After some algebraic handling, the algebraic expression for x in terms of r is x = 1 / r + 1 .
How to clear a variable within an algebraic formula
In this question we must make use of algebra properties to clear a variable within a formula only formed by algebraic form, there are no trascendent functions herein. Clearing variables consists in leaving such variables alone in one side of the equivalence. Now we proceed to present the procedure in detail:
r = 1 / (x - 1) Givenr = (x - 1)⁻¹ Definition of divisionx - 1 = r⁻¹ Compatibility with multiplication / Existence of multiplicative inverse / Associative, commutative and modulative properties.x = 1 / r + 1 Definition of division / Compatibility with addition / Existence of additive inverse / Commutative and modulative properties / ResultRemarkThe statement presents a typing omission, correct form is shown below:
Solve the equation r = 1 / (x - 1) for x in terms of r.
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Select the correct answer.
Based on the construction shown, what is the next step in the process of constructing parallel line CD?
A.
Using the same compass width that created the first arc, repeat the arc centered at point B.
B.
Using the same compass width that created the first arc, repeat the arc centered at point C.
C. Set the compass width to the distance between point E and where the arc crosses line AB.
D.Set the compass width to be where the arc intersects lines ECand EB.
The next step in the process of constructing parallel line CD is C. Set the compass width to the distance between point E and where the arc crosses line AB.
How to illustrate the information?It's important to draw a line parellel to line AB. Then, on should set compasses' width to the distance where the lower arc crosses the two lines.
After that, it's vital to move the compasses to where the upper arc crosses the transverse.
In conclusion, the correct option is C.
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Answer:
The answer is A
Step-by-step explanation:
-7(-w-1)-2 simplest form
(-2a²) (36³)
What’s do I simply using the properties of exponents
Answer:
-93312a²
Step-by-step explanation:
1) Simplify 36³ to 46656.
-2a² × 46656
2) Simplify 2a² × 46656 to 93312a².
-93312a²
Factor the polynomial expression 3x² + 2.
A. (√3x + √2i)(√3x - √/2i)
B. (3x + √2i)(3x - √2i)
C. (√3x + √2)(√3x - √2)
D. (√3x + i)(√√3x - i)
Answer:
[tex]\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
Step-by-step explanation:
Setting the expression equal to zero to find the roots,
[tex]3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}[/tex]
This means that
[tex]3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}[/tex]
Find the first four partial sums, s1,s2,s3,s4, and the nth partial sum of the squence an=log(nn+1).
The first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
In this question,
A sequence is a set of things (usually numbers) that are in order. A partial sum is the sum of part of the sequence.
The sequence is [tex]a_{n} =log(n^{n}+1 )[/tex]
The first four partial sum S₁, S₂, S₃, S₄ can be calculated by substituting n = 1,2,3,4 in the sequence.
S₁ can be calculated as
S₁ = a₁
⇒ [tex]a_{1} =log(1^{1}+1 )[/tex]
⇒ [tex]a_{1} =log(1+1 )[/tex]
⇒ [tex]a_{1} =log(2 )[/tex]
⇒ [tex]a_{1} =0.3010[/tex]
Now, S₁ = 0.3010
S₂ can be calculated as
S₂ = a₁ + a₂
⇒ [tex]a_{2} =log(2^{2}+1 )[/tex]
⇒ [tex]a_{2} =log(4+1 )[/tex]
⇒ [tex]a_{2} =log(5 )[/tex]
⇒ [tex]a_{2} =0.6989[/tex]
Now, S₂ = 0.3010 + 0.6989
⇒ S₂ = 0.9999
S₃ can be calculated as
S₃ = a₁ + a₂ + a₃
⇒ [tex]a_{3} =log(3^{3}+1 )[/tex]
⇒ [tex]a_{3} =log(27+1 )[/tex]
⇒ [tex]a_{3} =log(28)[/tex]
⇒ [tex]a_{3} =1.4471[/tex]
Now, S₃ = 0.3010 + 0.6989 + 1.4471
⇒ S₃ = 2.447
S₄ can be calculated as
S₄ = a₁ + a₂ + a₃ + a₄
⇒ [tex]a_{4} =log(4^{4}+1 )[/tex]
⇒ [tex]a_{4} =log(256+1 )[/tex]
⇒ [tex]a_{4} =log(257 )[/tex]
⇒ [tex]a_{4} =2.4099[/tex]
Now, S₄ = 0.3010 + 0.6989 + 1.4471 + 2.4099
⇒ S₄ = 4.8569
Hence we can conclude that the first four partial sums of the sequence are S₁ = 0.3010, S₂ = 0.9999, S₃ = 2.447, S₄ = 4.8569.
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pls help right now need pleaseee
Answer:
-1/2
Step-by-step explanation:
The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.
For a sample of size 300 from a population with the population proportion, p = 0. 45, compute μphat and σphat
For a sample of size 300 from a population with the population proportion, the μphat and σphat are 0.0287.
A share is an equation in which ratios are set equal to each other. for example, if there may be 1 boy and three women you can write the ratio as 1 : 3 (for each boy there are 3 women) 1 / 4 are boys and three / 4 are girls.
The formula for proportion is components /complete = percent/100. This system can be used to locate the percentage of a given ratio and to locate the lacking value of an element or an entire.
A proportion is generally written as equal fractions. for example: note that the equation has a ratio on each facet of the same signal. Every ratio compares the equal units, inches, and feet, and the ratios are equivalent due to the fact the devices are regular and equal.
Given 300 2 and p 0.45
p = 0.45 Up
and Õp-sqrt(p(1-p)/n) sqrt(0.45 * 0.55/300) sqrt(0.000825) =0.0287
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A casino offers the following game: you draw one card from a standard 52-card deck. If you draw a jack, you win $1.25. If you draw a queen, you win $3.25. If you draw a king, you win $4.5 dollars. If you draw any ace except the ace of spades, you win $6.5. If you draw the ace of spades, you win $7.75. The entry fee to play this game is $1.75. Compute the expected value of this gamble (include the entry fee in your expected value).
Let [tex]W[/tex] be the random variable for the winnings from playing the game once.
• There are 4 jacks in the deck, so you draw a jack with probability 4/52 = 1/13. In this case you "win" $1.25 - $1.75 = -$0.50.
• There are 4 queens, with draw probability 4/52 = 1/13 and winnings $3.25 - $1.75 = $1.50.
• There are 4 kings, with draw probability 4/52 = 1/13 and winnings $4.50 - $1.75 = $2.75.
• There are 4 aces, and 3 of these are not of the spade suit, so the probability of drawing any of these is 3/52 and you win $6.50 - $1.75 = $4.75.
• There is only 1 ace of spaces, with draw probability 1/52 and winnings $7.75 - $1.75 = $6.00.
• Adding these up, it follows that the probability of drawing any other card is 1 - (1/13 + 1/13 + 3/52 + 1/52) = 10/13, in which you have the privilege of "winning" -$1.75.
So, the probability mass function for [tex]W[/tex] is
[tex]\mathrm{Pr}(W=w) = \begin{cases} \dfrac1{13} & \text{if } w \in \{-\$0.50, \$1.50, \$2.75\} \\\\ \dfrac3{52} & \text{if } w = \$4.75 \\\\ \dfrac1{52} & \text{if } w = \$6.00 \\\\ \dfrac{10}{13} & \text{if } w = -\$1.75 \\\\ 0 & \text{otherwise} \end{cases}[/tex]
The expected winnings from playing one round of this game are
[tex]\Bbb E[W] = \displaystyle \sum_w w\,\mathrm{Pr}(W=w)[/tex]
[tex]\Bbb E[W] = \dfrac{-\$0.50 + \$1.50 + \$2.75}{13} + \dfrac{3\cdot\$4.75}{52} + \dfrac{\$6.00}{52} + \dfrac{10\cdot(-\$1.75)}{13}[/tex]
[tex]\Bbb E[W] \approx \boxed{-\$0.67}[/tex]
b. Write an expression equivalent to m+m+m+m that is a sum of two terms.
Type your answer in the box below.
Answer: I believe it is 4m
Step-by-step explanation:
m+m+m+m would be equivalent to 4m which is 4 times m
Step-by-step explanation:
It's like you're adding 1+1+1+1 which equals 4 so that's what I think
Elliott is standing at the top of a store escalator that leads to the ground floor below. the angle of depression from the top of the escalator to the floor is 36.84°, and the escalator is 15 feet long. how far is the top of the escalator from the ground floor? round your answer to the nearest foot. 9 feet 12 feet 20 feet 36 feet
The top of the escalator exists 9 feet far from the ground floor.
How to estimate how far is the top of the escalator from the ground floor?
Let h denote the distance between the top of the escalator from the ground floor.
We have existed given that the angle of depression from the top of the escalator to the floor stands 36.84°, and the escalator exists 15 feet long.
The side h exists opposite side and 15 feet side exists hypotenuse of a right triangle.
[tex]$&\sin =\frac{\text { Opposite }}{\text { Hypotenuse }} \\[/tex]
[tex]$&\sin \left(36.84^{\circ}\right)=\frac{h}{15} \\[/tex]
[tex]$&\sin \left(36.84^{\circ}\right) * 15=\frac{h}{15} * 15 \\[/tex]
[tex]$&0.599582468446 * 15=h \\[/tex]
8.993737 = h
[tex]$&h \approx 9[/tex]
Therefore, the top of the escalator exists 9 feet far from the ground floor.
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PLEASE HELP W THIS MATH QUESTION. correct answers only please
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
What is the quadratic equation behind two circular sections of equal area?
Herein we have two circular sections of equal area, whose expressions are described by the following geometric equations:
Semicircle
A = 0.5π · x² (1)
Half Semicircle
A = 0.25π · (x + 2)² (2)
By equalizing (1) and (2):
0.5π · x² = 0.25π · (x + 2)²
2 · x² = (x + 2)²
2 · x² = x² + 4 · x + 4
x² - 4 · x - 4 = 0
x² - 4 · x + 4 = 8
(x - 2)² = 8
x - 2 = ±√8
x = 2 ± √8
x = 2 ± 2√2
x = 2 · (1 ± √2)
x = 2 · (1 ± 1.41)
x₁ = 2 · 2.41 ∨ x₂ = 2 · (- 0.41)
x₁ = 4.82 ∨ x₂ = - 0.82
The values of x are x₁ ≈ 4.8 and x₂ ≈ - 0.8.
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PLEASE HELP IM SO STUCK
Answer:
y-9=-4(x+2)
Step-by-step explanation:
The point-slope formula is:
y-y1=m(x-x1)
m=-4 and use the point (-2, 9)
x1 y1
Plug in the information.
y-9=-4(x+2)
This is the equation written in point-slope form using the point (-2, 9).
Hope this helps!
The formula f(x 1) = two-thirds(f(x)) defines a geometric sequence where f(1) = 18. which explicit formula can be used to model the same sequence?
The explicit formula is Tn = 18[[tex]\frac{2}{3} ^{n-1}[/tex]]
here, we have to find n.
Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12
F(3) = 2/3 * f(2) = 2/3 * 12 = 8
F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3
F(5) = 2/3 * 16/3 = 32/9
These equations form a pattern.
That is Tn = (2/3)^(n-1)(18)
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Evaluate the following integral (Calculus 2) Please provide step by step explanation!
Answer:
[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=-\dfrac{2}{x+1}+\text{C}[/tex]
Step-by-step explanation:
Fundamental Theorem of Calculus
[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]
If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.
Given integral:
[tex]\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x[/tex]
Factor the denominator:
[tex]\begin{aligned}\implies x^2+2x+1 & = x^2+x+x+1\\& = x(x+1)+1(x+1)\\& = (x+1)(x+1)\\& = (x+1)^2\end{aligned}[/tex]
[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int \dfrac{2}{(x+1)^2}\:\:\text{d}x[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{1}{a^n}=a^{-n}[/tex]
[tex]\implies \displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x=\int 2(x+1)^{-2}\:\:\text{d}x[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $ax^n$}\\\\$\displaystyle \int ax^n\:\text{d}x=\dfrac{ax^{n+1}}{n+1}+\text{C}$\end{minipage}}[/tex]
Use Integration by Substitution:
[tex]\textsf{Let }u=(x+1) \implies \dfrac{\text{d}u}{\text{d}x}=1 \implies \text{d}x=\text{d}u}[/tex]
Therefore:
[tex]\begin{aligned}\displaystyle \int \dfrac{2}{x^2+2x+1}\:\:\text{d}x & = \int 2(x+1)^{-2}\:\:\text{d}x\\\\& = \int 2u^{-2}\:\:\text{d}u\\\\& = \dfrac{2}{-1}u^{-2+1}+\text{C}\\\\& = -2u^{-1}+\text{C}\\\\& = -\dfrac{2}{u}+\text{C}\\\\& = -\dfrac{2}{x+1}+\text{C}\end{aligned}[/tex]
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The price of a bus ticket to Saskatoon is $180. This bus has 56 seats. The bus company is considering dropping the bus fare as part of a promotion to increase the ridership on that route. Lately, the busses have only been at half capapcity. The bus company's research shows that for every $5 decrease they will gain 2 more riders.
a) define variables and set up an equation to represent this scenario
b) What is the maximum revenue the bus company can earn and what will be the cost of a ticket when the revenue is at a maximum
If the price of one ticket of bus is $180 and the bus has 56 seats then the maximum revenue that it can earn is $5107.6
Given that the price of a bus ticket to Saskatoon is $180 and the bus has 56 seats.
We are required to find the maximum revenue that the bus company can earn.
Suppose x represents the number of seats, y represents the total amount.
Price=$156
Seats=56
When the bus is of half capacity the bus seats will be 28.
As price decreases th rider gains 2 more.
Revenue equation.
y=(156.5x)(28+2x)-------------1
Expanding the equation.
y=4368-140x+312-10[tex]x^{2}[/tex]
Differentiating with respect to x.
dy/dx=0-140+312-20x
=172-20x
Put dy/dx=0
172-20x=0
x=8.6
Substitute the value of variable x in the equation 1.
y=(156-5x)(28+2x)
=$5107.6
Hence the maximum revenue that the bus company can earn is $5107.6.
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calculate the slope of the line in the graphs and show your work
calculate the slope of a line that passes through (1,4) and (5,8)
Answer:
7.a) 5
7.b) 1/2
8. 1
Step-by-step explanation:
7.
a)
Read the points on the graph (0, 0) and (1, 5).
slope = (5 - 0)/(1 - 0) = 5/1 = 5
b)
read the points on the graph (0, 0) and (4, 2).
slope = (2 - 0)/(4 - 0) = 2/4 = 1/2
8.
Points (1, 4) and (5, 8)
slope = (8 - 4)/(5 - 1) = 4/4 = 1
Find the ordered pair (s, t) that satisfies the system.
Answer:
s is antecedent t is consepuent
Help!! PLSS
what can be to total of 100% if divided by four percentage?
__%
__%
__%
__%
=100%
Step-by-step explanation:
I am not sure I understand your question (grammatically).
percentages are like any other numbers. they can be added, divided, ...
so, 100% or simply 100 : 100/4 = 25.
so, 4×25 = 100.
and 4×25% = 100%
I am really not sure if this is your question, but it fits to your table with 4 entries and 100% as result.
nts out of
10
Flag question
Instructions: Find the surface area of each figure. Round your answers to the nearest tenth, if necessary.
Surface Area:
Check
9 km.
7 km.
km²
6 km.
8 km.
11 km.
PLEASE HELP MEEEE
EXPLAIN
The Surface area of the triangular prism is: 318 km³.
What is a Triangular Prism?A triangular prism is a solid that has two triangular bases and three rectangular faces.
What is the Surface Area of a Triangular Prism?The surface area of a triangular prism is the sum of the areas of its two triangular bases and three rectangular faces.
The formula for the surface area of a triangular prism = (S1 +S2 + S3)L + bh, where:
Perimeter of the base = S1 + S2 + S3
Length of the prism = L
2 × Base Area = bh
Given the following:
s1 + s2 + s3 = 7 + 9 + 8 = 24 km
L = 11 km
bh = (9)(6) = 54 km²
Plug in the values
Surface area of the triangular prism = (24)11 + 54
Surface area of the triangular prism = 264 + 54
Surface area of the triangular prism = 318 km³
Thus, the Surface area of the given triangular prism in the diagram above is: 318 km³.
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Worth 15 points!!!!!!!!!!!!!!
Show that the curve x = 7 cos(t), y = 4 sin(t) cos(t) has two tangents at (0, 0) and find their equations
The equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
In this question,
The curves are x = 7 cos(t), y = 4 sin(t) cos(t)
Two tangents at (0, 0)
In this case, the parametric derivative of x and y are expressed in terms of t.
The first derivative dy/dx can be expressed as
[tex]\frac{dy}{dx}=\frac{\frac{dy}{dt} }{\frac{dx}{dt} }[/tex]
Now, dy/dt is obtained by differentiate y with respect to t,
[tex]\frac{dy}{dt}= 4[cos(t)(cos(t))+sin(t)(-sin(t))][/tex]
⇒ [tex]\frac{dy}{dt}= 4[cos^{2} (t)-sin^{2} (t)][/tex]
Now, dx/dt is obtained by differentiate x with respect to t,
[tex]\frac{dx}{dt} =7(-sin(t))[/tex]
⇒ [tex]\frac{dx}{dt} =-7sin(t)[/tex]
Thus, [tex]\frac{dy}{dx}=\frac{4[cos^{2}(t)-sin^{2}(t ) ]}{-7sin(t)}[/tex]
At (0,0) x = 0 and y = 0, Then
0 = 7 cos(t)
0 = 4 sin(t) cos(t)
and
cos(t) = 0
sin(t) cos(t) = 0
There are two values between -π and π which satisfy these equations simultaneously are
t = π/2
t = -π/2
The equation of a straight line given a point and its slope is
y-y₀ = m(x-x₀)
The two tangents lies at (0,0), so the equation becomes
y = mx
Then the two straight lines will be
y = m₁x and
y = m₂x
For t = π/2,
[tex]m_1=\frac{dy}{dx}=\frac{4[cos^{2}(\frac{\pi }{2} )-sin^{2}(\frac{\pi }{2} ) ]}{-7sin(\frac{\pi }{2} )}[/tex]
⇒ [tex]m_1=-\frac{4[0-1]}{7(1)}[/tex]
⇒ [tex]m_1=\frac{4}{7}[/tex]
For t = -π/2,
[tex]m_2=\frac{dy}{dx}=\frac{4[cos^{2}(-\frac{\pi }{2} )-sin^{2}(-\frac{\pi }{2} ) ]}{-7sin(-\frac{\pi }{2} )}[/tex]
⇒ [tex]m_2=-\frac{4[0-1]}{-7(1)}[/tex]
⇒ [tex]m_2=-\frac{4}{7}[/tex]
Thus the equations with tangents at (0,0) are [tex]y = \frac{4}{7} x[/tex] and
[tex]y = -\frac{4}{7} x[/tex].
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Sloane kicked a soccer ball off the ground at a speed of 36 feet per second. the height of the ball can be represented by the function h(t) = −16t2 36t where t is the time in seconds. . how many seconds did the ball travel before returning the ground? t = 0.44 seconds t = 2.25 seconds t = 16 seconds t = 36 seconds
The total time in seconds the ball will take to travel before returning the ground is 2.25 seconds.
What is factorisation?The breaking or breakdown of an entity (such as an integer, a matrices, or a polynomials) into a products of another unit, or factors, whose multiplication results in the original number, matrix, etc., is known as factorisation or factoring in mathematics.
Calculation for the time;
Let 't' be the time in second the ball will travel.
Let H(t) be the total height travelled by the ball.
The equation of the height is given as
[tex]H(t)=-16 t^{2}+36 t[/tex]
As soon as the ball will return to the ground the total height will become zero.
So, put equation of height equal to zero.
[tex]-16 t^{2}+36 t=0[/tex]
Factorise the above equation;
[tex]-16 t\left(t-\frac{9}{4}\right)=0[/tex]
Put each value equals to zero to get the value of time.
[tex]\begin{aligned}&t=0 \mathrm{sec} \\&t=9 / 4=2.25 \mathrm{sec}\end{aligned}[/tex]
As, time can not be zero
Therefore, the total time taken by the ball to return to the ground is 2.25 sec.
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A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
a =
b =
c =
d =
e =
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show logical relationships between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
The following have to be established:
a player can either be male or female
a player favors either the left or the right
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left
34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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If 3(x-3) = 5(2x + 1), then
x=-2
Step-by-step explanation:
Solution Given:
3(x-3) = 5(2x + 1)
Opening bracket we get
3x-9=10x+5
keeping common value in same side
-9-5=10x-3x
-14=7x
x=-14/7
x= -2
Answer:
-2 =x
Step-by-step explanation:
3(x-3) = 5(2x + 1)
To solve for x
Distribute
3x -9 = 10x +5
Subtract 3x from each side
3x-9-3x = 10x -3x+5
-9 = 7x+5
Subtract 5 from each side
-9-5 = 7x+5-5
-14 = 7x
Divide by 7
-14/7 = 7x/7
-2 =x
Select the correct answer. what is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11?
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
What is the probability that a person who exists older than 35 years contains a hemoglobin level between 9 and 11?Let the number of the person who is older than 35 years have a hemoglobin level between 9 and 11 be x.
From the given table it is clear that the total number of the person who is older than 35 years exists 162.
75+x+40 = 162
x+116 = 162
x = 162-116
x = 46
The number of people who are older than 35 years has a hemoglobin level between 9 and 11 exists at 46.
1. The probability that a person who exists older than 35 years has a hemoglobin level between 9 and 11 exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and 11 / Person who exists older than 35
P = 46/162 = 0.284
The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 exists at 0.284.
2. Person who is older than 35 years has a hemoglobin level of 9 and above exists 46 + 40 = 86.
The probability that a person who exists older than 35 years has a hemoglobin level of 9 and above exists
P = Probability who is older than 35 years has a hemoglobin level
between 9 and above / Person who is older than 35
P = 86/162 = 0.531.
The probability that a person who is older than 35 years has a hemoglobin level of 9 and above exists at 0.531.
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A sample is selected from a population with a mean of μ = 65 and a standard deviation of σ = 15. if the sample has n = 9 scores, what are the expected value of m and the standard error of m?
The Expected value of M is 65
The Standard error of M is 5
The mean of the distribution of sample means is called the expected value of M.The standard deviation of the distribution of sample means is called the standard error of M.Given,
The sample score, n = 9
The Standard deviation, σ = 15
Population mean, μ = 65
Then,
The Expected value of M = μ
∴ The Expected value of M = 65
The Standard error of M = σ/[tex]\sqrt{n}[/tex]
[tex]=\frac{15}{\sqrt{9} } \\\\=\frac{15}{3} \\=5[/tex]
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HELP!
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2.
The areas of the parallelograms can be compared as: A. The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
What is a parallelogram?A parallelogram refers to a geometrical shape and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.
How to calculate the area of a triangle?Mathematically, the area of a triangle can be calculated by using this formula:
Area = ½ × b × h
Where:
b represents the base area.h represents the height.How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula;
A = LW
Where:
A represents the area of a rectangle.l represents the length of a rectangle.w represents the width of a rectangle.Next, we would determine the area of the two parallelograms as follows:
Area of parallelogram 1 = Area of red-rectangular figure - Area of triangle A - Area of triangle B - Area of triangle C - Area of triangle D.
Substituting the given parameters into the formula, we have;
Area of parallelogram 1 = (6 × 6) - (½ × 4 × 2) - (½ × 2 × 4)- (½ × 4 × 2) - (½ × 2 × 4)
Area of parallelogram 1 = 36 - 4 - 4 - 4 - 4
Area of parallelogram 1 = 36 - 16
Area of parallelogram 1 = 20 units².
For parallelogram 2, we have:
Area of parallelogram 2 = Area of blue-rectangular figure - Area of triangle P - Area of triangle Q - Area of triangle R - Area of triangle S.
Substituting the given parameters into the formula, we have;
Area of parallelogram 2 = (8 × 4) - (½ × 2 × 2) - (½ × 6 × 2)- (½ × 2 × 2) - (½ × 2 × 6)
Area of parallelogram 2 = 32 - 2 - 6 - 2 - 6
Area of parallelogram 2 = 32 - 16
Area of parallelogram 2 = 16 units².
Difference = Area of parallelogram 1 - Area of parallelogram 2
Difference = 20 - 16
Difference = 4 units².
In conclusion, we can infer and logically deduce that the area of parallelogram 1 is 4 square units greater than the area of parallelogram 2.
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Charlie throws a ball up into the air. while the ball is airborne, which is the greatest force acting on the ball to slow it down?
The greatest force acting on the ball to slow it down is Gravitational force.
Which forces will act on the ball?When ball is thrown upwards then there will be two forces on the ball opposite to the motion of ball
1. Gravitational force (mg)
2. Air friction or air drag
Both forces are opposite to the motion of the ball and it will cause the decrease in the speed of the ball.
Now here due to less value of drag coefficient on the ball we will say that ball will decrease its speed more due to gravitational force compare to friction force of air.
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A recipe requires 3.5 teaspoons of sugar to make a tart. which equation shows the number of teaspoons of sugar, y, needed to make x tarts? x = 3.5y y = 3.5x y = 3.5 x x = 3.5 y
x = 3.5y equation shows the number of teaspoons of sugar, y, needed to make x tarts.
What is the linear equation in two variable?
Any equation which can be put in the form ax + by + c = 0, where a, b and c are real numbers, and a and b are not both zero, is called linear equation in two variable.
According to the given question
A recipe require 3.5 teaspoons of sugar to make a tart.
y represents the number of teaspoons of sugar.
x represents the number of tarts.
Now, for x tart 3.5y teaspoons of sugar required.
⇒ x = 3.5y
Hence, the linear equation in two variable that shows the number of teaspoons of sugar y, needed to make x number or tarts is x = 3.5y.
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A test consists of section A and section B. Section A has 15 questions and section B has 10 questions. The number of questions in section A is ____% if the questions in the test.
