Answer:
Approximately [tex]35.2[/tex] points.
Step-by-step explanation:
Let random variables [tex]X_{1},\, \dots,\, X_{30}[/tex] denote the score of those [tex]30[/tex] test-takers. These random variables are independently and identically distributed. In other words, the scores follow the same distribution and are independent from one other.
While the exact distribution of each score is unknown, the mean and variance of this distribution are given: [tex]\mu = 1083[/tex] and [tex]\sigma = 193[/tex].
By the Central Limit Theorem, the mean (average) [tex]\overline{X}_{n}[/tex] of a sufficiently large number of such observations would follow a normal distribution. The mean of that distribution would be [tex]\mu[/tex] (same as the mean of the observations) while the variance [tex]{\rm Var}(\overline{X}_{n})[/tex] would be [tex](\sigma^{2} / n)[/tex].
Take the square root of variance to find the value of the corresponding standard deviation:
[tex]\begin{aligned}& \sqrt{{\rm Var}(\overline{X}_{n})} \\ =\; & \sqrt{\frac{\sigma^{2}}{n}} \\ =\; & \sqrt{\frac{193^{2}}{30}}\\ \approx\; & 35.2\end{aligned}[/tex].
What is the area of the trapezoid? Enter your answer in the bOx
Solution:
Note that:
Area of trapezoid = Area of rectangle + 2(Area of triangle)Finding the area of the square.
Area of rectangle = LB=> Area of rectangle = (8)(6)=> Area of rectangle = 48 in²Finding the area of the 2 triangles.
Area of triangle = 1/2 x Base x Height=> Area of triangle = 1/2 x 4 x 6Since there are two triangles with the same base and height, we will multiply the area by 2 to cover the other triangle.
=> Area of 2 triangles = 2(1/2 x 4 x 6)=> Area of 2 triangles = 4 x 6=> Area of 2 triangles = 24Finding the area of the trapezoid.
Area of trapezoid = Area of rectangle + 2(Area of triangle)=> Area of trapezoid = 48 + 24=> Area of trapezoid = 72 in²Jeff has four credit cards with limits of $4,000, $9,000, $3,600 and $11,300 respectively. If he has all of his cards charged up to 85% of his credit limit, how much does he owe?
Answer:
Jeff would owe $23,715
Step-by-step explanation:
$4,000+$9000+$3600+$11300x 0.85 = $23,715
Find the value of x.
Answer:
-7
Step-by-step explanation:
∠D = ∠B
2x² + 7 = x² - 8x
2x² - x² + 8x + 7 = 0
x² + 8x + 7 = 0
(x + 7)(x + 1) = 0
x = -7 or -1
For x = -7, we have
x² - 8x = 49 + 56 = 105
2x² + 7 = 2*49 + 7 = 105 Right, x = -7 is an answer
For x = -1, we have
x² - 8x = 1 + 8 = 9 < 90
In the diagram angle B is > 90, so x = -1 is not the answer.
What is the surface area of this triangle prism
Answer:
Surface area = (Perimeter of the base × Length of the prism) + (2 × Base Area) = (S1 + S2+ S3)L + bh;
PLEASE HELP IM ALMOST DONE WITH THE CLASS
Answer: B
Step-by-step explanation:
What is the domain and range
Answer:
Its A
Step-by-step explanation:
LEARNING TASK 2 illustrate each of the following and label the diagram.
1. point B lies in plane M
2. line CD
3. point A
4. point F
5. line AT
ung tama po pls
Answer:
[tex]Please\ see\ attached\ photo[/tex]
Step-by-step explanation:
[tex]1.Plane\ is\ usually\ painted\ as\ a\ parallelogram,\ and\ the\ plane\ has\ infinite\ ductility.[/tex]
[tex]2.\ A\ line\ has\ no\ endpoints\ at\ both\ ends\ and\ can\ extend\ infinitely\ to\ both\ ends.[/tex]
[tex]3.\ Points\ are\ usually\ represented\ by\ dots[/tex]
[tex]4.\ Same\ as\ 3[/tex]
[tex]5.\ Same\ as\ 2[/tex]
I hope this helps you
:)
Quadrilateral GHIJ is similar to quadrilateral KLMN. Find the measure of side NK.
Figures are not drawn to scale.
Answer:
NK = 14.4
Step-by-step explanation:
Given the following question:
We know that the two sides are similar
JI = 3, NM = 7.2
The scale factor is 2.4 since....
[tex]3\times2.4=7.2[/tex]
Knowing the two sides are similar and if we multiply JI by 2.4, we get NM we can easily do the same for JG and NK.
JG = 6
[tex]6\times2.4=14.4[/tex]
[tex]=14.4[/tex]
NK = 14.4
Hope this helps.
1. THE CAR WAS BOUGHT BY MY BROTHER. Active or passive
Answer:
The sentence is passive.
(Btw this is English lol, not mathematics)
On Sandy's scale drawing of the school campus 2 inches equals 4 yards the distance between the swings and the tracks is 10 inches of the drawing and the distance between the track and the basketball court is 4 inches on the drawing how much farther is the track from the swings than from the basketball court in the actual distance?
Answer:
The answer would be 20 because 2x2=4 right so 10x2=20
Step-by-step explanation:
What’s the untit rate for 400 miles on 20 gallons
Answer:
20 miles per gallon
Step-by-step explanation:
We want a unit rate where
1 is in the denominator
so we divide top and bottom by 20
[tex]\frac{400 miles/20}{20 gallons/20}[/tex] = [tex]\frac{20 miles}{1 gallon}[/tex] = 20 miles a gallon
PLEASE PLEASE HELP
Connor needs 60 mL of a 19% acid solution for a science experiment. He has available a 21% solution and a 15% solution.
How many milliliters of the 21% solution and how many milliliters of the 15% solution should he mix to make the 19%
solution?
Answer:
Let x = ml of 21% solution
Let y = ml of 15% solution
ATQ,
x + y = 60.....(1)
or
0.21x + 0.15y = 0.6....(2)
Multiplying equation 1st by 0.21, we get,
0.21y+0.21y =12.6....(3)
subtracting equation 3
0.21y+0.21y =12.6
-0.21x +0.15y = 0.6
_________________
ㅤㅤㅤ 0.6y = 12
_________________
6y = 12
y = 20ml
x= 60-20 = 40 ml
Hence , Conner needs 20ml of 21% solution & 40ml of 15% solution
what is 8 & 3/4 x 3
(I need this today!)
3/4 x 3 = 9/4
Since you need to multiply first you add the 8 later after you solve the multiplication
8 9/4
Answer:
26 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
8[tex]\frac{3}{4}[/tex] = [tex]\frac{(8x4)+3}{4}[/tex] = [tex]\frac{35}{4}[/tex]
[tex]\frac{35}{4}[/tex] x [tex]\frac{3}{1}[/tex] = [tex]\frac{105}{4}[/tex] = 26.25 = 26 [tex]\frac{1}{4}[/tex]
A farmer had a total of 700 goats and sheep. If he sold of his goats and
400 sheep, he would have an equal number of goats and sheep left. How
many more sheep than goats did he have in the beginning?
Answer:
300 rxc icz ugv ddhhbs hhjo
What is the trigonometric ratio for sin C?
Enter your answer, as a simplified fraction.
Answer:
(9/40)
Step-by-step explanation:
Sin is Opposite/Adjacent
sin(C) = AB/BC
We can find the value of AB by using the Pythagorean Theorem:
a^2 + b^2 = c^2
(80)^2 + b^2 = (82)^2
b = 18
sin(C) = 18/80 or (9/40)
Is negative one a rational number?
Answer: -1 is a rational number.
Step-by-step explanation: -1 is a rational number because it is an integer. An integer can be any number, such as -5, 5, 0, 3, etc.
Rational numbers can also be perfect squares (i.e square root of 25), it can be repeating decimals or decimals in general.
Irrational numbers are numbers that cannot be written as a fraction OR that are imaginary.
Irrational numbers would be repeating decimals that do not have the same values repeated, such as Pi. Pi cannot be written as a fraction, only estimated. Irrational numbers can also be imaginary numbers such as the square root of -4. There is no number in this world that can multiply itself and become -4. A negative times a negative is positive, and a positive times a positive is a positive. This means the square root -4 is imaginary and therefore irrational.
Answer:
Yes.
Step-by-step explanation:
All integers, fractions, whole numbers & natural numbers fall into the category of rational numbers.
How are integers rational numbers?
The definition of rational numbers says that any number that can be written in the form of p/q, where p & q are integers & q is not equal to 0 are categorised into rational numbers. This is in the form of the fraction. We know that, by dividing the integers by 1, we'll get them as a fraction. Sp, integers are rational numbers.
For example:
- 1 = -1/1 (p/q form; so it's a rational number)
________
Hope it helps ⚜
What is the area of the figure At the right explain how you found your answer use the formula A = 1/2 bh to find the area of the triangle and A = bh for the area of a parallelogram
By comparing the figure with simpler shapes (rectangles and triangles) we will see that its area is 30ft^2.
How to get the area?
The area of the figure will be equal to the difference between the area of a 5ft by 10 ft rectangle, and the area of the 3 triangles that can be formed.
The area of a 5ft by 10ft rectangle is:
A = 5ft*10ft = 50ft^2
For the 3 triangles we have:
2 triangles with a base of 5ft - 3ft = 2ft, and a height of 10ft/2 = 5ft.
(these are the two left triangles).
Remember that for a triangle of base b and height h, the area:
A = b*h/2
Then for each of these triangles, the area is:
A' = (2ft*5ft)/2 = 5ft^2
And we have two of these, so the areas add up to 10ft^2.
For the right triangle, we can see that its base measures 10 ft, and its height is of 2 ft, then its area is:
A'' = (10ft*2ft)/2 = 10ft^2
Then the area of the figure is:
Area = A - 2A' - A'' = 50ft^2 - 2*(5ft^2) - 10ft^2 = 30ft^2
If you want to learn more about areas, you can read:
https://brainly.com/question/24487155
Si un gramo de chocolate vale$38.25¿cuánto costarán 750 gramos?
Answer:
28687.5
Step-by-step explanation:
Un gramo equivale a $38,25, por lo que si tenemos 750 de esos gramos, tendríamos que multiplicarlos para obtener el costo total.
Utilize graphing to find the solution to
the following system of equations.
y = 2x 1 AND y = x - 3
-
([?], [])
Step-by-step explanation:
Thr solution to a system of equations when graphing is the point of intersection of teh lines
Find the value of x, y, and z, in the rhombus below.
Answer:
Step-by-step explanation:
please help me answer this asap thank you
In circle N chord CD is 18. Find the length of the radius to the nearest tenth.
The radius of the given circle is 12.1 (correct to the nearest tenth), computed using chord properties.
We assume the radius of this circle to be x.
By the theorem saying that a perpendicular from the center of the circle to a chord, bisects the chord, we can say that CE = ED = 0.5CD = 0.5*18 = 9.
Now, we know that NC = NA = radius of the circle = x.
We are given that AE = 4.
Therefore, NE = NA - AE = x - 4.
Now, in right-angled triangle NEC, by Pythagoras theorem, we can say that,
NC² = CE² + NE²
or, x² = 9² + (x - 4)²
or, x² = 81 + x² - 8x + 16
or, x² - x² + 8x = 97
or, 8x = 97
or, x = 97/8 = 12.125 ≈ 12.1 (correct to the nearest tenth, that is, rounding off up to one decimal place).
Learn more about chord properties at
https://brainly.com/question/13950364
#SPJ10
A farmer needs to mix 12 ounces of fertilizer for every 10 pounds of soil. How many pound of fertilizer will the farmer need to make a mix that contains 120 pounds of soil?
If A= [
4 3 1
8 6 2
1 1 5
]
ii) Is it possible to determine the inverse of the matrix? If possible find the
inverse of the matrix
Answer:
√384 esa es la respuesta ayudame a mi porfa
What is the perimeter of a square that has a side of 20
Answer:
80 cm
Step-by-step explanation:
perimeter = Side × 4 = 20 × 4 = 80 cm
I hope you understand...
work out the area of the parallelogram
Answer:
b x h
Step-by-step explanation:
hi guys can u pls help me thank u
Answer:
D. Knowing that 5^2 + 9^2 < 12^2, draw the 5 cm side and the 9 cm side
with a right angle between them. The 12 cm side will fit to form a
right triangle
Step-by-step explanation: mark me brainliest!!
Hypotenuse = h
Altitude = lBase = bl²+b²=h²
Here 6²=369²=8112²=14415²=225
From the above it is clear that81+144=225⇒9²+12²=15²
30 more than the quotient of b and c
Answer:
b/c+30
Step-by-step explanation:
Evaluate - (3-1)(3-2).
A. -27
B. 27
C. -1/27
D. 1/27
Choose the inequality that represents the following graph.HELP HELP HELP
Solution:
It should be noted:
If the starting point of the inequality is half shaded, the sign will be < or >.If the starting point of the inequality is fully shaded, the sign will be ≤ or ≥.We can tell that:
The inequality will either have an < or > sign.The blue line tells us that the value of x must be greater than -1.This clearly tells us that the inequality is x > -1
In conclusion:
Option C is correct.
Someone help and please make sure the answer right pls, pls help I’m confused
Answer:
it's the third bubble
Step-by-step explanation:
Answer:
n³ - 2n² - 3n + 2 + (2 / x - 4)
Step-by-step explanation:
n^4 - 6n³ + 5n² + 14n - 6
(n - 4) x n³
n^4 - 6n³ + 5n² + 14n - 6
-n^4 + 4n³
-2n³ + 5n² + 14n - 6
(n - 4) x -2n²
-2n³ + 5n² + 14n - 6
2n³ - 8n²
-3n² + 14n - 6
(n - 4) x -3n
-3n² + 14n - 6
3n² - 12n
2n- 6
(n - 4) x 2
2n - 6
-2n + 8
R. 2 / x - 4
I hope this helps!