Answer:
Approximately [tex]0.012[/tex] (that's approximately [tex]1.2\%[/tex].)
Step-by-step explanation:
The question did not specify the exact distribution of the size of those images. However, the sample size [tex]n = 80[/tex] is a rather large number. Assume that:
the sizes of these [tex]80[/tex] images follow the same distribution, with mean [tex]\mu = 0.5[/tex] megabytes and standard deviation [tex]\sigma = 0.2[/tex] megabytes.the size of each image is independent of one another.If both assumptions are met, the central limit theorem would apply. This theorem would suggest that the sum of the sizes of these [tex]80[/tex] image (a random variable) will approximately follow a normal distribution. The mean of that sum would be approximately [tex]n\cdot \mu= 80 \times 0.5[/tex]. The standard deviation of that sum would be approximately [tex]\sigma\, \sqrt{n} = 0.2\times \sqrt{80}[/tex].
Let [tex]\displaystyle \Sigma X[/tex] denote the sum of these eighty sizes.
Under these assumption, [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left(n\, \mu,\, \sigma\,\sqrt{n}\right)[/tex].
That is: [tex]\displaystyle \Sigma X \stackrel{\text{app.}}{\sim} \mathrm{N}\left({80\times 0.5},\, \left(0.2\times \sqrt{80}\right)^2}\right)[/tex].
The question is asking for the probability [tex]P(49 \le \Sigma X \le 53)[/tex]. Therefore, calculate the [tex]z[/tex]-score that corresponding to [tex]\Sigma X = 49[/tex] and [tex]\Sigma X = 53[/tex]:
For [tex]\Sigma X = 49[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{49 - 80 \times 0.5}{0.2\times \sqrt{80}} = 2.25[/tex].For [tex]\Sigma X = 53[/tex], the [tex]z[/tex]-score would be [tex]\displaystyle \frac{\sum X - n\, \mu}{\sigma \sqrt{n}} = \frac{53 - 80 \times 0.5}{0.2\times \sqrt{80}} = 3.25[/tex].Make use of a [tex]z[/tex]-table to find these two probabilities:
[tex]P(X \le 49) = P(Z < 2.25) \approx 0.98778[/tex].[tex]P(X \le 53) = P(Z < 3.25) \approx 0.99942[/tex].Calculate the probability that this question is asking for:
[tex]\begin{aligned}& P(49 \le \Sigma X \le 53) \\ &= P(\Sigma X < 53) - P(\Sigma X < 49) \\ & \approx 0.99942 - 0.98778 \approx 0.012 = 1.2\%\end{aligned}[/tex].
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Answer:
y = 64
Step-by-step explanation:
The angles are supplementary, that is sum to 180° , thus
2(x + 6) + y = 180 ← substitute x = 52
2(52 + 6) + y = 180
2(58) + y = 180
116 + y = 180 ( subtract 116 from both sides )
y = 64
Write the slope-intercept form of the equation of the line through the given point and slope.
Point: (1, -3)
Slope: -4
Answer:
y=-4x+1
Step-by-step explanation:
Graph (1,-3)
Go down 4 over one/ up left one
Get y-intercept
Then BOOM you got it
Answer:
y = -4x + 1
Step-by-step explanation:
We are given that a line has a slope of -4 and a point (1, -3).
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept.
As we are already given the slope, we can immediately plug its value into the equation.
Substitute -4 as m in the equation.
y = -4x + b
Now we need to find b.
As the equation passes through the point (1, -3), we can use its values to help solve for b.
Substitute 1 as x and -3 as y.
-3 = -4(1) + b
Multiply.
-3 = -4 + b
Add 4 to both sides
1 = b
Substitute 1 as b in the equation.
y = -4x + 1
Topic: writing the equation of the line (slope-intercept form)
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A large rectangle is made by joining three identical small rectangles as shown.
The perimeter of one small rectangle is 21cm. The width of one small rectangle is x cm.
Work out the perimeter of the large rectangle. The final line of your answer should be the form, perimeter of large rectangle is ...cm
Answer: 35 cm
Step-by-step explanation:
As shown in the image attached, the A large rectangle is made by joining three identical small rectangles,
The width of one small rectangle is x cm and the length of one small rectangle is 2x cm. Therefore the perimeter of the small rectangle is given as:
2(length + width) = Perimeter
2(2x + x) = 21
2(3x) = 21
6x = 21
x = 21/6 = 3.5 cm
x = 3.5 cm
From the image attached, the width of the large rectangle is 2x (x + x) and the length is 3x (2x + x). Therefore, the perimeter of the large rectangle is:
2(length + width) = Perimeter
2(3x + 2x) = Perimeter
Perimeter = 2(5x)
Perimeter = 10x
Perimeter = 10(3.5)
Perimeter = 35 cm
Step-by-step explanation:
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
Simplify the expression 12 a to B minus AAA +582B minus to a B minus 4AB2 minus 6AB plus to a plus 3AB
Question:
Simplify:
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Answer:
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]
Step-by-step explanation:
Given
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Required
Simplify
[tex](12a^2b-8a+5a^2b-2ab)-(4ab^2-6ab+2a+3ab)[/tex]
Open brackets
[tex]12a^2b-8a+5a^2b-2ab-4ab^2+6ab-2a-3ab[/tex]
Collect Like Terms
[tex]12a^2b + 5a^2b - 4ab^2 - 8a - 2a + 6ab - 3ab- 2ab[/tex]
[tex]17a^2b - 4ab^2 - 10a + ab[/tex]
Solve for n.
below
.....................
Answer:
n = 12
I hope this helps!
Is 0,4,8,12 an arithmetic sequence?
3/5+(-7/5)= can someone help me with this please
Answer:
[tex]-\frac{4}{5}[/tex]
Step-by-step explanation:
Because both of the fractions have a common denominator they can be subracted without any other work.
Please help I'll give brainlest
Which of the following is 1,215 divisible by? Select all that apply.
A.3
B.2
C.9
D.10
E.5
F.8
G.4
H.6
Answer: A,C,E
Step-by-step explanation:
All of the other answers give you a decimal.
Answer:
ACEStep-by-step explanation:
A
1215 divided by 3 = 405
B
1215 divided by 9 = 135
C
1215 divided by 5 = 243
*The other answers can give a decimal answer.
Can two fraction with the same numerator and different denominators be equal? Use words and numbers to explain.
Step-by-step explanation:
Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal.
The two fractions with the same numerator and different denominators can not be equal.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A division number is a number that addresses the piece of the entire, where the entire can be any number. It is a numerator and a denominator.
The fraction is in the form of a numerator and denominator. The two fractions can be equal if and only if their numerator and denominator are equal.
The two divisions with similar numerators and various denominators can not be equivalent.
More about the Algebra link is given below.
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What’s the value of x? :/
Answer:
[tex] x = 27 [/tex]
Step-by-step explanation:
According to congruent chords and arcs theorem, if [tex] \overline{XY} \cong \overline{ZY} [/tex] then [tex] \arc{XY} \cong \arc{ZY} [/tex].
This means that [tex] \arc{XY} = \arc{ZY} = (6x - 20) degrees [/tex]
Thus:
[tex] \arc{XY} + \arc{ZY} + \arc{ZX} = 360 [/tex] (full circle = 360°)
[tex] \arc{XY} = (6x - 20) [/tex]
[tex] \arc{ZY} = (6x - 20) [/tex]
[tex] \arc{ZX} = 76 [/tex]
Plug in the values into the equation
[tex] (6x - 20) + (6x - 20) + 76 = 360 [/tex]
[tex] 6x - 20 + 6x - 20 + 76 = 360 [/tex]
Add like terms
[tex] 12x + 36 = 360 [/tex]
Subtract 36 on both sides
[tex] 12x = 360 - 36 [/tex]
[tex] 12x = 324 [/tex]
Divide both sides by 12
[tex] x = 27 [/tex]
on Wednesday, James slept for [tex]\frac{3}{8}[/tex] of the day.
how many hours did James spend sleeping?
Answer:
I believe he slept for 9 hours of the day
Step-by-step explanation:
⅜ of 24
24 ÷ 8 = 3
3 × 3 = 9
The number of hours James slept is 9 hours.
What is an expression?In mathematics, an expression is a combination of symbols and numbers, often containing variables, that represents a quantity or a relationship between quantities.
Expressions can be simple or complex, and they can involve a variety of mathematical operations such as addition, subtraction, multiplication, and division.
The number of hours will be calculated as,
E = ⅜ of 24
E = 3 x ( 24 ÷ 8 )
E = 3 × 3
E = 9 hours
Therefore, the number of hours will be 9.
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Solve the equation.
S- (- 20) = 19
Answer:
s = -1
Explanation:
s − (−20) = 19
[ Simplify both sides of the equation ]
s + 20 = 19
[ Subtract 20 from both sides ]
s + 20 − 20 = 19 − 20
s = −1
- PNW
f(x) = x^2 + 2x – 4
f(3) = ?
Answer:
11
Step-by-step explanation:
f(3)=(3)^2+2(3)-4
f(3)=9+2(3)-4
f(3)=9+6-4
f(3)=15-4
f(3)=11
Looking for geometry proof help on a problem with parallelograms and an isosceles triangle
Answer:
Step-by-step explanation:
30. Given: rectangles QRST and RKST
Prove: ΔQSK is isosceles
An isosceles triangle is a triangle which has two sides and two angles to be equal.
Thus,
From rectangle QRST, the diagonals of rectangles are similar.
i.e RT ≅ QS (diagonal property)
Also, RT ≅ SK (opposite sides of rectangle RKST)
Thus,
RT ≅ QS ≅ SK
Therefore,
ΔQSK is an isosceles triangle.
31. Given: Rectangles QRST, RKST and JQST
Prove: JT ≅ KS
From rectangle QRST, the diagonals of rectangles are similar.
i.e RT ≅ QS (diagonal property)
But,
JT // QS and RT // KS
Thus,
JT ≅ QS (opposite sides of rectangle JQST)
also,
RT ≅ KS (opposite sides of rectangle RKST)
So that,
JT ≅ QS ≅ RT ≅ KS
Therefore,
JT ≅ KS
Which substitution method should be the best used to solve which system of equations
Answer: 6x+2y=1
Step-by-step explanation:
because it just is
What is the area of a hexagon with a side length of 10? it also has a rectangle in it with other measurements but the question is asking for the area of the hectagon.
Answer:
there is a formula for a hexagon .. it's
Area = 3[tex]\sqrt{3\\}[/tex]/2 * [tex]length^{2}[/tex]
where length is the length of one side, assuming all sides are equal
Step-by-step explanation:
3*[tex]\sqrt{3}[/tex]/2= 7.348469228.........
since the length is 10... the length squared is 100
then the total area of the hexagon is 734.8469228...... [tex]units^{2}[/tex].. what ever they are
if you want to work with some concepts.. you could also say that a hexagon is just a box with the corners cut off and the triangles that are missing are the equilateral right triangles with a hypotenuse of 10 . and since 2 pieces of those triangles make a square.. you can subtract two squares of that size from the bigger box that the hexagon fits into. this is a long way to figure this out but might be good for trigonometry practice :)
it will also be 734.8463288..... see if you can work that out :)
Find the average rate of change from x = 2 to x = 6 for the function f(x) = 3^x and select the correct answer below.
180
- 180
- 720
720
======================================================
Work Shown:
f(x) = 3^x
a = 2 = lower value of the interval
b = 6 = upper value of the interval
c = average rate of change of f(x) from a to b
c = ( f(b) - f(a) )/(b - a) ..... note how this mimics the slope formula
c = ( f(6) - f(2) )/(6 - 2)
c = ( 3^6 - 3^2 )/4
c = ( 729 - 9 )/4
c = 720/4
c = 180
The average rate of change from x = 2 to x = 6 for f(x) = 3^x is 180
A music store marks up the instruments it sells by 30%.
If the price tag on a trumpet says $104, how much did the store pay for it?
A. $ 58.50
B. $ 80
C. No, it did not mark up 30%.
Step-by-step explanation:Since,
A. We have,
Mark up percentage = 30%
Actual price = $ 45,
B. We have,
SP = $ 104,
C. We have,
AP = $ 75,
SP = $100,
Thus, mark up percentage =
= 33.33 %
Hence, store did not mark up the price by 30%.
Mr.Farrar spent a total of $43.87 after tax on new clothes at a clothing store. He brought 1 pair of sandals for $8.02 t-shirts fo $9.49 each and 1 pair of jeans. The tax on the purchase was $2.87 how much did Mr.Farrar pay for the pair of jeans?
Answer:
43.87 - 8 = 35.87 (sandals)
9.49 + 9.49 = 18.98 ( for two t-shirts)
35.87 - 18.98 = 16.89 (t-shirts)
16.89 - 2.87 = 14.02 (taxes)
Andrea payed $14.02 for a pair of jeans
Hopes this helps you!
Step-by-step explanation:
The high temperatures for two consecutive days were 83°F and 79°F. If the average(mean) high temperaature, including a third day, was greater than 82°F, then what was the high temperature on the third day? Write an inequality representing the problem.
Answer:
83F+79F+X
----------------- >82F
3
Step-by-step explanation:
X is the unknown temp, which is the third day. adding all those up and dividing that by 3 will give you the average. if the average is above 82F, then you just add a > symbol showing that its higher than 82F
Find the size of the angle 2 x
Answer:
Given - Angles measure 2x , X and 3x
To find - Measures of 2x
Solution -
2x + X = 180° ( forming linear pair )
3x = 180°
x = 180/3
x = 60°
2x = 2 × 60 = 120°
Answer:
120°
plz give brainlist
Step-by-step explanation:
since 2x and x form a straight angle you get the equation
2x + x = 180
combine like terms
3x = 180
devide by 3
x = 60
evaluate 2x
2(60) = 120
Kevin and his children went into a restaurant and he bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $2.25. He bought 3 times as many hotdogs as drinks.
Answer:
He bought 6 hotdogs and 2 drinks
Step-by-step explanation:
System of Equations
Kevin and his children went into a restaurant and bought $31.50 worth of hotdogs and drinks. Each hotdog costs $4.50 and each drink costs $2.25.
To solve the system of equations, we'll call the variables:
x = number of hotdogs
y = number of drinks
The first condition yields the equation:
4.50x + 2.25y = 31.50 [1]
It's also known he bought 3 times as many hotdogs as drinks, thus:
x = 3y [2}
Substituting [2] in [1]:
4.50(3y) + 2.25y = 31.50
Operating:
13.5y + 2.25y = 31.50
15.75y = 31.50
y = 31.50/15.75
y = 2
And
x = 3*2 = 6
He bought 6 hotdogs and 2 drinks
A veterinarian prescribes Benadryl for a dog with allergies. The recommended dosage is 3 mg per kg per day to be given in two doses. If your golden retriever weighs 67 lbs., how much Benadryl should he get in each dose? Round to nearest milligram.
Answer:
Each dose should be of 5.05 milligrams.
Step-by-step explanation:
To solve the present problem, it is necessary to first establish the equivalence between pounds and kilograms. Thus, 1 pound is equal to 0.453 kilograms. Therefore, the dog weighs about 30.35 kilograms (67 x 0.453), with which, since 3 milligrams must be applied for each kilogram of the animal's weight, 10.1 milligrams of Benadryl (30.35 / 3) should be applied.
Now, since Benadryl is applied in two doses, each of these doses should be 5.05 milligrams (10.1 / 2).
What is the slope of a horizontal line?
Answer:
Slope of a horizontal line. When two points have the same y-value, it means they lie on a horizontal line. The slope of such a line is 0, and you will also find this by using the slope formula.
A pipe is leaking in the school bathroom . it leaked 3 gallons of water in 6 hours.
Find the constant of proportionality
Answer:
0.5 gallons per hour
Step-by-step explanation:
Find the LCM of the denominators in these fractions
5/6 and 1/14
Answer:
35/42 and 3/42
Step-by-step explanation:
Multiply by 3.
HOPE THIS HELPS :)
The LCM of the denominators in the fractions 5/6 and 1/14 is 42.
What is Least Common Multiple(LCM)?The least common multiple is defined as the least positive integer that is dividable by both given numbers.
A group's Least Common Multiple (LCM) is the smallest number that is a multiple of all the numbers.
To find the least common multiple (LCM) of two numbers, you can list the multiples of each number and find the smallest number that is a multiple of both.
The multiples of 6 are 6, 12, 18, 24, 30, and so on. The multiples of 14 are 14, 28, 42, 56, and so on. The smallest number that is a multiple of both 6 and 14 is 42, so the LCM of 6 and 14 is 42.
Therefore, the denominators in the fractions 5/6 and 1/14 have an LCM of 42.
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Which graph below represents the solution to the inequality 6 x − 12 − x ≤ 3
Answer:
The solution is:
[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]
The graph of the solution is attached below.
Both the number line and graph is attached below.
Step-by-step explanation:
Note: you missed to add the graph options. Therefore, I am solving the inequality and adding the corresponding graph which would anyways clear your concept.
Given the inequality expression
[tex]6\:x\:-\:12\:-\:x\:\le \:3[/tex]
Group like terms
[tex]6x-x-12\le \:3[/tex]
Add similar elements: 6x-x=5x
[tex]5x-12\le \:3[/tex]
Add 12 to both sides
[tex]5x-12+12\le \:3+12[/tex]
simplify
[tex]5x\le \:15[/tex]
Divide both sides by 5
[tex]\frac{5x}{5}\le \frac{15}{5}[/tex]
simplify
[tex]x\le \:3[/tex]
Therefore, the solution is:
[tex]6x-12-x\le \:3\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x\le \:3\:\\ \:\mathrm{Interval\:Notation:}&\:(-\infty \:,\:3]\end{bmatrix}[/tex]
The graph of the solution is attached below.Both the number line and graph is attached below.
The value of y varies directly with the value of x. When y = 18, x = 3.
What is the value of x when y = 54?
Answer:
9
Step-by-step explanation:
y is 6 times x, so if you divide 54 by 6, you get 9. Hope this helps :)
Last month, Jennifer earned $143 for her after-school job. If she was paid $6.50 per hour, how many hours did Jennifer work?
A.18 hours
B.20 hours
C.22 hours
D. 24 hours
Answer:
22 hours.
Step-by-step explanation:
Using algebra:
6.5x = 143
6.5 6.5
x = 22