According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.
What exactly does "normal distribution" mean?A data collection with a normal distribution is put up so that the majority of the values cluster in the middle of the range and the remaining values taper off symmetrically in either direction.Because the probability density graph of the normal distribution resembles a bell, it is frequently referred to as the bell curve. In honor of the German mathematician Carl Gauss, who initially characterized it, it is often referred to as the Gaussian distribution.The normal distribution defines how a variable's values are distributed, just like any probability distribution does. Because it accurately depicts the distribution of values for many natural occurrences, it is the most significant probability distribution in statistics.
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Use the remainder theorem to find the remainder when 3x^4 - 5x^2 - 20x + 8 is divided by x - 1.-414-140
SOLUTION
The given equatiion is:
[tex]3x^4-5x^2-20x+8[/tex]To be divided by x-1
set the expression to zero:
[tex]\begin{gathered} x-1=0 \\ x=1 \end{gathered}[/tex]Substitute x=1 into the polynomial:
[tex]3(1)^4-5(1)^2-20(1)+8[/tex]This gives:
[tex]3-5-20+8=-14[/tex]Therefore the remainder is -14.
211, 207, 203, ...
Find the 38th term.
The 38th term of the sequence is 63
How to calculate the 38th term ?The first step is to write out the parameters
The first term (a) = 211
The common difference (d) = 207 - 211
= -4
The 38th term of the sequence can be calculated as follows
a₃₈ = a + (n-1)d
a₃₈ = 211 + (38-1)(-4)
a₃₈ = 211 + 37(-4)
a₃₈ = 211 - 148
a₃₈ = 63
Hence the 38th term is 63
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HELP PLS ASAP,,ITS DUE REALLY SOON
.........THX
Altitudes and depths are measured with respect to sea level. Sea level corresponds to an altitude of 0. Determine the distance which separates a plane flying at an altitude of 3 250m and a submarine travelling at a depth of 326m below sea level.
Answer:3576m
Step-by-step explanation:
3250+326=3576
The profit for a certain commodity, n, where n is in units, is given by the functionP(n) =25n^2 + 300n + 1125At the break-even point, the profit is zero, i.e., P(n) = 0. Find the number of units where the break-even point is located, i.e., find n when P(n) = 0.The number of units, n, where the break-even point is located, isHint: Did you factor the GCF? Then reduce your equation to smaller coefficients?
Given the function:
[tex]P\mleft(n\mright)=-25n^2+300n+1125[/tex]You know that "P" is the profit for a certain "n" commodity (in units).
You need to find the value of "n" when:
[tex]P(n)=0[/tex]In order to find it, you can follow these steps:
1. Substitute this value into the function:
[tex]P(n)=0[/tex]Then:
[tex]\begin{gathered} 0=-25n^2+300n+1125 \\ \\ -25n^2+300n+1125=0 \end{gathered}[/tex]2. Divide both sides of the equation by -25:
[tex]\begin{gathered} \frac{-25n^2}{(-25)}+\frac{300n}{(-25)}+\frac{1125}{(-25)}=\frac{0}{(-25)} \\ \\ n^2-12n-45=0 \end{gathered}[/tex]3. Factor the equation by finding two numbers whose Sum is -12 and whose Product is -45. These are 3 and -15, because:
[tex]\begin{gathered} 3-15=-12 \\ \\ (3)(-15)=-45 \end{gathered}[/tex]Then:
[tex](n+3)(n-15)=0[/tex]4. Set up these two equations:
[tex]\begin{gathered} n+3=0\text{ (Equation 1)} \\ \\ n-15=0\text{ (Equation 2)} \end{gathered}[/tex]5. Solving form "n" from each equation, you get:
[tex]\begin{gathered} n+3=0\text{ }\Rightarrow n_1=-3 \\ \\ n-15=0\Rightarrow n_2=15 \end{gathered}[/tex]Since the number of units cannot be negative, the answer is:
[tex]n=15[/tex]Rewrite as a simplified fraction.3.16
The decimal number 3.16 in the form of the simplest fraction is 79/25.
The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.
Consider the decimal number,
Let x = 3.16
Then,
x = 3.16 = 316/100
The fraction then can be simplified as,
x = ( 158 × 2)/ (50 × 2)
x = 158/50
x = ( 79 × 2)/ ( 25 × 2 )
x = 79/25
Hence, the number 3.16 in the simplest fraction is 79/25.
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given f(x) = -x -4 find f (-2)
Answer:
-2
Step-by-step explanation:
f(-2) = -(-2) - 4
= 2-4
= -2
Find the values of the variables and the measure of the angles.
Since ∠GFE is a right triangle, we can conclude:
[tex]\begin{gathered} b+32=90 \\ b=90-32 \\ b=58 \end{gathered}[/tex]the sum of the internal angles of a triangle is 180, therefore, for the triangle GHF:
[tex]\begin{gathered} 55+a+b=180 \\ \text{ Since b=58} \\ 55+a+58=180 \\ a+113=180 \\ a=67 \end{gathered}[/tex]Finally, for the triangle GEF:
[tex]\begin{gathered} a+90+d=180 \\ 67+90+d=180 \\ 157+d=180 \\ d=180-157 \\ d=23 \end{gathered}[/tex]Solve the word problem below. Enter your answer, using the slash (/) as the
fraction bar.
Students were asked to choose their favorite season and 3/10 chose either spring or summer. If 1/10 chose spring, what fraction chose summer? (Please show a solution)
When asked which season they preferred, just 3/10 of the students selected either spring or summer. 2/5 fraction went with summer if 1/10 chose spring.
Given that,
When asked which season they preferred, just 3/10 of the students selected either spring or summer.
We have to find what fraction went with summer if 1/10 chose spring.
To find the fraction we have to add the students selected in spring or summer.
3/10+1/10
Denominator are equal numerator can add
(3+1)/10
By adding
4/10
By doing the division
2/5
Therefore, the fraction is 2/5.
2/5 fraction went with summer if 1/10 chose spring.
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Write an inequality that represents the velocity of an object that has a mass of 30 kilograms and creates a momentum of at least 15 kg(m/s)
The inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
The relation between the mass(m) of an object with momentum(p) and velocity(v) is given by the equation
p=m × v .
In the question,
it is given that
the mass of the object = 30 Kg
the momentum required is at least 15 Kg(m/s).
let the velocity of the object " v " .
Substituting values in the formula ,
we get ,
15 = 30×v
the word at least in inequality is represented by " ≥ " .
So , the inequality becomes
15 ≥ 30×v
Therefore , the inequality that represents the velocity of an object that has mass of 30 Kg and creates a momentum of at least 15 Kg(m/s) is 15 ≥ 30×v .
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Find the length of side BC.
Give your answer to 3 significant figures.
C
A
71°
6.3 cm
B
From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
What is trigonometric function?The trigonometric functions are real functions that relate the angle of a right-angled triangle to side length ratios. They are widely used in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many others.The values of all trigonometric functions based on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.From the given diagram, the size of side BC is 19.4 rounded to 3 significant figures
Given
The right angle triangle with a side and an angle
We must find out the hypotenuse BC
We are given with adjacent side AB
Let's use trigonometric ratio
[tex]$&\cos (B)=\frac{\text { adjacent }}{\text { hypotenuse }} \\[/tex]
[tex]$&\cos (71)=\frac{A B}{B C} \\[/tex]
[tex]$&\cos (71)=\frac{6.3}{B C} \\[/tex]
[tex]$&B C \cos (71)=6.3 \\[/tex]
[tex]$&B C=\frac{6.3}{\cos (71)}[/tex]
Use the calculator to find out BC
BC=19.3508
Round the answer to 3 significant figures
So BC= 19.4
Length of side BC = 19.4
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playing blackjack. blackjack, or twenty-one as it is frequently called, is a popular gambling game played in casinos. a player is dealt two cards. face cards (jacks, queens, and kings) and tens have a point value of 10. aces have a point value of 1 or 11. a 52-card deck contains 16 cards with a point value of 10 (jacks, queens, kings, and tens) and four aces. a. what is the probability that both cards dealt are aces or 10-point cards? b. what is the probability that both of the cards are aces? c. what is the probability that both of the cards have a point value of 10? d. a blackjack is a 10-point card and an ace for a value of 21. use your answers to parts (a), (b), and (c) to determine the probability that a player is dealt blackjack. (hint: part (d) is not a hypergeometric problem. develop your own logical relationship as to how the hypergeometric probabilities from parts (a), (b), and (c) can be combined to answer this question.)
The probabilities for the ace cards are 0.1433, 0.0045, 0.0905, 0.0482.
what is a blackjack card game?
It derives from the Twenty-One line of gambling banking games and utilises 52-card decks.
Face cards and number 10: 16 cards have point value 10 Ace cards:
4 cards have point value 1 or 11 total number of cards =
Part a)
P(Ace or 10 point card has following cases)
case l: both are Ace cards = (4/52)*3/51 =
0.0045
Case II: both are 10 point cards = (16/52)*(15/51) =
0.0905
Case III: first card Ace, second card 10 point = (4/52)*(16/51 0.0241 Case IV: first card 10 pt, second card Ace: = (16/52)"(4/51) = 0.0241
Total = 0.1433
Part b) P(both cards are Ace) = (4/52)*(3/51) = 0.0045
Partc) P(both cards have point value 10) = (16/52) * (15/51) = 0.0905
Part d) P(Ace and 10 point) = 0.0241+0.0241 = 0.0482
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Find the value of x, y, and z. (see picture)
z=72°+57°(EXTERIOR ANGLES OF A TRIANGLE)
z=129°
x+57°=180°(ANGLES ON A STRAIGHT LINE)
x=180°-57°
x=123°
y+72°=180°(ANGLES ON A STRAIGHT LINE)
y=180°-72°
y=108°
HOPE THIS HELPS.
Solve the following Radical Equation (Square root). Show all work.
At their going out business sale, Bill’s Bikes sold 36 bikes and had 58 left. Which equation could be used to find x, the number of bikes the store had originally.
The equation that could be used to find x, the number of bikes the store had originally, is (x-94) = 0.
According to the question,
We have the following details:
Bill has sold 36 bikes and is left with 58 bikes more.
Now, the number of bikes the store had originally is given to be x.
So, we have:
x = Number of bikes sold + Number of bikes left
x = 36+58
x = 94
x-94 = 0 (94 was positive on the right hand side. So, it is negative on the left hand side.)
Hence, the equation that could be used to find number of original bikes in Bill's store is x-94 = 0.
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Which angle pairs include the named angle?
what is 3 (6+99) - 45
Given:
[tex]3(6+99)-45[/tex]What is AC?
A √162 = 12.7
B√98 = 9.9
C√117 ≈ 10.8
D√72 = 8.5
The most appropriate choice for distance formula will be given by Length of AC = [tex]\sqrt{72} = 8.5 units[/tex]
What is distance?
Distance is a measurement of how far apart two objects or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over").
What is distance formula?
Distance formula is used to find the distance between two points.
Let A and B be two points with coordinate [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] respectively
Distance between A and B = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Here,
Coordinate of A = (1, 1)
Coordinate of E = (4, 4)
Coordinate of C = (7, 7)
Length of AE =
[tex]\sqrt{(4-1)^2 + (4-1)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]
Length of EC =
[tex]\sqrt{(7-4)^2 + (7-4)^2}\\\sqrt{9 + 9}\\\sqrt{18}\\3\sqrt{2} units[/tex]
Length of AC = Length of AE + Length of EC
= [tex]3\sqrt{2} + 3\sqrt{2} = 6\sqrt{2} units[/tex] =[tex]\sqrt{72} units = 8.5 units[/tex]
Fourth option is correct
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HELP ASAP Arrange the dot plots in descending order based on standard deviation
Answer:
its true because standard deviation is the only way out to find any solution
Determine the slope of a line passing through the given points. If the slope is undefined, write undefined. Enter your answer as a decimal if necessary. a. ( 5 , − 4 ) and ( 0 , 1 ) b. ( − 1 , 8 ) and ( 7 , 10 ) c. ( − 4 , 12 ) and ( − 4 , 5 ) Tools are not currently accessible
The slope of the given line that runs through the points are:
1. Defined
2. Defined
3. undefined.
What is an Undefined Slope of a Line?An undefined slope of a line can be described as the slope of a vertical line that has no run but only rise. That is, the x-coordinates do not change even though the y-coordinates of the line are changing.
Thus, the change in x-coordinates is always 0.
Slope = change in y / change in x.
a. (5 , − 4) and (0 , 1):
Slope = (-4 - 1)/(5 - 0)
Slope = -5/5 = -1 [the slope is defined]
b. (−1 , 8) and (7 , 10):
Slope = (10 - 8)/(7 -(-1))
Slope = 2/8
Slope = 1/4
c. (-4, 12) and (-4, 5)
Slope = (12 - 5)/(-4 -(-4))
Slope = 7/0 [cannot divide, therefore, the slope is undefined]
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In triangle XYZ, angle Y is right and sin X =5/13. Which of the following trig. Ratios are correct?
In triangle XYZ, angle Y is right and sin X =5/13 the correct trigonometry ratios are
tan Z = 12/5cos Z = 5 / 13How to determine the correct trigonometry ratioInformation given in the question include
In triangle XYZ
angle Y
sin X = 5 / 13
A right angle triangle has three sides namely Adjacent, Opposite and Hypotenuse
from Sin X = opposite = Hypotenuse = 5 / 13
we have that
opposite = 5
Hypotenuse = 13
Using Pythagoras theorem
Hypotenuse^2 = opposite^2 + Adjacent^2
13^2 = 5^2 + Adjacent62
Adjacent = √(169 - 25)
Adjacent = 12
The correct options are tan Z = 12/5 and cos Z = 5 / 13
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Line s has a slope of 1/3 Line t is perpendicular to line s. What is the slope of line t?
The line t has a slope of the value of -3
How to determine the slope of line t?The lines are given as
Line s and line t
The slope of line s is given as
Slope of line s = 1/3
Also, from the question;
We understand that line s and line t are perpendicular lines
The condition for perpendicular lines is represented as
The product of the slopes of the lines = -1
This means that
Slope of line s * Slope of line t = -1
This gives
1/3 * Slope of line t = -1
Divide both sides by 1/4
Slope of line t = -3
Hence, the slope is -3
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Ashley saved money every month last year. The table below shows how much money she saved each month.
Dollars Saved
Month Money Saved (in dollars)
January
96
February
38
March
162
April
65
May
178
June
112
July
57
August
143
September
135
October
104
88
22
November
December
What is the mean absolute deviation of amounts she saved?
A.18
B.39
C.23
D.156
The mean absolute deviation of the amount $39
What is Mean Absolute Deviation?
The average distance between each data value and the mean is known as the mean absolute deviation (MAD) of a data set. A measure of variance in a data set is the mean absolute deviation. We may determine how "spread out" the values in a data collection are by looking at the mean absolute deviation.
Given,
The amount she saved throughout the year
January 96
February 38
March 162
April 65
May 178
June 112
July 57
August 143
September 135
October 104
November 88
December 22
The mean of the data will be = 96+38+162+65+178+112+57+143+135+104+88+22/12
= 1200/12
=100
The mean would be 100
|data - mean value| = 96-100 = 4
38-100 = 62
162-100 = 62
65-100 = 35
178-100 = 78
112-100 = 12
57-100 = 43
143-100 = 43
135-100= 35
104-100 = 4
88-100 = 12
22-100 = 78
Now, sum of |data - mean values| = 468
The mean absolute deviation:
= sum of |data - mean values| / number of values
= 468 / 12
= 39
Hence, the mean absolute deviation of amounts she saved is $39
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Find the volume of a cone with a base radius of 5 ft and a height of 10 ft.
Write the exact volume in terms of it, and be sure to include the correct unit in your answer.
The volume of cone is 261.79 ft³
Solution:
To solve Volume of cone we need radius and height of cone,
Base Radius of cone = 5 ft
Height of cone = 10 ft
Formula for Volume of cone V = π r² h/3
So,
The radius of cone is 5ft and
height of cone is 10ft ,
Volume V= π × 5ft² × 10ft/3
= 261.79939 ft³
Equation :
V = π r² h/3V= volume , π= 3.14 , r= radius , h= heightTo learn more about Volume of cone refer:
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8% turned into a fraction
Answer: 0.8
Step-by-step explanation: 0.8 as a fraction is expressed as 4/5
hope this helps
Answer: 2/25 or 8/100.
Step-by-step explanation:
If f(x)=5x^2-x-4 and g(x)=x-6What (f+g)(x)=And(f+g)(9)=
Explanation
given
[tex]\begin{gathered} f(x)=5x^2-x-4 \\ g(x)=x-6 \end{gathered}[/tex]Step 1
a) (f+g) (x)
here we need to find a new function ( f+g) (x), this is the sum of the functions f and g, so to find it just add g(x) to f(x)
hence
[tex]\begin{gathered} (f+g)(x)=5x^2-x-4+x-6 \\ add\text{ like terms} \\ (f+g)(x)=5x^2-10 \end{gathered}[/tex]so
[tex](f+g)(x)=5x^{2}-10[/tex]Step 2
now, we have to evaluate that function for x= 9
so
[tex]\begin{gathered} (f+g)(x)=5x^{2}-10 \\ evaluate\text{ for x=9} \\ replace\text{ and calculate} \\ (f+g)(9)=5(9)^2-10 \\ (f+g)(9)=5(81)-10=405-10 \\ (f+g)(9)=395 \end{gathered}[/tex]so
[tex](f+g)(9)=395[/tex]I hope this helps you
Find the equation of the line that goes through the points (-15,70) and (5,10).
[tex](\stackrel{x_1}{-15}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{10}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{10}-\stackrel{y1}{70}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-15)}}} \implies \cfrac{-60}{5 +15} \implies \cfrac{ -60 }{ 20 } \implies - 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{70}=\stackrel{m}{- 3}(x-\stackrel{x_1}{(-15)}) \implies y -70= -3 (x +15) \\\\\\ y - 70 = -3x - 45\implies {\Large \begin{array}{llll} y = -3x+25 \end{array}}[/tex]
the lenght of a flower is 529 cm covet it to m
The information is in the photo. Please help. Goodnight .
The ratio of hexagons to triangles is 2/1.
What are Ratios?The ratio is the relationship or comparison between two amounts of the same unit to determine how much larger one number is than the other. A ratio is a mathematical term that compares two comparable or dissimilar numbers by division. If you want to compare one data point (A) to another data point (B), your formula would be A/B.Given:
In the figure,
Number of hexagons = 4
Number of triangles = 2
We have to determine the ratio of hexagons to triangles.
Ratio = Number of hexagons/Number of triangles
Ratio = 4/2
Reducing it we get,
Ratio = 2/1
Therefore, the required ratio is 2/1.
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Solve the equation b over 24 equals negative 6 for b.
Answer:
b=-144
Step-by-step explanation:
b/24=-6
cross multiplication
b=24×-6
=-144
Tell whether x and y show direct variation. Explain your reasoning if so, find k
y+3=x+6
yes; The equation can be written as y=kx, k = 1
yes; The equation can be written as y = kx, k = 3
No The equation can be written as y
kx, k = 9
no; The equation cannot be written as y = kx.
Answer:
A
Step-by-step explanation:
I just need points bro, Bob bob bob bob bob bob bob bob bob
