The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4.
a) What is the probability that a single student randomly chosen form all those taking the test scores 80 or higher?
b) What is the probability that the sample mean score of 64 randomly selected student is 80 or higher?
c) What is the probability the sample mean score of 64 randomly selected students is between 74 and 76?
Answer:
The appropriate solution is:
(a) 0.1056
(b) 0
(c) 0.9544
Step-by-step explanation:
The given values are:
Mean,
[tex]\mu = 75[/tex]
Standard deviation,
[tex]\sigma = 4[/tex]
(a)
⇒ [tex]P(x>80)=1-(x<80)[/tex]
[tex]=1-P[\frac{x-\mu}{\sigma} <\frac{80-75}{4} ][/tex]
[tex]=1-P[\frac{x-\mu}{\sigma} <\frac{5}{4} ][/tex]
[tex]=1-P(z<1.25)[/tex]
By using the table, we get
[tex]=1-0.8944[/tex]
[tex]=0.1056[/tex]
(b)
According to the question, the values are:
[tex]n[/tex] = 64
[tex]\mu_\bar{x}[/tex] = 75
Now,
⇒ [tex]\sigma_\bar{x}[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
= [tex]\frac{4}{\sqrt{64} }[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]0.5[/tex]
⇒ [tex]P(\bar {x} >80 ) = 1 - P(\bar x <80 )[/tex]
[tex]=1 - P[\frac{(\bar x-\mu_\bar x)}{\sigma \bar x} < \frac{80-75}{0.5} ][/tex]
[tex]=1-P(z<10)[/tex]
By using the table, we get
[tex]=1-1[/tex]
[tex]=0[/tex]
(c)
As we know,
⇒ [tex]\sigma_\bar x[/tex] = [tex]\frac{\sigma}{\sqrt{n} }[/tex]
= [tex]\frac{4}{\sqrt{64} }[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]0.5[/tex]
then,
= [tex]P(74< \bar x <76)[/tex]
= [tex]P[\frac{74-75}{0.5} < \frac{\bar x-\mu \bar x}{\sigma \bar x} < \frac{76-75}{0.5} ][/tex]
= [tex]P(-2<z<2)[/tex]
= [tex]P(z<2)-P(z<-2)[/tex]
By using the table, we get
= [tex]0.9772-0.0228[/tex]
= [tex]0.9544[/tex]
PLEASE HELPPPP select the expression that represents the following statement: Multiply 8 by 1 less than 5. (4 points)
Group of answer choices
(8 x 1) − 5
8 x (5 − 1)
1 − (8 x 5)
8 − (5 x 1)
By using PEDMAS rule, (8 x 1) − 5 is the expression represents the given statement.
What is PEDMAS rule?The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEDMAS: Parentheses, Exponents, Division and multiplication, Addition and Subtraction.
According to the question
Multiply 8 by 1 less than 5.
Rewriting the mathematical expression using order of operations using PEDMAS rule
= (8 x 1) − 5
(8 x 1) − 5 is the expression represents the given statement.
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Is the enlargement shown below a dilation…. Please I need help ASAP
Marcy will earn 3 rewards points for each movie she attends. Which equation represents the relationship between y, the total points and x the number of movies?
Answer:
y=3x
Step-by-step explanation:
An average human heart beats 60 times per minute. If an average person lives to the age of 75, how many times does the average heartbeat in a lifetime?
There should be ( ) heartbeats per lifetime.
(Enter your answer as a decimal number. Round to two decimal places.)
Answer:
The average number of beats in a lifetime would be 2,365,200,000
Step-by-step explanation:
To find the amount we need to take basic steps. The first step is multiplying the number of beats to find out how many are in an hour. Since there are 60 in a minute and 60 minutes in an hour, multiply the two.
60 beats * 60 minutes = 3,600 beats per hour.
Now multiply the amount of beats in an hour by the number of hours in a day.
3,600 * 24 hours = 86,400 beats per day
Now multiply the number of days in a year. Technically there is 365 1/4 in a year, but we'll use the flat rate of 365 since that is generally the accepted answer.
86,400 * 365 days = 31,536,000 beats per year
And now we take that number and multiply by the number of years that he lines
31,536,000 * 75 years = 2,365,200,00 beats in a lifetime
The heart beats 236,520, 000 times in a lifetime.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas. This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
An average human heart beats 60 times per minute.
Now, the amount of beats in an hour by the number of hours in a day.
= 3,600 x 24 hours
= 86,400 beats per day
Again, the amount of beats per year
= 86,400 x 365 days
= 31,536,000 beats per year
So, the heart beats
= 31,536,000 x 75 years
= 236,520, 000 beats in a lifetime
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Please answer this question!!!!!
Jacinta has 2 blue marbles , 4 red marbles and 5 green marbles in a bag, all the marbles are the same size, she will select one marbles from the marble from the bag without looking what is the possibility that Jacinta will choose the green marble
Jacinta has 2 blue marbles , 4 red marbles and 5 green marbles in a bag, all the marbles are the same size, she will select one marbles from the marble from the bag without looking what is the possibility that Jacinta will choose the green marble
The possibility that Jacinta will choose the green marble is 45.5%
What is probability?Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event.
Given that, Jacinta has 2 blue marbles, 4 red marbles and 5 green marbles in a bag, all the marbles are the same size,
We need to find the possibility that Jacinta will choose the green marble,
So, here we will use the concept of probability, probability tell us the chances of happening of an event.
The formula =
Probability = favorable outcomes / total outcomes.
Here, the favorable outcomes = green marble (5)
The total outcomes = total number of marbles = 5+4+2 = 11
So, P(getting the green marble) = 5/11 = 0.454545 = 45.5%
Hence, the possibility that Jacinta will choose the green marble is 45.5%
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Write an expression for each of these expressions:
A. Divide 36 by a
B. Subtract b from 55.
C. Add 18 to c.
D. Multiply 49 by d.
E. Divide e by 62
F. Subtract 71 from f.
es
Answer:
A. 36 ÷ a
B. 55 - b
C. 18 + c
D. 49 · d
E. e ÷ 62
F. f - 71
The population of a town grows uniformly at the rate of 4% every year. In how many years will the population of the town grow from 15,62,500 to 17,57,600?
Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.
What is percentage?A figure or ratio that is stated as a percentage of 100 is referred to as a percentage in mathematics. However, the percent symbol ("%) is usually used to denote it." The percent amount is flat. When the numerator is 100, percentages are really just fractions. Put the standard form (%) next to a number to show that it is a percentage. For instance, if you correctly respond to 75 out of questions in total on a test, you receive a 75% (75/100).
Here,
Given: 1757600 more people overall
Population as of now: 1562500
According to the issue,
=> 1562500[tex](1 + 4/100 )^{n}[/tex] = 1757600
=> [tex](26/25)^{n}[/tex] = 1757600/ 1562500
=> [tex](26/25)^{n}[/tex]= [tex](26/25)^{3}[/tex]
On comparing,
n=3
Therefore , the solution of the given problem of percentage comes out to be time n = 3 years.
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Keshawn is organizing textbooks on his bookshelf. He has a Spanish textbook, a biology textbook, a history textbook, and a writing textbook. How many different ways can he line the textbooks up on his bookshelf?
Answer: four textbooks
Step-by-step explanation:
*ANSWER TWO FOR BRAINLIEST*
Question 1 (multiple choice worth 4 points)
(08.05) Which of the following ordered pairs represents the solution to the system given below?
x - 4y = 7
5x + 9 = 6
A) (3, -1)
B) (3, 1)
C) (1, -3)
D) (-1, -3)
Question 2 (multiple choice Worth 4 points)
(08.05) Maria wants to solve the following system using the elimination method:
4x + 9y = 59
x + y = 17
What number should the equation x + y = 17 be multiplied by to eliminate y?
A) 4
B) -4
C) 9
D) -9
Answer:
why u delete the answer biro it was being record ...72+ comments
If I bought 3 shirts that cost the same and I got a coupon for 10 dollars off and I spent 65 altogether what equation can be used to find the cost of the shirt
Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period, while 1% of individuals living in the suburbs move to the city during a one-year period. Assuming that this process is modeled by a Markov process with two states: city and suburbs.
a. Prepare the matrix of transition probabilities.
b. Compute the steady-state probabilities.
c. In a particular metropolitan area, 40% of the population lives in the city, and 60% of the population lives in the suburbs. What population changes do your steady-state probabilities project for this metropolitan area?
Answer:
a) City Suburbs city 0.98 0.02 , Suburbs 0.01 0.99
b) 0.333 , 0.667
c ) Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population
Step-by-step explanation:
2% living within the city limits move to suburbs
1% living within the suburbs move to the city
a) Matrix of transition probabilities
City Suburbs city 0.98 0.02 , Suburbs 0.01 0.99
b) Steady -state probabilities
attached below
steady state probabilities = 0.333 , 0.667
c) Determine the population changes the steady-state probabilities
Using the steady-state probabilities, There will be an increase in the Suburb population and a decrease in City population i.e. a decrease from 40% to 33%
Reciprocal of following expression is *
3/5×(10+35/24)
Answer:
8/55
Step-by-step explanation:
The answer to that equation is 55/8, and the reciprocal is that improper fraction flipped.
The box plots below compare the number of points two basketball players scored per game over 25 games last season. WHich statement is supported by the information in the box plots above?
it's down there
Answer:
im not helping you cuz ur pfp
Step-by-step explanation:
Ayudaaaaa porfavor
Convertir las unidades de medida
8 000 m = _______ km
4 000 g = _______ kg
3 000 m = ________ km
7 m = _________ cm
30 mm _________ cm
10 cm ________ mm
70 mm ___________ cm
10 L = ____________ ml
800 cm = _________ m
6 kg = __________ g
Considering as a side of ∆CBD, express its length in terms of variables representing side lengths and angle measures in ∆CBD. Show your work.
The value of the common length BD would be 8 units, approximately.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The AD line is perpendicular to the line AC.
The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
So, We know that
Sin A = BD / AB
Sin A = BD / c
c Sin A = BD
Substitute angle A = 53.13 and c = 10.
BD = (10) Sin (53.13)
BD = 10 (0.79)
BD = 7.99
BD ≈ 8
The question was incomplete, but the complete question is given below.
Considering line BD as a side of ABD, express its length in terms of variables representing side lengths and angle measures in ABD. Show your work.
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Solve by factoring
-3x^2-11x+2=0
Answer:
x = -11, 2/3
Step-by-step explanation:
-3x^2-11x+2=0
-(3x^2+11x-2) = 0
3x^2 + 11x - 2 = 0
3x^2 + 33x - 22x - 2 = 0 ==> 33-22=11 and 33/11=3 and -22/11=-2
3x(x + 11) - 2(x + 11) = 0 ==> factor
(3x - 2)(x + 11) = 0
3x - 2 = 0 x + 11 = 0
3x = 2 x + 11 - 11 = 0 - 11
{ x = 2/3 x = -11 } ==> x = -11, 2/3
To order tickets online to a hockey game
Answer:
I'm not quite sure what the question is here but in order to buy tickets to a hockey game, you can type the hockey team or game into the web browser and select their website then select the time and dates you'd like to see the game
Hope this helps!
Larry graphs the inequality x less-than negative 5 using the steps below.
Step 1: Draw a number line, and place an open circle at –5.
A number line going from negative 10 to 0. An open circle is at negative 5.
Step 2: Shade to the left of –5 to represent less than –5.
A number line going from negative 10 to 0. An open circle is at negative 5. Everything to the left of the circle is shaded.
Step 3: Check work by substitution.
x = negative 5
Negative 5 less-than negative 5 False
Larry concludes that he must have shaded the number line in the wrong direction. Which best describes the situation?
Larry’s graph is incorrect. He should have used a closed circle at –5.
Larry’s graph is incorrect. He should have shaded to the right of –5 because the numbers less than –5 are to the right of –5.
Larry’s graph is correct. He should have checked his work using a number to the left of –5.
Larry’s graph is correct. He should have checked his work using a number to the right of –5.
Mark this and return Save and Exit Next Submit
Answer:
D
Step-by-step explanation:
James divides a piece of poster board into equal sections and uses the shaded sections for an art project
The value of a sculpture is $950. The value increases by 15% a year. Find the value in 8 years.
Answer:
1,140
Step-by-step explanation:
because first you have to cross multiply the 15*950 and then divide it by 100 and you get 1,140
please make me brainist lol
4-56 Determine the magnitude of the moments of the force F about the x. y, and z axes Solve the problem (a) using a Cartesian vector approach and (b) using a scalar approach
(a) As of the Cartesian vector approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].
(b) Using a scalar approach, Moment about axes are [tex]M_x = 13\ Ft-lb[/tex], [tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex].
What is a vector?Vector is defined as the quantities that have both magnitude and direction is called a vector quantity and the nature of the quantity is called a vector.
here,
[tex]\vec F = 4 \hat i + 12\hat j -3 \hat k\\ \vec B = 4 \hat i + 3\hat j - 2 \hat k\\[/tex]
Scalar approach,
moment about the x-axis is given by,
[tex]M_x = B_yF_z - ZF_y\\M_x = 3(-3)-(-2)(12)\\M_x = 13\ Ft-lb[/tex]
Similarly,
[tex]M_y = 4\ Ft-lb,[/tex] and [tex]M_z = 36\ Ft-lb[/tex]
Vector approach,
Moment about the x-axis is given by,
[tex]M_x = U_x \times[ {\vec B \times \vec F]}\\M_x = \left[\begin{array}{ccc}1&0&0\\4&3&-2\\4&12&-3\end{array}\right][/tex]
The above expression given is of determinate, when solving the above determinate,
[tex]M_x = 13\ Ft-lb[/tex]
Similarly,
[tex]M_y = 4\ Ft-lb[/tex] and [tex]M_z = 36\ Ft-lb[/tex],
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Need help plz need to turn in before 12?!?!?!
Answer:
C = π (4yd)
C = 12.6yd
Step-by-step explanation:
Translate the sentence into an equation.
Five times the sum of a number and 9 equals 3.
Use the variable y for the unknown number.
Answer: To translate the given sentence into an equation, we can start by replacing the words "five times the sum" with the mathematical expression "5(x + 9)". Then, we can replace the word "number" with the variable y, to get:
5(y + 9) = 3
Next, we can distribute the 5 to obtain:
5y + 45 = 3
Finally, we can subtract 45 from both sides to solve for y:
5y = -42
y = -42/5
y = -8.4
Therefore, the equation that represents the given sentence is y = -8.4.
Step-by-step explanation:
Mr. Hughes gave 5/14
of his savings to his son, 2/3 of the remainder to his daughter, and the rest to his wife.
If his wife got $900, what were his savings?
Answer:
His savings were of $4,200.
Step-by-step explanation:
Mr. Hughes gave 5/14 of his savings to his son, 2/3 of the remainder to his daughter, and the rest to his wife:
This means that the son and daughter amount is:
[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14})[/tex]
As [tex]\frac{9}{14}[/tex] is the remained that his son did not get. So
[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14}) = \frac{15}{42} + \frac{18}{42} = \frac{33}{42}[/tex]
Fraction his wife got:
[tex]1 - \frac{33}{42} = \frac{42}{42} - \frac{33}{42} = \frac{9}{42}[/tex]
If his wife got $900, what were his savings?
Total savings are x, wife got [tex]\frac{9}{42}[/tex] of x. So
[tex]\frac{9x}{42} = 900[/tex]
[tex]9x = 900*42[/tex]
[tex]x = \frac{900*42}{9}[/tex]
[tex]x = 100*42[/tex]
[tex]x = 4200[/tex]
His savings were of $4,200.
How many whole months will it take for a motorbike valued at £2550 to depreciate to less than £1200 if depreciation is at a rate of 5% per month?
It will take roughly 15.7 months to drop in value to less than £1200 if the current value of the bike is £2550.
How to find the present value of bike?You can use the following formula to calculate how many months it will take for a motorbike with a value of £2550 value to drop to under £1200:
n = (1200 - 2550) ln / ln (1 - 0.05)
Where 0.05 denotes the 5% monthly depreciation rate, ln is indeed the natural logarithm function, and n refers to the number of months.
When we enter the values, we will get:
n = (1200 - 2550 - 1 - 0.05) / ln(1 - 0.05) = about 15.7 months
The motorcycle will take approximately 15.7 months to drop in value to less than £1200.
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Describe the error in each problem below. 36÷3+(3²•2)36÷3+9•2 36÷12•2 3•2 6
Answer:
Step-by-step explanation:
In the last part of the problem, you have to follow PEMDAS.
Instead of you added before dividing. After the step of 36÷3+9x2 you have to divide.
AMERICA EATS 350 PIZZA SLICES EVERY SECOND HOW MANY DO THEY EAT IN HALF IN HOUR
630,000
Step-by-step explanation:
350x60=21,000
21,000x30=630,000
3 times a number minus 12 is equal to
5 times the number plus 15,
Find the number,
Answer:
-13.5
Step-by-step explanation:
take number as x
3x-12=5x+15
-2x=27
x=27/-2
x=-13.5