the mpg (miles per gallon) of a certain compact car is normally distributed with a mean of 31 and a standard deviation of 1.2. what is the probability that the mpg for a randomly selected compact car would be more than 30?
The probability that a compact car's randomly chosen mpg would be higher than 30 is 0.797.
Given data;
A certain compact car's mpg (miles per gallon) has a mean of 31 and a standard deviation of 1.2 and is regularly distributed.
We need to get the probability that the mpg for a randomly selected compact car would be more than 30.
Therefore;
Mean = μ = 31
Standard deviation = σ = 1.2
Let;
P(X > 30) = P(X - 31/1.2 > 30 - 31/1.2)
= P(Z > -0.833)
= 0.797
Hence, the probability that the mpg for a randomly selected compact car would be more than 30 is 0.797.
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Separate 25 into two parts so that one part is 13 less than the other part.
NEED HELP QUICKLY!!
Answer:
One number is 19 and the other is 6
Step-by-step explanation:
25 = x + (x- 13)
25 = x + x - 13
38 = 2x
19 = x
x = 19
25 - 19 = 6
write the quotient as a power. a^21/a
the quotient as a power. a^21/a is a^20.
What is Power?
In mathematics, power defines a base number raised to the exponent, where base number is the factor which is multiplied by itself and exponent denotes the number of times the same base number is multiplied.
What is quotient?
The number we obtain when we divide one number by another is the quotient.
What is exponential function?
An exponential function is a mathematical function of the following form: f ( x ) = a x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e , which is equal to approximately 2.71828.
Given that,
a^21/a
quotient as power = a^21/a
= a^(21-1)
= a^20
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Factorise a squared - a -20
Answer:
(a-5)(a+4)
Step-by-step explanation:
[tex]a^{2}[/tex]-a-20
[tex]a^{2}[/tex]+4a-5a-20
a(a+4) -5(a+4)
(a-5)(a+4)
(30 x 5) + (9 x 5) =
150 + 45 = 195
Answer:
thats correct
Step-by-step explanation:
if our circadian clocks are not reset each morning by exposure to light, they: a. tend to run a cycle that is a little longer than 24 hours b. tend to run a cycle that is a little shorter than 24 hours c. tend to run on a 12-hour cycle d. still run exactly on a 24-hour cycle
If our circadian clocks are not reset each morning by exposure to light, they a. tend to run a cycle that is a little longer than 24 hours.
Chronobiology, the study of the body's circadian rhythms, contends that our daily routine, including when we eat, exercise, go to bed, and are exposed to light, may have a significant impact on how our bodies function on a day-to-day basis.
According to the National Institute of General Medical Sciences, circadian rhythms are the normal physical, mental, and behavioral changes that take place in the body on a 24-hour cycle, typically in reaction to light and darkness. One illustration is resting at night and remaining awake during the day.
You might not be able to avoid daytime sleep and evening work if you work an overnight shift or other irregular hours. According to Wright, those people should pay extra close attention to making other healthy decisions a priority, such as getting enough exercise and quitting smoking.
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At the beginning of a chemistry experiment, the volume of liquid in a container was 3 milliliters. During the experiment, the volume dropped to
2.1 milliliters. Find the percent of decrease.
Answer:
30%
Step-by-step explanation:
To calculate the percent of change, you find the amount of change and divide that my the original amount
[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3 As a percent, this would be 30%
Factor the expression using the GCF.
The expression $32z-48$ factored using the GCF is
Answer:
16(2z-3) or GCF: 16
Step-by-step explanation:
32z-48 has a GFC of 16
16(2z-3)
Answer:
$16(2z-3)
Step-by-step explanation:
Prime factorization:
32: 2*2*2*2*2
48: 2*2*2*2*3
Notice any similarities:
2*2*2*2=16
$32z-$48 = $16(2z-3)
Find the value of x.
79
118°
109
Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
Find the value of x ?y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
answer is B
x = 108 and y = 109
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The value of X is 108 and the value of y is 109. The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division.
Find the value of x ?Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.
y = 180 -71 = 109
x = 360 - (81+100+71)
x = 360 -252
x = 108
Therefore the value of x and y is x = 108 and y = 109
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1. Why is identifying
the domain and range important when
defining a function?
Identifying the domain and range is important when defining a function because domain gives all the input values and range gives all the output values a function can take. It is very essential to know domain and range of a function.
Domain are represented by independent variable and are graphed on x coordinate of the axis.
Range are dependent values and are graphed on y axis of the graph.
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so what is 9/4 divided by 6/5
Answer:
45/20
Step-by-step explanation:
Answer:
9/4 divided by 6/5 is 15/8
Step-by-step explanation:
9/4 ÷ 6/5 turns into 9/4 × 5/6 which is the reciprocal
9/4 × 5/6 = 45/24
Divide the numerator and denominator by 3 to get 15/8
15/8 is in its simplest form
Jenna and Becca were both selling cookies door to door. Jenna sold 8 boxes of cookies for every 3 boxes of cookies Becca sold. Combined,they sold a total of 385 boxes of cookies. How many boxes did each girl sell?
the sum of the number of factors of n and n2 is 34. how many such distinct numbers such that n<150 exist?
The total 18 numbers such that n<150 exist, if the sum of the numbers of factors of N and N^2 is 34
Let me give you an example. 12. Both 2- 2 times and 3- 1 times are factors of 12.
Factors in total (2+1)*(1+1)=6
It will have 2- 4 times and 3-2 times for 122.
15 total factors of 5*3
Situation 1: N = xy
attempting a reverse strategy for N*N Factors in 35=5*7 are x-4 times and y-6 times.
Regarding N-x-2 and Y-3 timings.
There are a total of (2+1)*(3+1)=12 factors.
Situation 2
Since N2 has 34 factors if N2 is raised to the power of 34, there are 17 factors for N.
Consequently, 17+1 = 18 factors in total.
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3 (2− k) = −3k + 2
I need this for class
The value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
According to the question,
We have the following expression:
3 (2− k) = −3k + 2
Now, we will multiply 3 into the bracket:
6-3k = -3k+2
Now, moving -3k from the left hand side to the right hand side will result in the change of the sign from minus to plus:
6-3k+3k = 2
Now, 3k will get subtracted from 3k. So, we do not have any variable left for this equation.
Hence, the value of k for the expression, 3 (2− k) = −3k + 2, does not exist.
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mandy begins bicycling west at 30 miles per hour at 11:00 a.m. if liz leaves from the same point 20 minutes later bicycling west at 36 miles per hour, when will she catch mandy?
The time at which Liz will catch up with Mandy is 1 pm.
Here we have to find the time when Mandy and Liz meet.
Let t be the time taken by Liz to meet Mandy
Given:
Speed of Mandy = 30mile/hr
Speed of Liz = 36 miles/hr
Formula:
Speed = Distance/ time
Distance by Mandy = 30t
Distance by Liz = 36( t - 20/60)
As the distance covered by both is the same. So we have
30t = 36( t - 1/3)
6t = 12
t = 2
2 hours past 11 am is 1 pm.
Therefore Liz catch Mandy at 1 pm.
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Round to the nearest hundredth. 44.242
Answer:
44.24
Step-by-step explanation:
The 2 in the thousandths place is lower than 5 therefore it does not round the 4 to a 5
Answer:
44.24
Step-by-step explanation:
hopes this helps please mark brainliest
79 ala decena mas cercana
Answer:
80
Step-by-step explanation:
Miguel's class just held a class election. 70% of the 30 students in the class voted. How many students voted?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 30}}{\left( \cfrac{70}{100} \right)30}\implies 21[/tex]
Answer: 21
Step-by-step explanation:
70% of 30 students is 21
Hope this helped :)
A baseball diamond is a square that measures 90ft on each side. Write and expression for the distance from 2nd base to home plate in square root form using a^2+b^2=c^2, then give the answer rounded to the nearest tenth
If a baseball diamond is a square that measures 90ft on each side. The expression for the distance from 2nd base to home plate in square root form isc =√ (90)² + (90)² and the distance is 127ft.
How to find the distance?Using the Pythagoreans theorem formula
c= √ a²+b²
Where:
c = length of hypotenuse
a and b = length of the sides of the right triangle
Let plug in the formula
c =√ (90)² + (90)²
c =√ 8100 +8100
c =√16200
c = 127.3
c = 127 ft (Approximately)
Therefore the distance is 127ft.
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if saint cloud is growing according to the equation pn= 200(1.03)n where n is years after 2010, and the population is measured in thousands. find when the population will be 400 thousand.
In 2267 year, this population would be 400000.
From the question, we have
population is growing as Pn = 200*(1.03)n
substituting the value, we get
400000 = 200*(1.03)n
2000 = 1.03n
ln(2000) = n*ln(1.03)
n = ln(20000) / ln(1.03)
n = 257.15
2010 + 257.15 = 2267 year , this population would be 400000.
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Describe in words where cube root of 24 would be plotted on a number line.
100 points and brainliest
Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.
Step-by-step explanation:
b. Which of these products has the same value as 4(12)? Select all that apply.
A.
8(6)
B.
76
C.
316
D.
12(4)
E.
124
Answer:
A and D
Step-by-step explanation:
8(6) means 8x6 so that's 48
and 12(4) is the same as 4(12) so that should be simple enough
Need help ASAP find the value of x in the triangle below
Answer:
x = 12
Step-by-step explanation:
Creating an equationAngles in a triangle add up to 180 degrees.
This means that 6x - 19 + 3x + 7 + 84 = 180
Solving for x6x - 19 + 3x + 7 + 84 = 180
==> combine like terms
9x + 72 = 180
==> subtract 72 from both sides
9x = 108
==> divide both sides by 9
x = 12
in 1950, the world population was 2560 million people. in 1960, the population was 3040 million people. assume that world population grows in constant relative proportion. (a) what is the relative growth rate, k? [3p] (b) use the model to predict the population in 2020.
(i) Relative growth rate, k = 48 million people/ year
(ii) Population in 2020 is given by 5920 million people.
Given that in 1950, the population of world was 2560 million.
In 1960, the population of world was 3040 million people.
Also it is mentioned that, world population grows in constant relative proportion.
So, the difference between time = 1960 – 1950 = 10 years
The growth in population = 3040 mil – 2560 mil = 480 million
So the relative growth rate of population is = 480/10 = 48 million/year
Now N be the new population, k be the relative population growth rate, all figures in millions. And t be the time in years passes since 1950.
Then the mathematical model is,
N = 2560 + kt
So for 2020, t = 2020-1950 = 70
k = 48
So, N = 2560+48*70 = 5920
So the population in 2020 is 5920 million people.
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(b) Write down the value of 12⁰
(c) Write down the value of 3-²
Answer:
b) 1 c) 0.1Step-by-step explanation:
b) The value of 12⁰ will be?
→ 12⁰ = ?
→ 12⁰ = 1
Hence, the solution is 1.
c) The value of (3)^(-2) will be?
→ (3)^(-2) = ?
→ (3)^(-2) = 0.1
Hence, the solution is 0.1.
Find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
6, (2, 8) 7, (2,10)
The equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
We know that the equation of a line with gradient m and y-intercept is:
y = mx + c.
We need to find the equation of each of the straight lines, given its gradient and the coordinates of a point on the line.
We know the point-slope form of equation of line,
(y - y1) = m(x - x1)
For m = 6 and (x1, y1) = (2, 8)
(y - 8) = 6(x - 2)
y - 8 = 6x - 12
y = 6x - 4
For m = 7 and (x1, y1) = (2, 10)
(y - 10) = 7(x - 2)
y - 10 = 7x - 14
y = 7x - 4
Therefore, the equation of the straight lines are:
For m = 6 and (x1, y1) = (2, 8) => y = 6x - 4
For m = 7 and (x1, y1) = (2, 10) => y = 7x - 4
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help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
HELP ME PLS IM STRUGGLING
1. If 1(-1) for the polynomial f(z) = 2z+z²-5 is-2, can you use the Factor Theorem to find the other factor?
No, because (x+1) is not a factor of the polynomial f(z) = 22 +2²-5,
Yes, because (x + 1) is a factor of all degree 4 polynomials.
No, because-2 is not an irrational number.
Yes, because-2 is the opposite of the leading coefficient of f(z) = 2x¹ +2²-5.
Answer: yes, because -2 is the opposite of the leading coefficient
Step-by-step explanation:
i took a sample of the grade point averages for students in my class. for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89. the standard error for the sample was:
The standard error for the sample was 0.13 when "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89."
What is standard error?The standard deviation of a statistic's sampling distribution, or an estimate of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean. By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.
Here,
The standard error=standard deviation/√number of samples
=0.65/√25
=0.65/5
=0.13
When "for the 25 students, the standard deviation of grade points was 0.65 and the mean was 2.89," the standard error for the sample was 0.13.
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Which of the following is(are) the solution(s) to |5x + 2| = 8 ?
Answer:
x = -2 ; x = 6/5
Step-by-step explanation:
5x + 2 >=0
5x >= -2
5/5 x >= -2/5
x >= -2/5
if x >= -2/5
5x +2 = 8
5x = 8 -2
5x = 6
5/5 x = 6/5
x = 6/5
if x < -2/5
-5x -2 = 8
-5x = 8+2
-5x = 10
-5/-5 x = 10/-5
x = -2