Answer:
86.64%
Step-by-step explanation:
We solve for the above question using z score formula
z score formula = z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
For x = 350, μ = 500, σ = 100
z score = 350 - 500/100
= -150/100
= -1.5
Using the z score for normal distribution
Probability (z = -1.5) = P(x = 350).
= 0.066807
For x = 650, μ = 500, σ = 100
z score = 650 - 500/100
= 150/100
= 1.5
Using the z score for normal distribution
Probability (z = 1.5) = P(x = 650).
= 0.93319
The probability of people who write this exam and obtain scores between 350 and 650
P < 350 < x < 650 = P(x ≤ 650) - P(x ≤ 350)
= P(z = 1.5) - P(z = -1.5)
= 0.93319 - 0.066807
= 0.866383
Therefore, the percent of people who write this exam and obtain scores between 350 and 650 is
0.866383 × 100
= 86.6383%
Approximately ≈ 86.64%
1. The number of pizzas consumed per month by university students is normally distributed with a mean of 12 and a standard deviation of 4. What is the probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month?
Answer:
0.00621
Step-by-step explanation:
To solve for this question: we would be making use of the z score formula.
z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation
Step 1
Find the Standard Error
From the above question, we are given number of samples, hence, the standard deviation we would use for our z score is Standard error.
Standard error = Standard deviation/√n
Where n = number of samples = 25
Standard deviation = 4
Standard error = 4/√25
= 4/5
= 0.8
Step 2
Calculate the z score
Since we are given number of samples in the question,
z score = z = (x - μ)/σ
where
x is the raw score = 14
μ is the population mean = 12
σ is the standard error = 0.8
z score = 14 - 12/0.8
z score = 2.5
Step 3
We find the Probability.
The probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is calculated as:
We find the Probability of the Z score 2.5 using a Z table.
P(z = 2.5) = P(x ≤ 14) = 0.99379
P(x > 14) = 1 - P(x<14)
= 1 - 0.99379
= 0.0062097
Approximately ≈ 0.00621
Therefore, the probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is
0.00621
A 92-ft tree casts a shadow that is 120 ft long. What is the angle of elevation of the sun?
Answer:
The angle of elevation of the sun is 38°
Step-by-step explanation:
We can set up the diagram for the the question by interpreting it, you can check the diagram at the attached file.
We can see that after the interpretation of the question we arrived at a triangle,. Where the vertical side represent the 92-ft. which is the height of the tree and the horizontal side represent the 120 ft. which is the shadow's lenght. Then the angle of elevation of the sun can ba calculated using tangent ratio, from our knowledge of trigonometry
Tan(θ )= opposite/adjacent
Where our opposite =92ft
Adjacent= 120ft
Tan(θ ) =92/120
θ =tan-1( 92/120)
θ = 37.48°
Therefore, the angle of elevation of the sun If we round up our decimal value to the nearest 10th, we have θ = 38°
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answer:
change f(x) to y, switch x and y, and solve for y
y = √(x -4)
x = √(y - 4)
x² = y - 4
x² + 4 = y
y = x² + 4
f⁽⁻¹⁾ = x² + 4, where x ≥ 4
is it possible to roll a six sided number cube to generate a set of ten ordered pairs and have it graph a function?
Answer:
maybe
Step-by-step explanation:
It depends on your strategy for determining ordered pairs.
A straightforward interpretation of the problem would say 1 roll gives an x-value, and the next roll gives the corresponding y-value. If that is the strategy, in 10 rolls, there will be repeats of the x-value. So, the pairs cannot represent a function.
__
If you adopt a different strategy, such as using the rolled number as the tens digit of the x-value, and sequentially assigning the numbers 0 to 9 to the units digit of the x-value, then all of the x-values will be different. Regardless of how you arrive at the y-values, the result will always be a function when graphed.
__
Basically, any strategy that makes it likely that the x-values will be different makes it likely that the relation will be a function. Otherwise, it is unlikely (or impossible) that the relation will be a function.
Is the a discrete random variable, a continuous random variable, or not a random variable? response to the survey question "Did you smoke in the last week?" A. It is a discrete random variable. B. It is a continuous random variable. C. It is not a random variable.
Answer:
The correct answer is:
It is a discrete random variable. (A)
Step-by-step explanation:
Discrete Random Variables are variables that have distinct values. The number of variables that can be taken on can be counted. in this example, the variables to the question Did you smoke in the last week? is one of two possibilities; yes or no. Apart from these two values, there is no other possibility for the variables, hence it is a discrete random variable
Continuous Random Variables are values that can take on any value between distinct values, even up to infinity. The number of values that the variables can take on cannot be counted or listed. For example, is there are variables for the possible temperature that a particular city can take on in a day, the values are continuous random variables because the values do not have any distinct value, and the possibilities cannot be counted. the possibilities can be; anywhere between 20°C to 50°C. between these two, temperatures, you can have infinite possibilities; 20.1, 30.5, 40.8, etc. Hence the values cannot be counted, it is thus a continuous random variable.
Answer:
c not random variable
Step-by-step explanation:
what is the greatest common factor of 60 , 8
Answer:
4
Step-by-step explanation:
The factors of 8 are 1, 2, 4, and 8.
60 is not divisible by 8, but it is divisible by 4: 4 * 15 = 60. So the GCF of 60 and 8 is 4.
Using the number 98,045,132.706
(a) The digit 8 is in the
place.
(b) The digit 3 is in the
place.
Answer:
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
Step-by-step explanation:
Given:
98,045,132.706
9 is in the ten million position
8 is in the one million position
0 is in the hundred-thousand position
4 is in the ten-thousand position
5 is in the one-thousand position
1 is in the hundred position
3 is in the tens position
2 is in the one position
. Decimal
7 is in the tenth position
0 is in the hundredth position
6 is in the thousandth position
Therefore,
A. The digit 8 is in the place one million position
B. The digit 3 is in the place tens position
Let y = (2 6) and u = (7 1). Write y as the sum of a vector in Span(u) and a vector orthogonal to .
The question is missing. Here is the complete question.
Let y = [tex]\left[\begin{array}{ccc}2\\6\end{array}\right][/tex] and u = [tex]\left[\begin{array}{ccc}7\\1\end{array}\right][/tex]. Write y as the sum of a vector in Span(u) and a vector orthogonal to u.
Answer: y = [tex]\left[\begin{array}{ccc}\frac{21}{10} \\ \frac{3}{10} \end{array}\right] + \left[\begin{array}{ccc}\frac{-1}{10}\\ \frac{57}{10} \end{array}\right][/tex]
Step-by-step explanation: The sum of vectors is given by
y = [tex]y_{1}[/tex] + z
where [tex]y_{1}[/tex] is in Span(u);
vector z is orthogonal to it;
First you have to compute the orthogonal projection [tex]y_{1}[/tex] of y:
[tex]y_{1}[/tex] = proj y = [tex]\frac{y.u}{u.u}.u[/tex]
Calculating orthogonal projection:
[tex]\left[\begin{array}{c}2\\6\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}9\\6\end{array}\right][/tex]
[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex].[tex]\left[\begin{array}{c}7\\1\end{array}\right][/tex] = [tex]\left[\begin{array}{c}49\\1\end{array}\right][/tex]
[tex]y_{1} = \frac{9+6}{49+1}.u[/tex]
[tex]y_{1} = \frac{15}{50}.u[/tex]
[tex]y_{1} = \frac{3}{10}.u[/tex]
[tex]y_{1} = \frac{3}{10}.\left[\begin{array}{c}7\\1\end{array}\right][/tex]
[tex]y_{1} = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]
Calculating vector z:
z = y - [tex]y_{1}[/tex]
z = [tex]\left[\begin{array}{c}2\\6\end{array}\right] - \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right][/tex]
z = [tex]\left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]
Writing y as the sum:
[tex]y = \left[\begin{array}{c}\frac{21}{10} \\\frac{3}{10} \end{array}\right] + \left[\begin{array}{c}\frac{-1}{10} \\\frac{57}{10} \end{array}\right][/tex]
graph the inequality 7< y -3x < 11
Answer:
X=5 Y=-4
Step-by-step explanation:
To determine customers opinion of their pricing, Home Depot randomly selects 60 check out lines during a certain week and surveys all customers in the check out line.
What type of sampling is used?
A. Systematic
B. Stratified
C. Convenience
Answer:
Cluster sampling
Step-by-step explanation:
The sampling technique used by Home Depot to select randomly 60 check out lines during a certain week in order to determine customers opinion of their pricing is called cluster sampling.
Cluster sampling is a sampling technique which is obtained by dividing the population into groups and selecting all individuals from within a random sample of the groups.
I think you omitted some options from the question which should include cluster sampling as the answer is not included in the options you gave in the question.
What is the value of y in the equation 6.4x + 2.8y = 44.4, when x = 3?
Answer:
y = 9
Step-by-step explanation:
So if x = 3, we can sub that into the equation.
This gives us:
6.4 (* 3) + 2.8y = 44.4
so:
19.2 + 2.8y = 44.4
25.2 = 2.8y
so
y = 9
Answer: 9
Step-by-step explanation: plug 3 into the x, then use the order of operations/ pemdas to solve. first multiply 6.4 and 3 (=19.2) then subtract the answer from 44.4 (now the equation is 2.8y=25.2) then divide 2.8 from 25.2 to get x alone and you are left with x=9
The lines given by the equations 3y + 2x = 7 and y = mx − 11 are perpendicular. Find m
Answer:
[tex]m=\frac{3}{2}[/tex]
Step-by-step explanation:
When two lines are perpendicular, their slopes will be opposite reciprocals:
[tex]-3[/tex] → [tex]\frac{1}{3}[/tex]
[tex]\frac{1}{4}[/tex] → [tex]-4[/tex]
Solve the first equation for y to rewrite in slope-intercept form:
[tex]y=mx+b\\\\3y+2x=7\\\\3y+2x-2x=7-2x\\\\3y=-2x+7\\\\\frac{3y}{3}=\frac{-2x}{3} +\frac{7}{3} \\\\y=-\frac{2}{3}x+\frac{7}{3}[/tex]
m is the slope, so the slope of this line is [tex]-\frac{2}{3}[/tex]. The opposite reciprocal is [tex]\frac{3}{2}[/tex], therefore, m is [tex]\frac{3}{2}[/tex]
How to solve this brainteaser
Answer:
last row equals 333
Step-by-step explanation:
The clock showing time 9:00 should be worth 9 points, and the clock showing 3:00 should be worth 3 points, giving for the first row:
9 + 9 + 3 = 21
the three equal calculators showing 1234 are worth 10 points each:
1+2+3+4 = 10
and 10 + 10 + 10 = 30
the light bulbs should be 15 points each then giving 15 + 15 - 15 = 130 - 15 = 15 Notice also that they all have 5 rays of light coming out (so a 3 points per ray)
Now for the bottom line we have:
9 + (1+2+2+4) times 3 * 12 (only four rays on each bulb thus 4 * 3 = 12)
Notice we added the figures that appear in the calculator.
9 + 9 * 36 = 333
Shota is a dangerous fellow who likes to go rock climbing in active volcanoes. One time, when he was 303030 meters below the edge of a volcano, he heard some rumbling, so he decided to climb up out of there as quickly as he could. He climbed up at a constant rate. After 4.54.54, point, 5 seconds, he was 7.57.57, point, 5 meters below the edge of the volcano How fast did Shota climb? In total, how long did it take Shota to reach the edge of the volcano?
Answer:
5m/s;
6 seconds
Step-by-step explanation:
Given the following :
Initial position = 30 m below
He climbed at a constant rate, and was 7.5 m below after 4.5 s.
Distance climbed or covered in 4.5 seconds :
(Initial position - current position)
(30 - 7. 5)m = 22.5 meters
Using the relation:
Speed = distance covered / time taken
Therefore,
Shota's speed = 22.5m / 4.5s = 5m/s
Time taken to reach edge of volcano :
Distance left to cover = 7.5m
Speed = 5m/s
Time required to cover remaining distance :
= distance / speed
= (7.5m ÷ 5m/s) = 1.5s
Total time to reach edge :
(4.5 + 1.5)s = 6 seconds
Answer:
5m/s
6 seconds
Step-by-step explanation:
did it on khan
What is 3,000 is 1/10 of
Answer:
30000
Step-by-step explanation:
3000 / (1/10) = w
3000*10/1 = w
30000 = w
probe:
30000*1/10 = 3000
then:
30000
is 1/10
of
30000
Please help ill give brainlest
Answer & Step-by-step explanation:
For this problem, we have to find the equations that have a value of 10 for the variable y. Immediately, we can eliminate some answers. We can eliminate A, D, and E because they all have a different value for the variable y. So, that leaves us with answer choices B and C.
In order to check to see if we are correct, let's plug in 10 for the y in answer choices B and C.
B:
8 = 18 - y
8 = 18 - 10
8 = 8
C:
60 = 6y
60 = 6(10)
60 = 60
So, as you can see, we are correct and we have successfully found the correct answer to the given problem.
Answer:
B and C
Step-by-step explanation:
We want to find the equations where y=10 is a solution. Let's plug 10 into each equation and solve.
A. y+11=22
10 +11 =22
Add 10 and 11.
21 ≠ 22
21 does not equal 22. This choice is incorrect.
B. 8= 18-y
8=18-10
Subtract 10 from 18.
8=8
8 equals 8. This choice is correct.
C. 60=6y
60=6(10)
Multiply 6 and 10.
60=60
60 equals 60. This choice is correct.
D. y/5=4
10/5=4
Divide 10 by 5.
2≠4
2 does not equal 4. This choice is incorrect.
E. 10y=20
10(10)=20
Multiply 10 and 10.
100≠20
100 does not equal 20. This choice is incorrect.
The equations where y=10 is a solution are B. 8=18-y and C. 60=6y
(5x+3)(7x-7) how do find x
Answer:
12x-4
Step-by-step explanation:
combine like terms. the 5x with the 7x (=12x) and the 3 witht the -7 (-4) hope this helps!!
how many terms are in the exspression 4{8+3x]
2 terms
Step-by-step explanation:
4[8+2x]
=4*8+4*2x
=32+8x
therefore there are 2 terms
hope it helps u if yes pls mark brainliest
Answer:
The first factor (4) consists of one (1) term, "4".
The second factor (8 +3x) consists of two (2) terms, "8" and "3x".
Write 1.653 x 10-4 as an ordinary number.
Answer:
1.4×10−5=0.000014
Step-by-step explanation:
Because the exponent of the 10 term is a negative number you need to move the decimal point to the left 5 positions;
1.4×10−5=0.000014
The ordinary number is 0.0001653.
The given number is: [tex]1.653*10^{-4}[/tex]
We know that for [tex]10^{-4}[/tex] we have to move the decimal to the left by 4 units.
So the ordinary number will be: 0.0001653.
Learn more: https://brainly.com/question/16236436
simplify 3×+1(2×-1)2-1(6×)
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Answer = [tex]\boxed {x - 2}[/tex]
[tex]3x +1(2x-1)2-1(6x)[/tex]
= [tex]\boxed {3x + 1 . ( 2x - 1 ) . 2 - 1 (6x) = x - 2}[/tex]
Steps :
[tex]3x + 1 . (2x - 1) . 2 - 1 . (6x)[/tex]
Remove the parentheses : [tex](a) = a[/tex]
[tex]= 3x + 1 * (2x- 1) * 2 - 1 * 6x[/tex]
Multiply the numbers : [tex]1 * 2 = 2[/tex]
[tex]= 3x + 2 ( 2x - 1 ) * 6x[/tex]
Multiply the numbers : [tex]1 * 6 = 6[/tex]
[tex]= 3x + 2 ( 2x - 1 ) -6x[/tex]
Expand: [tex]2 (2x - 1) : 4x - 2[/tex]
[tex]2 ( 2x - 1 )[/tex]
Apply the distributive law : [tex]a (b - c) = ab - ac[/tex]
[tex]a = 2, b = 2x, c = 1 \\= 2 * 2x - 2 * 1[/tex]
Simplify [tex]2 * 2x - 2 * 1 : 4x - 2[/tex]
= [tex]= 4x - 2[/tex]
[tex]= 3x + 4x - 2 - 6x[/tex]
Simplify [tex]3x + 4x - 2 - 6x : x - 2[/tex]
= [tex]x - 2[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
What is 8 3/5 graphed on a number line
PLZ I NEED HELP ASAP CUZ IM ON A TIMER!
Answer:
Step-by-step explanation:
8 3/5 on a number line is between 8 and nine
idk how to draw a number line on a computer so ill just tell you how
1. divided the spaces between 8 and 9 into 5 sections ( 3/5 )
2. then mark 3 of those 5 spaces and put a dot or a line at where the 3rd space ends
000KS
c. Sumana runs a tea shop and she buys 7.5L of milk everyday. If she
uses 4.75L of milk in the morning and the remaining milk in the
evening. Find the quantity of milk she uses in the evening
Answer:
2.75 L
Step-by-step explanation:
This is the problem of subtraction.
Total Milk sumana has = 7.5 l
Milk used in the morning = 4.75 L
Milk left for evening = Total Milk sumana has - Milk used in the morning
Milk left for evening = 7.5 l - 4.75 l = 2.75 L
Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression line? About the unexplained variation?
r=0.864
a) Calculate the coefficient of determination.
(Round to three decimal places as needed.)
b) What does this tell you about the explained variation of the data about the regression line?
c) What % of the variation can be explained by the regression line.
(Round to one decimal place as needed.)
About the unexplained variation?
d) What % of the variation is unexplained and is due to other factors or to sampling error.
(Round to one decimal place as needed.)
Answer:
Kindly check explanation
Step-by-step explanation:
Given the Coefficient of correlation (r) = 0.864
The Coefficient of determination (R^2) :
0.864^2 = 0.747 ( 3 decimal places)
B) the Coefficient of determinationR^2 tells about the proportion of variation in the dependent variable that is predicted by the independent variable, Hence, a proportion of about 0.75 should fall within the regression line.
C) percentage variation explained :
Coefficient of determination * 100%
0.747 * 100% = 74.7%
D) unexplained variation due to other factors or sampling error :
(total variation - explained variation) = (100 - 74.7)% = 25.3%
7 1/8 + 1/6, reduced to lowest terms
Answer:
Step-by-step explanation:
7 3/24 + 4/24
7 7/24
Y=x-1 4x+8=y solve the system
To rent a certain meeting room, a college charges a reservation fee of $ 46 and an additional fee of $ 6.40 per hour. The chemistry club wants to spend at most $ 78.00 on renting the meeting room. What are the possible amounts of time for which they could rent the meeting room? Use t for the number of hours the meeting room is rented, and solve your inequality for t .
Answer:
Up to 5 hours
Step-by-step explanation:
Given:
One off fee = $46Hourly rent = $6.4 / hrAmount limitation= $78Equation to reflect the condition:
78 = 46 + 6.4t6.4t = 78 - 466.4t = 32t = 32/6.4t = 5 hours maxSo, the meeting room can be rented for up to 5 hours with $78
A market woman purchased a number of plates for GH 150.00. Four of the plates
4
got broken while transporting them to her shop. By selling the remaining plates at a
profitof GH€ 1.00 on each, she made a total profit of GH€ 6.00. How many
plates did she purchase?
Answer: 160 plates.
Step-by-step explanation:
The woman bought N plates for GH€ 150.00
4 of the plates where broken, so she has N - 4 plates to sell.
She sold each one of the N - 4 plates for GH€ 1, then after all the N- 4 plates were sold, the total money that she has is:
(N - 4)*GH€1 = GH€ (N - 4)
And the total profit (profit is the difference between the final amount of money that she gets, and the initial payment) is GH€ 6, then we have that:
GH€ (N - 4) - GH€ 150.00 = GH€ 6
ignoring the units, we have:
N - 4 - 150 = 6.
N = 6 + 154 = 160.
She bought 160 plates.
Keith has 39 books in his library. He bought several books at a yard sale over the weekend. He now has 84 books in his library. How many books did he buy at the yard sale ?
Answer:
total books in library = 39
books bought from yard sale = ??
Total book in library now = 84
Now,
books bought from yard sale= 39-84
= 45
A box contains 12 balls: 8 red and 4 black. Two extractions are made without replacing the extracted ball to the box before the second extraction. Do you find the probability of drawing a ball of each color?
Answer:
16/33
Step-by-step explanation:
The probability that the first ball is red and the second ball is black is:
8/12 × 4/11 = 8/33
The probability that the first ball is black and the second ball is red is:
4/12 × 8/11 = 8/33
So the total probability of drawing one ball of each color is 8/33 + 8/33 = 16/33.
jamal bought donuts and cupcakes. he bought three times as many donuts as cupcakes. cupcakes cost .50 cent each and donuts cost a $1.00 each. jamaal spent $10.00 total. how many cupcakes did he buy? how many donuts did he buy?
Answer: He bought 4 cupcakes and 12 donuts
Step-by-step explanation:
He bought three times as many donuts as cupcakes so we could represent that by the equation d= 3c where d is donuts and c is the cupcakes.
If cupcakes also cost 50 cent and donuts cost a dollar each and he spent a total of 10 dollars then we could also represent that by the equation
0.50d + 1c = 10
Now combine use the two equations and solve for d and c
d= 3c
0.50d + 1c =10 substitute d in the first equation into the second equation.
0.50(3c) + 1c =10
1.5c + 1c =10
2.5c = 10
c= 4
In this case he bought a total of 4 cupcakes and to find the total of donuts that he bought we multiply that by 3 because he bought three times as much as that.
d= 3 * 4
d = 12