The surface area of the given rectangular prism with a length 7cm , width 2cm and height 6cm is equal to 136cm².
As given in the question,
Dimensions for a given rectangular prism are:
Length = 7cm
Width = 2cm
Height = 6cm
Surface area of the given rectangular prism is equal to
= 2 ( length × width + width × height + height × length )
Substitute the value in the formula we get,
= 2 ( 7 × 2 + 2 × 6 + 6 × 7 )
= 2 ( 14 + 12 + 42 )
= 2 ( 68 )
= 136 cm²
Therefore, the surface area of the rectangular prism is equal to 136cm².
The complete question is :
Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm,
and a height of 6 cm.
What is the surface area of Hannah's rectangular prism?
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Given the equation of a circle, identify the center and the radius.
(x − 9)² + (y+4)² = 36
-
Center:
Radius:
How many ways can you arrange 5 numbers?.
In 120 ways 5 numbers can be arranged through permutations.
Define permutation.A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation." The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given,
In following ways 5 numbers can be arranged through permutations,
5!
5 × 4 × 3 × 2×1
120
In 120 ways 5 numbers can be arranged through permutations.
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Which special segments go through a midpoint?.
Bisectors are the special segments that pass through the mid point of the lines or line segments.
A bisector is the line, line segment or ray that intercepts and/or divided lines or line segments into two equal line segments and thus passes through the midpoint of the given line segment or line segments.
There can be infinite bisector for one particular line or line segment at multiple angles.
The bisector that intercepts and/or cuts a line in half, passes through the midpoint when it is perpendicular (making an angle of 90°) to the line segment is known as the Perpendicular Bisector.
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a relaxed student rolls a fair, 6-sided die in the morning. if he rolls a 1, then he does his laundry immediately (with zero days of delay). otherwise, he delays for one day and repeats the experiment the following morning. let r be the number of days a relaxed student delays laundry. what is ex(r)
The expectation of the required random variable is Ex(r) for the given number of days when a relaxed student delays for laundry is Ex(r) = 5.
As given in the question,
6-sided fair die was rolled by relaxed student
Rolls of fair die represents 1 it mean laundry is done ( no delay in laundry)
Count the number of days when laundry gets done = 1 / (1 /6)
= 6
Number of days when laundry gets delays = 6 - 1
= 5
Probability of laundry delay = 5/6
Expectation of the required number of random variables
Ex(r) = [tex]\sum\limits^\infty_0 {P_{r} } \,[/tex]
= [tex]\frac{5}{6} + (\frac{5}{6}) (\frac{5}{6}) +....[/tex]
= (5/6)( 1+ ( 5/6) + (5/6)(5/6) + (5/6)(5/6)(5/6) +...)
= [tex]( 5/ 6)[ \frac{1}{1- (\frac{5}{6} )}][/tex]
= 5
Therefore, the number of days when relaxed student delays for laundry is equal to Ex(r) = 5.
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How do you solve linear systems using linear combinations?.
a system of two linear equations is solved by combining the two equations to eliminate one of the variables.
Using the linear combination method, a system of two linear equations is solved by combining the two equations to eliminate one of the variables. Once one of the variables is eliminated, an equation with only one variable is left, e.g., 2x=2, and it is very simple to see that in this case, x=1
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What are the roles of political parties at the national state and local levels ?.
A political party is made up of people who band together to run the government, win elections, and shape public policy. Currently, the two major parties in Congress are the Democratic and Republican.
The actions of the parties?Political parties act as a conduit between the governed and the ruling class. They educate the public, arouse inspiration, and pique interest in and engagement in public affairs. Their main duty is to suggest candidates for elected office.
What is self-annuncement?Self-annuncation, in which a candidate for office only declares their candidacy, is the earliest method of nominating in American politics.
The national chairman, a national committee, the national convention, and two congressional campaign committees make up the party's overall organizational structure. The party is decentralized at the state level, and state legislation generally determines how it is structured.
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What does dilated by a scale factor of 3 mean?.
a skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing. write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position. write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km). write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).
The expressions are written as
(a) The expression from east side of ski trail to reach skier's current position is θ = π/2 + 3.1 × t
(b) The expression for skier's distance to east of ski trail is 1.9 × cos(π/2 + 3.1 × t) km .
(c) The expression for skier's distance to north of ski trail is 1.9 × sin(π/2 + 3.1 × t) km .
In the question ,
it is given that ,
the radius of the circular ski trail is = 1.9 km
The Skier starts from the Northern most point
the radians that is sweeped in per hour is = 3.1 radians per hour
that means the angular speed is = 3.1 radians per hour ,
Part(a)
From the above data the expression in terms for t that represents number of radians swept out from each side of ski trail to reach skier's current position is written as ,
θ = π/2 + 3.1 × t
Part(b)
From the above data , expression in terms of t to represent skier's distance to the east of ski trail is written as ,
we know that , x = rcosθ
Substituting the value of θ from part(a) ,
we get ,
= 1.9 × cos(π/2 + 3.1 × t) km
Part(c)
From the above data , expression in terms of t to represent skier's distance to the north of ski trail is written as ,
we know that , y = rsinθ
Substituting the value of θ from part(a) ,
= 1.9 × sin(π/2 + 3.1 × t) km
Therefore , The expressions are (a) for radians is θ = π/2 + 3.1 × t
(b) the distance to the east is 1.9 × cos(π/2 + 3.1 × t) km ,
(c) the distance to the north is 1.9 × sin(π/2 + 3.1 × t) km .
The given question is incomplete , the complete question is
A skier skis ccw along a circular ski trail that has a radius of 1.9 km. she starts at the northern most point of the trail and travels at a constant speed, sweeping out 3.1 radians per hour. let t represent the number of hours since she started skiing.
(a) write an expression in terms of t to represent the number of radians that would need to be swept out from the east side of the ski trail to reach the skier's current position.
(b) write an expression in terms of t to represent the skier's distance to the east of the ski trail (in km).
(c) write an expression in terms of t to represent the skier's distance to the north of the ski trail (in km).
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Warp-O Corporation common stock has a market price of
$45
per share. Warp-O has a beta of 1.4. The rate of return on Treasury bonds is currently
6%
and the retum on the S\&.P 500 is
13%
. What is the required rate of return on Warp-O common stock? a)10.2%
d)24.2%
b)13.0%
e)35.1%
c)15.8%
Option c 15.8% is the required rate of return for Warp-O common stock.
Given,
The market price of share = $45
Beta = 1.4
The rate of return on Treasury bonds = 6%
Market rate of return = 13%
We have to find the required rate of return on Warp-O common stock;
Here,
Rate of return = The rate of return on Treasury bonds + beta × (market rate of return -The rate of return on Treasury bonds )
= 6% + 1.4 × (13% - 6%)
= 6% + 1.4 ×7%
= 6% + 9.8%
= 15.8%
That is,
The required rate of return on Warp-O common stock is option c 15.8%
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What is the base of an triangle that has an area of 24 square units and a height of 12 units
Answer:
The base equals 4 units².
Step-by-step explanation:
Formula:
A = hbB/2
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Answer:
base = 4 units
Step-by-step explanation:
[tex]A=bh/2\\bh=2A[/tex]
[tex]b=2A/h[/tex]
Replace values:
[tex]b=2(24)/12=48/12[/tex]
[tex]b=4[/tex]
Hope this helps
How many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram?.
If there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.
We need to find how many kilograms are there in 4. 21 pounds if there are 2. 2 pounds in 1 kilogram. This can be calculated by using unitary method.
There are 2. 2 pounds in 1 kilogram,
We need to find the kilograms are there in 4. 21 pounds
If there are 2. 2 pounds in 1 kilogram,
Then, 1 pound is 1/2.2 kilogram
1 pound = 0.4545
4.21 pound is (1/2.2) 4.21 kilogram
4.21 pound is 1.91 kilogram.
Therefore, if there are 2. 2 pounds in 1 kilogram then there are 1.91 kilograms in 4.21 pounds.
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Unless specified, all approximating rectangles are assumed to have the same width.
Evaluate the upper and lower sums for f(x) = 6 - x², -2 ≤x≤ 2,
with n = 2, 4, and 8. Illustrate each case with a sketch similar to the figure shown below. (Round your answers to two decimal places.)
The upper sum is 24 and the lower sum is 8 for the given function
f(x) = 6 - x², -2 ≤x≤ 2.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given,
f(x) = 6 - x²
-2 ≤x≤ 2
When n=2, partition of interval -2, 0, 2
When x=-2, f(-2)=6-4
f(-2)=2
x=0, f(0)=6-0
f(0)=6
x=2, f(2)=6-4
f(2)=2
Upper sum= M₁S₁+M₂S₂
=6(2)+6(2)
=24
Lower sum=m₁ s₁+m₂ s₂
=2(2)+2(2)
=8
Therefore, upper sum=24 and lower sum= 8
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(20 pts) Basic Probability (a) (4 pts) Which of the following expressions is guaranteed to be 1, given two random variables X and Y, and no independence or conditional independence assumptions between them are given? For each expression, show why and why not it is guaranteed to be 1 . -y∑ P(X=x∣Y=y)-x∑ P(X=x∣Y=y)x∑y∑ P(X=x∣Y=y)-x∑P(X=x)+ y∑P(Y=y)(b) (4 pts) Given two Boolean random variables A and B , where P(A)= 21 ,P(B)= 4 1, andP(A∣¬B)= 31, apply Bayes's rule and calculate the value ofP(A∣B)
After applying Baye's Rule , the value of P(A/B) is 1 , the correct option is (d) .
In the question ,
it is given that ,
probability of A is P(A) = 1/2 ,
P(B) is = 1/3 , and
P(A/~B) = 1/4
we know that Baye's Rule for any two events A and B is ,
P(A/B) = (P(B/A) × P(A))/ P(B)
Substituting the values of P(A) and P(B) from above in the Baye's Rule ,
we get ,
P(A/B) = 3/2 × P(B/A)
given that P(A/~B) = 1/4 ,
and we know that , P(B/A) = 1 – P(~B/A) ....equation(1)
by Baye's rule ,
P(~B/A) = (P(A/~B) × P(~B)) / (P(A))
= (1/4 * 2/3 )/(1/2)
= 1/3
Substituting it in equation(1) , we get
P(B/A) = 1 - 1/3
= 2/3
Substituting the value of P(B/A) in P(A/B) = 3/2 × P(B/A) ,
we get ,
P(A/B) = 3/2 × 2/3
P(A/B) = 1
Therefore , the value of P(A/B) is 1 .
The given question is incomplete , the complete question is
Given two Boolean random variables, A and B, where P(A) = 1/2 , P(B) = 1/3, and P(A/~B) = 1/4 , Apply Baye's Rule and calculate the value of P(A/B) ?
A. 1/6
B. 1/4
C. 3/4
D. 1
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An engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78 Does this data suggest that the population mean strength of the components differs from 50? Set up an appropriate hypothesis test to answer this question.
The population mean strength of the components differs from 50 is 0.304.
In the given question, an engineer selected 30 components at random and measure their strengths. 34,54,73,38,89,52,75,33,50,39,42,42,40,66,72,85,28,71,52,47,41,36,33,38,49,51,55,63,72,78
We have to check does this data suggest that the population mean strength of the components differs from 50 and we have to set up an appropriate hypothesis test to answer this question.
Sample size n = 30
Claim : The population mean strength of the components differs from 50.
Null and alternative hypothesis:
H(0): μ = 50
H(A): μ≠50
As the population standard deviation is unknown (not given) , t-test can be used .
Test Statistic :
t = (X-μ)/(S/√n)
To find the sample mean we find the average of the given sample.
So
X = 34 + 54 + 73 + 38 + 89 + 52 + 75 + 33 + 50 + 39 + 42 + 42 + 40 + 66 + 72 + 85 + 28 + 71 + 52 + 47 + 41 + 36 + 33 + 38 + 49 + 51 + 55 + 63 + 72 + 78/ 30
X = 53.267
Now finding the standard deviation using the excel.
SD = 17.1101
To find the SD we use the formula =STDEV(B1:C15)
Now putting the value in the formula of Test Statistic
t = (X-μ)/(S/√n)
t = (53.267-50)/(17.1101/√30)
After solving:
t=1.046
P-value :
As the alternative hypothesis H(A) is of not equal to type , this is two tailed test.
Degrees of freedom = n-1 = 30 -1 = 29
df =29
Using Excel function , =TDIST( t , df , number of tails )
=TDIST( 1.046 , 29 , 2 )
=0.304201657
Rounding to three decimal places
= 0.304
P-value = 0.304
Hence, the population mean strength of the components differs from 50 is 0.304.
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riteria used to allocate fixed costs to a department include: relative benefits question 6 options: relative benefits ability to bear equity all of the above
Option (d) is correct. Criteria for assigning fixed costs to sectors include relative utility, sustainability, and fairness.
Fixed cost and allocation:
Fixed costs are costs that are essentially constant and do not change with fluctuations in the output of the relevant sector. Fixed costs are borne by the company and exist independently of business activities. Rent, insurance, and depreciation are examples of fixed costs. Cost attributes help identify, total, and assign costs to cost objects.
Fixed cost allocation involves identifying the beneficiaries of outputs and allocating costs to beneficiaries in proportion to the benefits received. Fixed costs can also be allocated in relation to the payer's ability to bear the allocated costs. Fairness is a criterion met where cost allocation is the basis for determining a satisfactory price (such as government contracts).
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Select the correct answer.
What is the simplified form of this expression?
(-x² + x) + (4x²-x-1)
a 3x²-1
b -5x² + 2x + 1
c -3x²2² +1
d 5x²+2x-1
Answer:
its A
Step-by-step explanation:
-x²+x+(4x²-x-1)
-x²+x+4x²-x-1
-x²+4x²-1
3x²-1
A local tennis club has an annual tournament to raise money. they allow a total of 128 players to enter. each round eliminates half the players. how many players will be left after 5 rounds?
The total of 4 players left after 5 rounds.
Given information,
Given that a neighborhood tennis club holds a fundraising competition every year. A total of 128 players are permitted to enter. In each round, half the participants are eliminated.
The function will be written as,
[tex]F(x) = 128e^x[/tex]
To know how many players left after 5 rounds,
Round 1 ⇒ 128/2 = 64
Round 2 ⇒ 64/2 = 32
Round 3 ⇒ 32/2 = 16
Round 4 ⇒ 16/2 = 8
Round 5 ⇒ 8/2 = 4
Hence, 4 players will be left after 5 rounds.
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BBQ Corp. had a 3:1 stock split ratio. Pre-split the company had 1.35 Million outstanding shares at a price of $72.45 per share.
What is the price per share of BBQ Corp. stock post-split?
The price per share of BBQ Corp. after there has been a stock split, or post - split, is $24. 15
How to find the price after a stock split?When there is a stock - split, then each of outstanding shares that a company has, is divided into a number of shares that is determined by the stock split ratio.
The price of the individual shares are also divided into the same ratio as the shares.
This means that the price per share for BBQ Corp. post - split is:
= Price per share before split / 3
= 72. 45 / 3
= $24. 15
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8. transistors produced by one machine have a lifetime which is exponentially distributed with mean 100 hours. those produced by a second machine have an exponentially distributed lifetime with mean 200 hours. a package of 12 transistors contains 4 produced by the first machine and 8 produced by the second. let x be the lifetime of a transistor picked at random from this package. find: a) p(x 200 hours); b) e(x); c) var(x)
The transtors produced by one machine have a lifetime which is Exponentially Distributed. let X be the lifetime of a transistor.
a) P(X≥200 hours) = 0.29
b) E(x) = 166.7
c) Var(x) = 12222.22
We have given the exponential distribution of lifetime of transtors produced by one machine
So, X∼Exp(x)
a) The probability density function is
f(x)=m × e⁻ᵐˣ
The number e = 2.71828182846e
we have , mean , u = 100 for first machine
and it follows that
P(X≥200) = e⁻²·⁴¹² + e⁻¹·⁸¹² = 2e⁻²≈0.29.
(b) By the tower property of conditional expectation, E(X) = E[E(X|Y)] = XyE(X|Y=y)
pY(y)=E(X|Y= 1)P(Y= 1) +E(X|Y= 2)P(Y= 2).
Again using the conditional distributions of X|Y, we have E(X|Y= 1) = 100, E(XY= 2) = 200.
Hence,E(X) = 100·412+ 200·812=5003≈166.7.
(c) The general formula for a random variable depending on a parameter is:
Var(X) = E(Var(X|Y)) + Var(E(X|Y))
In this case, Y is a random variable which is "100" with a probability of 1/3 and "200" with a probability of 2/3, and X is an exponential distribution with mean Y.
Var(X|Y) = Y² so E(Var(X|Y)) = (1/3)100² + (2/3) 200² = 90000/9
E(X|Y) = Y, so Var(E(X|Y)) = Var(Y) = E(Y²) - E(Y)² = 30000 - (500/3)² = (30000 * 9 - 250000)/9
= 20000/9
Var(X) = 110000/9 = 12222.22
Hence, a) the P(X≥200) = 0.29
b) E(x) = 166.7
c) var(x) = 12222.22
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The difference of the square of a number and 18 is equal to 3 times that number. Find the negative solution.
[tex]x=number\hspace{5em}x^2=\textit{squared number} \\\\\\ \stackrel{\textit{difference of }x^2\textit{ and 18}}{x^2~~ - ~~18}~~ = ~~\stackrel{\textit{three times }x}{3x} \\\\\\ x^2-3x-18=0\implies (x-6)(x+3)=0\implies x= \begin{cases} 6\\\\ -3 ~~ \checkmark \end{cases}[/tex]
in macroland there is $12,000,000 in currency. the public holds 60% of the currency and banks hold the rest as reserves. if banks' desired reserve/deposit ratio is 25.0 percent, deposits in macroland equal and the money supply equals .
If banks' desired reserve/deposit ratio is 25.0 percent, deposits in macro land are $28800000 and the money supply is $36000000
The deposit ratio is the rate sum of money (stores) that commercial banks must not loan out or invest, the reserve ratio is as a rule fixed by the central banks to control inflation and the volume of cash in circulation inside a given country in a particular time.
Initial bank deposit= 60% of 12000000 = 7200000, The reserve/deposit will calculate as follows (25.0 /100%)=0.25 and If banks desired to keep 25.0 it deposit ratio will be : 1/0.25*7200000= 28800000
So the money supply will be the desired deposited :
=28800000+ 7200000 =36000000
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Using the equation of the model:
a. About 150.4 thousand students studied in abroad in 2011.
b. About 467.5 thousand students would be studying in abroad in 2018.
How to Make Predictions Using the Equation of a Model?An example of an equation of a model that can be used to make predictions or determine the value of one variable, is the equation that models the number of college students who studied abroad each year. This is given as y = 123.1(1.069)^x, here, we have:
y representing the number of students from a country in thousandsx representing the number of years after 1998Using the equation, y = 123.1(1.069)^x, we would solve the following:
a. 2001 after 1998 would be x = 3 years. Therefore, substitute x = 3 into the equation y = 123.1(1.069)^x to find the number of students that are studying abroad in 2001:
y = 123.1(1.069)^3 = 150.4
This implies that about 150.4 thousand students studied in abroad in 2001.
b. 2018 after 1998 would be x = 20 years. Therefore, substitute x = 20 into the equation y = 123.1(1.069)^x to find the number of students that would be studying abroad in 2018:
y = 123.1(1.069)^20 = 467.5
This implies that about 467.5 thousand students studied in abroad in 2018.
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A rectangle has a height of 10 and length of 8. the unshaded regions inside the rectangle include a rectangle with length of 5 and height 2, a triangle with base of 4 and height of 8, and a square with side lengths of 4. all other regions are shaded. tara is playing a party game in which a tiny ball is dropped into a rectangular box. to win the game, she must guess where the ball will stop. what should she guess to maximize her chances of winning? which word describes the likelihood of the ball stopping in a square or rectangular shaped area?
Answer:
shaded area
unlikely
Step-by-step explanation:
She should guess a shaded portion of a rectangle that has a height of 10 and a length of 8 to maximize her chances of winning. The unlikely word describes the likelihood of the ball stop.
First, we need to find the areas of all the regions.
The area of the shaded rectangle = Length x Breadth = 10 x 8 = 80 square units
Area of unshaded rectangle = Length x Breadth = 5 x 2 = 10 square units
Area of unshaded triangle = 1/2 x base x height = 1/2 x 4 x 8 = 32/2 = 16 square units
Area of unshaded square = Side^2 = 4^2 = 16 square units
The area difference between the shaded and unshaded areas = The area of the shaded rectangle - (Area of unshaded rectangle + Area of unshaded triangle + Area of the unshaded square)
The area difference between the shaded and unshaded areas = 80 - (10 + 16 + 16)
The area difference between the shaded and unshaded areas = 80 - 42 = 38
As we see that the area of the shaded region is 38 more than the unshaded region so to maximize her chances of winning she should guess the shaded region or area.
Probability percentage of the shaded rectangle = 80/122 x 100 = 65.57%
Probability percentage of an unshaded rectangle = 10/122 x 100 = 8.20%
Probability percentage of an unshaded triangle = 16/122 x 100 = 13.11%
Probability percentage of an unshaded square = 16/122 x 100 = 13.11%
The unlikely word describes the likelihood of the ball stopping in a square or rectangular-shaped area because one is shaded and unshaded and the other is only unshaded. So, both are having different probabilities because of shape, area, and portion.
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Do you agree with all equilateral triangles are similar to isosceles triangles why justify with an example?.
Yes, I agree with all equilateral triangles are similar to isosceles triangles because Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.
Define triangle.When three straight lines come together, a triangle is created. Every triangle has three corners and three sides (angles). The vertex of a triangle is the intersection of two sides. Each polygon has a unique name depending on how many sides it has. For instance, the polygon with three sides is known as a triangle since the word "tri" denotes the number three. Additionally, the name of the polygon suggests that it contains three angles. "Poly" is a prefix that means many.
Given,
All equilateral triangles are similar to isosceles triangles,
Since equilateral triangles have three equal sides and isosceles only have two, all equilateral triangles are in fact isosceles.
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The universal set, &, and set W are defined below.
{= {all integers}
W= {a : 3 <2<10}
Select all of the statements below that are true.
The statements which are true is 4∈W, 7.5∈W and W= ∅
What does the term "universal set" mean?
A set that contains elements from all related sets, without any repetition of elements, is known as a universal set (typically denoted by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.
What are the 8 different kinds of sets?
Empty set, finite set, singleton set, equivalent set, subset, power set, universal set, superset, and infinite set are the various types of sets.
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The average annual salary in pennsylvania was $25,000 in 1992. assume that salaries were normally distributed for a certain group of wage earners, and the standard deviation of this group was $3,000. find the probability that for a randomly selected sample of 10 individuals, the mean salary was less than $24,000.
Answer:
0.6293
Step-by-step explanation:
The [tex]z[/tex] score for $24000 is [tex]\frac{24000-25000}{3000} \approx 0.333[/tex].
[tex]P(z<0.333)=0.6293[/tex]
Elliot loves carrot chips and buys one ounce bags to pack with her lunch. According to the label, there are an average of 25 chips per ounce. Elliot suspects that the true average is higher and decides to investigate. She selects 12 bags of chips (which she is willing to consider a random sample) and finds the sample average number of chips per bag is 26.6 with a sample standard deviation of s = 4.6. What is the associated standard score for this hypothesis test? z-2.05 2-4.17 2-26.6 - 1.20 MacBook Air 000 000 F4 F5 F6 F7 F8 F9 a
Using the test statistic z, the value of z is 1.20.
In the given question,
Given:
Sample Size(n) = 12
Population Mean([tex]\mu[/tex]) = 25
Standard Deviation(S) = 4.6
Statistic of intereset(x) = 26.6
The test statistic z is
[tex]z=\frac{x-\mu}{\frac{s}{\sqrt{{n}}}}[/tex]
Putting the value
[tex]z=\frac{26.2-25}{4.6/\sqrt{12}}[/tex]
z = 1.6/(4.6/3.46)
z = 1.6/1.329
z = 1.20
Hence, the value of z is 1.20.
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What does :: mean in math?.
:: means average mean in mathematics.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find what is :: in maths
Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations and any other mathematical objects, and assembling them into expressions and formulas.
: : is a mathematical notation, it is called as double colon and it is used to find the average mean.
a:b: : c:d
In the above expression it acts as an equivalent ration between a:b and c:d
Hence, :: means average mean in mathematics.
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there are three different cars that you could buy. they differ in initial cost, annual operating costs, and life. your minimum acceptable rate of return is 14%. use the ror method to select the best alternative.
You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%
Given,
There are three different cars that you could buy. They differ in initial cost, annual operating costs, and life. Your minimum acceptable rate of return is 14%. Use the ROR method to select the best alternative.
Alternative A B C
Initial Cost 10,000 8,000 5,000
Annual Cost 1,000 1,500 1,500
Life 8 years 8 years 5 years
Here,
Rate of Return of car A = (10,000 - 1000 x 8) / 100 = 2000/100 = 20%
Rate of Return of car B = (8,000 - 1500 x 8) / 100 = -4000/100 = -40%
Rate of Return of car B = (5,000 - 1500 x 5) / 100 = -2500/100 = -25%
That is,
You can buy car A, because the acceptable rate is 14% and here car A has a rate of 20%
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How do you know if a system has one solution or infinitely many?.
If you try to solve an equation and receive a variable or a number equal to itself, the problem has an unlimited number of solutions.
There are an infinite number of solutions to the equation system when two lines coincide with the same y-intercept. If the slope and y-intercept of the two lines coincide, they actually belong to the same line. Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the two lines that make up a linear system cross each other once, the system has a single solution. When the two lines are identical, as in the cases of y=x+3 and 2y=2x+6, a linear system has several (infinite) solutions. When the lines never cross (i.e., they are parallel and have the same slope), a linear system cannot be solved.
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