False, As the sample size is increased, the standard deviation of a sampling distribution of the sample's mean drops.
The term "standard error" also refers to the sample mean's standard deviation. The high dimensionality theorem establishes that as sample size increases, the sample mean's sampling distribution becomes more or less normal.
Using the formula below, the sample mean's standard deviation is determined.
σ ÷ √n
where n is the sample size and would be the population standard deviation.
As the denominator, or n, increases, the standard variance of the sample average would also decrease, as shown by the aforementioned calculation.
It follows that the standard deviation of a sample's average decreases as the sample size grows.
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for g(x)=x to the power of 2 minus x, find g(x) when x=-2
The value of the function g(x) when x = -2 is 6
How to evaluate the function?The definition of the function is given as
g(x)=x to the power of 2 minus x
Rewrite the above function properly
So, we have the following representation
g(x) = x² - x
To find the function g(-2), we set the value of x in the equation g(x) = x² - x to -2
This is represented by
Calculate g(x), when x = -2
Substitute -2 for x in the equation g(x) = x² - x
So, we have the following equation
g(-2) = (-2)² - (-2)
Evaluate the exponents
This gives
g(-2) = 4 - (-2)
Evaluate the sum
g(-2) = 6
Hence, the value of the function is 6
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Aiden ha $3 worth of dime and quarter. He ha 2 more dime than quarter. Determine the number of dime and the number of quarter that Aiden ha
The number of dime and the number of quarters that Aiden have are 10 and 8 respectively.
How to find the number of dime and quarter?Aiden ha $3 worth of dime and quarter. Aiden has 2 more dime than quarter. The number of dime and the number of quarter that Aiden has can be calculated as follows:
let
x = number of quarter
y = number of dime
Therefore,
y = 2 + x
y - x = 2
0.1y + 0.25x = 3
Multiply equation(ii) by 10
y - x = 2
y + 2.5x = 30
subtract equation(i) from equation(ii)
3.5x = 28
x = 28 / 3.5
x = 8
Hence,
y = 2 + 8
y = 10
Therefore,
number of dime = 10
number of quarters = 8
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PLEASE HELP ASAP I NEED TO GET THIS DONE!!
Answer:
B and D
Step-by-step explanation:
A is wrong because x has a negative exponent
C is wrong because x is a denominator
h(x)=x²+3x-2; 12-h(7)
How would I input 12-h(7) in place of x to solve this function?
Solve for 12 - h(7)
First find h(7)
h(7) = 7^2+3(7)-2
h(7) = 49 + 21 - 2
h(7) = 68
12 - 68 = - 56
12 - h(7) = -56.
I'm not sure if the question wants h(-56) as well, but just plug that in.
H(-56)=2966
hope this helps :)
arturo can have pizza for dinner on any four of the next eight days. how many different ways can he select the days on which to have pizza?
Arturo can select the days on which to have pizza in 70 ways using combination rule if he chooses any four of the next eight days.
What is combination?
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
In combinations, one can select the items in any order.
Number of combination of a objects chosen from n objects
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
According to the given question:
To select 4 days out of the next 8 days, use combination rule
ⁿCₐ = [tex]\frac{n!}{a! (n-a)!}[/tex]
⁸C₄ = [tex]\frac{8!}{4! (8-4)!}[/tex]
⁸C₄ = (8x7x6x5x4x3x2x1)/(4x3x2x1)(4x3x2x1)
⁸C₄ = (8x7x6x5)/(4x3x2x1)
⁸C₄ = 70
Therefore there are 70 ways Arturo can select the 4 days out of 8 to have pizza for dinner.
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rachel and robert run on a circular track. rachel runs counterclockwise and completes a lap every 9090 seconds, and robert runs clockwise and completes a lap every 8080 seconds. both start from the same line at the same time. at some random time between 1010 minutes and 1111 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fourth of the track, centered on the starting line. what is the probability that both rachel and robert are in the picture?
The probability that both Rachel and Robert are in the picture is 3/16.
The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.
Given that
Rachel and Robert both begin at the same point
Rachel completes a lap every 90 seconds.
Robert completes a lap every 80 seconds.
The photographer captures 1/4th of the track, centered on the starting line.
As a result, the photo captures 1/8th of the track on either side of the starting line.
The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.
Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.
Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.
Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).
Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.
i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.
Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}
= {90/8}/60
= 3/16
Therefore the probability that both Rachel and Robert are in the picture is 3/16
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Triangle ABC is congruent to triangle XYZ. Side BC corresponds to what side in triangle XYZ?
Answer:
Side BC is congruent to side YZ
Please help!! Asap screenshot below.
the equation 32divided ? =8 she says the value of ? is 4 does ella answer make sense ?
Ella answer makes sense because the value of ? is 4
How to determine the value of ? in the equation make sense?
Given: the equation 32 divided ? =8 she says the value of ? is 4
32 / ? = 8
Let x represent ? in the equation, thus:
32 / x = 8 cross multiply
8x = 32
x = 32/8
x = 4
Since x = 4. This implies ? = 4
Also, the value that divides 32 to give is 4
Since the value of ? is 4. Therefore, Ella's answer makes sense
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[tex]x-4/5-x+1/6=1/3[/tex]
The equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions.
What is an equation?
A equation in mathematics is a mathematical statement depicting that the values of two mathematical expressions are equal. Some examples representing equations are -
y = 5x + 4
2x + 3y = 5x + 8π
cos(ny) = sin(πx)
Given is the following equation -
x - 4/5 - x + 1/6 = 1/3
We have -
x - 4/5 - x + 1/6 = 1/3
x - x - 4/5 + 1/6 = 1/3
- 4/5 + 1/6 = 1/3
Now, [x] will cancel out for ever possible value of [x], therefore, it will have infinitely many solutions
Therefore, the equation → x - 4/5 - x + 1/6 = 1/3 will have infinitely many solutions
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Solve :-
[tex]7a - 3 = 3 + 6a[/tex]
Answer:
A=6Step-by-step explanation:
7a-3=3+6aMove 6a to the other side
7a-6a-3=3Subtract 7a and 6a
a-3=3use inverse operations. So add 3 on both sides
a-3+3=3+3~~~~~~~~~Now we have the answer which is a=6Answer:
a = 6
Step-by-step explanation:
The given equation is,
→ 7a - 3 = 3 + 6a
Now the value of a will be,
→ 7a - 3 = 3 + 6a
→ 7a - 6a = 3 + 3
→ a = 3 + 3
→ [ a = 6 ]
Hence, the value of a is 6.
Which equation represents a line which is perpendicular to the line y=2x-5y
A. 2x−y=−4
B. 2y−x=4
C. x+2y=-6
D.2x+y=-2
Answer:
c
Step-by-step explanation:
To find a perpendicular line, you must compare the slopes. With the equation y=2x-5, we're looking for the inverse/opposite slope of -1/2.
Option A still has a slope of 2. Option B, when everything is in the format of mx+b = y format is -x-4=-2y. which gives us 1/2 but not -1/2. C when everything is on the right side gives us -2y=x-6. Divide both sides by -2 to get the y by itself and you're left with y = -1/2x+3. Now we found the equation that gives us the -1/2 slope we were looking for.
Write the equation of the line is fully simplified slope intercept form
Answer:
y = - 2x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 5, 11) and (x₂, y₂ ) = (6, - 11) ← 2 points on the line
m = [tex]\frac{-11-11}{6-(-5)}[/tex] = [tex]\frac{-22}{6+5}[/tex] = [tex]\frac{-22}{11}[/tex] = - 2
the line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - 2x + 1 ← equation of line
Write an equation in point-slope form for the line that passes through each point
with the given slope. Then graph the equation.
1. (-6, -3), m = -1
2. (-7, 6), m = 0
3. (-2, 11), m=4/3
The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
the graph of the line is shown below .
In the question ,
point on the line and slope of the line is given
So , equation will be
Part(1)
(-6, -3), m = -1
(y -(-3)) = -1(x -(-6))
y + 3 = -1(x + 6)
y + 3 = -x - 6
y = -x -6 -3
y = -x -9
the equation is y = -x -9 .
Part(2)
(-7, 6), m = 0
(y - 6) = 0(x -(-7))
y - 6 = 0(x + 7)
y - 6 = 0
y = 6
the equation is y = 6
Part(3)
(-2, 11), m=4/3
(y - 11) = (4/3)(x -(-2))
y - 11 = (4/3)x + 8/3
y = (4/3)x + 8/3 + 11
y = (4/3)x + 41/3
the equation is y = (4/3)x + 41/3
the graph of all the three equations are shown below .
Therefore , The equation of the line passing through
(1) point (-6, -3) and m = -1 is y = -x -9 .
(2) point (-7 , 6) and m = 0 is y = 6 ,
(3) point (-2 , 11) and m = 4/3 is y = (4/3)x + 41/3 .
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Choose ALL answers that describe the quadrilateral UVWX if UV = 31,
VW = 67, WX = 45, XU = 56, m/U = 146°, m/V = 54°, m/W = 95°,
and m/X = 65°.
Parallelogram
□ Quadrilateral
Rectangle
Rhombus
Square
Trapezoid
The correct option ; Quadrilateral, has the given information describing quadrilateral UVWX.
What is meant by the term Quadrilateral? A polygon comprising four sides, 4 angles, and 4 vertices is called a quadrilateral.There are some aspects that all quadrilaterals share. These attributes are:There have been four of them.There have been four of them.360° is the summation of all interior angles.There have been two diagonals in them.For the given values in the question;
In the quadrilateral UVWX
Sides are;UV = 31,VW = 67, WX = 45, XU = 56, Angles are-m/U = 146°, m/V = 54°, m/W = 95°,and m/X = 65°.As, none of the sides are equal to other and none of the angles are equal to the other.
Thus, the this information shows the values are given for quadrilateral.
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The table shows the probabilities that a biased dice will land on 2, on 3,
on 4, on 5 and on 6.
Number on dice
Probability
1
2
0.1
3
0.17
4
5
6
0.08 0.16 0.14
Paulo rolls the biased dice 300 times.
Work out an estimate for the total number of times the dice will land on 1 or on 5
The total number of times the dice will land on 1 or on 5 is 153.
What is probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.All of the probabilities will add up to 1. This gives us the equation.
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1
P(1) + 0.17 + 0.08 + 0.16 + 0.14 + 0.1 = 1
P(1) + 0.65 = 1
P(1) = 1 - 0.66
P(1) = 0.35
We now need to find the probability of 1 or 5.
P( 1 or 5) = P(1) + P(5)
= 0.35 + 0.16
= 0.51
We now use the predicting outcomes formula
Expected = P( 1 or 5) * No. of times
= 0.51 * 300
= 153
Hence, the total number of times the dice will land on 1 or on 5 is 153.
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street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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Which equation represents a line that is parallel to the line y = -2/3x + 5? Pls Hurry :/
The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21
How to find the equation of a line?The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.
Lines are parallel when they have the same slope.
Using slope intercept form,
y = mx + b
where
m = slopeb = y-interceptTherefore,
y = - 2 / 3 x + 5.
The slope of the equation is - 2 / 3.
Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.
2x - 3y = 21
add 2x to both sides of the equation
2x + 2x - 3y = 21 + 2x
- 3y = 2x + 21
divide both ides by - 3
- 3y / - 3 = 2x / -3 + 21 / - 3
y = - 2 / 3 x - 7
Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
If the equation 2(x-7) = 36, then the value of x is 13 and 1
The equation is
[tex](x-7)^2[/tex] = 36
The equation is defined as the statement the connect the two expression with an equal sign.
We know the square of 6 is 36
[tex]6^2[/tex] = 36
Substitute the value in the equation
[tex](x-7)^2=6^2[/tex]
Apply square root in the both side of the equation
[tex]\sqrt{(x-7)^2} = \sqrt{6^2}[/tex]
Then the equation will become
x - 7 = ± 6
If the value is +6
x - 7 = 6
Add both side of the equation by 7
x - 7 +7 = 6+7
x = 13
If the value is -6
x - 7 = -6
Add both side of the equation by 7
x - 7 + 7 = -6 + 7
x = 1
Hence, If the equation 2(x-7) = 36, then the value of x is 13 and 1
The complete question is:
Given [tex](x-7)^2=36[/tex], find the value of x.
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a pyramid with a square base is cut by a plane that is parallel to its base and 22 units from the base. the surface area of the smaller pyramid that is cut from the top is half the surface area of the original pyramid. what is the altitude of the original pyramid?
The altitude of the original pyramid is about 75.11 units
Given that,
Let h stand in for the original pyramid's height. The cut-off top then stands at a height of (h -22). The square of the scale factor for height is the scale factor for area, therefore we get :
Altitude of Pyramid means The slant height of a regular pyramid is its lateral face's height. Slant height in a non-rectangular pyramid is not specified. When determining the height (or altitude) of a regular, right pyramid, the vertex (the top) is used as the point perpendicular to the base. The base will intersect at this position.
(Height ratio)^2 = 1/2
((h -22)/h) ^ 2 = 1/2
(h-22) / h = 1/[tex]\sqrt{2}[/tex]
h-22 = h /[tex]\sqrt{2}[/tex]
h = 75.11 units
Consequently, the original pyramid's altitude is around 75.11 units.
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suppose you paid $4 for a bet on a horse and, as a result, you will win $110 if your horse wins a given race. find the expected value of the bet (in $) if the odds that the horse will win are 3 to 12.
The expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8
What is expected value?
Expected value is the predictive value of all the possibilities that occur by multiplying the value by the probability.
Winning probability = odds / total outcomes
= 3 / (3 + 12)
= 3 / 15
= 0.2
Now, we need to calculate expected value.
= winning probability x amount won - losing probability x amount lost
= 0.2 x 110 - (1 - 0.2) x 4
= 22 - 3.2
= 18.8
Thus, the expected value of the bet if the odds that the horse will win are 3 to 12 is $18.8
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what is the difference between independent samples and related samples when dealing with two samples
The difference between an independent sample and a dependent sample is that the dependent sample for one set of items is paired measurement while measurements made on two samples are termed an independent sample.
In statistics, while considering two samples and conducting a hypothesis test, one should be aware of which type of test should be conducted based on samples whether they are dependent or independent. If the value of another sample is affected by any one sample then the samples are dependent. If no information can be deduced from the other sample using one sample then the samples are independent.
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The rectangular frame is made from 5 straight pieces of metal.
The weight of metal is 1.5kg per metre.
Work out the total weight of the metal in the frame.
Answer:
weight = 57 Kg
Step-by-step explanation:
We require to find the length of the diagonal (d) piece of metal
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
d² = 8² + 6² = 64 + 36 = 100 ( take square root of both sides )
d = [tex]\sqrt{100}[/tex] = 10
the length of the 5 pieces is then
8 + 8 + 6 + 6 + 10 = 38 m
the total weight of the 5 pieces is then
weight = 38 × 1.5 Kg = 57 Kg
- 4≤2w + 2 and 3w+1 <4
Answer:
[tex] - 3 \leqslant w < 1[/tex]
Step-by-step explanation:
as shown in picture attached
I NEED HELP ASAP :
if a volume of an object varies directly with its width and if the volume is 16, while the with is 4 what is k?
The value of k is 4.
What is Proportion ?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Volume= 16
Width = 4
So, we can write the relation as
Volume= k (width)
k = Volume/ width
k= 16/4
k = 4
Hence, the value of k is 4.
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What is the nature of the roots for y=2x^2- 5? Use the discriminant to determine the nature of the roots.
The nature of the roots for y=2x²- 5 is there are 2 distinct real roots.
What is the nature of roots?
The nature of the roots of the quadratic can fall into one of three categories depending on the value of the discriminant
Δ > 0 means there are 2 distinct real roots.
Δ = 0 means there are 2 equal real roots or 1 distinct real root.
Δ < 0 means there are no real roots, but 2 complex roots.
Here,
The discriminant of a quadratic is the expression inside the radical of the quadratic formula.
b² - 4ac
Substitute the values of a, b, and c.
Evaluate the given equation to find the discriminant, we get
= 0 - 4×2×(-5)
= 41
> 0
Since the discriminant is greater than 0
Hence, there are 2 distinct real roots.
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Drew painted his uncle's barn on saturday. it took him 7 hours to paint the whole barn, and his uncle paid him 133 dollars for his work. what was drew's pay rate, in dollars per hour?
The total amount paid in dollars per hour is $19.
Unitary Method:
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
It is given that the total amount given by the uncle is $133 for the work done by Barn for 7 hours.
We have to find the amount paid per hour.
Total amount given = $133
Number of hour Barn work = 7 hours
Amount paid per hour = 133/ 7
= $ 19
Therefore the amount paid per hour is $19.
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length and width of a rectangle that maximises the enclosed area are 800 yards. The maximum area is 640,000 square yards.
In the given question we have to find the maximum area of the rectangular area.
Liana has 3200 yards of fencing to enclose a rectangle.
As we know that the perimeter of rectangle
P= 2(l+b)
Let length of the rectangle is x yards and width is y yards.
So the equation should be
2(x+y) = 3200
Divide by 2 on both side we get
x+y = 1600................(1)
From the area of rectangle is
A = xy
From the equation the value of y is 1600-x.
Now putting the value of y
A = x(1600-x)
A = 1600x-x^2
On differentiating
dA/dx = 1600-2x
Putting dA/dx=0
1600-2x=0
Subtract 1600 on both side we get
-2x= -1600
Divide by -2 on both side we get
x = 800 yards
Now putting the value of x in the y=1600-x
y=1600-800
y=800 yards
So the maximum area is
A= 800*800
A= 640,000 square yards
Hence, the length and width of a rectangle that maximises the enclosed area are 800 yards. 640,000 square yards is the maximum area.
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Total revenue is determined by price
multiplied by output. What is the total
revenue for 95 goods each priced at
$8?
A. $760
B. $450
C. $930
Answer:
A. $760
Step-by-step explanation:
Price: $8
Amount of goods; 95
revenue = price x total units
$8 x 95 = $760 revenue
Cual es el número que sigue en la sucesión 1,3,4,7,11,18
Answer:
29
Step-by-step explanation:
1+3= 4
3+4=7
4+7=11
7+11=18
11+18=29