The Central Limit Theorem states that over a large number of samples, the sampling average of the sample means would be closer to the population mean.
What does the Central Limit Theorem state?The Central Limit Theorem states that for a random variable X, with mean given by [tex]\mu[/tex] and standard deviation given by [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
This means that over a large number of trials, i.e., of samples from the population, the mean of the sample means will be close to the population mean, with a small standard error, as the standard error is inversely proportional to the square root of the sample size.
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please help to find the value of x and explain how to get it in simple terms.
SOLUTION
From the image above
[tex]\begin{gathered} z^2=6^2+3^2\ldots\text{ by pythagora's rule } \\ z^2=36+9 \\ z^2=45 \\ z=\sqrt[]{45} \end{gathered}[/tex]Considering the bigger right angle triangle,
[tex](3+x)^2=y^2+45[/tex]We can obtain the expression of y from the smaller right angle triangle,
Using pythagora's rule, we have
[tex]y^2=6^2+x^2[/tex]Then, recall
[tex](3+x)^2=y^2+45[/tex]Substite the expression for y², we have
[tex](3+x)^2=6^2+x^2+45[/tex]Expand the paranthesis, we have
[tex]\begin{gathered} 9+6x+x^2=x^2+36+45 \\ \text{Subtract x}^2from\text{ both sides } \\ 9+6x=36+45 \\ \end{gathered}[/tex]subtract 9 from both sides, we have
[tex]\begin{gathered} 6x+9-9=81-9 \\ 6x=72 \end{gathered}[/tex]Divide both sides by 6, we obtain
[tex]\begin{gathered} \frac{6x}{6}=\frac{72}{6} \\ \text{Then} \\ x=12 \end{gathered}[/tex]Therefore
Answer: x= 12
What is the slope of this line?
What is the slope of this line?
Enter your answer as a whole number or a fraction in simplest form in the box.
Answer: 1
Step-by-step explanation: Rise over run, Rise/run. The rise is how much the line goes up or down vertically. The run is how far the line goes until it intersects through a square. The slope is 1 because if you look at the line specifically at the first dot, you just have to go down one and right one as it intersects the square to find the slope.
Please help last question and super confused!! ASAP
Given the function:
h(x) = -2/3x+4/5
Find the following values
A) h(3)
B) h(4)
C) h(-1/2)
A line passes through the points (–3, –4) and (6, 2).
A coordinate plane.
What is the x-intercept of this line?
Answer:
x intercept is -3
Step-by-step explanation:
We need to find the equation for the line First we find the slope m = (y2-y1)/(x2-x1) = (2- -4)/(6- -3) = (2+4)/(6+3) =6/9 = 2/3 The we can write the equation y= mx+b y = 2/3x +b We can substitute in (6,2) 2 = 2/3(6) +b 2 =4+b Subtract 4 from each side 2-4 =b b =-2 y = 2/3 x-2 We want to find the x intercept, so set y =0 and solve for x 0 = 2/3x -2 Add 2 to each side 0-2 = 2/3x Multiply each side by 3/2 to isolate x -2 *3/2 = 2/3x * 3/2 -3 =x The x intercept is -3
9) Determine the domain and range of the function represented in the graph. A. Domain: – 1
we know that
The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y
so
In this problem
The domain is the interval {-1,3}
so
[tex]-1\leq\text{ x }\leq3[/tex]The range is the interval {-4,5}
so
[tex]-4\leq\text{ y}\leq5[/tex]answer Option A
3 What is the range of the function shown
in the graph?
Answer:
D y < 8
Step-by-step explanation:
the range is the interval or set of all valid y (functional result) values.
we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.
8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").
and therefore we cannot say y <= 8.
we have to use y < 8.
A recent math test had an average score of 75, with a standard deviation of 10. What percentage of people scored an 85 or higher?16%34%50%, 13.5%
Answer:
16%.
Explanation:
In a recent math test:
• The average score = 75
,• Standard Deviation = 10
To find: The percentage of people who scored an 85 or higher, P(X>85).
First, find the z-score when X=85.
[tex]z-score=\frac{X-\mu}{\sigma}[/tex]Substitute the given values:
[tex]z=\frac{85-75}{10}=\frac{10}{10}=1[/tex]The people who scored an 85 or higher are 1 standard deviation away from the mean.
[tex]13.5\%+2.35\%+0.15\%=16\%[/tex]The percentage of people who scored an 85 or higher is 16%.
Find the average rate of change of his annual salary between 2017 and 2020
We were told that the salary, t years after 2015 is given by the function,
S(t) = 3100t + 56000
When considering 2017, the number of years, t from 2015 is 2017 - 2015 = 2
We would substitute t = 2 into the function and find S(2)
Thus,
S(2) = 3100 x 2 + 56000 = 6200 + 56000 = 62200
When considering 2020, the number of years, t from 2015 is 2020 - 2015 = 5
We would substitute t = 2 into the function and find S(2)
Thus,
S(5) = 3100 x 5 + 56000 = 15500 + 56000 = 71500
Thus, we can say that
when
x1 = 2, y1 = 62200
when x2 = 5, y2 = 71500
Recall,
slope or average rate of change = (y2 - y1)/(x2 - x1)
average rate of change = (71500 - 62200)/(5 - 2) = 9300/3
average rate of change = 3100
The last option is correct
Match each equation to one of the lines
5x + 3y = 20
The graph of the linear function 5x + 3y = 20 is given at the end of the answer.
How to graph a linear function?To build the graph of a linear function, we identify two points on the line, and then plot a line passing through them.
In this problem, the function is:
5x + 3y = 20.
The points that we are going to choose are the intercepts. The x-intercept is the value of x when y = 0, hence:
5x = 20
x = 20/5
x = 4.
Meaning that point (4,0) is on the graph of the function.
The y-intercept is the value of y when x = 0, hence:
3y = 20
y = 20/3
y = 6.67.
Meaning that point (0, 6.67) is on the graph of the function.
The graph is plotted with a line passing through the points (4,0) and (0, 6.67).
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Find the value of x .
Answer:
x = 113
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
here n = 8 , then
sum = 180° × 6 = 1080°
sum the interior angles and equate to 1080
x + 137 + 144 + 139 + 123 + 150 + 142 + 132 = 1080
x + 967 = 1080 ( subtract 967 from both sides )
x = 113
This is the only question I’m stuck on can someone explain and help me
Answer:
x = 58°
∠P = 58°
∠PQR = 64°
Step-by-step explanation:
If you add the two nonadjacent angles together they will equal the exterior angle. Setup up an equation using that info.
[tex]58 +x=2x[/tex]
Solve for x.
[tex]58 +x-x=2x-x\\58=x[/tex]
Since ∠P is the same as x, ∠P = 58°
To find ∠PQR, add ∠P and ∠R together and then subtract from 180°. You subtract from 180° because the sum of the three angles of a triangle equal 180°.
58 + 58 = 116
180 - 116 = 64°
∠PQR = 64°
Amira is younger than Marques. Their ages are consecutive integers. Find Amira's age if the sum of Amira's age and 2 times Marques's age is 38.
Amira's age is 12 years when Amira is younger than Marques and their ages are consecutive integers and the sum of Amira's age and 2 times Marques's age is 38.
According to the question,
We have the following information:
Amira is younger than Marques.
Their ages are consecutive integers.
The sum of Amira's age and 2 times Marques's age is 38.
Now, let's take Amira's age to be x years.
Then, Marques's age will be (x+1) years.
So, we have:
x + 2(x+1) = 38
x + 2x + 2 = 38
3x+2 = 38
3x = 38-2 (Moving 2 from the left hand side to the right hand side will result in the change of the sign from plus to minus.)
3x = 36
x = 36/3
x = 12 years
Hence, Amira's age is 12 years.
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Find the velocity of the car at the end of a drag race. Round to the nearest whole number.
Answer:
183 miles per hour.
Explanation:
The estimated velocity(v) at the end of a drag race is modeled using the formula below:
[tex]v=234\sqrt[3]{\frac{p}{w}}[/tex]Given:
• The horsepower, p = 1311
,• The weight (in pounds), w = 2744 pounds.
Substitute into the formula above:
[tex]\begin{gathered} v=234\sqrt[3]{\frac{1311}{2744}}=182.9 \\ v\approx183\text{ miles per hour} \end{gathered}[/tex]The velocity is approximately 183 miles per hour.
( f - 12) + Pf decreased by the sum of 12 and p is it correct?
The sum of 12 and P can be written as 12 + P
Then, f decreased by the sum of 12 and P can be written as:
f - (12 + P)
Answer: it isn't correct, the correct answer is f - (12 + P)
suppose a large shipment of televisions contained 9% defectives. if a sample of size 393 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%? round your answer to four decimal places.
The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624, or 96.24%.
We must comprehend the central limit theorem and the normal probability distribution in order to answer this query.
Distribution of Normal Probabilities
The z-score formula can be used to address problems with normal distributions.
The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:
The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p-value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.
Imagine that 9% of a huge shipment of televisions were defective.
As a result, the sample size has a p value of 0.09
As a result, n=393
Standard deviation and the mean
u=p= 0.09
s= sqrt(p(1-p)/n)
s=sqrt(0.09*0.91/393)= 0.0144
What is the likelihood that the sample percentage and population proportion will deviate by less than 3%?
The ratio of 0.09 - 0.03 = 0.06 to 0.09 + 0.03 = 0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p-value of Z when X = 0.06.
X = 0.12
By the Central Limit Theorem
Z= x-u/s
Z=2.08 has a p-value of 0.9812
X = 0.06
Z= x-u/s
Z=-2.08 has a p-value of 0.0188
0.9812 - 0.0188 = 0.9624
Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.
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Answer:
Step-by-step explanation:
The probability that the sample percentage will deviate from the population proportion by less than 3% is 0.9624.
Distribution of Normal Probabilities
The z-score formula can be used to address problems with normal distributions.
The z-score of a measure X in a set with mean and standard deviation can be calculated as follows:
The Z-score calculates how far a measure deviates from the mean by standard deviation. We look at the p- value linked with this Z-score after determining the Z-score by consulting the z-score table. This p-value represents the probability that the measure's value is less than X, or the percentile of X. 1 is subtracted from the p-value, giving us the likelihood that the value of the metric exceeds X.
Imagine that 9% of a huge shipment of televisions were defective.
As a result, the sample size has a p value of 0.09
As a result, n=393
Standard deviation and the mean u=p=0.09 s= sqrt(p(1-p)/n)
s=sqrt(0.09*0.91/393)=0.0144
The ratio of 0.09 -0.03=0.06 to 0.09 + 0.03 =0.12 is the result of subtracting the p-value of Z when X = 0.12 from the p- value of Z when X = 0.06.
X = 0.12
By the Central Limit Theorem
Z=x-u/s
Z-2.08 has a p-value of 0.9812
X = 0.06
Z=x-u/s
Z=-2.08 has a p-value of 0.0188
0.9812 -0.0188=0.9624
Therefore, The probability that the sample proportion and population proportion will deviate by less than 3% is 0.9624, or 96.24%.
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Write an expression for the calculation triple 4 and then add 6 times 6
Answer:
4x3+6x6=48
Step-by-step explanation:
PEMDAS
4x3=12
6x6=36
12+36=48
therefore, the answer is 48
If there are 16 successful outcomes in a sample with a size of 50, what is the
sample proportion?
OA. 0.55
OB. 0.16
OC. 0.34
OD. 0.32
The sample proportion is option(d) i.e, 0.32
What is Proportion?
A proportion is an equation in which two ratios are set equal to each other.
Given,
Number of successful outcomes = 16
Total number of outcomes = 50
The sample proportion =
Number of successful outcomes / Total number of outcomes
Sample proportion = 16 / 50
= 0.32
Hence, the sample proportion is option(d) i.e, 0.32
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There were 42 boys and 28 girls in a photography club. Then, 6 more girls joined the club. What was the ratio of the numbers of boys to the numbers of girls in the end? Express the ratio in its simplest form.
Given:
There are given that a total of 42 boys and 28 girls in the photography club.
Explanation:
According to the question:
We need to find the ratio.
So,
We can see a total of 28 girls and 6 more girls.
So,
The total number of girls is:
[tex]28+6=34[/tex]Then,
The numbers of boys to the numbers of girls in the end is:
[tex]\frac{42}{34}=\frac{21}{17}[/tex]Final answer:
Hence, the ratio is shown below:
[tex]21:17[/tex]
Evaluate the inverse when y=4. Show all of your work.
The inverse of the function y = 4ˣ is f⁻¹(x) = ㏑x / ㏑4.
What is termed as the inverse of the function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function "f" takes x to y, then its inverse will take y to x. The inverse function is signified by f-1 or F-1 if the function is signified by 'f' or 'F'. Here, (-1) should not be confused with exponent or reciprocal.For the given question;
The function is given as;
y=4ˣ
Interchange the variables of the function.
x = 4∧y
Taking log both side.
㏑ x = ㏑(4∧y)
Using the power rule of log function.
㏑ x = y㏑(4)
y = ㏑ x/㏑(4)
Now, replace y with f⁻¹(x).
f⁻¹(x) = ㏑ x/㏑(4)
Thus, the inverse of the function y = 4ˣ is found to be f⁻¹(x) = ㏑x / ㏑4.
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The correct question is-
Evaluate the inverse when y=4ˣ. Show all of your work.
3.2+2(-1.5)-3.4
(pls solve by doing the order of operations)
(step by step pls)
AS per the order of operations, the value of the expression 3.2+2(-1.5)-3.4 is -3.2
Order of operations:
Order of operations states the rule that tells the correct sequence of steps for evaluating a math expression.
The order using PEMDAS:
Parentheses,
Exponents,
Multiplication and Division (from left to right),
Addition and Subtraction (from left to right).
Given,
Here we have the expression. 3.2+2(-1.5)-3.4
Now, we have to use the order of operations concept in order to solve it.
The highest priority for the order of operation is brackets and the next priority is for division and multiplication,
So, here we have to solve those things first, then we get,
=> 3.2 + (-3) - 3.4
We know that (+) x (-) = -, so, the expression is rewritten as,
=> 3.2 - 3 - 3.4
The next priority is for addition and subtraction,
So, the result is,
=> 3.2 - 6.4
=> -3.2
Therefore, the resulting number is -3.2
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A virtual environment created by game engine renders non-character objects
more efficiently than it renders characters. If the assumption is that 72
percent of objects must be devoted to non-character objects and this reset
cache is set at 67 non-character objects, how many objects can be
characters before the cache resets?
Answer:18
Step-by-step explanation:
Find the measure of
Answer: 93°
Step-by-step explanation:
[tex]\angle A \ and\ \angle B\ are\ vertical\ angles.\ Hence,\ \angle A \ = \ \angle B\\\\2x+19=3x-18\\\\2x+19+18=3x-18+18\\\\2x+37=3x\\\\2x+37-2x=3x-2x\\\\37=x\\\\Thus,\ x=37\\\\m\angle A=(2(37)+19)^0\\\\m\angle A=(74+19)^0\\\\m\angle A=93^0\\\\[/tex]
Rewrite as a simplified fraction.
\large{0.8\overline{95} = {?}}0.8
95
=?
0.895 with 95 repeating on and on as a simplified fraction can be re-written as 887/990.
How to determine the fractional equivalent of this repeating decimal?By critically observing the given number, we can reasonably and logically deduce that it has three (3) repeating digits. Since this number has three (3) repeating digits, we would have to multiply n by 1000 as follows:
1000n = 0.895
1000n = 895.95 .......equation 1.
10n = 8.95 .......equation 2.
Subtracting equation 2 from equation 1, we have:
1000n - 10n = 895.95 - 8.95
990n = 887
Dividing both sides by 990, we have:
n = 887/990
Simplified fraction, n = 887/990.
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Complete Question:
Write 0.895 with 95 repeating on and on as a simplified fraction.
Someone please help!
Answer:
Step-by-step explanation:
1. b. (2,14)
2. a. (-1,4)
3. c. (-2,2)
Answer: 1. b
2. a
3. c
Step-by-step explanation:
We will change the second equation to y form, then we get:
2x - y = - 6
- y = -2x - 6
y = 2x + 6
Then we plug in each point to see whether it fixes the equations.
a) 1. y = 3x + 8
4 ?= 3(-1) + 8
4 ?= -3 + 8
4 x 5
a) 2. y = 2x + 6
4 ?= 2(-1) + 6
4 ?= -2 + 6
4 = 4
Point a is a solution of the second equation, but not a solution for the first equation.
b) 1. y = 3x + 8
14 ?= 3(2) + 8
14 ?= 6 + 8
14 = 14
b) 2. y = 2x + 6
14 ?= 2(2) + 6
14 ?= 4 + 6
14 x 10
Point b only fits the first equation, but does not fix (not a solution) of the second equation.
c) 1. y = 3x + 8
2 ?= 3(-2) + 8
2 ?= -6 + 8
2 = 2
c) 2. y = 2x + 6
2 ?= 2(-2) + 6
2 ?= - 4 + 6
2 = 2
Point c fits both the first equations and the second equations.
Someone please help with this math problem?
Both equations' solutions are found at the point (-2, 2). When point (-1,4), the 2x-y=-6 yields the correct point. The second equation is as a result. The point (2, 14) is the answer to the first equation because it provides the answer to the first equation but not the second.
What is equation?The word equation and its cognates in other languages may have slightly different meanings; for example, in French an equation is defined as containing one or more variables, while in English any well-formed formula consisting of two expressions related with an equals sign is an equation. An equation is a formula that expresses the equality of two expressions by connecting them with the equals sign =. Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that satisfy the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations.
3x-y=-8
2x-y=-6
given points are (-1,4), (2,14), (-2,2)
On solving the equation,
3x-y=-8
-(2x-y=-6)
x=-2
y=2
The point (-2,2) is the solution to both equations.
The point (-1,4) on putting in the 3x-y=-8 will not give solution but when put in the 2x-y=-6, it gives the result. so it the solution to second equation.
The point (2,14) is the solution to the first equation as it gives the answer to first but not to the second equation.
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What is the measure of C?
Please show your work if you want to be brainiest!
The measure of ∠C in the given triangle is 58°.
According to the question,
We have the following information:
ACD is a triangle where we have BD as an altitude on the side AC.
Now, we know that the altitude on any side makes an angle of 90° or in other words, it can be said that it makes a right angle.
Now, we have two right-angled triangle: ABD and CBD.
We have ∠ADB = 32°.
Now, ∠CDB will also be equal to 32° because the altitude bisects the angle (in two equal parts).
We know that the sum of the three angles in a triangle is 180°.
In ΔCBD, we have:
∠B + ∠C + ∠CDB = 180°
90° + ∠C + 32° = 180°
∠C + 122° = 180°
∠C = (180-122)°
(Moving 122 from the left hand side to right hand side will result in the change of sign.)
∠C = 58°
Hence, the measurement of ∠C in the given triangle is 58°.
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How can the rate of a reaction be decreased?
O adding a catalyst
O lowering the temperature
O increasing the amount of reactants
O having more surface area
The shape below is enlarged using a scale factor of 3 and centre (3,7) to give the dashed shape.
What are the coordinates of B'?
The point B has a coordinates of (-3, 7) after the dilation
How to determine the coordinates of the point B?From the question, the coordinates of the point B are given as
B = (1, 7)
The scale factor of dilation is given as
k = 3
The center of dilation is given as
Center = (3, 7)
The rule of the dilation is calculated using
B' = (k(x - a) + a, k(y - b) + b)
Where
(a, b) = (3, 7)
k = 3
(x, y) = (1, 7)
So, we have
B' = (3 * (1 - 3) + 3, 3 * (7 - 7) + 7)
Evaluate
B' = (-3, 7)
Hence, the coordinates of the point B is (-3, 7)
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[3] How many solutions does the system of equations have? y = 5x - 6 y = 5x + 2
The system of equations has no solution when solving with elimination or substitution
so No solution is the answer
checking
y = 5x -6 ------(1)
y =5x +2------(2)
5x +2 = 5x-6
5x -5x = -6 -2
0 =-8
hence there is no solution since all variables are eliminated
Model Real Life A healthcare worker
has 3 shifts each week. The route from
her house to the hospital is 9.9 miles
and the route back to her house is
10.5 miles. About how far does she
travel for work each week?
She travels 61.2 miles for work each week.
What is addition?Addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
We have been given that the healthcare worker has 3 shifts each week. The route from her house to the hospital is 9.9 miles and the route back to her house is 10.5 miles.
The distance from her house to the hospital = 9.9 miles
The distance back to her house = 10.5 miles.
The total distance travel in one shift = 9.9 + 10.5 = 20.4 miles
The total distance travel in 3 shift = 3 x 20.4 = 61.2 miles
Hence, She travels 61.2 miles for work each week.
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