Assume that the random variable X is normally distributed, with mean =60 and standard deviation=8 Compute the probability P(X < 75).
Answers
The probability that X is less than 75 P(X < 75) is approximately 0.9693, or 96.93%.
What is probability?
To compute the probability P(X < 75) when X is normally distributed with mean = 60 and standard deviation = 8, we need to standardize the value 75 and then use a standard normal distribution table or calculator to find the corresponding probability.
The standardized value of 75 is:
z = (75 - 60) / 8 = 1.875
Using a standard normal distribution table or calculator, we can find that the probability of a standard normal variable being less than 1.875 is approximately 0.9693.
Therefore, P(X < 75) = P(Z < 1.875) = 0.9693, where Z is a standard normal variable.
So the probability that X is less than 75 is approximately 0.9693, or 96.93%.
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Related Questions
What's the simplified expression of -2a-3 bº?
Answers
Answer:
-2a - 3
Step-by-step explanation:
bº equals 1 due to the zero exponent.
Thus, -2a-3 bº simplifies to -2a - 3.
Answer:
−2/a^3
Step-by-step explanation:
MATH PLEASE HELP
Paul wants to put a fence around his vegetable garden in the backyard. The price of fencing is $1.65 per linear foot. Given a diagram of his vegetable garden below, how much will it cost him for the fencing?
Answers
Answer:
$122.10Step-by-step explanation:
Note cm is changed to ftPerimeter of the garden:
P = 2(14 + 23) = 74 ftThe price of fencing:
74*$1.65 = $122.10Rewrite in logarithmic form 19^2 = 361
Answers
Answer:
\(\log_{19}{361}=2\)
Step-by-step explanation:
We know that taking logarithms performs the transformation ...
\(b^e=x\\\\e\cdot\log{b}=\log{x}\quad\text{take logs}\\\\e=\dfrac{\log{x}}{\log{b}}\quad\text{divide by $\log{b}$}\\\\\log_b{x}=e\quad\text{use the change of base formula}\)
Then for b=19, e=2, x=361, we have
\(\boxed{\log_{19}{361}=2}\)
Given =(5,-2, 3) and >= (1, 1, 2) find an ordered triple that represents 3u - 2v.
Answers
The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).
To find an ordered triple representing \(3u - 2v\),
where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),
we can perform the following operations:
\(3u = 3(5, -2, 3)\)
\(3u = (15, -6, 9)\)
\(2v = 2(1, 1, 2)\)
\(2v = (2, 2, 4)\)
Now, subtracting 2v from 3u gives:
\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)
\(3u - 2v = (15-2, -6-2, 9-4)\)
\(3u - 2v = (13, -8, 5)\)
Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).
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A scientist is monitoring cell division and notes that a single cell divides into 4 cells within one hour. During the next hour, each of these cells divides into 4 cells. This process continues at the same rate every hour. What type of function could be used to represent this situation?
Answers
As a result, the functiοn that represents this situatiοn is \($y=4^{x}$\), where x is the number οf hοurs since the οbservatiοn began.
What is functiοn?In mathematics, a functiοn appears tο be a relatiοnship amοng twο οf the numerical sets where each member οf the οriginal set (knοwn as the dοmain) is assοciated with a particular member οf the third part (called the range). In οther wοrds, a functiοn takes input by οne set and prοvides pοwer frοm anοther.
The attribute x has frequently been used tο represent inputs, and the variable y has been used tο represent οutputs. A methοdοlοgy οr a graph can be used tο represent a functiοn. Fοr example, the fοrmula y = 2x + 1 represents a linear mοdel whereby each x-value yields a unique value οf y.
This situatiοn cοuld be represented by an expοnential functiοn.
Starting with a single cell, we have fοur cells after οne hοur and fοur cells after twο hοurs. We have 4 x 4 x 4 = 64 cells after three hοurs.
\($y=a*b^{x}$\)
where y represents the number οf cells, x represents the number οf hοurs, and a and b represent cοnstants. In this case, an is 1 (because we start with οne cell) and b is 4. (since each cell divides intο 4 cells). As a result, the functiοn that represents this situatiοn is:
\($y=4^{x}$\)
where x is the number οf hοurs since the οbservatiοn began.
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GIVING BRAIN LIST
Hiroko wants to know how much money students in her school band typically spend on their instruments. She plans to survey a sample of the population. Will each approach result in a sample that is representative of the population? Explain Please! Thank You!
Answer the following 3 questions from a to c.
Thanks Again!
a. Surveying all of the flute players in the band
b. Surveying all band members whose first names start with J or M
c. Surveying two band members from each school in her city
Answers
Answer:
Option C would be better than the others.
Step-by-step explanation:
She wants to learn about band members from a sample of the population. Option a isn't enough because flute players aren't the only ones who should be surveyed, she needs to know about all band members. B isn't right, it isn't logical to just survey people with names starting with J or M. So, c would be just right since she's surveying 2 band members from each school so she would get information from a sample of the population and not just from her school.
The instructor noted the following scores on the last quiz of the semester for 8 students. Find the range of this data set 59,61,83,67,81,80,81,100
Answers
answer: the range is 41.
to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.
then we subtract the minimum from the maximum.
59 - 100 = 41.
1A ball is launched vertically upward at 19.6
meters per second from a 102.9 meter tall
building. The height of the ball is modeled by the
function f(t) = -4.0t² + 19.6t + 102.9. How many
seconds after launch does the ball strike the
ground?
Answers
The time after which the ball strike the ground is \(t = \frac{49(5+\sqrt{5}) }{100}\) or;\(t = \frac{49(5-\sqrt{5}) }{100}\) seconds.
The speed of the ball when launched vertically upward is 19.6 m/s².
The acceleration of the ball, g = - 9.8 m/s²
The final velocity of the ball will be 0 m/s since the ball will reach the maximum height and the ball stops.
u = 0 m/s
Using the equation of motion,
v² = u² + 2as
v² = u² + 2(-g)s
v² = u²- 2gh
( 19.6 )² = 0 - 2(10)h
384.16 = -20h
h = - 19.208 m
Therefore, the total height reached by the ball is 102.9 + 19.208 = 122.108 m
Now, the function for the height of the ball is:
f(t) = - 4t² + 19.6t + 102.9
122.108 = - 4t² + 19.6t + 102.9
- 4t² + 19.6t + 102.9 - 122.108 = 0
- 4t² + 19.6t - 19.208 = 0
4t² - 19.6t + 19.208 = 0
Multiplying by 1000 on each side of the equation.
4000t² - 19600t + 19208 = 0
Solving the quadratic equation,\(t =[\frac{ - ( - 19600 ) \pm \sqrt{(-19600)^{2}-4(4000)(19208)} }{2(4000)} ]\)
Therefore,
\(t = \frac{49(5+\sqrt{5}) }{100}\) or;
\(t = \frac{49(5-\sqrt{5}) }{100}\)
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this week Jada bought a 3 1/2 pound of cat food. her cat eats 5/8 of a pound each day. show your work and remember to include units. check your work with multiplication
Answers
Answer:
5 days.
Step-by-step explanation:
The food will last her 5 days.
\(3\frac{1}{2}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}-\frac{5}{8}\)
\(=1\frac{5}{8}-\frac{5}{8}-\frac{5}{8}\)
\(=1-\frac{5}{8}\)\(=\frac{3}{8}\)
3 1/2 cups as a multiplication expression using the unit 1 cup
Answers
Answer:
4 1/2
Step-by-step explanation:
From a population of 200,000,000 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is
Answers
Answer:
The standard error of the mean = 2
Step-by-step explanation:
Given that:
The standard deviation σ = 14
The sample size n = 49
The sample mean \(\overline x\) = 56
The formula for calculating the standard error can be expressed as:
\(S.E = \dfrac{\sigma}{\sqrt{n}}\)
\(S.E = \dfrac{14}{\sqrt{49}}\)
\(S.E = \dfrac{14}{7}\)
S.E = 2
Therefore, the standard error of the mean = 2
The residual plot shows the residuals for the day of the month and the amount in Kali’s checking account. Which statement best assesses the linearity of the relationship between the day of the month and account balance if the scatterplot appears to be reasonably linear?
A) Because the residual plot has an obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.
B) Because the residual plot has an obvious pattern, and the scatterplot appears linear, it is not appropriate to use the line of best fit to predict the account balance based on the day of the month.
C) Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.
D) Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is not appropriate to use the line of best fit to predict the account balance based on the day of the month.
Answers
The best assessment of the linearity of the relationship between the day of the month and account balance would be "Because the residual plot has no obvious pattern, and the scatterplot appears linear, it is appropriate to use the line of best fit to predict the account balance based on the day of the month."The correct answer is option C.
When assessing linearity, it is important to examine both the scatterplot and the residual plot. The scatterplot is used to visualize the relationship between the variables, while the residual plot helps us assess the appropriateness of a linear model by examining the pattern of the residuals (the differences between observed and predicted values).
If the scatterplot appears reasonably linear, it suggests that there is a linear relationship between the variables. In this case, since the scatterplot appears linear, it supports the use of a linear model to predict the account balance based on the day of the month.
Furthermore, the residual plot is used to check for any patterns or systematic deviations from the line of best fit. If the residual plot exhibits no obvious pattern and the residuals appear randomly distributed around zero, it indicates that the linear model captures the relationship adequately.
Therefore, if the residual plot shows no obvious pattern, it provides further evidence in favor of using the line of best fit to predict the account balance based on the day of the month.
In conclusion, when the scatterplot appears linear and the residual plot shows no obvious pattern, it is appropriate to use the line of best fit to predict the account balance based on the day of the month.
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Answer:
person above
Step-by-step explanation:
the obvious
Use implicit differentiation to find an equation of the tangent line to the curve
sin(x+y)=4x−4y at the point (π,π)
Answers
Answer:
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
Step-by-step explanation:
o find the equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) using implicit differentiation, we can follow these steps:
Differentiate both sides of the equation with respect to x:
cos(x+y) * (1 + dy/dx) = 4 - 4dy/dx
Simplify by grouping the terms with dy/dx on one side and the rest on the other side:
cos(x+y) * (1 + dy/dx) + 4dy/dx = 4
Substitute x = π and y = π, since we want to find the equation of the tangent line at the point (π,π):
cos(2π) * (1 + dy/dx) + 4dy/dx = 4
Simplify:
-5dy/dx = 4 - cos(2π)
dy/dx = -4/5
Use the point-slope form of the equation of a line to write the equation of the tangent line:
y - π = (-4/5)(x - π)
Simplify:
y = (-4/5)x + (8/5) + π
The equation of the tangent line to the curve sin(x+y) = 4x - 4y at the point (π,π) is y = (-4/5)x + (8/5) + π.
The United States Senate Committee on Commerce, Science, and Transportation consists of 23 members, 12 Republicans and 11 Democrats. The Surface Transportation and Merchant Marine Subcommittee consists of 8 Republicans and 7 Democrats. How many ways can members of the Subcommittee be chosen from the Committee?
Answers
The number of ways members of the Subcommittee can be chosen from the Committee is 12,077,462,720.
What is number?Number is a mathematical object used to count, measure, and label. It is a concept used in math, science, and everyday life. Number has been around since the dawn of time and is an integral part of the universe. Numbers can be used to identify objects, measure quantities, and understand relationships between things. They are also used to represent abstract concepts, such as money, time, and space. Numbers can be used to solve problems and make decisions.
The number of ways members of the Subcommittee can be chosen from the Committee is equal to the number of combinations of 8 Republicans and 7 Democrats out of the total 23 members. This can be calculated using the combination formula, which is:
C(23, 8) x C(15, 7) = 12,077,462,720
The combination formula is defined as C(n,r) = n!/(r!(n-r)!), where n is the total number of members in the Committee (23) and r is the number of Republicans and Democrats from the Subcommittee (8 and 7, respectively). In this case, the n! term is equal to 23!, which is 8,314,814,080, and the r! term is equal to 8! x 7!, which is 40,320. Therefore, 12,077,462,720 is the total number of ways members of the Subcommittee can be chosen from the Committee.
This number can also be interpreted as the number of possible permutations of the 8 Republicans and 7 Democrats within the Subcommittee. This means that there are 12,077,462,720 ways to assign the 8 Republicans and 7 Democrats to the Subcommittee, without changing the number of Republicans and Democrats in the Subcommittee.
In conclusion, the number of ways members of the Subcommittee can be chosen from the Committee is 12,077,462,720. This number can be calculated using the combination formula, and it represents the number of possible permutations of the 8 Republicans and 7 Democrats within the Subcommittee.
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Jim bought a new freezer last winter. When he plugged it in at noon the temperature
inside the freezer was 21°C. That night the temperature inside the freezer was -15°C. By
how many degrees Celsius did the temperature change?
Answers
Answer:
The temperature inside the freezer dropped 36°C.
Step-by-step explanation:
You need to subtract the new temperature from the old temperature to get the difference. That's a pretty cool freezer! (Pun intended!)
I hope this helps!
Any tips for a gaming addicted brother? :-/
Answers
Answer:
Step-by-step explanation:
I would take his phone for a bit and also reduce screen time to 6 hours a week at MOST. It would help a lot.
Tony is 5 years older than Noelle. In 2 years the sum of their ages will be 69. How old is Tony now?
Answers
Solution:
Note that:
T = 5 + NT + 2 + N + 2 = 69Substitute the given values into the equation.
T + 2 + N + 2 = 69=> 5 + N + 2 + N + 2 = 69=> 2N + 9 = 69=> 2N = 69 - 9=> 2N = 60=> N = 30=> T = 5 + 30=> T = 35Tony is 35 years old.
Una sala de cine de New York vende las entradas para niños a 3 dólares y las de los adultos a 5 dólares. Si para ver una película pueden ingresar tanto niños como adultos y en un día
ingresan 345 espectadores, recaudando por concepto de venta de boletas 1365 dólares. Se
puede afirmar que el número de niños y adultos que ingresaron fue:
Answers
A la sala de cine ingresaron 180 niños y 165 adultos.
¿Cuántos niños y adultos ingresaron a una sala de cine?
De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:
3 · x + 5 · (345 - x) = 1365
Donde x es el número de niños que asistieron a la sala de cine.
Ahora despejamos la variable correspondiente mediante propiedades algebraicas:
3 · x + 1725 - 5 · x = 1365
1725 - 2 · x = 1365
2 · x = 1725 - 1365
2 · x = 360
x = 180
Ahora, el número de adultos es:
y = 345 - 180
y = 165
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6. The California Tiger Salamander is an endangered species, which decreases at the rate of 4.6% per year in a habitat that currently has 60 of them. Write an exponential function and find how many California Tiger Salamanders will be left after 4 years.
7. Factor and solve the following equation 2x2 + x - 21 = 0.
8. Alvin throws the football to a receiver who jumps up to catch the ball. The height of the ball over time can be represented by the quadratic equation -4.9t2 + 7.5t + 1.8 = 2.1 . This equation is based on the acceleration of gravity -4.9 m/s2, the velocity of his pass is 7.5 m/s and releases the football at a height of 1.8 meters, and the height where the receiver catches the ball of 2.1 meters. Put the equation in standard form and then solve by using the quadratic equation.
9. Examine the graph of f(x) and the table that contains values of g(x). Which function has a greater rate of change over the interval [0,2]? Explain your answer.
Answers
\(\rule{2000pt}{1000000pt}\)
Simplify this expression:2x + 3 – (5 – 6x).
Answers
Answer:
8x - 2
Step-by-step explanation:
2x + 3 - (5 - 6x) ← distribute parenthesis by - 1
= 2x + 3 - 5 + 6x ← collect like terms
= (2x + 6x) + (3 - 5)
= 8x + (- 2)
= 8x - 2
Please A milligram is a small unit of measure for mass in the metric system. There are 1,000 milligrams in 1 gram. btw
Which amount is greater than 12 grams?
1,200 milligrams
1,300 milligrams
12,000 milligrams
13,000 milligrams
Answers
Answer:n the metric system, "milli" means 1/1,000 and "kilo" means 1,000. This means that a milligram is 1/1,000 of a gram, and a kilogram is 1,000 grams. So a kilogram is much heavier than a milligram; in fact, a kilogra
Step-by-step explanation:
Suppose the function h(x) = 2x - 9 is translated up 5 units to become a new function,
Xx). What's the equation of the new function?
A) x) = 7x-4
B)(x) = 2x - 14
C)(x) = 7x-9
D) (x)=2x-4
Answers
According to the given data the equation of the new function is (D) f(x) = 2x - 4.
What is meant by equation?An equation is a mathematical statement that indicates that two expressions are equal. It contains an equals sign "=" and may involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponentiation, etc.
According to the given information:If we translate the function h(x) = 2x - 9 up by 5 units, the new function f(x) will have the form:
f(x) = h(x) + 5
Substituting the definition of h(x) into this equation, we get:
f(x) = 2x - 9 + 5
Simplifying, we have:
f(x) = 2x - 4
Therefore, the equation of the new function is (D) f(x) = 2x - 4.
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Write 6^4 in expanded form. Then evaluate.
Answers
Answer:
expanded form: 6x6x6x6
answer: 1296
Step-by-step explanation:
Country A has an exponential growth rate of 4.3% per year. The population is currently 4,079,000, and the land area of Country A is 19,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answers
The number of years it would it take for there to be one person for every square yard is 108,325.68 years.
How many years would it take for there to be one person for every square yard?When there is one person for every square yard, it means that the population and land area are equal in value.
Number of years = (In FV / PV) / r
FV = future populationPV = present populationr = rate of growth(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years
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\(2\frac{2}{5}\)
![[tex]2\frac{2}{5}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/nSZSZg3zmCUNAEMOQdOssFzMEjvuV4vy.png)
Answers
A fraction is a way to describe a part of a whole. The decimal form of 2 2/5 is 2.4.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The decimal form of 2 2/5 can be written as,
2 2/5 = 2 + 2/5 = 2 + 0.4 = 2.4
Hence, the decimal form of 2 2/5 is 2.4.
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Help me please I need to do it faster
Answers
Answer:
0.25M + 0.75B + 1.25C - 50 = total money raised
Step-by-step explanation:
0.25 for each muffin so if 78 are sold we do 78*0.25 = 19.5
0.75*56 = 42 for brownies
1.25*30 = 37.5
19.5+42+37.5 = 99
99 -50 = 49
if there are 18 triangles in a polygon how many sides has the polygon
Answers
The number of sides of a polygon that has 18 triangles would be 20 sides.
How to find the number of sides ?To determine the number of sides in a polygon consisting of 18 triangles, we can calculate the sum of the interior angles. Each triangle has total interior angle sum of 180 degrees, and since there are 18 triangles, the sum of those angles would be 18 multiplied by 180, which comes to 3, 240 degrees.
Applying the given formula for calculating the interior angles of a polygon, we obtain that (n - 2) multiplied by 180 stands for the sum of all angles within it, with n being the number of sides.
Hence, rearranging the equation gives n :
n = (sum of interior angles ÷ 180) + 2
n = (3240 ÷ 180) + 2 = 20
There must be precisely 20 sides in that particular polygon.
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an isosceles triangle has an angle of 9x+1 and another of 88, find x
Answers
Answer:
Step-by-step explanation:
2(9x+1)+88=180
9x+1+44=90
9x=90-45=45
x=5
Rodrigo's hair is 10 2/7 inches long. The barber trims 1/4 inch. About how long is his his hair now ?
Answers
10/27 - 1/4 = 10.03 in decimals.
help me please
The water pressure on a submerged object is given by P = 64d, where P is the pressure in pounds per square foot, and d is the depth of the object in feet.
a. solve the formula for d.
b. Find the depth of a submerged object if the pressure is 672 pounds per square foot.
Answers
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
What is a function?A function can be defined as an expression, law or rule that shows the relationship between two variables.
Given the role as;
P = 64d
Where;
P stands for pressure in pounds per square foot.
The object's depth, d, is expressed in feet.
Now let's center the formula on the variable "d."
Both sides of the equation are divided by the variable "d64-based "'s coefficient. This is carried out so that the variable can stand on its own.
We have.
P/64 = 64d/64
d = P/ 64
If there is pressure, P is equivalent to 672 pounds per square foot.
When the value of the variable is inserted into the formula, we obtain;
d = P/64
Then,
d = 672/64
Discover the quotient.
d = 10. 5 ft.
Therefore,
The water pressure on a submerged object is given by P = 64d, then the value d is 10.5 feet.
a. D = P/64 is the solution to the formula's "d" subject.
b. The depth of a submerged object at a pressure of 672 pounds per square foot is 10. 5 feet.
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