Option B. The rule of sampling distribution that is listed here that can be said to be false is Sampling distributions get wider (I.e. have greater variability) with increasing sample size.
What is meant by sampling distribution?The probability distribution of a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution. It outlines a variety of potential possibilities for a statistic, such as the mean or mode of a population's mean or mode of some variable.
It could be regarded as the statistical distribution for all feasible samples drawn from the same population with a particular sample size. The population's underlying distribution, the statistic under consideration, the sampling technique utilized, and the sample size used all have an impact on the sampling distribution.
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Factor 5x^2+22x+8
Worth a large grade point, please help
You can subtract the right side and factor the result, or you can factor the left side then see what happens.
... 5x² +22x +8 = 5x +2
... 5x² + 2x +20x +8 = 5x +2 . . . . split the x term so we can factor by grouping
... x(5x +2) +4(5x +2) = (5x +2)
Now we can subtract the right side and finish the factoring.
... x(5x +2) +(4 - 1)(5x +2) = 0
... (x +3)(5x +2) = 0 . . . . . the factorization of your equation
_____
If we start by subtracting the right side, we are looking to factor ...
... 5x² +17x +6 = 0
... 5x² +2x +15x +6 = 0 . . . . . split the x-term to help factoring by grouping
... x(5x +2) +3(5x +2) = 0 . . . factor pairs of terms
... (x +3)(5x +2) = 0 . . . . . . . . combine the results
______ _____
Factoring quadratics with the leading coefficient not equal to 1 is similar to factoring when it is equal to 1. Here, (after subtracting the right side), we are looking for factors of 5·6 = 30 that add to 17, the coefficient of the x-term.
... 30 = 1·30 = 2·15 = 3·10 = 5·6
The sums of these factor pairs are 31, 17, 13, 11. We see that the factor pair (2, 15) is the one we want, as its sum is 17. You will note these are the numbers used to divide the x-term for factoring by grouping. We rewrote 17x as 2x +15x. (There are other ways to use these numbers, but this is perhaps the easiest to see and remember.)
Answer:
(5x + 2)(x + 4)
Step-by-step explanation:
So, we have the equation [tex]5x^2+22x+8[/tex] right?
To get the [tex]x^2[/tex] we are going to need 'something' x in the first x slots of our factor form, like this:
(?x ± ?)(?x ± ?)
5 is a prime number, so one of the x's will be a 5x, and the other one a 1x:
(5x ± z)(x ± q)
z * q must be 8, and 5 * q + z must be 22
2 * 4 is 8
Let's plug these values in:
(5x + 2)(x + 4)
Let's multiply this out:
[tex]5x^2+22x+8[/tex]
This matches with our original equation!
So, our answer is:
(5x + 2)(x + 4)
Find the standard deviation of the sampling distribution of sample means using the given information. Round to one decimal place, if necessary.
μ=77 and σ=14; n=64
The standard deviation of the sampling distribution of sample means using the given information is 1.8
What does the mathematical term "rounding" mean?
Rounding is a method for estimating a specific number in a situation. To determine how to round a number, look at the next digit in the appropriate position; if it is less than 5, round down, and if it is greater than 5, round up. The precise rounding of decimal figures is referred to as "rounding decimals."
What are the guidelines for rounding off decimal numbers?
To locate the rounding digit, look at its right side.
If the right-side numbers are less than 5, consider them to be equal to zero.
The digit on the right is increased by one and the other digits are treated as zero if the right-side digits are greater than or equal to 5.
The population standard deviation divided by the square root of the sample size, or n, gives the standard deviation of the sampling distribution of sample means, or x, for any given population. Therefore:
For the provided data, the sampling distribution's standard deviation of sample means is [tex]\frac{14}{\sqrt{64} }[/tex], or 1.8.
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A set of notations (SSS, SAS, ASA and RHS) is used to describe/prove
that two triangles are congruent.
For each pair of triangles shown, select the correct statement.
a)
A: Congruent (SSS)
B: Congruent (SAS)
C: Congruent (ASA)
D: Congruent (RHS)
b)
58
68
54
68
9.2 cm
54
Not drawn
to scale
Not drawn
to scale
9.2 cm
58
68*
58
68*
54
A: Congruent (SSS)
B: Congruent (SAS)
C: Congruent (ASA)
D: Congruent (RHS)
E: Not congruent
F: Could be congruent
E: Not congruent
F: Could be congruent
b)
A
3. What is the proper ordering
(from greatest to least) of the
following numbers?
I.58/67
II.0.58%
III.58%
IV.5.8%
O I, III, II,
O III, IV, II, I
O I, III, IV, II
O IV, I, III, II
Answer:
C) I, III, IV, II
Step-by-step explanation:
Convert each number into a decimal:
[tex]\textsf{I.} \quad \dfrac{58}{67}=0.86567...[/tex]
[tex]\textsf{II.} \quad 0.58\%=\dfrac{0.58}{100}=0.0058[/tex]
[tex]\textsf{III.} \quad 58\%=\dfrac{58}{100}=0.58[/tex]
[tex]\textsf{IV.} \quad 5.8\%=\dfrac{5.8}{100}=0.058[/tex]
Comparing the tenths of all the numbers, 8 is the biggest tenth, so 58/67 is the largest number.
The next biggest tenth is 5, so 58% is the next largest number.
The two remaining numbers have zero tenths, so compare their hundredths. 5 is the largest hundredth, so 5.8% is the next largest number. Therefore, 0.58% is the smallest number.
Therefore, the given set of numbers in order from greatest to least is:
I, III, IV, IIAnswer:
c) I, III, IV, II
Step-by-step explanation:
Values of l, ll, lll & lV respectively,
→ 58/67, 0.58%, 58%, 5.8%
→ 0.87, 0.0058, 0.58, 0.058
Arranging them in descending order,
→ 0.87 > 0.58 > 0.058 > 0.0058
→ 0.87, 0.58, 0.058, 0.0058
→ l, lll, lV, ll
Hence, the option (c) is correct.
The graph of an exponential function passes through (2,100) and (4,2500). Find the function that describes the graph
Step-by-step explanation:
Form of an exponential function is
[tex]y = a \times b {}^{x} [/tex]
where a is the initial value, and b is the rate of growth
We know that when x=2
[tex]100 = a \times b {}^{2} [/tex]
when x=4
[tex]2500 = a \times b {}^{4} [/tex]
If we divide these two quantities we would get
[tex]25 = b {}^{2} [/tex]
[tex]b = 5[/tex]
So our rate of common growth is 5,
so b=5
[tex]y = a \times 5 {}^{x} [/tex]
We need to find the initial value, this means we solve for a.
[tex]100 = a \times 5 {}^{2} [/tex]
[tex]100 = a \times 25[/tex]
[tex]4 = a[/tex]
So our equation is
[tex]y = 4(5) {}^{x} [/tex]
or
[tex]y = 4 \times 5 {}^{x} [/tex]
The exponential model A=371.4e^0.0241 describes the population, A, of a county in millions, t years after 2003. Use the model to determine when the population of the country will be 677 million
After 598 years the population of the country will be 677 million
The exponential model of the population is
A = 371.4 e^ (0.0241×t)
Where A is the total population in t years
t is the number of years
The population of the country = 677 million
677 million = 677e^8
Therefore the exponential equation will be
6.77 × [tex]10^8[/tex] = 371.4e^(0.0241t)
e^(0.0241t) = 6.77 × [tex]10^8[/tex] / 371.4
Divide the terms
e^(0.0241t) = 1822832.526
0.0241t = ln(1822832.526)
t = ln(1822832.526) / 0.0241
Divide the terms
t = 598.17
t ≈ 598 years
Hence, after 598 years the population of the country will be 677 million
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Please help me!!!!!!!!
Answer & Step-by-step explanation:
This question is just a matter of reading the graph correctly. There is really no explanation for this question. But I'll try my best.
1997 for age 65 or older
Bachelor's degree or higher: The yellow bar starts at 75% and ends at 100%
To find how much percent of people 65 or older had a bachelor's degree in 1997, you subtract...100-75 = 25%
College/associate degree: 75 - 54 = 21%
High school graduates: 54 - 22 = 32%
Less than a High school diploma: 22 - 0 = 22%
Total: 25+21+32+22 = 100%
2007 for age 65 or older
Bachelor's degree or higher: 100 - 69 = 31%
College/associate degree: 69 - 46 = 23%
High school graduates: 46 - 13 = 33%
Less than a High school diploma: 13 - 0 = 13%
Total: 31+23+33+13 = 100%
Hope this helped :)
Winners buys a jacket from a manufacturer. Manufacturer offers 45% trade discount. Winners want to price the jacket for $150. What price should Winners pay for the jacket?
Question 1 options:
$82.50
55.60
53.50
$62.50
The price that Winners wants to pay for the jackets is $82.50
How to find the price that Winners wants to payThe question is a percentage problem, percentage deals with a fraction hundred and used as follows
45%
= 45 percent
= 45 / 100
= 0.45
The factor 0.71 is a discount factor so we subtract from 1
1 - 0.45 = 0.55
The price Winner wants to pay
= 0.55 * 150
= $82.50
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The product of two factors is 1. One of the factors is 1. Can you tell what the other factor is?
A. Yes; the other factor is 0 since 0 × 1 = 1.
B. Yes; the other factor is 1 since 1 × 1 = 1.
C. No; any number times 0 is 0, so there is no way to know what the other factor is.
D. No; any number times 1 is 1, so there is no way to know what the other factor is.
Answer:
The correct answer is: B. Yes; the other factor is 1 since 1 × 1 = 1.
Step-by-step explanation:
Solve the inequality
Answer: None of these
Step-by-step explanation:
[tex]3^x+2 > -1\\\\3^x > -3\\\\3^x \geq 0 \forall x \in \mathbb{R} \implies x \in (-\infty, \infty)[/tex]
Resuelva:
1) |3 x-1|-|2 x+5-(5-x)|=0
2) |2(x+1)-4|=|2-2(2-x)|
3) |x-2/4|-1/3=x
4) 1/2|x-3|-1=|x-3|+2
The solutions to the absolute functions |3x - 1| - |2x + 5 - (5 - x)| = 0, |2(x + 1) - 4| - 4| = |2 - 2(2 - x)|, |(x - 2) / 4| - 1/3 = x and 1/2|x - 3| - 1 = |x - 3| + 2 are 1/6, 1, 2/15 and no solutions respectively
Absolute FunctionAn absolute value function is a function in algebra where the variable is inside the absolute value bars. This function is also known as the modulus function and the most commonly used form of the absolute value function is f(x) = |x|, where x is a real number. Generally, we can represent the absolute value function as, f(x) = a |x - h| + k, where a represents how far the graph stretches vertically, h represents the horizontal shift and k represents the vertical shift from the graph of f(x) = |x|. If the value of 'a' is negative, the graph opens downwards and if it is positive, the graph opens upwards.
In the questions given;
Question 1
|3x - 1| - |2x + 5 - (5 - x)| = 0
x = 1/6
Question 2
|2(x + 1) - 4| - 4| = |2 - 2(2 - x)|
x = 1
Question 3
|(x - 2) / 4| - 1/3 = x
x = 2 / 15
Question 4
1/2|x - 3| - 1 = |x - 3| + 2
This equation does not have a solution
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People were surveyed about pizza toppings. The results are shown in the Venn diagram. How many people like sausage or mushrooms?
a. 11
b. 30
c. 23
d. 12
The number of people that like sausage or mushrooms as shown in the Vann diagram is 30.
What is a Venn diagram?Venn diagrams are diagrams used to visually depict sets, relationships between sets, and operations on sets
To determine the number of people that like sausage or mushrooms from the Vann diagram, we use the Formula below.
Formula:
n (S ∪ M) = n (S) + n (M) − n (S ∩ M) ................. Equation 1
Where:
S = SausageM = Mushrooms∩ = Union∩ = Intersectionn (S ∪ M) = Number of people that like sausage and mushroomsn (S) = Number of Elements in the set Sn (M) = Number of element in set Sn (S ∩ M) = Number of element for S intersection MFrom the diagram,
Given:
n (S) = Add up all the numbers inside the circle for Sausage = 4+6+8+3 = 21 n (M) = Add up all the numbers inside the circle for Mushrooms = 5+4+4+8 = 21n (S ∩ M) = Add up all the numbers in side the region where the circle for Sausage and the circle for Mushrooms intersect. = 4+8 = 12Substitute these values into equation 1
n (S ∪ M) = 21+21-12n (S ∪ M) = 42-12n (S ∪ M) = 30Hence, the people who like sausage or mushrooms is 30
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The cost of
maintaing libraries is 90.00
and this met from the expenditure on
Schools which is 6000.00. what percentage
Correct to
3 significant figures of the
expenditure on schools is spent on maintaining
Libraries ?
Answer the questions below about the following function
f(x) =log₄(x)
what is the domain of f(x)
what is the range of f(x)
what is the x-intercept of f(x)? enter your answer as an ordered pair. if no x-intercept exists, enter none
what it the equation of the vertical asymptote
Which function has a greater y-intercept?
Answer:
Step-by-step explanation:ask a pro
Which inequality is equivalent to x-6/x+5 ≥ x+7 /x+3? -13/x²+8x+15 ≥0 2x²+9x+17/x²+8x+15 ≥0 -15x-53/x²+8x+15 ≥0 9x+17/x²+8x+15 ≥ 0
The inequality (x - 6) / (x + 5) ≥ (x + 7) / (x + 3) is equivalent to (-15x - 53) / x² + 8x + 15 ≥ 0
Equivalent InequalityTwo or more inequalities are equivalent inequalities if they have the same solution set. Similar to equivalent equations, applying properties of Inequality to an inequality produces an equivalent inequality.
In the given inequality
(x - 6) / (x + 5) ≥ (x + 7) / (x + 3)
This can be reduced to
x < -5 or -53/15 ≤ x < -3
In the options given;
(-15x - 53) / x² + 8x + 15 ≥ 0 has the same reduction of x < -5 or -53/15 ≤ x < -3.
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Robbin's thumbnail is 1 5/8 centimeters long her pinky nail is 4/5 centimeters long. How much longer is robins thumbnail that pinky nail
A way to measure things is the metric system. Calculations and research use it all around the world.
What is Metric Units?In the metric system, the following units are used to measure length, weight, and capacity:
Length: There are five units of measurement for length, width, and height: the millimeter (mm), decimeter (dm), centimeter (cm), meter (m), and kilometer (km).Debit card thickness and length measurements, fabric length measurements, and distances between cities are a few examples.
Weight: Using instruments, we can determine an object's weight in grams (g) and kilograms (kg).The weight of fruits or our own body weight are two examples.
It is possible to measure how much liquid an object can hold using milliliters (ml) and liters (l).Calculating the volume of water in a water tank or the amount of juice in a juice can are two examples.
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The function f(x) is graphed below. How many points on the graph represent a relative minimum? PLEASE need help i don't understand. Need help NOWWW!!!
The relative minimum from the given graph is located at d.
Given that, the function [tex]f(x)[/tex] is graphed below.
What are relative minimum and maximum?A relative maximum point is a point where the function changes direction from increasing to decreasing (making that point a "peak" in the graph). Similarly, a relative minimum point is a point where the function changes direction from decreasing to increasing (making that point a "bottom" in the graph).
A relative minimum of a function is all the points x, in the domain of the function, such that it is the smallest value for some neighborhood. These are points in which the first derivative is 0 or it does not exist.
From the given graph, point d is a relative minimum.
Hence, the relative minimum from the given graph is located at d.
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21. Plot the numbers on the number line below. A.-5 1/2 B -6.3 C. -5.8 D. -6 7/10 E. -4.9 F. -6 9/10
The number line that contains each of these points marked is given by the image presented at the end of the answer.
How to plot numbers on a number line?It depends if the number to be plotted is an integer or if it is a decimal.
If the number is an integer number, then the symbol is just marked over the point representing the number.If the number is a decimal, we have to find between which two integers the decimal is located, and then verify the proportion to plot the number.The numbers that will be plotted in this problem are defined as follows:
A = -5.5, hence halfway between -6 and -5.B = -6.3, hence between -7 and -6, and closest to -6.C = -5.8, between -6 and -5, to the left of A, hence closest to -6.D = -6 and 7/10 = -6.7, also between -7 and -6, closest to -7, hence to the left of B.E = -4.9, hence slightly to the right of -5.F = -6 and 9/10, also between -7 and -6, and to the left of D.A similar problem, also featuring the number line, is presented at brainly.com/question/24644930
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Three of the exterior angles of an n-sided
polygon are 50° each,
two of its interior
angles are 127° and 135°,
and the remaining
interior angles are 173° each. Find the value of n.
Answer:
[tex]n=126[/tex]
Step-by-step explanation:
Using the formula for the sum of the angles of an [tex]n[/tex]-sided polygon, the sum of the angles is [tex]180(n-2)[/tex] degrees.
An exterior angle is supplementary to the corresponding interior angle. Using the given angle measures, the sum of the angles is [tex]2(180-50)+127+135+173n=522+173n[/tex] degrees.
Equating these two results,
[tex]180(n-2)=522+173n \\ \\ 180n-360=522+173n \\ \\ 7n-360=362 \\ \\ 7n=882 \\ \\ n=126[/tex]
Answer:
n=126
Step-by-step explanation:
180(n−2)=522+173n
180n−360=522+173n
7n−360=362
7n=882
n=126
Cheese production in a country is currently growing at a rate of 3% per year. The equation y=7.1(1.03)ˣ models the cheese production in the country from 2003 to 2009 . In this equation, y is the amount of cheese produced, in billions of pounds, and x represents the number of years after 2003.
a. Estimate the total cheese production in the country in 2006.
b. Assuming this equation continues to be valid in the future, use the equation to predict the total amount of cheese produced in the country in 2014.
a. The total cheese production in the country in 2006 was about _____ billions of pounds.
(Round to the nearest tenth as needed.)
There were 7.76 billion chees produced until 2006 and 8.99 billion cheese produced until 2014.
What is a model?The mathematical model can be used in the solving of a particular problem. Most importantly, we could use the mathematical models to be able to solve a problem or make predictions about the future.
We can now use the model that is shown as ;y=7.1(1.03)ˣ where x = the number of years after 2003.
a) For the year 2006, we can see that the number of years that ahs past is three years hence;
y = 7.1(1.03)^3
y = 7.76 billion chees
b) For 2014 we have 8 years thus we can write;
y = 7.1 (1.03)^8
y = 8.99 billion cheese
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The line 2y=3x intersects the ellipse x^2/8+y^2/18 = 1 at the points Q and R. What is the length of segment QR?
The distance between the points Q and R is 7.211 units.
What is an ellipse?In geometry, an ellipse is a two-dimensional shape, that is defined along its axes. An ellipse is formed when a cone is intersected by a plane at an angle with respect to its base. It has two focal points.
Given an equation of ellipse x²/8+y²/18 =1, a line 2y = 3x intersect the ellipse at points Q and R,
x²/8+y²/18 =1........ (i)
2y = 3x....... (ii)
Use eq 2 in 1, we get
x²/8+(3x/2)²/18 = 1
On solving, we get,
x²/4 = 1
x = ±2
And,
(2y/3)²/8+y²/18 = 1
On solving, we get,
y = ±3
Therefore, we got, y1 = 3, y2 = -3, x1 = 2 and x2 = -2
Using the distance formula, D = √(x1-x2)²+(y2-y1)²
QR = √(-2-2)²+(-3-3)² = 7.211
|QR| = 7.211
Hence, The distance between the points Q and R is 7.211 units.
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Let U={b, c, d, e, f, g, h} and A={b, f, g, h}. Use the roster method to write the set A'
A'= {____ }
(Use a comma to separate answers as needed.)
The roster method to write the set A' will be {c, d, e}.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
Let U = {b, c, d, e, f, g, h} and A = {b, f, g, h}.
The roster method to write the set A' will be given as,
A' = U - A
A' = {b, c, d, e, f, g, h} - {b, f, g, h}
A' = {c, d, e}
The roster method to write the set A' will be {c, d, e}.
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Mr. Perez bought a living room showcase listed at 150,580 Pesos but discounted into 127,993 pesos. What was the rate of the discount?
Step-by-step explanation:
Mr. Perez bought a living room showcase listed at 150,580 Pesos but discounted into 127,993 pesos. What was the rate of the discount?
(150,580 - 127,993) / 150,580 = 15%
What is the correct answer to this question?
In accordance with Pythagorean theorem, no point is 4 units away from point M.
What point is 4 units away from point M?
In this problem we find the coordinates of points A, B, C, whose coordinates are (- 4, 2), (2, 7) and (8, - 6), respectively, and the location of point M, whose coordinates are (- 4, - 6), all set on Cartesian plane. We need to determine if at least one of those three points (A, B, C) are four units away from point M. This can be checked by means of Pythagorean theorem:
AM = √[(- 4 - 2)² + [- 6 - (- 4)]²]
AM = √[(- 6)² + (- 2)²]
AM = 2√10 = √40
BM = √[(- 4 - 2)² + (- 6 - 7)²]
BM = √[(- 6)² + (- 13)²]
BM = √205
CM = √[(- 6 - 8)² + [- 4 - (- 6)]²]
CM = √[(- 14)² + 2²]
CM = 10√2 = √200
There is no point that is four units away from point M.
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Identity the property of equality that was used for each step
Addition property
Subtraction property
Multiplication property
Division property
Transitive property
Symmetric property
Substitution property
Reflexive property
Distributive property
The property of equality that are used in each step is:
What is meant by Division property?According to the division property of equality, if both sides of an equation are divided by a common real integer that is not equal to zero, the quotients remain equal. The formula for this is as follows: If a, b, and c are real numbers, with a = b and c 0 respectively, then a c = b c.
Have you ever wondered what rules you have to follow when dealing with inequalities? The division property of inequality is one of those laws, and it basically states that if you divide one side of an inequality by a number, you can divide the other side of the inequality by the same amount.
2((2X/5)+8)= 4(14-(X/5))
2((2X/5)+8)/2= 4(14-(X/5))/2 ---------Division property
(2x/5+8)=2(14-x/5)
((2x/5)+8)=(28-(2x/5) ---------Distributive property
(2x/5)+8+(2x/5)=28-(2x/5)+(2x/5) --------Addition property
(4x/5)+8=28
(4x/5)+8-8=28-8 ---------subtraction property
4x/5=20
(4x/5)×(5)=20×(5) ---------Multiplicative property
4x=100
4x/4=100/4 --------- Division property
x=25 ----------Symmetric property
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-2.1666666666666665
as a fraction
4 1/5-(3 3/5-2 3/3) of 3/11
Step-by-step explanation:
This is the answer.
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What is a formula for the nth term of the given sequence?
80, 100, 125
[tex]a_n=80\left(\frac{5}{4}\right)^{n-1}[/tex]is the formula for the nth term of the given sequence.
What is sequence?
In mathematics, a sequence is a list of components, usually numbers, where the components' order is important.
Here, everything fits into a predetermined pattern. In real life, we encounter sequences frequently.
Sequences include things like house numbers in a row, income increases over time (by a set dollar amount or percentage), book pages, etc.
A list of numbers (or other components) that follow a specific pattern is called a sequence.
Olivia, for instance, has been given a job with a starting monthly pay of $1,000 and a $500 annual raise.
Are you able to determine her monthly pay for the first three years? $1000, $1500, and $2000 will be the amounts.
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Connor has already written 15 pages of his new young adult novel and he will write more today. He expects to write 2.5 pages per hour
Write an equation that shows the relationship between the number of hours Connor spends writing today,X, and the total number of pages, y.
The required equation is y = 2.5x + 15 which shows the relationship between the number of hours Connor spends writing today,X, and the total number of pages.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that Connor has already written 15 pages of his new young adult novel and he will write more today. He expects to write 2.5 pages per hour
Let x represents the number of hours Connor spends writing today and y represents the total number of pages,
According to the given situation, we can write the equation as:
⇒ y = 2.5x + 15
Therefore, the required equation is y = 2.5x + 15.
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