value of x in the diagram?
April ought some sports drinks and slices of pizza for her friends. She bought 3 more sports drinks than slices of pizza. If her total was $21.25, how many sports drinks did she purchase?
(1 sports drink is $1.75, one pizza slice is $2.75)
{System of Operations}
s= p+3
(number of sports drinks= s)
(pizza slices= p)
in
2. Susan is divorced and has one child that she pays for. She will file her taxes as a head of
household for federal income tax and single for state tax purposes. Susan's gross income is
$48,500. Susan lives in Louisiana
Answer:
what si the questions
Step-by-step explanation:
please help HEYMLMUM
Answer:
A.
Step-by-step explanation:
The price of a 6-minute phone call is 1.80 what is the price of a 17-minute phone call
Answer:
$5.10
Step-by-step explanation:
Ratios:
[tex]\frac{6}{1.8} =\frac{17}{x} \\\\6x=30.6\\x=5.1[/tex]
Help please, not sure how to do this...
Answer:
8.38
Step-by-step explanation:
The underlined number is in the hundredths place, so that means that we're going to round there. That means that you look at the number to its right and if it's lower than 5, it stays the same. However, if it's 5 or higher, you round it up. For example, if the number was 8.386, we would round it to 8.39.
Linear or Non Linear
The cost to ride in a taxi that initially charges $4 plus $0.25 per half mile
given the f(x)=x+2 g(x)=3x²-1 what is (fg) (x)?
Answer:
(f·g)(x) = 3x² + 1Step-by-step explanation:
Given:
f(x)=x+2, g(x)=3x²-1To find:
(f·g) (x) = ?Solution:
(f·g)(x) = f(g(x)) = f(3x²-1) = (3x²-1) + 2 = 3x² + 1(f·g)(x) = 3x² + 1