the scores of 8 grade students in math test are normal distributed with a mean of 57.5 abs a standard deviation of 6.5 from thus data, we can conclude that 68% of the students received scores between 34 or 51 and 64 or 68.
Answers
We need to calculate the Z-score of the given values.
I'll draw the normal distribution curve for this example
Z-score of 34
\(\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ Z=\frac{34-57.5}{6.5}=-3.615 \end{gathered}\)If we use a Z table, we can see that a value of Z=-3.615 corresponds to an area of 0.00015
Z-score of 51
\(Z=\frac{51-57.5}{6.5}=-1\)Again, using the Z table, when Z=-1, the area below the curve is 0.15866.
If we substract 0.15866 and 0.00015, we obtain the area between 51 and 34, as shown below
\(0.15866-0.00015=0.15851\)In percentage: 15.851%
Now, let's proceed with 64 and 68
Z-score of 64:
\(Z=\frac{64-57.5}{6.5}=1\)This value represents an area to the left of: 0.84134
Z-score of 68:
\(Z=\frac{68-57.5}{6.5}=1.62\)which corresponds to an area to the left of: 0.94738
Again, we must substract those two values to obtain the areal between 68 and 64
\(0.94738-0.84134=0.10604\)In percentage, this is equal to 10.604%
I will upload an image of Z table in case you want to double check...
Now, in order to conclude the question... we need to check if "68% of the students received scores between 34 or 51 and 64 or 68."
We already know that between 34 and 51 there are 15.851% of students and between 64 and 68 there are 10.604%, which adds a value of 26.455%
In conclusion, the information given is wrong, because it is 26.455% and not 68%
Related Questions
using the digits 4,5,6,and 7,write the greatest 4 digit number you can without repeating any of the digits.
Answers
Answer:
7,654
Step-by-step explanation:
Arrange the digits in order to create the highest possible number.
7000 + 600 + 50 + 4 = 7654
Give the equation of the circle centered at the origin and passing through the point (4, 0).
Answers
\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)
\(\qquad \tt \rightarrow \: x² + y² = 16\)
____________________________________
\( \large \tt Solution \: : \)
The distance between the centre and the point through which the circle is passing is equal to the radius of the circle.
so, let's use distance formula here :
\(\qquad \tt \rightarrow \: \sqrt{(y2 - y1) {}^{2} + (x2 - x1) {}^{2} } \)
\(\qquad \tt \rightarrow \: \sqrt{(0 - 0) {}^{2} + (4 - 0) {}^{2} } \)
\(\qquad \tt \rightarrow \: \sqrt{0 + (4) {}^{2} } \)
\(\qquad \tt \rightarrow \: \sqrt{ {4}^{2} } \)
\(\qquad \tt \rightarrow \: 4 \: \: units\)
Now, let's write the equation of circle in standard form :
\(\qquad \tt \rightarrow \: (x - h) {}^{2} + (y - k) {}^{2} = r {}^{2} \)
h = x - coordinate of circle k = y - coordinate of circle r = radius of circle\(\qquad \tt \rightarrow \: (x - 0) {}^{2} + (y - 0) {}^{2} = {4}^{2} \)
\(\qquad \tt \rightarrow \: {x}^{2} + {y}^{2} = 16 \)
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
this is rlly easy but im lazy and dont wana answer it, i mark brainliesttttt tyyy ❤️
Answers
Answer:
C and D is correct
Step-by-step explanation:
C: Debit is negative, and if you add 27 to -14, you get 13 which is Maria's account.
D: Its the same thing but opposite. 13 minus 27 is -14.
♡ Hope it helps ♡
Answer:
both c and d
Step-by-step explanatioin
nobody is answering my question so im saving up like 100 points so someone will actually do it so ye
2.2 2.1.4 a Given that A and B are complementary angles and 7 cos A-3 = 0. Determine WITHOUT the use of a calculator, the value of: 7 cos B-3 tan A. (4)
Answers
30 POINTS!!! Louie is trying to find a rectangular canvas for his art project. Its diagonal must measure 23.3 inches and form a 31° angle with the bottom of the canvas. What is the height of the canvas? Round your answer to the nearest inch. 12 inches 14 inches 24 inches 27 inches
Answers
Answer:
12 inches
Step-by-step explanation:
Given
\(\theta = 31^{\circ}\)
\(diagonal = 23.3\ in\)
Required
Determine the height of the canvas
The question is illustrated using the attached image.
Using the attachment as a point of reference, the height is calculated from
\(sin \theta = \frac{opp}{hyp}\)
This gives:
\(sin 31^{\circ}= \frac{h}{23.3}\)
Make h the subject
\(h = 23.3 * sin(31^{\circ)\)
\(h = 23.3 * 0.5150\\\)
\(h = 11.9995\)
\(h = 12\ inches\)
A rectangle has right angles as its interior angles. Secondly, when you draw a diagonal and has its angle with bottom, then you get a right angled triangle with known angle.
The height of the rectangle is given by:
Option D: 12 inches
Given that:There is a rectangular canvas.The angle that the diagonal of the rectangle makes with bottom is 31° The length of diagonal = 23.3 inchesTo find:The height of that rectangular canvas.
Using the right angle triangle and sine ratio to find height of canvas:I have attached a figure below which you can refer.
The triangle ABC is right angled triangle. Using the sine ratio from angle A's viewpoint:
\(sin(A) = \dfrac{BC}{AC}\\\\ sin(31^\circ) = \dfrac{h}{23.3}\\\\ h \approx 0.515 \times 23.3\\ h \approx 12 \: \rm inches\)
Thus, the height of the specified canvas is 12 inches.
Thus, Option D: 12 inches is correct.
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2(w+3)-14=6(32-3w)...
Answers
2(w+3) - 14 = 6(32 - 3w)
open the parenthesis
2w + 6 - 14 = 192 - 18w
collect like term
2w + 18w = 192 -6 + 14
20w = 200
Divide both-side of the equation by 20
w = 10
A camel drank 2 1/2 gallons of water in 1/4 hour. What was the average rate in gallons per hour at which the camel drank?
Answers
Answer:
10 gallons per hour
Step-by-step explanation:
1/4x4=1. 2 1/2x4=10. Hope it helps!
help please the question is uploaded
Answers
The expression for y is y = (-1/4)(cos 8x + 2 cos 4x) + C, where C is the constant of integration.
What is integration?
Integration is a fundamental concept in calculus that involves finding the antiderivative of a function
To find y, we need to integrate the given expression with respect to x:
∫ dy/dx dx = ∫ 5 cos² 4x sin 4x dx
y = ∫ cos² 4x sin 4x d(4x) (using u-substitution, where u = 4x)
y = ∫ cos² u sin u du
Now, we can use the identity cos²θ = (1/2)(1 + cos2θ) to simplify the integral:
y = ∫ (1/2)(1 + cos2u) sin u du
y = (-1/4)(cos2u - 2 cos u) + C (using integration by substitution)
y = (-1/4)(cos2(4x) - 2 cos 4x) + C
y = (-1/4)(cos 8x + 2 cos 4x) + C
Therefore, the expression for y is y = (-1/4)(cos 8x + 2 cos 4x) + C, where C is the constant of integration.
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When Tyee runs the 400 meter dash, his finishing times are normally distributed with a mean of 61 seconds and a standard deviation of 1.5 seconds. If Tyee were to run 39 practice trials of the 400 meter dash, how many of those trials would be faster than 62 seconds, to the nearest whole number?
Answers
To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.
We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.
The z-score formula is:
z = (x - μ) / σ
Where:
x = value (62 seconds)
μ = mean (61 seconds)
σ = standard deviation (1.5 seconds)
Calculating the z-score:
z = (62 - 61) / 1.5
z ≈ 0.6667
Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.
Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.
To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:
Number of trials = Proportion * Total number of trials
Number of trials = 0.7461 * 39
Number of trials ≈ 29.08
Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.
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Simplify: 7/6 x −3/28 Also, find the reciprocal of the answer.
Answers
Answer:
Simplify = 7x/6 - 3/28
Reciprocal = 6x/7 - 28/3
Step-by-step explanation:
Add x to the top of the first fraction to combine them.
To find the reciprocal you flip the numbers. So the numerator is the bottom and the dominator is the top.
2/9=?/18=?/27 help pleace thank u so much
Answers
Answer:Not there yet
Step-by-step explanation: Think about it your close 2/9 = nothing why do numbers determine our grades so don't answer if anything flunk out of school
A round pencil is sharpened to a cone shape at both ends.calculate the volume of the pencil if the two radius is 1.2 and heights are 8cm
Answers
Answer:
A round pencil is sharpened at both ends the hight of the pencil is 16cm the length of the pencil is 1cm the radius of the two sharpened ends is 16cm 1.2cm
Calculate the volume using the value 22/7.
Step-by-step explanation:
The question what function matches the graph?
A) linear
B) exponential
C)Geometric
D)Quadratic
Answers
What is the 24th term of -21, -14,-7,0,7,…
Answers
Answer:
140
If that's wrong, try 147
Step-by-step explanation:
With this brief sequence of numbers, we can see that the function is linear, and increases by 7 each term, with the first term at -21, and therefore, the "0th" term, or the y-intercept, at -28. With this information we can create a function in slope intercept form (y=mx+b):
\(y=7x-28\\\),
where our m (slope) is 7, and our b (y-intercept) is -28.
If this doesn't make sense, then the easiest way is to just keep adding seven to the previous number until you get to the 24th term.
Hope this helps!
Tarek buys a pomegranate with 314 seeds. He buys a second pomegranate
that has more seeds. The number of seeds in the second pomegranate is
made of the digits 6, 3, 1, and 4, but not in that order.
Part A If the value of 1 is 100 times greater in the second pomegranate, in
what place should the 1 be written in the second number? Explain
how you know
Answers
Answer:
1 goes in the thousands place in the second number.
Step-by-step explanation:
In the first pomegranate, the 1 is in 314, so it is in the tens place.
In the second pomegranate, the value of the 1 is 100 times the value of the 1 in the first pomegranate, so since 100 × 10 = 1000, it must be in the thousands place. Therefore, the number of seeds in the second pomegranate is 1abc, where 1 is in the thousands place, and abc represent the digits 3,4, and 6, but we do not know in which order.
The sale price S (in dollars) of an item is given by the formula S=L-rL, where L is the list price (in dollars) and r is the discount rate (in decimal form).I’ve already solved problem (a) although I’m not sure if it’s correct but I need help with problem (b)The list price of the shirt is $30 and the sale price is $18. What is the discount rate?
Answers
Since the equation of the sale price S is
\(S=L-rL\)a)
To solve for r add rL to both sides
\(\begin{gathered} S+rL=L-rL+rL \\ S+rL=L \end{gathered}\)Subtract S from both sides
\(\begin{gathered} S-S+rL=L-S \\ rL=L-S \end{gathered}\)Divide both sides by L
\(\begin{gathered} \frac{rL}{L}=\frac{L-S}{L} \\ \\ r=\frac{L-S}{L} \end{gathered}\)b)
Since the list price of the shirt is $30, then
L = 30
Since the sale price is $18, then
S = 18
Substitute them in the equation of r to find it
\(\begin{gathered} r=\frac{30-18}{30} \\ \\ r=\frac{12}{30} \\ \\ r=\frac{2}{5} \\ \\ r=0.4 \end{gathered}\)The discount rate is 0.4
The Ozzie Chocolate Company is preparing to offer a new product in its candy offerings, the Minty Dark Chocolate Bite bar. Material costs per new candy bar are
$0.25 for chocolate, $0.02 for sugar, and $0.03 for mint flavoring. Labor costs of the new product are approximately $0.15 per bar. Adding a production line devoted to the new candy will cost $250,000 per year.
(a) If the sales price is $1.40 per candy bar, how many must the company make per year in order to break even? Assume that each bar made is sold at full price.
(b) What is the company's profit or loss if they make and sell 270,000 candy bars at the $1.40 price in the first year?
(c) About 20% of the food consumed in the U.S. is imported. Production in many industries has been offshored. What ethical issues do companies face when presented with the decision to move operations?
Answers
Answer:
a) 263,158
b) $164,500
c) Ethical issues companies face when deciding to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
Step-by-step explanation:
a)
Total cost = (0.25 + 0.02 + 0.03 + 0.15) x + 250,000
Total revenue = 1.40x
Setting the two equations equal to each other and solving for x, we get:
(0.45)x + 250,000 = 1.40x
0.95x = 250,000
x ≈ 263,158
b)
If the company sells 270,000 candy bars at $1.40 each, the total revenue generated is:
270,000 * $1.40 = $378,000
The total cost of producing 270,000 candy bars is:
(0.25 + 0.02 + 0.03 + 0.15) * 270,000 + $250,000 = $213,500
Therefore, the company's profit is:
$378,000 - $213,500 = $164,500
c)
Ethical issues companies face when presented with the decision to move operations: job loss for employees, poor working conditions and exploitation of workers, negative environmental impact,...
What value correctly fills in the blank so that the expressions are equivalent?
18 + 45 = x (2+5)
2
3
7
9
Answers
Answer: X = 9
Step-by-step explanation:
Multiply x all in the expression and then combine like terms, add the two terms together on the left side and you are left with
63 = 7x
divide 63 by x to get x alone to get x = 9
A golfer wants to determine if the type of driver she uses each year can be used to predict the amount of improvement in her game. Which variable would be the explanatory variable?a. The type of driverb. The number of holes she playsc. The rating of the golferd. The improvement in her game
Answers
Answer:
The type of driver
Step-by-step explanation:
The term known as '' response variable'' is use in describing a variable that changes when you alter an examination or a test. Just like its name implies, it is the ''response'' that one gets when the other variable that is the Explanatory Variable are being altered.
In this question, the golfer will have to be changing the type of drivers that she is using in order to be able to know whether these changes in drivers will increase her game performance. Hence, the Explanatory Variable is the type of driver in which the golfer changes which is being use to define the performance of the golfer.
Find the area of OP. Leave your answer in terms of .
A. 14 cm2
B. 77 cm2
C. 147 cm2
D. 497 cm2
Answers
Answer:
D. 49
Step-by-step explanation:
The area of a circle is pi times the radius squared (A = pi r^2).
so putting in your numbers given you get 7^2
which equals 49
Which of the following options have the same value as 10 % , percent of 33?
Answers
Answer:
3.3
Step-by-step explanation:
33 x .10 = 3.3
One jar of spaghetti sauce is made with 1/4 of a cup of tomatoes. How many full jars of spaghetti sauce can be made with 3 cups of tomatoes?
Answers
Answer:
you can make 12 cans of them
A map shows the scale 0.5 cm = 6 mi. If
the map measures 9.5 cm between two
points, what would the actual distance
be, in miles?
Answers
The scale on the map is given as 0.5 cm = 6 mi, which means that 1 cm on the map represents 6 miles in reality. This can also be written as 1:6, where the numbers before and after the colon represent the proportion of the map distance to the actual distance.
Since the map measures 9.5 cm between the two points, this is 9.5 times the map distance represented by 1 cm. So the actual distance is 9.5 times the actual distance represented by 1 cm on the map, or 9.5 * 6 = <<9.5*6=57>>57 miles.
Therefore, the actual distance between the two points is 57 miles.
hhhhhhhhhhhhhhhheeeeeeeeeeeeeeeeeeeeeeeeeelllllllllllllllllpppppppppppp
Answers
Answer:
yesss???
Step-by-step explanation:
Answer:yes
Step-by-step explanation:
An expression is shown below: 3pf2 − 21p2f + 6pf − 42p2 Part A: Rewrite the expression by factoring out the greatest common factor. (4 points) Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
Answers
The expression factoring out the greatest common factor is (3pf - 21p²)(f + 2).
We have the expression as
3pf² - 21p²f + 6pf - 42p²
Now, factorising the expression as
= 3pf² + 6pf - 21p²f - 42p²
= 3pf(f +2) - 21p²(f + 2)
= (3pf - 21p²)(f +2)
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PLEASE HELP ME ANSWER THIS PROBLEM
Answers
Answer:
9
Step-by-step explanation:
because 3*4=12 then divide 108 by 12 giving you 9
A wire that is centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed into the shape of a square.
Answers
Using properties of square,
a. Equation for total area = 2x² - 16x + 64
b. Area will be minimum for the value of x = 0
c. Minimum area will be 64cm².
Define a square?With four equal sides, a square is a quadrilateral. There are numerous square-shaped objects in our immediate environment. The equal sides and 90° internal angles of each square form serve as indicators of its identity.
Total length of wire = 32cm.
Now side of one square is given as x.
Perimeter of big square will be = 4x.
Now perimeter of small square = 32- 4x.
Side of small square = (32-4x)/4
= 4(8-x)/4
= 8-x
Area of big square = x × x
= x².
Area of small square = (8-x) ².
Now Total area, A(x) = x² + (8-x) ²
= x² + 64 + x² - 16x
= 2x² - 16x + 64
The side length that will minimize the area will be, x = 0.
Minimum area of the total figure will be = 64cm²
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A rectangle has a perimeter of 28 feet. The width of the rectangle is two foot less than the length of the rectangle. What is the width of the rectangle?
Answers
Step-by-step explanation:
perimeter of a rectangle = 2×length + 2×width = 28 ft
width = length - 2
length = width + 2
2×(width + 2) + 2×width = 28
2×width + 4 + 2×width = 28
4×width + 4 = 28
4×width = 24
width = 6 ft
and the length is width + 2 = 6+2 = 8 ft.
Stefan borrowed twice as much on his 8 % car loan as on his 7% student loan. The annual interest
on the car loan is $360 more than the interest on the student loan. How much did Stefan borrow on
each loan?
a. Write an equation about the principals on the loans, using for the amount of money he borrowed
for his car and y for the amount of money he borrowed for his student loan.
b. Write another equation about the interest on the loans.
c. Solve your system and answer the question for much he borrowed at each rate.
Car: $
Student: $
Answers
Answer:
Stefan borrowed $8000 on his car loan and $4000 on his student loan.
Step-by-step explanation:
a. Let x be the amount of money Stefan borrowed on his car loan and y be the amount he borrowed on his student loan. According to the problem, Stefan borrowed twice as much on his car loan as on his student loan, so x = 2y.
b. The annual interest on the car loan is $360 more than the interest on the student loan. We can set up an equation as follows:
0.08x - 0.07y = 360
c. Substituting x = 2y from equation (a) into equation (b), we get:
0.08(2y) - 0.07y = 360
0.16y - 0.07y = 360
0.09y = 360
y = 4000
So, Stefan borrowed $4000 on his student loan. Using equation (a), we can find the amount he borrowed on his car loan:
x = 2y = 2(4000) = 8000
Therefore, Stefan borrowed $8000 on his car loan and $4000 on his student loan.
Please help, I have no idea on what I’m doing for this question! Ill mark the brainiest!
Answers
Q=98
P=25
R=57
STEP BY STEP EXPLANATION AND DOUBLE CHECKING:
1. Because you’re trying to find the variable for INTERNAL angles, all the angles will add up to 180. So, you put all the angles = 180
5x+3+3x+x+6=180
2. Add up all like terms
5x+3+3x+x+6 —> 9x+9=180
3. Subtract 9 from both sides
9x+9=180 —> 9x=171
4. Divide
9x=171 —> x=19.
TO DOUBLE CHECK THE ANSWER:
Plug 19 into all the variables.
ANGLE Q —> 5x+3 —> 5*19+3 —> 98
ANGLE P —> x+6 —> 19+6 —>25
ANGLE R —>3x —> 3*19 —> 57
Hope i helped :)