The probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
We can use the Central Limit Theorem and the standard normal distribution to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample means will approach a normal distribution, regardless of the distribution of the population.
Since we have a sample of 80 observations, we can assume that the sample mean follows a normal distribution with a mean of 1460 (the population mean) and a standard deviation of:
Standard deviation of the sample mean
= population standard deviation ÷ [tex]\sqrt {sample size[/tex]
[tex]= 270 \div \sqrt{80} = 27[/tex]
So the standard deviation of the sample mean is 27.
We can now standardize the interval between 1300 and 1400 by subtracting the mean and dividing it by the standard deviation of the sample mean.
[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59
[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22
We need to find the area under the standard normal distribution curve between Z1 and Z2.
Using a standard normal table or a calculator with the standard normal distribution function, we can find the probability that a random variable from the standard normal distribution is between -2.59 and -2.22. This probability is approximately 0.0134 or 1.34%.
Therefore, the probability that the sample mean is between 1300 and 1400 is approximately 1.34%.
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decide whether the function is a polynomial function. If so right it in standard form and state it’s degree type in leading coefficient if so write it in standard form and state its degree type in leading coefficient P(x)=-3x^2+10-4x
For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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Select the interval where the graph h is negative.
Answer: C
Step-by-step explanation:
Based on the graph, we know that it is negative if it is under the x-axis. It is also indicated by the negative labels.
A: incorrect
Looking at choice A, it says the interval is from -3<x<-2. This means we have to find x=-3 and x=-2. On the graph, that interval is above the x-axis, so it is positive, not negative.
B: incorrect
Looking at choice B, it says the interval is from 2<x<3. This means we have to find x=2 and x=3. On the graph, that interval is above the x-axis, so it is positive, not negative.
C: correct
Looking at choice C, it says the interval is from 4<x<5. This means we have to find x=4 and x=5. On the graph, that interval is under the x-axis, so it is negative.
Therefore, C is the correct answer.
Anybody know the answer to this? this is due very soon :(
Answer:
Step-by-step explanation:
7,80
Which fraction is equivalent to 1/2? Use the number line to help answer the question
Answer:
4/8
Step-by-step explanation:
Approximately 3.4% of Americans are vegetarian. If we ask a random sample of 36 people, what is the probability that exactly 4 of them are vegetarian?
Answer:
0
Step-by-step explanation:
Given: 3.4% of Americans are vegetarian.
sample size = 36 people
Therefore, 3.4% of 36 = 1.224.
Hence, out of 36 people only 1.224 people which is approximately 1 is vegetarian.
So, the probability of exactly 4 people being vegetarian out of 36 people would be zero.
As out of 36 only 1 was vegetarian.
Hence, the correct answer would be 0
How is 0.1363636363636363636... written as a fraction in simplest form?
.
Answer:
3/22
Step-by-step explanation:
There's a very neat trick for this kind of problem.
First, choose a letter to represent the number.
n = 0.1363636...
Observe that there is a 2-digit block that repeats ("36"), but that block does not repeat immediately to the right of the decimal point. Do two muliplications, one to put the decimal point in front of the repeating block, the other to put the decimal point after the block.
10n = 1.363636...
1000n = 136.363636...
Here comes the cool part: subtract the first equation from the second.
990 n = 135 See? The repeating decimal parts, all lined up as they are, subtract to zeros.
Finally, n = 135/990 = 15/110 = 3/22
Perform the indicated operation. Be sure the answer is reduced.
2a + 1 5 2a-3
———— + — - ——— =
3a 4 6a^2
Find two numbers if thier sum is -11 and there difference is 41. PLS HELP ME
Answer:
x = 15
y = -26
Step-by-step explanation:
x + y = -11
x - y = 41
let x = 41 + y
substitute:
41 + y + y = -11
2y = -52
y = -26
x -26 = -11
x = 15
Does anyone know c & d please
Answer:
c = 100 or 10^2
d = 3125 or 5^5
Step-by-step explanation:
c. the answer for C is 10^2 because you just subtract the exponents same goes for d.
the ball rolls downhill, its kinetic energy increases and its potential energy ________
Maximum
Minimum
.
The Ball Rolls Downhill, It's Kinetic Energy Increases And It's Potential Energy Maximum.
Hope Helps! :)
[tex] \: \: [/tex]
the sum of 8 times a number and 6 is 3
Answer:
Sum means '+'
is means '='
a number means 'x'
3x + 6 = 8
I hope this helped!
compared to the cost of each share in 1960.
Company
1960 Cost
2010 Cost
Company A
$0.65
$9.75
Company B
$0.25
$3.80
Company C
$0.45
$3.78
The cost of each share of stock in Company A was nothing times as much in 2010.
(Type an integer or a decimal.)
Answer:
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explajyhgftdcsesdxqadfadrfswfeedfrsdx:
10% of 84 is what number?
Answer:
8.4 is 10% of 100
Step-by-step explanation:
84 is 100%
x is 10 %
x= 84*10/100= 8.4
Johhny earns $2,334.50 from his job each month. He pays $1,437 for monthly expenses. Johnny is planning a vacation in 3 months' time that he estimates will cost $1,750 total. How much will Johnny have leftover from three months of saving once he pays for his vacation?
Answer:
2,302,63
Step-by-step explanation:
................
Answer:
942.50
Step-by-step explanation:
First, multiply 2334.50 by 3 to get 7003.50. Then multiply 1437x3= 4311
7003.50-4311=2692.50 Then take away 1750. 2692.50-1750=942.50
I hope this helps! UWU
-2x+20y=-18
8x+10y=-18
Answer:
x = -1
y = -1
Step-by-step explanation:
This is a system of equations- the set up of the problem lends well to using the elimination method. There are always many ways of solving a system of equations, both in methods and different strategies within each method. The problem isn't necessarily complete but I can assume you're being asked to solve for x and y values.
divide the first equation by -2. this means we can use elimination to cancel out the y value, and is also our simplest option (rather than multiplying the second equation by -2.
-2x + 20y = -18 --> x - 10y = 9
x - 10y = 9
8x + 10y = -18
Using the elimination method to essentially add the parts of the equations together, this comes out to 9x = -9 , meaning x = -1 .
We can then return to our original equations, and substitute -1 for x (either equation will work, but the second one is simpler and therefore the better option).
8 (-1) +10y = -18
-8 + 10y = -18
10y = -10
y = -1
CHECKING
Substitute both x and y values back into the original equations to check them. the sides should be equal if our values are correct.
-2 (-1) + 20 (-1) = -18
Our first equation works: 2 - 20 = -18
8 (-1) + 10 (-1) = -18
The second equation works as well: -8-10= -18
Which equation has 3 as a solution set *?
The equation 3x - 9 = 0 has 3 as a solution out of all the given equations in the options.
Check the solution of equation 3x - 9 = 0
3x - 9 = 0
3x = 9
x = 3
Check the solution of equation 4x - 3 = 0
4x - 3 = 0
4x = 3
x = 3/4
Check the solution of equation 5x - 10 = 0
5x - 10 = 0
5x = 10
x = 10/5
x = 2
Check the solution of equation 7x - 49 = 0
7x - 49 = 0
7x = 49
x = 49/7
x = 7
Thus, only 3x - 9 = 0 satisfy the solution x = 3.
Hence, the correct option is A.
--The given question is incomplete, the complete question is
''Which equation has 3 as a solution set?
A. 3x - 9 = 0
B. 4x - 3 = 0
C. 5x - 10 = 0
D. 7x - 49 = 0''--
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The endpoints of a line segment AB are (1, -6) and (5, -6). The equation of a line BC is
y=x-11. Is triangle ABC a right triangle? Justify your answer.
No, triangle ABC is not a right triangle. The equation of a line BC "y=x-11" is a line with slope of 1, which means it has an angle of 45 degrees with respect to the x-axis. The segment AB has a slope of 0, which means it is parallel to the x-axis. A right triangle's legs must be perpendicular, therefore a line with a slope of 1 and a line with a slope of 0 cannot be the legs of a right triangle.
A RIGHT TRIANGLEA right triangle is a triangle in which one of the angles is 90 degrees. In order for a triangle to be a right triangle, the two sides (or legs) that form the 90-degree angle must be perpendicular to each other. Perpendicular lines have slopes that are negative reciprocals of each other.
In this case, the equation of the line segment AB is "y = -6", which means it is parallel to the x-axis. The slope of a line parallel to the x-axis is 0. On the other hand, the equation of the line BC is "y = x - 11", which means it has a slope of 1. A slope of 1 means that the line is at a 45 degree angle with respect to the x-axis.
Since the slopes of the two lines are not negative reciprocals of each other (0 and 1), the legs of the triangle cannot be perpendicular. Therefore, triangle ABC cannot be a right triangle.
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h=?ft
what is the correct answer
Answer:
h = 4 ft
Step-by-step explanation:
the area (A) of a parallelogram is calculated as
A = bh ( b is the base and h the perpendicular height )
here b = 8 and h = 3 , then
A = 8 × 3 = 24 ft²
Now consider the other base b = 6 with perpendicular height h , then
6h = 24 ( divide both sides by 6 )
h = 4
i will rank brainliest!!
Answer:
WO = 10
NE = 90
NT = 42
Step-by-step explanation:
scale factor of 6
a builder wishes to fence in 60,000m of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost 20 per meter, while the fence for the other three sides will cost 10 per meter. how much of each type of fence should the builder buy to minimize the cost of the fence
The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.
To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.
To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:
2x + 2y = 60,000
To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:
60,000 - x = 3x + 2y
The total length of the three sides that are not the front is 3x + 2y.
Now we can calculate how much the builder will pay for each type of fence:
Cost of front fence = $20/m * x = $20xCost of other three sides = $10/m * (3x + 2y) = $30x + $20yTotal cost of the fence = $20x + $30x + $20y = $50x + $20y
To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.
However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:
x meters of $20/m fence for the front side3x + 2y meters of $10/m fence for the other three sides.This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.
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please help me if you can! ( links= report )m
Answer:
Volume (V) = 2522.0 mm^3
Step-by-step explanation:
The volume of cylinder is :
V = π r 2 h
We know that the height (h) is 19.
We also know the radius (r) is 13/2 = 6.5
So,
V = π 6.5^2*19
V = 2522.0 mm^3
can someone please tell which congruency do you use and how?
To prove that ΔABC is isosceles.
Properties of an isosceles triangle.An isosceles triangle is a type of triangle in which the length of its two sides, and measure of its two internal angles are equal. When a bisector of an angle is drawn to one of the internal angles of the triangle, two congruent triangles of corresponding properties are produced.
To prove that ΔABC is isosceles, we have:
<CAD ≅ <BAD (definition of an angle bisector)
CD ≅ BD (definition of a midpoint)
AC ≅ AB (congruent sides of an isosceles)
<ACD ≅ <ABD (congruent internal angles of an isosceles)
<ADC ≅ <ADB (definition of right angle)
Therefore it can be concluded that;
ΔABC is an isosceles triangle (Angle-Side-Side theorem)
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From midnight to 2:00 am, the temperature dropped 1.4 °c each hour. If the temperature at 2:00am was 11.2 °c, what was the temperature at midnight
The temperature at midnight as required to ve determined in the task content is; 14°C.
What is the temperature at midnight as required to be determined from the given information.According to the task content; the temperature was 11.2°C at 2 : 00am.
However, since the temperature dropped 1.4 °c each hour; we have that;
In the two hours between midnight and 2:00am, the total temperature drop is; 2 × 1.4°C = 2.8°C.
On this note, the temperature at midnight can be evaluated as; 11.2°C + 2.8°C = 14°C.
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Please help me solve this problem. I attached a pic of it.
Answer:
Surveying every 5th customer that enters the yogurt shop
Step-by-step explanation:
•225+225 = ?
•5/25 = ?
•78-8 = ?
•13*1 = ?
Step-by-step explanation:
hope it is helpful to you
A stack of identical 8-centimeter-by-10-centimeter rectangular playing cards is sitting on a table. The stack is 1 centimeter high and has a volume of 80 cubic centimeters. The table is bumped and the stack of cards is shifted so that the stack is no longer a right rectangular prism, but all of the cards are still part of the stack.
Which of the following statements are true of the shifted stack of cards? Select all that apply.
A) The shifted stack of cards has a volume of 80 cubic centimeters because it has the same base area and height.
B) The area of a card at any location in the stack remains the same.
C) The width of the stack from the leftmost edge to the rightmost edge will remain 10 centimeters because the volume is the same.
D) Cavalieri’s principle cannot be applied to the volume of the stack because the stack is a rectangular prism instead of a cylinder.
E) The area of the middle card in the stack is 40 square centimeters because it is half of 80.
Answer: A, B, C.
If the stack of cards are shifted so it is not straight, it still has everything the same.
dont even know where to start
Answer:
[tex] \displaystyle M = ( 3,1 )[/tex]
Step-by-step explanation:
we are given the endpoint i.e P and Q of a line segment
we want to figure out the Midpoint of the Line segment
in order to do so we can use Midpoint formula given by
[tex] \displaystyle M = \bigg( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2}}{2} \bigg)[/tex]
so let
[tex]x_1=-2\\x_2=8\\y_1=-2\\y_2=4[/tex]
substitute
[tex] \displaystyle M = \bigg( \frac{ - 2 + 8}{2} , \frac{ - 2 + 4}{2} \bigg)[/tex]
simplify addition:
[tex] \displaystyle M = \bigg( \frac{ 6}{2} , \frac{ 2}{2} \bigg)[/tex]
simplify division:
[tex] \displaystyle M = ( 3,1 )[/tex]
hence,
the Midpoint of the line segment is (3,1)
Number 9 is very confusing for me
Answer:
The value of x is 2/7 or 0.285
Step-by-step explanation:
Here, we will make equivalent expressions in the equation that all have equal bases.
6²⁽⁶ˣ⁻¹⁾ = 6⁵ˣ
Since, The bases are the same i.e., 6. So, exponent are also same
2(6x - 1) = 5x
Solve for x
12x - 2 = 5x
12x - 5x - 2 + 2 = 5x - 5x + 2
7x = 2
7x/7 = 2/7
x = 2/7 = 0.285
Thus, The value of x is 2/7 or 0.285
For verification
36⁶ˣ⁻¹ = 6⁵ˣ
36⁶⁽⁰°²⁸⁵⁾ ⁻ ¹ = 6⁵⁽⁰°²⁸⁵⁾
36¹°⁷¹ ⁻ ¹ = 6¹°⁴²⁵
36⁰°⁷¹ = 6¹°⁴²⁵
12.7 = 12.7
Hence, L.H.S = R.H.S
VERIFIED!!
Please help!! I will give brainliest and no links!! Also please do it in a picture model “standard algorithm” please do both questions!
Find the quotient of 4,611 divided by 21.
Answer:
1. 219.571428571
2. 150.314285714
Can you help me with this