Answer:
15.85%
Step-by-step explanation:
Empirical rule states that for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviation and 99.7% falls within three standard deviation.
Given mean (μ) = 41 months, standard deviation (σ) = 5 months
One standard deviation = μ ± σ = 41 ± 5 = (36, 46)
Therefore 68% falls within 36 months and 41 months
Two standard deviation = μ ± 2σ = 41 ± 2(5) = (31,51)
Therefore 95% falls within 31 months and 51 months
Three standard deviation = μ ± 3σ = 41 ± 3(5) = (26, 56)
Therefore 99.7% falls within 26 months and 56 months
The percentage of cars that remain in service between 46 and 51 months = 32%/2 - 0.3%/2 = 16% - 0.15% = 15.85%
Find the measure of the missing angle
128°
Help plz
Answer:
52 degrees
Step-by-step explanation:
a line is 180 degrees so just subtract 128 from 180 which is 52
Suppose f(x) = x^3 +3. Find the graph of f(2/3x)
Answer:
First, when we have a function f(x), an horizontal dilation of scale factor k, is written as:
g(x) = f(x/k)
Then f((2/3)*x) is an horizontal dilation of scale factor 3/2 of the function f(x).
(The graph will be a little bit wider than the graph of f(x))
Also, knowing that f(x) = x^3 + 3
Then:
f((2/3)*x) = ( (2/3)*x)^3 + 3
= (8/27)*x^3 + 3
And the graph of this function is shown below:
The number of employees in each industry in Seattle was recorded and rounded to the nearest
10 thousand. The results are displayed in the dot plot above. According to the dot plot, what is
the median number of employees, in thousands?
Answer:
20
Step-by-step explanation:
In the question, "35 is what percent of 40?" what is the 35?
Answer:
35 is the 'is' and 40 is the 'of'
Step-by-step explanation:
is/of = %/100
35/40 = x/100
cross-multiply to get:
40x = 3500
x = 3500/40
x = 87.5
3(2^2x+3)-5(2^x+2)-156=0
Answer: [tex]x=3.0206[/tex]
Step-by-step explanation:
Given
[tex]3(2^{2x}+3)-5(2^x+2)-156=0[/tex]
Replace [tex]2^x[/tex] by [tex]y[/tex]
We can write
[tex]\Rightarrow 3(y^2+3)-5(y+2)-156=0\\\Rightarrow 3y^2+9-5y-10-156=0\\\Rightarrow 3y^2-5y-157=0\\\\\Rightarrow y=\dfrac{5\pm \sqrt{25-4(3)(-157)}}{2\times 3}\\\\\Rightarrow y=\dfrac{5+43.69}{6}\\\\\Rightarrow y=8.115\\\Rightarrow 2^x=8.115\\\therefore \quad x=3.0206[/tex]
HELP ASAP
Solve for x.
x = [?]
X - 6
8x + 24
Answer:
x=18
Step-by-step explanation:
Both angles are supplementary angles and form 180
Set your formula up as following
(x-6) + (8x+24) = 180
x+8x-6+24=180
9x=180+6-24
9x=162
x=162/9
x=18
Now substitute 18 for x to get your angles and check your work .
177*((177+(9-4+7)) +90/8=
Answer:
33464.25
Step-by-step explanation:
Using BODMAS : brackets, division, multiplication, addition
[tex]177\times ((177+(9-4+7)) +\frac{90}{8}\\\\177\times (177+12) +\frac{90}{8}\\\\177\times 189 +\frac{90}{8}\\\\\\177 \times 189 + 11.25\\\\33453 + 11.25\\\\33464.25[/tex]
Answer:
35444.25
Step-by-step explanation:
OFC by computing them
Find the area of a triangle with a height of 5 ft and a base of 4 ft.
Answer:
5 x 4 = 20, 20 divided by 2 ( x 1/2 ) = 10
Step-by-step explanation:
Formula area of a Triangle:
B(base) x H(height) x 1/2(basically just dividing by 2)
match the equation below
I REALLY NEED HELP PLS HELP ME ON THIS MATH
Answer:
Ok, we can define a function as a relation that maps elements from a set (the domain) into elements from another set (the range), such that each element in the domain can be mapped into only one element of the range.
2) Here you choose the autographed poster, and we know that each one of these costs $10.
So, if the artist sold x posters, then he/she would earn x times $10:
earnings = $10*x
So we can create a function:
f(x)
such that f(x) represents the total earnings of the artist for selling x posters.
And we already know the equation for the earnings, so the function will be:
f(x) = $10*x
3) Now, it asks us if the values:
-2, -1, 0, and 1
be appropiate for the domain of the function.
Remember that x represents the number of posters that the artist sold.
Then, if we take x = -2 or x = -1 (like the first two given values) this would mean that the artist sold a negative number of posters, which has no real sense in the situation given. So we can conclude that these values should not be in the domain of the function.
For the other two cases, 0 and 1, these two can be in the domain, because these represent the case where the artist sold only one poster and the case where the artist did not sell any poster (that are two possible cases)
Please help. Image up top.
Answer:
6/5t + 4/15s - 3
Step-by-step explanation:
(-4/5t + 5/3s) + (-3 -7/5s + 2t)
You can only add like terms together so convert like terms to have the same denominator:
(-4/5t + 25/15s) + (-3 - 21/15s + 10/5t)
Get rid of the parentheses:
-4/5t + 25/15s - 3 - 21/15s + 10/5t
Combine like terms:
6/5t + 4/15s - 3
What is the area, in square units, of trapezoid AEDC shown below?
Area of this trapezoid is 264 unit²
What is the area of a trapezoid?Area: ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides.
Given perpendicular distance as 12 and parallel sides as 20,24 units respectively.
Thus Area is (20+24 /2) ×12=264 units²
Hence, the Area of trapezoid is 264 unit²
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Stanley attempted to simplify the expression below.
−4●(2.5x−1.25)−3x
His work, step by step, is shown below.
Step 1: −4●{(2.5x+(−1.25)}−3x
Step 2:−10x+(−5)−3x
Step 3:−10x−3x+(−5)
Step 4: −13x−5
In which step did he make his first error simplifying the expression?
Help If you know the answer plz!
Answer:
2
Step-by-step explanation:
Answer:
2t
Step-by-step explanation:
3t-t is the same as 3-1, so it equals 2t
Simplify.
Rewrite the expression in the form z”. Z5 • Z6
Answer:
Simplify.
Rewrite the expression in the form z”. Z5 • Z6Simplify.
Rewrite the expression in the form z”. Z5 • Z6
Answer:
Simplify.
Rewrite the expression in the form z”. Z5 • Z6Simplify.
Rewrite the expression in the form z”. Z5 • Z6
PLZZZZ HELP!!!
First to answer will get brainly!!!PLZZZZZZ
Answer:
-7
Step-by-step explanation:
What is the domain of f?
Bacteria are taking over the kitchen sink. Right now, there are 375 microbes of bacteria. They double every hour.
Is the function describe above a growth or decay function?
Answer: The function described in this scenario above is a “Growth Function”
Have a nice day!
I NEED THIS QUICK no links !!!!! (math)
answer: the answer is c
the ratio of colored papers to white papers is 3/8 if there are 48 white papers, how many coloured papers are there
The number of coloured papers as per the given problem is 18.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
Given that,
The ratio of coloured papers to white papers is 3/8.
And, the number of white papers is 48.
Suppose, the number of coloured papers be x.
Then, as per the question the following equation can be obtained,
3/8 = x/48
=> x = 3/8 × 48
=> x = 18
Hence, the number of coloured papers is 18.
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Find the measure of angle C
Answer:
ajnasnnanananandbabbabbansbansbz svabsvsb
Create a step function for the following graph, be sure to watch holes in the graph. NEED HELP ASAP!
Answer:
See below
Step-by-step explanation:
This is a piece-wise function.
4, -4≤ x ≤ -2
f(x) = 2, -2 ≤ x < 2
-3, 2 ≤ x ≤ 4
Expand and combine like terms.
(4m^5) – 5m^6) (4m^5 + 5m^6) =
Answer:
[tex]16m^{10} -25m^{12}[/tex]
Step-by-step explanation:
hope this helps :)
The expand and combination like terms (4m^5) – 5m^6) (4m^5 + 5m^6) is -9m^12 + (16)m^10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The equation=(4m^5) – 5m^6) (4m^5 + 5m^6)
Now,
To expand the expression, we need to multiply each term inside the first parentheses by each term inside the second parentheses. This gives us:
(4m^5 - 5m^6) (4m^5 + 5m^6) = 4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6
To simplify the expression, we need to use the exponent rule that a^b * a^c = a^(b + c) and combine the terms that have the same base and exponent. This gives us:
4m^5 * 4m^5 + 4m^5 * 5m^6 - 5m^6 * 4m^5 - 5m^6 * 5m^6 = 16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6)
To further simplify the expression, we need to add the exponents and simplify the coefficients. This gives us:
16m^(5 + 5) + 20m^(5 + 6) - 20m^(6 + 5) - 25m^(6 + 6) = 16m^10 + 20m^11 - 20m^11 - 25m^12
To combine like terms, we need to add or subtract the coefficients of the terms that have the same base and exponent. This gives us:
16m^10 + 20m^11 - 20m^11 - 25m^12 = (16 - 25)m^12 + (20 - 20)m^11 + (16)m^10
= -9m^12 + (0)m^11 + (16)m^10
= -9m^12 + (16)m^10
Therefore, the equation will be equal to -9m^12 + (16)m^10.
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What is the height h of the flagpole in meters?
A. 10m
B. 12m
C. 18m
D. 20m
What is the volume of the rectangular prism?
A recipe for lemonade requires 10 parts of water to every 6 parts of lemon juice. How many cups of water should be added to 30 cups of lemon juice to make the lemonade? I dont understand how many "parts" of water = 1 cup
Answer:
50 cups
Step-by-step explanation:
ratio of water to juice = 10 : 6 = 5 : 3
amount of cup = (5 x 30) / 3 = 50
If the interest of a sum at 7.5% p.a in 4 years is Rs. 1050, find the sum
~Refer to the attachment for the solution.
[tex] \to \bf { Sum = 3500 } [/tex]
You take a bus from your neighborhood to your school. The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m. The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m. You arrive at the bus stop at 7:33 a.m. Find the probability that you missed both the express bus and the local bus. Express your answer as a fraction in simplest form.
Answer:
[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.
Step-by-step explanation:
Uniform distribution:
An uniform distribution has two bounds, a and b.
The probability of getting a value lower than x is:
[tex]P(X < x) = \frac{x - a}{x - b}[/tex]
The express bus arrives at your neighborhood at a random time between 7:30 and 7:36 a.m.
6 minutes, so [tex]a = 0, b = 6[/tex]
You arrive at 7:33, so if x < 3, you lose the express bus:
[tex]P_E = P(X < 3) = \frac{3 - 0}{6 - 0} = \frac{3}{6} = \frac{1}{2}[/tex]
The local bus arrives at your neighborhood at a random time between 7:30 and 7:40 a.m.
10 minutes, so [tex]a = 0, b = 10[/tex]
[tex]P_B = P(X < 3) = \frac{3 - 0}{10 - 0} = \frac{3}{10}[/tex]
Find the probability that you missed both the express bus and the local bus.
[tex]p = P_E*P_B = \frac{1}{2}*\frac{3}{10} = \frac{3}{20}[/tex]
[tex]\frac{3}{20}[/tex] probability that you missed both the express bus and the local bus.
The probability that you missed both the express bus and the local bus is 3/20
The individual probability of a uniform distribution is calculated as:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
For the express bus
At 7:30 am, a = 0
At 7:36 am, b = 6
You arrived at 7:33 am; this means that:
x = 3
For you to miss the express bus, it means that the express bus left before 7:33 am.
i.e. x < 3
So, the probability that you miss the express bus is:
[tex]P(X < 3) = \frac{3 - 0}{6 - 0}[/tex]
[tex]P(X < 3) = \frac{3}{6}[/tex]
[tex]P(X_E < 3) = \frac{1}{2}[/tex]
For the local bus
At 7:30 am, a = 0
At 7:40 am, b = 10
You arrived at 7:33 am; this means that:
x = 3
For you to miss the local bus, it means that the local bus left before 7:33 am.
i.e. x < 3
So, the probability that you miss the local bus is:
[tex]P(X < 3) = \frac{3 - 0}{10 - 0}[/tex]
[tex]P(X_L < 3) = \frac{3}{10}[/tex]
So, the probability that you miss both bus is:
[tex]P(Both) = P(X_E < 3) * P(X_L < 3)[/tex]
This gives
[tex]P(Both) = \frac 12 * \frac 3{10}[/tex]
[tex]P(Both) = \frac 3{20}[/tex]
Hence, the probability that you missed both the express bus and the local bus is 3/20
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Classify this expression
Answer:
8.
[tex]8. - 1. - 44 [/tex]
9
A survey of 125 freshmen business students at a local university produced the results listed below. How many students took history and math, but not music? 30 took history; 32 took math; 33 took music; 14 took history but not math; 9 took math and music; 13 took history and music; 2 took all three
Answer:
Total Number of students taking Math and History and not music are 68.
Number of students who took both math and history at the same time is 6.
Step-by-step explanation:
History = 30
Math = 32
Music= 33
Math and Music= 9
History and Music= 13
History and Music and Math = 2
History but not math = 14
We have to find students taking history and math but not music.
Total number of students = 125
From the figure number of students taking Math and History and not music are
=30+6+32= 68
Number of students who took both math and history at the same time is 6.