Answer: 32 is the answer to the expression you provided.
Step-by-step explanation:
[tex]2^3\times2^2\\2\times2\times2\times2\times2\\4\times4\times2\\16\times2\\\rightarrow32[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{E}\textsf{quation:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\huge\boxed{S}\textsf{olving:}[/tex]
[tex]\mathsf{2^3 \times 2^2}[/tex]
[tex]\mathsf{= 2\times2\times2 \times2\times2}[/tex]
[tex]\mathsf{= 4\times4\times2}[/tex]
[tex]\mathsf{= 16\times2}[/tex]
[tex]\mathsf{= 32}[/tex]
[tex]\huge\boxed{T}\textsf{herefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{32}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which function is represented in the
graph below?
Answer:
Option 2
Step-by-step explanation:
There is an amplitude of 1/2, a period of pi, and a non-zero y-intercept.
The diagram shows a cuboid. 4 cm 12 cm x cm the volume of the cube is 120cm² calculate the value of x
Answer:
The value of x will be 2.5cm.
Step-by-step explanation:
Greetings !Volume = Length*Width*Height
where,
Volume=120cm³Length=12cmWidth=xHeight=4cm[tex]v = l \times w \times h \: ...substitute \: values \\ 120cm {}^{3} = 12cm \times w \times 4cm \\ 120cm {}^{3} = 48cm {}^{2} \times w \: ...divide \: both \: \\ sides \:by \: 48cm {}^{2} \\ \frac{120cm {}^{3} }{48cm {}^{2} } = w \\ w = 2.5cm[/tex]
Analysis and observations in these two graphs
By critically observing the graph, we can infer and logically deduce the following points:
The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line) was constant.Graph 1 (thin-dashed line) is essentially a linear graph.What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
This ultimately implies that, the data of a linear graph are directly proportional and as such, as the value on the x-axis increases or decreases, the values on the y-axis also increases or decreases.
By critically observing the graph which models the changes in temperature over a specific period of time (in years), we can infer and logically deduce the following points:
The linear function is given by y = 0.0169x + 32.485.The initial temperature for both data is greater than 32°C.The final temperature for both data is less than 33.5°C.Between 1980 and 2020, the temperature for graph 2 (thick-continuous line) was constant.Graph 1 (thin-dashed line) is essentially a linear graph.In conclusion, there are four (4) points of intersection on this graph.
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The hollenbecks own a square lot with area 3600 square meters. they plan to fence just three sides of this lot. how many meters of fence must they purchase?
Answer: 180 meters
Step-by-step explanation: To solve this we need to find the square root of 3600. 6x6 = 36 so we know the square root is 60. That means that each side of the square lot is 60 meters. If they fence 3 sides they will need to purchase 60x3= 180 meters of fence.
Match the graph of the function with the function rule.
y = 3 • 2x
y = 2 • 3x
y = 1 • 3x
y = 4 • 3x
By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)
What is the equation behind the exponential curve seen in the graph?In this question we have the graph of a exponential function, whose expression have to be found based on the definition of exponential function:
y = a · bˣ (1)
Where:
a - Initial value of the exponetial function.b - Base of the exponential function.x - Independent variabley - Dependent variableNow we find the values for a and b:
Initial value (x = 0, y = 3)
3 = a · b⁰
a = 3
Base of the exponential function (x = 1, a = 3, y = 6)
6 = 3 · a
a = 6 / 3
a = 2
By applying the definition of exponential function, we find that the function f(x) = 3 · 2ˣ match with the graph of the picture. (Correct choice: A)
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Alexa is a basketball player at East High. At a recent game, she made some three point shots and some two point shots. Alexa scored a total of 18 points and made 3 times as many two point shots as three point shots. Determine the number of three point shots Alexa made and the number of two point shots she made.
Answer:
6 2 point shots 2 3 points
Step-by-step explanation:
3 two point shot 1 3 point shot = 9
6 two point shot 2 3 point shot =18
Please help with this question on a acellus thanks!
Using the law of sines, it is found that the measure of angle x is given as follows:
x = 69.9º.
What is the law of sines?Suppose we have a triangle in which:
The length of the side opposite to angle A is a.The length of the side opposite to angle B is b.The length of the side opposite to angle C is c.The lengths and the sine of the angles are related as follows:
sin(A)/A = sin(B)/B = sin(C)/C
Considering the given triangle, the following relation can be established:
sin(x)/11 = sin(28º)/x
Hence, applying cross multiplication:
sin(x) = 2sin(28º)
sin(x) = 0.938943126
x = arcsin(0.938943126)
x = 69.9º.
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1
Select the correct answer.
Which expression is equivalent to x+y+x+y+ 3(y+5)?
OA. 2x+5y+5
OB. 2x+y+30
OC. 2x+ 5y + 15
OD. 2x+3y + 10
what is the correct solution to the original inequality?
-4(5/2 + 3/2x) > 8
pls help LP 69 credits
Answer:
x < - 3 or x ∈ (-∞, -3)==============================
GivenInequality:
[tex]-4(\cfrac{5}{2} +\cfrac{3}{2}x) > 8[/tex]SolutionSteps1. Distribute:
[tex]-4(\cfrac{5}{2}) -4(\cfrac{3}{2}x) > 8[/tex]2. Multiply:
[tex]-10-6x > 8[/tex]3. Collect like terms:
[tex]-10-8 > 6x[/tex]4. Addition:
[tex]-18 > 6x[/tex]5. Divide both sides by 6:
[tex]-3 > x[/tex] or [tex]x < -3[/tex]Interval notation for this solution is:
x ∈ (-∞, -3)Answer:
[tex]x < -3[/tex]
Interval notation: (-∞, 3)
Step-by-step explanation:
Given inequality:
[tex]-4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right) > 8[/tex]
Divide both sides by -4 (remembering to change the direction of the inequality sign, since we are dividing by a negative):
[tex]\implies \dfrac{ -4 \left(\dfrac{5}{2}+\dfrac{3}{2}x\right)}{-4} > \dfrac{8}{-4}[/tex]
[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x < -2[/tex]
Subtract ⁵/₂ from both sides:
[tex]\implies \dfrac{5}{2}+\dfrac{3}{2}x-\dfrac{5}{2} < -2-\dfrac{5}{2}[/tex]
[tex]\implies \dfrac{3}{2}x < -\dfrac{9}{2}[/tex]
Multiply both sides by 2:
[tex]\implies \dfrac{2 \cdot 3}{2}x < -\dfrac{2 \cdot 9}{2}[/tex]
[tex]\implies \dfrac{\diagup\!\!\!\!2 \cdot 3}{\diagup\!\!\!\!2}x < -\dfrac{\diagup\!\!\!\!2 \cdot 9}{\diagup\!\!\!\!2}[/tex]
[tex]\implies 3x < -9[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3} < \dfrac{-9}{3}[/tex]
[tex]\implies x < -3[/tex]
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Austin keeps a right conical basin for the birds in his garden as represented in the diagram. The basin is 40 centimeters deep, and the angle between the sloping sides is 77°. What is the shortest distance between the tip of the cone and its rim?
177.8 centimeters.
What is the formula for cos θ?The symbol for it is Cosθ, and it has the following form: adjacent/hypotenuse = cosθ. In other words, it divides the length of the hypotenuse by the length of the neighboring side, which is the side next to the angle (the longest side of a right triangle).When working with right-angled triangles, the Cos Theta Formula is particularly helpful. The Cosine of an angle in a right triangle is always equal to the hypotenuse's length divided by the length of the neighboring side. This makes it an excellent tool for resolving Cosine-related issues.The shortest distance between the tip of the cone and its rim:
cos θ= base/Hypotenuse
cos 77°=[tex]\frac{40}{H}[/tex]
[tex]0.22495=\frac{40}{H}[/tex]
[tex]H=177.8[/tex]
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The shortest distance between the tip of the cone and its rim exits 51.11cm.
What is the shortest distance between the tip of the cone and its rim?If you draw a line along the middle of the cone, you'd finish up with two right triangles and the line even bisects the angle between the sloping sides. The shortest distance between the tip of the cone and its rim exists in the hypotenuse of a right triangle with one angle calculating 38.5°. So, utilizing trigonometry and allowing x as the measurement of the shortest distance between the tip of the cone and its rim.
Cos 38.5 = 40 / x
Solving the value of x, we get
Multiply both sides by x
[tex]$\cos \left(38.5^{\circ}\right) x=\frac{40}{x} x[/tex]
[tex]$\cos \left(38.5^{\circ}\right) x=40[/tex]
Divide both sides by [tex]$\cos \left(38.5^{\circ}\right)$[/tex]
[tex]$\frac{\cos \left(38.5^{\circ}\right) x}{\cos \left(38.5^{\circ}\right)}=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
simplifying the above equation, we get
[tex]$x=\frac{40}{\cos \left(38.5^{\circ}\right)}[/tex]
x = 51.11cm
The shortest distance between the tip of the cone and its rim exits 51.11cm.
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What happens when you reflect a shape over the x-axis and then the y-axis. What is the one transformation that could have been performed to achieve the same result?
Answer:
Rotate 180 degrees with the center the origin (0,0)
Step-by-step explanation:
Try drawing a small square in the first quadrant, then reflect it like the direction. If you use tracing paper and and copy the figure, you will see that if you rotate the figure at the origin, it will land on the same spot as the translations.
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
The surface area of the given figure is 288 km²
Calculating surface areaFrom the question, we are to determine the surface area of the figure
The given figure is a square-base pyramid
Surface area of the pyramid = (10×10) + 4× 1/2(10×9.4)
Surface area of the pyramid = (100) + 2(94)
Surface area of the pyramid = 100 + 188
Surface area of the pyramid = 288 km²
Hence, the surface area of the given figure is 288 km²
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A grandfather's age in years is the same as his granddaughter's age is months. Together, they are 91 years old. How old is the grandfather?
Answer:
Step-by-step explanation:
The picture below shows a pole and its shadow:
A pole is shown with a right triangle side. The right triangle has hypotenuse 113 cm and base 15 cm.
What is the height of the pole?
112 centimeters
100 centimeters
98 centimeters
64 centimeters
The answer is 112 centimeters.
As this problem represents a right triangle, here we need to apply the Pythagorean Theorem.
h = √113² - 15²h = √12769 - 225h = √12544h = 112 centimetersQuestion 8
725
A cable measures inch outside diameter and has a wrap of cotton that is 1000
1000
65
inch thick and covering of rubber insulation that is inch thick. What is the
diameter of the copper conductor (wire)?
Based on the thickness of the rubber insulation and outside diameter, the diameter of the copper conductor is 0.376 inch.
What is the copper wire's diameter?The diameter of the copper wire can be found by the formula:
= Outer diameter - ( 2 x cotton insulation) - (2 x rubber insulation)
Solving gives:
= 500/ 1,000 - (2 x 12/ 1,000) - (2 x 50 / 1,000)
= 0.5 - (2 x 0.12) - (2 x 0.05)
= 0.376 inch
= 376 / 1,000 inch
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find the size of each of the angles marked with letter
Answer: ||||||| n=41° |||||| m=59° IIIII p=260° IIII
Step-by-step explanation:
Alternate angle:
<m=<59°
m=59°
<n=<41°
n=41°
______________
p+41°+59°= 360°
p+100°=360°
p=360°-100°
p=260°
Answer:
n = 49
m= 31
p= 280
Step-by-step explanation:
41 + n = 90
n= 90 -41 = 49
59 + m = 90
m = 90 - 59 = 31
Hope this helps!
p + n + m = 360
p = 360 - 49 - 31 = 280
ramiro has filled 1/3 or 50 gallons of his fish tank. find the total capacity of the fish tank
Answer:
150
Step-by-step explanation:
because full capacity is 3/3, therefore you time 50 by 3, which will be 150 gallons
How did doves view the conflict in Vietnam?
O As a vital Cold War battleground in the fight for democracy
O As a localized civil war that should not include the US
O As the first step in acquiring territory in Southeast Asia
O As a means to achieving Johnson's Great Society
The view of war doves with respect to the Vietnam War was that: B. as a localized civil war that should not include the United States of America (US).
What is the Vietnam War?The Vietnam War is also referred to as Second Indochina War or the Vietnam conflict and it can be defined as a short, costly, protracted and divisive conflict between the communist government of North Vietnam and South Vietnam, which ended on the 30th of April, 1975.
Based on historical information and records, the Vietnam War officially started on the 1st of November, 1955 in the following locations:
VietnamCambodiaNorth VietnamSouth VietnamLaosSouth East AsiaIn conclusion, we can infer and logically deduce that the view of war doves with respect to the Vietnam War was that it is a a localized civil war and as such should not include the United States of America.
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The sum of 2 numbers is 73, and their difference is 11.
Find the numbers.
Answer: 42 and 31
Step-by-step explanation:
Let x be one number and y be the other.
We will write mathematical equations for these two numbers.
The sum of 2 numbers is 73.
x + y = 73
Their difference is 11.
x - y = 11
See attached for the graph.
The point of intersection is our solution.
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}[/tex]
Step-by-step explanation:
To find y-intercept of a graph, we have to substitute x = 0 to find it - consider each functions:
First Choice
[tex]\displaystyle{f(x) = 2x(x+14)-64}\\\\\displaystyle{f(0) = 2\cdot 0(0+14)-64}\\\\\displaystyle{f(0) = 0\cdot 14-64}\\\\\displaystyle{f(0) = -64}[/tex]
Second Choice
[tex]\displaystyle{f(x) = (x+4)^2+2x}\\\\\displaystyle{f(0) = (0+4)^2 + 2(0)}\\\\\displaystyle{f(0) = 4^2}\\\\\displaystyle{f(0) = 16}[/tex]
Third Choice
[tex]\displaystyle{f(x) = (x-16)^2 + 4}\\\\\displaystyle{f(0) = (0-16)^2 + 4}\\\\\displaystyle{f(0) = (-16)^2 + 4}\\\\\displaystyle{f(0) = 256 + 4}\\\\\displaystyle{f(0) = 260}[/tex]
Fourth Choice
[tex]\displaystyle{f(x) = -2(x-3)^2 + 2}\\\\\displaystyle{f(0) = -2(0-3)^2 + 2}\\\\\displaystyle{f(0) = -2(-3)^2 + 2}\\\\\displaystyle{f(0) = -2\cdot 9 + 2}\\\\\displaystyle{f(0) = -18+2}\\\\\displaystyle{f(0) = -16}\\[/tex]
Therefore, fourth choice is correct.
Which test point holds true for the inequality 3/2y-2x>=1? Where does the shaded area lie for this inequality? The test point holds true for this inequality. The shaded area for the inequality lies the boundary line.
The test That holds true for this inequality is given as 1/4 and 1
How to solve for the inequality3/2 y - 2x > 1
The goal is to make y the subject
then
3/2 y > 2x + 1
We have to divide through the equation by 3/2
Such that y > 4/3 x + 2/3
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-2x + 7x +34 = -2(1-7x)
[tex]\boldsymbol{\sf{-2x + 7x +34 = -2(1-7x) \ \ \longmapsto \ \ [Add \ -2x+7x]}}[/tex]
[tex]\boldsymbol{\sf{5x+34=-2(1-7x)}}[/tex]
Use the distributive property to multiply −2 by 1−7x.
[tex]\boldsymbol{\sf{5x+34=-2+14x}}[/tex]
Subtract 14x on both sides.
[tex]\boldsymbol{\sf{5x+34-14x=-2}}[/tex]
Combine 5x and −14x to get −9x.
[tex]\boldsymbol{\sf{-9x+34=-2 }}[/tex]
Subtract 34 from both sides.
[tex]\boldsymbol{\sf{-9x=-2-34 \ \ \longmapsto \ \ \ [Subtract] }}[/tex]
[tex]\boldsymbol{\sf{-9x=-36}}[/tex]
Divide both sides by −9.
[tex]\boldsymbol{\sf{x=\dfrac{-36}{-9} \ \ \longmapsto \ \ [Split] }}[/tex]
[tex]\red{\boxed{\boldsymbol{\sf{\blue{Answer \ \ \longmapsto \ \ x=4 }}}}}[/tex]
[tex] \quad\quad\quad \huge \underline{ \tt{ANSWER}}[/tex]
[tex]\quad\quad\quad\quad\quad\quad[/tex]
[tex]\tt{- 2x + 7x + 34 = - 2(1 - 7x)}[/tex]
[tex]\tt{5x + 34 = - 2(- 7x + 1)}[/tex]
[tex]\tt{5x + 34 = - (- 2 * 7x + 2)}[/tex]
[tex]\tt{5x + 34 = - (- 14x + 2)}[/tex]
[tex]\tt{(5x + 34) + (- 34 - 14x) = (14x - 2) + (- 34 - 14x)}[/tex]
[tex]\tt{5x + 34 - 34 - 14x = 14x - 2 - 34 - 14x}[/tex]
[tex]\tt{5x - 14x + 34 - 34 =14x-14x-2 - 34}[/tex]
[tex]\tt{- 9x = - 36}[/tex]
[tex]\tt{\frac{9x}{9} = \frac{36}{9}}[/tex]
[tex]\tt{x = 4}[/tex]
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
B {3/2, -5/3}
Step-by-step explanation:
6x² + x - 15 = 0
6x² + 10x - 9x - 15 = 0
2x(3x + 5) - 3(3x + 5) = 0
(3x + 5)(2x - 3) = 0
3x + 5 = 0 or 2x - 3 = 0
3x = -5 or 2x = 3
x = -5/3 or x = 3/2
Answer: B {3/2, -5/3}
Answer:
[tex]\left\{\dfrac{3}{2},\ -\dfrac{5}{3}\right\}[/tex]
Step-by-step explanation:
Given quadratic equation: [tex]6x^2+x-15=0[/tex]
[tex]\implies a=\textsf{6},b=\textsf{1},c=\textsf{-15}[/tex]
..................................................................................................................................................
[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]
..................................................................................................................................................
Step 1: Substitute the given values into the formula and simplify.
[tex]\implies x=\dfrac{-{(\textsf1})\pm \sqrt{\textsf{(1)}^2-4(\textsf{6}){(\textsf{-15})}}}{2{(\textsf{6})}}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{1-4(-90)}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{1+360}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm \sqrt{361}}{12}[/tex]
[tex]\implies x=\dfrac{-1\pm 19}{12}[/tex]
Step 2: Separate into two cases.
[tex]x_1=\dfrac{-1+19}{2}[/tex]
[tex]x_2=\dfrac{-1-19}{2}[/tex]
Step 3: Solve both cases.
[tex]\implies x_1=\dfrac{-1+19}{12}=\dfrac{18}{12}=\dfrac{6\times3}{6\times2}=\boxed{\dfrac{3}{2}}[/tex]
[tex]\implies x_2=\dfrac{-1-19}{12}=\dfrac{-20}{12}=\dfrac{-4\times5}{4\times3}=\boxed{-\dfrac{5}{3}}[/tex]
The solutions to this quadratic are: [tex]x_1=\dfrac{3}{2},\ x_2=-\dfrac{5}{3}[/tex]
..................................................................................................................................................
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13. The average age of a high school freshman is 14.5. How many days old is the average high
school freshman?
Answer:
5296.125 days
Step-by-step explanation:
1 year = 365.25 days
14.5 years × 365.25 days/year = 5296.125 days
Find the polar equation of an ellipse with its focus at the pole and vertices at (−1,0) and (3,0).
The polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
The vertices of ellipse are (−1,0) and (3,0).
The polar equation of an ellipse can be represented as
[tex]r=\frac{ep}{1+ecos\theta}[/tex]
where e is the eccentricity.
Eccentricity, e = [tex]\frac{c}{a}[/tex]
c is the distance from the center to the focus and a is the distance from the center to the vertex
[tex]c=\frac{3-(-1)}{2}[/tex]
⇒ [tex]c=\frac{4}{2}[/tex]
⇒ c = 2
[tex]a=\frac{3+(-1)}{2}[/tex]
⇒ [tex]a=\frac{2}{2}[/tex]
⇒ a = 1
Then, e = [tex]\frac{2}{1}[/tex]
⇒ e = 2
Now, the polar equation of an ellipse becomes as,
⇒ [tex]r=\frac{2p}{1+2cos\theta}[/tex] ------- (1)
Now plug in a vertex point such as (-1,0) and solve for p,
⇒ [tex]-1=\frac{2p}{1+2cos0}[/tex]
⇒ [tex]-1=\frac{2p}{1+2(1)}[/tex] [∵ cos 0 = 1]
⇒ [tex]-1=\frac{2p}{3}[/tex]
⇒ [tex]-3=2p[/tex]
⇒ [tex]p=-\frac{3}{2}[/tex]
Thus the polar equation of an ellipse (1) becomes as,
⇒ [tex]r=\frac{2(-\frac{3}{2} )}{1+2cos\theta}[/tex]
⇒ [tex]r=-\frac{3}{1+2cos\theta}[/tex]
Hence we can conclude that the polar equation of an ellipse is [tex]r=-\frac{3}{1+2cos\theta}[/tex].
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Amanda increased the amount of protein she eats everyday from 48g to 54 g By what percentage did Amanda increase the amount of protein she eats
Step-by-step explanation:
she increased the amount from 48g to 54g. that is 54-48 = 6g.
so, the question really is, how many % of 48 is 6 ?
100% = 48g
1% = 100%/100 = 48/100 = 0.48g
how many % are 6g ?
as many as how often 1% (0.48g) fits into 6g :
6 / 0.48 = 12.5%
Consider a binomial experiment. if the number of trials is increased, what happens to the expected value? To the standard deviation? Explain
The expected value or mean of binomial distribution is also increased by increasing the number of trials.
The standard deviation of binomial distribution is also increased by increasing the number of trials.
According to the question
There is binomial experiment.
The condition given in the question is 'if the number of trials is increased, what happens to the expected value and to the standard deviation'.
We all know,
In binomial distribution, The mean or expected value is given by np whereas the variance is given by np(1 - p) where (1 - p) taken as q is the probability of failure and p is the probability of success.
The standard deviation of binomial distribution is [tex]\sqrt{npq}[/tex].
From the expected value formula we can see that number number of trials is directly proportional to mean or expected value.
Thus we can say that
If the number of trials is increasing, then the expected value is also increasing.
From the standard deviation of binomial distribution we can see that if the number of trials increasing then the standard deviation also increasing because standard deviation is directly proportional to number of trials.
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Use euler’s method. i. e. to find the approximate values of the solution for yʹ=y(3−ty), y(0)=0. 5,h=0. 1, 0≤t≤0. 5
The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.
In this question,
The differential equation is
yʹ=y(3−ty) ------- (1)
Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.
By Euler's method,
[tex]y_{n+1}=y_n+hf_n[/tex]
where [tex]f_n=f(t_n,y_n)[/tex]
For, t = 0, y = 0,
[tex]y_{1}=y_0+hf_0[/tex] and
[tex]f_0=f(t_0,y_0)[/tex]
Substitute in equation 1,
⇒ f(0,0.5) = 0.5(3-(0)(0.5))
⇒ f(0,0.5) = 0.5(3-0)
⇒ f(0,0.5) = 0.5(3)
⇒ f(0,0.5) = 1.5
Then, [tex]y_{1}=y_0+hf_0[/tex] becomes,
⇒ y₁ = 0.5 + (0.1)(1.5)
⇒ y₁ = 0.5 + 0.15
⇒ y₁ = 0.65
For, t = 1, y = 1,
[tex]y_{2}=y_1+hf_1[/tex] and
[tex]f_1=f(t_1,y_1)[/tex]
⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))
⇒ f(0.1,0.65) = 0.65(3-0.065)
⇒ f(0.1,0.65) = 1.90
Then, [tex]y_{2}=y_1+hf_1[/tex] becomes,
⇒ y₂ = 0.65+(0.1)(1.90)
⇒ y₂ = 0.84
For t = 2, y = 2,
[tex]y_{3}=y_2+hf_2[/tex] and
[tex]f_2=f(t_2,y_2)[/tex]
⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))
⇒ f(0.2,0.84) = 0.84(3-0.168)
⇒ f(0.2,0.84) = 2.3788
Then, [tex]y_{3}=y_2+hf_2[/tex]
⇒ y₃ = 0.84+(0.1)(2.3788)
⇒ y₃ = 1.0778
For t = 3, y = 3,
[tex]y_{4}=y_3+hf_3[/tex] and
[tex]f_3=f(t_3,y_3)[/tex]
⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))
⇒ f(0.3,1.0778) = 1.0778(3-0.32334)
⇒ f(0.3,1.0778) = 2.8848
Then, [tex]y_{4}=y_3+hf_3[/tex] becomes
⇒ y₄ = 1.0778+(0.1)(2.8848)
⇒ y₄ = 1.3584
For t = 4, y = 4,
[tex]y_{5}=y_4+hf_4[/tex] and
[tex]f_4=f(t_4,y_4)[/tex]
⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))
⇒ f(0.4,1.3584) = 1.3584(3-0.5433)
⇒ f(0.4,1.3584) = 3.3372
Then, [tex]y_{5}=y_4+hf_4[/tex] becomes
⇒ y₅ = 1.3584 + (0.1)(3.3372)
⇒ y₅ = 1.6921
For t = 5, y = 5,
[tex]y_{6}=y_5+hf_5[/tex] and
[tex]f_5=f(t_5,y_5)[/tex]
⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))
⇒ f(0.5,1.6921) = 1.6921(3-0.84605)
⇒ f(0.5,1.6921) = 3.6447
Then, [tex]y_{6}=y_5+hf_5[/tex] becomes
⇒ y₆ = 1.6921 + (0.1)(3.6447)
⇒ y₆ = 2.05657
Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.
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Pls help …. Need it immediately ….
The answer is 10.73 years.
Here, the formula we can use is :
[tex]\boxed {Children = \frac{Boys+Girls}{2}}[/tex] (for the average)
Substitute the values mentioned in the question.
10.54 = (10.35 + Girls)/2
21.08 = 10.35 + Girls
Girls = 10.73 years
The mean salary at a local industrial plant is $29,300 with a standard deviation of $5400. The median salary is $24,500 and the 63rd percentile is $29,600.
Step 1 of 5: Based on the given information, determine if the following statement is true or false.
Approximately 63% of the salaries are less than or equal to $29,600
Step 2 of 5: Based on the given information, determine if the following statement is true or false.
Joe's salary of $39,320 is 1.80 standard deviations above the mean.
Step 3 of 5: Based on the given information, determine if the following statement is true or false.
The percentile rank of $25,000 is 50.
Step 4 of 5: Based on the given information, determine if the following statement is true or false.
Approximately 13% of the salaries are between $29,300 and $29,600.
Step 5 of 5: If Tom's salary has a z-score of 0.5, how much does he earn (in dollars)?
The true and false statement about the mean salary is illustrated below.
How to illustrate the information?The true false statement about the mean salary include:
Approximately 63% of the salaries are less than or equal to $29,600Joe's salary of $39,320 is 1.80 standard deviations above the mean.The percentile rank of $25,000 is 50.Approximately 13% of the salaries are between $29,300 and $29,600.When Tom's salary has a z-score of 0.5, the amount that he earns will be:
0.5 = (x - 29300)/5400
0.5 × 5400 = x - 29300
2700 = x - 29300
x = 29300 + 2700.
x = 32000
The amount he earns is 32000.
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