The table below represents the number of NFL teams that won or lost their first game of the season. What is the probability that a team selected won their first game, given the team is from the AFC?

Answer:

okay the answer is b[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The approximate difference in mass between these two animals is 154,000 kg.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a broad area of study that includes a wide range of topics, such as equations, inequalities, functions, polynomials, matrices, and more.

Algebraic expressions are composed of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. Equations, on the other hand, are mathematical statements that assert the equality of two algebraic expressions. Inequalities are mathematical statements that assert the relationship between two algebraic expressions using the symbols "<", ">", "<=", or ">=".

Functions in algebra are mappings from one set of numbers to another set of numbers that obey certain rules. These rules may involve properties such as continuity, differentiability, and invertibility.

The difference in mass between these two animals is:

1.7 x 10⁵ kg - 8 x 10⁴ kg = 1.54 x 10⁵ kg

Therefore, the approximate difference in mass between these two animals is 154,000 kg.

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Answer:

Adian would pick 396 apples in 36 minutes.

Step-by-step explanation:

Therefore, in 1 minute, Adian picks 11 apples.

In 36 minutes, he will pick:

11 apples/minute x 36 minutes = 396 apples.

Therefore, Adian would pick 396 apples in 36 minutes.

Answer:

396 apples

Step-by-step explanation:

adian picks apples at the rate of 11 apples every minute

So in order to find out how many he picks in 36 minutes we just multiply 36 by 11

36 x 11 = 396 apples in 36 minutes

Hope this helps!

Brainliest and a like is much appreciated.

Answer:

270

Step-by-step explanation:

360×3/4=270 as per given information in the qustion a complete circle is 360 so then 3/4 × 360

Handy should produce 5400 units of C1 and 5600 units of C2 and the production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.

1. To develop a production plan for Handy, we need to calculate the expected demand for each component under each scenario. This is done by multiplying the demand for each scooter by the number of components used in its production, and then multiplying by the probability of each scenario occurring.

Expected demand for C1 = (600 x 6 x 0.3) + (400 x 6 x 0.4) + (300 x 6 x 0.3) + (200 x 10 x 0.3) + (400 x 10 x 0.4) + (500 x 10 x 0.3) = 5400

Expected demand for C2 = (600 x 10 x 0.3) + (400 x 10 x 0.4) + (300 x 10 x 0.3) + (200 x 4 x 0.3) + (400 x 4 x 0.4) + (500 x 4 x 0.3) = 5600

Therefore, Handy should produce 5400 units of C1 and 5600 units of C2.

2. To determine whether Handy should retool its production system to develop C3, we need to compare the expected cost of production with and without the new component.

Without C3:

Expected cost = (5400 x $8) + (5600 x $12) = $43,200 + $67,200 = $110,400

With C3:

Expected cost = (5400 x $14) + (5600 x $14) = $75,600 + $78,400 = $154,000

Since the expected cost of production with C3 is higher than without C3, Handy should not retool its production system to develop the new component. The production plan should remain the same, with 5400 units of C1 and 5600 units of C2 being produced.

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Answer:

The area of the parallelogram is 630.4 square units, to the nearest tenth.

Step-by-step explanation:

The formula to find the area of a parallelogram is:

[tex]A=bh[/tex]

where b is the base and h is the height.

For the given parallelogram ABCD, BC and AD are the bases and h is the height. Therefore, we need to calculate the height, h, before we can calculate the area of the parallelogram.

The height of the parallelogram is also the side opposite angle 62° in the right triangle of the given diagram. As we also know the hypotenuse of this triangle, we can use the sine trigonometric ratio to find "h".

[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]

Given:

Therefore, the expression for h is:

[tex]\implies \sin 62^{\circ}=\dfrac{h}{21}[/tex]

[tex]\implies h=21\sin 62^{\circ}[/tex]

Given the base of the parallelogram is 34 units, substitute b = 34 and the expression for h into the formula for the area:

[tex]\begin{aligned}\implies \textsf{Area}&=34 \cdot 21\sin 62^{\circ}\\&=630.424581...\\&=630.4\; \sf square\;units\;(nearest\;tenth) \end{aligned}[/tex]

Therefore, the area of the parallelogram is 630.4 square units, to the nearest tenth.

Answer: The farmer has 1377 sheeps.

Step-by-step explanation:

Farmer loses sheeps due to drought = 32½% of 2400

32½% of 2400

= 65 × 2400 × 1

2100

After cutting it will be,

65×12

=780

Number of sheeps that are left with him = 2400 - 780

=1620

After that,

The farmer loses due to sickness = 15% of 1620

15% of 1620

= 15 × 1620

100

After cutting it will be,

3 × 81

= 243

Total amount of sheeps that the farmer loses = 780 + 243

= 1023

Now the number of sheeps he has is 2400-1023

= 1377

Answer:

Step-by-step explanation:

Correct option is B)

Center is the point of intersection of diagonals.

⇒2x−3y=5

⇒3x−4y=7

Solving simultaneous equation, x=1,y=−1

Center =(1,−1)

For radius r ( let )

⇒r=

π

154

​

​

  ⇒

22

154

​

×7

​

=7

Equation -

⇒(x−1)

2

+(y+1)

2

=7

2

⇒x

2

+1−2x+y

2

+1+2y=49

⇒x

2

+y

2

−2x+2y=49−2

⇒x

2

+y

2

−2x+2y=47

Hence, the answer is x

2

+y

2

−2x+2y=47.

Answer:

To find the Maclaurin series for $f(x) = xe^x$, we can use the formula for the Maclaurin series of $e^x$ and differentiate the product term by term:

$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$

$$xe^x = x \sum_{n=0}^\infty \frac{x^n}{n!} = \sum_{n=0}^\infty \frac{x^{n+1}}{n!}$$

So the first few terms of the Maclaurin series for $f(x)$ are:

$$f(x) = xe^x = x + x^2 + \frac{x^3}{2} + \frac{x^4}{3} + \frac{x^5}{24} + \cdots$$

To find the radius of convergence, we can use the ratio test:

$$\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n\to\infty} \left| \frac{x^{n+2}/(n+1)!}{x^{n+1}/n!} \right| = \lim_{n\to\infty} \frac{|x|}{n+1} = 0$$

Since the limit is less than 1 for all values of $x$, the Maclaurin series converges for all values of $x$, and the radius of convergence is infinite.

We will have $840 and $2142 respectively. The solution has been obtained by using simple interest.

What is simple interest?

Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest.

We know that amount after simple interest is given by

A = P (1 + rt)

We are given that $700 are deposited in an account with an annual interest rate of 4%.

Here,

P = $700

r = 4%

t = 5 years

On substitution, we get

⇒A = 700 (1 + (0.04 * 5))

⇒A = 700 (1 + 0.2)

⇒A = 700 (1.2)

⇒A = $840

Similarly, in the second case,

P = $1800

r = 3.8%

t = 5 years

On substitution, we get

⇒A = 1800 (1 + (0.038 * 5))

⇒A = 1800 (1 + 0.19)

⇒A = 1800 (1.19)

⇒A = $2142

Hence, we will have $840 and $2142 respectively.

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The amount repaid in the three months of the loan amount $24,000 with a condition of 20% repayment is equal to $11,712.

Percent of amount Maricarmen has to pay = 20% of the loan each month.

This implies  Maricarmen pay 0.2 times the loan amount each month.

Amount Maricarmen will pay in the first month is equal to,

0.2 x $24,000 = $4,800

Amount left after the first payment,

$24,000 - $4,800 = $19,200

In the second month, Maricarmen will pay,

0.2 x $19,200 = $3,840

Amount left after the second payment,

$19,200 - $3,840 = $15,360

In the third month, Maricarmen will pay,

0.2 x $15,360 = $3,072

Amount left after the third payment,

$15,360 - $3,072 = $12,288

total amount paid in three months,

$4,800 + $3,840 + $3,072 = $11,712

Therefore, after three months Maricarmen will have repaid a total of  $11,712 of the loan.

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Apart from each other 3.33 hours

To determine at what time the freight and express trains will be 600 km apart from each other, we must first determine the distance covered by each train. We can then use these distances to determine the total distance between the two trains at any given time.In this problem, we are given the following information:A freight train leaves the main station heading east at an average speed of 100 km/h.An hour later, an express train leaves the same station heading west at an average speed of 170 km/h.We are asked to determine the time at which they will be 600 km apart from each other.We can use the following formula to determine the distance covered by each train:D = RTwhere:D is the distance coveredR is the average speedT is the time takenTo find the distance covered by the freight train, we can use the following formula:D1 = RT1where:D1 is the distance covered by the freight trainR is the average speed of the freight trainT1 is the time taken by the freight trainTo find the distance covered by the express train, we can use the following formula:D2 = RT2where:D2 is the distance covered by the express trainR is the average speed of the express trainT2 is the time taken by the express trainNow, let's determine the distances covered by each train:D1 = 100(T1+1)D2 = 170T2We know that the total distance between the two trains is 600 km, so we can use the following equation to solve for the time at which they will be 600 km apart:D1 + D2 = 600100(T1+1) + 170T2 = 600100T1 + 170T2 + 100 = 600100T1 + 170T2 = 500(100/170)T1 + T2 = 5.9 hoursThe time taken by the freight train is T1 + 1, so we can substitute T1 + 1 for T1 in the equation above to solve for T1:T1 + T2 = 5.9100(T1+1)/170 + T2 = 5.9T1 + 1 + 1.7T2 = 5.9T1 + 1.7T2 = 4.9T1 = (4.9 - 1.7T2)/1.9Now, we can substitute this value of T1 into the equation we used earlier to solve for T2:100T1 + 170T2 = 500100((4.9 - 1.7T2)/1.9) + 170T2 = 500T2 ≈ 2.33Therefore, the time at which the two trains will be 600 km apart from each other is approximately 2.33 hours after the express train leaves the main station. To find the exact time, we need to add this value to the time at which the express train left the main station:Time = 1 + 2.33 = 3.33 hoursTherefore, the two trains will be 600 km apart from each other 3.33 hours after the express train leaves the main station.

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The answer of the given question based on finding roots are  roots of the equation are -3, 3/2, and 1.

Synthetic division is  shortcut method used to divide  polynomial by  linear factor of  form (x-a), where "a" is a constant. It is  simplified method of polynomial long division, and it is especially useful when dividing by linear factor, as it avoids the need to write out all  powers of x.

We list the factors of the leading coefficient 2 and the constant term 9:

Factors of 2: ±1, ±2

Factors of 9: ±1, ±3, ±9

Possible rational roots are: ±1, ±2, ±3, ±9

Using synthetic division with x = -1, we get:

-1 | 2 1 -12 9

-2 1 11

2  -1    -1  20

The remainder is not zero, so x = -1 is not a root of the equation.

Using synthetic division with x = -2, we get:

-2 | 2 1 -12 9

-4 6 -88

2  -3    -6 -79

The remainder is not zero, so x = -2 is not a root of the equation.

Using synthetic division with x = -3, we get:

-3 | 2 1 -12 9

-6 15 -9

2  -5     3  0

The remainder is zero, so x = -3 is a root of the equation. This means that (x + 3) is a factor of the equation.

Using polynomial long division, we get:

2x³ + x² - 12x + 9 = (x + 3)(2x² - 5x + 3)

quadratic factor can  factored further we get:

2x² - 5x + 3 = (2x - 3)(x - 1)

Therefore, roots of  given equation is:

x = -3 (root obtained earlier)

x = 3/2 (from 2x - 3 = 0)

x = 1(from x -1=0)

For the given equation 2x³ + x² - 12x + 9 = 0, the factors of the leading coefficient 2 are ±1, ±2, and the factors of the constant term 9 are ±1, ±3, ±9. Therefore,  possible rational roots of  equation are:

±1/1, ±3/1, ±1/2, ±3/2, ±9/2, ±1/9, ±3/9, ±9/9

Using synthetic division or other methods, we can check that the real rational roots of the equation are -3, 3/2, and 1.which we found in part (a).

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Answer:

Without more information about the specific survey and population being surveyed, it is difficult to provide a precise answer to this question. However, I can provide some general information on how probabilities can be calculated in surveys.

Assuming that the survey is a representative sample of college students and that the question about difficulty falling asleep is a binary (yes/no) question, we can calculate the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week as follows:

1. Determine the total number of surveyed college students who answered the question about difficulty falling asleep.

2. Determine the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week.

3. Divide the number of surveyed college students who reported having a hard time falling asleep on 3 or more days in the last week by the total number of surveyed college students who answered the question about difficulty falling asleep.

For example, if 1,000 college students were surveyed and 800 of them answered the question about difficulty falling asleep, and 200 of those 800 reported having a hard time falling asleep on 3 or more days in the last week, then the probability of a surveyed college student having a hard time falling asleep on 3 or more days in the last week would be 200/800, or 0.25, or 25%.

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

A ratiο is an οrdered pair οf numbers a and b, written a / b where b dοes nοt equal 0. A prοpοrtiοn is an equatiοn in which twο ratiοs are set equal tο each οther. Fοr example, if there is 1 bοy and 3 girls yοu cοuld write the ratiο as 1 : 3 (fοr every οne bοy there are 3 girls).

A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria:

Linearity: The graph must shοw a straight line passing thrοugh the οrigin (0,0). This means that as οne variable increases, the οther variable increases in prοpοrtiοn.

Cοnstant ratiο: The slοpe οf the line (i.e., the change in the y-variable divided by the change in the x-variable) must be cοnstant thrοughοut the entire graph.

This cοnstant ratiο represents the prοpοrtiοnality cοnstant between the twο variables.

Hence,  A graph shοws a prοpοrtiοnal relatiοnship if it meets the fοllοwing twο criteria Linearity and Cοnstant ratiο.

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For XY and BD are parallel lines,

a) Complete sentence: Angle XBC = 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.

b) The angle XBC is 55 degrees due to the equal sides XB = XC, and angle BXC is 125 degrees as the sum of angles in a straight line is 180 degrees.

Working out angle BXC:

Angle XBC = 55 degrees (given)

Angles XBC and BXC form a straight line, so:

Angle BXC = 180 - 55 = 125 degrees (sum of angles in a straight line)

Reasoning for each angle:

Angle XBC is given as 55 degrees because XB = XC and angles opposite to equal sides of a triangle are equal.

Angle BXC is found by subtracting the given angle XBC from the sum of angles in a straight line (180 degrees).

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The question is -

XY and BD are parallel lines.

X is a point on AB and C is a point on BD.

XB = XC.

a) complete this sentence.

Angle XBC = 55 Degrees Because . . .

b) Work out angle BXC.

give a reason for each angle you work out.

Answer:

Step-by-step explanation:

Which statement best compares and contrasts the two formats?

The infographic shows the movement of water visually, while the text describes it.

The infographic would be less appealing to visual learners than the text.

It is impossible to understand the infographic without the text.

The text is more accurate than the infographic.

The conditional probability that a randomly chosen student studies every day, given that the student passes a math test is O P(M|S). The correct option is A.

P(M|S) is the probability that a randomly chosen student passes a math test given that the student studies every day. But, the question is asking for the probability that a student studies every day given that the student passes a math test.

Considering an P(M|S) situation,
Option D: P(SM) is incorrect because it means the probability that both events S and M occur simultaneously.
Option C: P(S) and P(M) is incorrect because it shows the probabilities of two individual events, not the probability of one event given that the other event has occurred.
Option B: P(M AND S) is incorrect because it means the probability that both events M and S occur simultaneously.

The given problem is based on Conditional Probability Notation to Describe Events. The notation used for conditional probability is P(A|B). Where A and B are two events, the notation represents the probability of event A occurring, given that event B has occurred. Conditional probability can be described as the probability of one event happening given that another event has already happened.

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Answer:2.333...

Step-by-step explanation:

A tangent meets a radius (also works with diameters) at 90°.

This means (98 - 3x) = 90

98 = 90 + 3x

8 = 3x

x = 8 / 3 = 2.3333333......

Step-by-step explanation:

Arc   wxv is 360 - 176 = 184 degrees

  this makes angle  98-3x  = 1/2  (184)  = 92°

    ( 98 -3x )°= 92°

          - 3x = -6

               x = 3  

Answer:

2

Step-by-step explanation:

The correct answers are x³ + 19 x² + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0.

Given:

A box with dimensions 3 cm × 5 cm × 11 cm

Current volume of given box = 3×5×11 = 165 cm^3

New volume of box = (3+x) × (5+x) × (11+x)

= (15 + 8 x + x²) × (11+x)

= 165 + 103 x + 19 x^2 + x³

For volume to be 300 cm³

=> x³+ 19 x² + 103 x + 165 = 300

=> x³ + 19 x² + 103 x - 135 = 0

For volume to be 900 cm³ -

=> x³ + 19 x² + 103 x + 165 = 900

=> x³ + 19 x²+ 103 x - 735 = 0

Therefore, x^3 + 19 x^2 + 103 x - 135 = 0 and x³ + 19 x² + 103 x - 735 = 0 are the solution.

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The method used to prove the values of the variables consists of solving the equations as presented in the following section.

An equation is a statement of equivalence between two expressions which is indicated by joining them with an '=' sign.

8. Statement [tex]{}[/tex]                                     Reasons

(5·y - 1)/2 = 7 [tex]{}[/tex]                                 Given

5·y - 1 = 2 × 7 [tex]{}[/tex]                                Multiplicative property of equality

5·y = 2 × 7 + 1 = 10 [tex]{}[/tex]                        Additive property of equality

5 = 10/5 = 2 [tex]{}[/tex]                                  Division property of equality

9. Statement [tex]{}[/tex]                                     Reasons

10·k - 4 = 2·k - 20 [tex]{}[/tex]                               Given

10·k = 2·k - 20 + 4 = 2·k - 16   [tex]{}[/tex]            Additive property of equality

10·k - 2·k = 8·k = -16  [tex]{}[/tex]                          Subtraction property of equality

k = -16/2 = -8 [tex]{}[/tex]                                       Division property of equality

10. Statement [tex]{}[/tex]                                           Reasons

-8·(w + 1) = -5·(w + 10) [tex]{}[/tex]                               Given

-8·w - 8 = -5·w - 50   [tex]{}[/tex]                                 Distributive property of equality

-5·w + 8·w = 3·w = 50 - 8 = 42  [tex]{}[/tex]                Subtraction property of equality

4 = 42/3 = 14 [tex]{}[/tex]                                             Division property of equality

11. Statement [tex]{}[/tex]                                                      Reasons

14 - 2·(x + 8) = 5·x - (3·x - 34) [tex]{}[/tex]                   Given

14 - 2·x - 16 = 5·x - 3·x + 34   [tex]{}[/tex]                    Distributive property of equality

2·x + 2·x = 4·x = -2 - 34 = -36  [tex]{}[/tex]                 Subtraction property of equality

x = -36/4 = -9 [tex]{}[/tex]                                            Division property of equality

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Answer:

Angie is 20, Mandy is 42.

Step-by-step explanation:

Angie's current age = x

Mandy's current age = y, also x + 22

Mandy's age in 2 years = 2x+2

2x + 2 = x + 22

x + 2 = 22

x = 20

y = x + 22

y = 20 + 22

y = 42

Answer: 1456 square yds

Step-by-step explanation: Please mark brainliest and give thanks!

Answer:728

Step-by-step explanation:

V=abc=19*14*c=266c=3724

c=14

S=(19c+14c+14*19)=33c+266=33*14+266=728

Answer:

Step-by-step explanation:

If we call 1999 year 0, then 2010 would be year 11. This makes the coordinates for our problem (0, 43129) and (11, 56780). That means that the initial value, a, is 43129 and we can use that to solve for b.

[tex]56780=43129(b)^{11[/tex]

Divide both sides by 43129 to get

[tex]1.31651557=b^{11[/tex] and take the 11th root on your calculator to get that

b = 1.025314051

Not sure how you need to round that.

Santina drive 14 miles more than Carole. The owner needs to buy 8 bags this week. John bought 48 individual can of cola.

Mile is measurement unit of land or any surface. We use it to calculate the distance.

Now we have to calculate these questions,

a. Santina drive 203 miles and Carole drive 189 Miles.

Santina drive 14 miles more than Carole.

b. A restaurant uses 80 pounds of potatoes per week and the owner buys the potatoes in 10 pound bags.

So, Number of bags, 80/10 = 8 bags.

The owner needs to buy 8 bags this week.

c. Six-packs of cola were on sale at a grocery store (i.e. 6 cola in pack) and he buy 8 six-packs of cola.

Total number of cola can = 8 X 6 = 48 cola can

John bought 48 individual can of cola.

d. Lori read 85 pages last weekend, 135 pages during the week, and 98 pages this weekend.

So, total number of pages read by Lori = 85 + 135 + 98

= 318

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The value of the indicated trigonometric ratio.

cosβ is equal to 0.9167

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

the side CA = 22 is adjacent to the angle β while BA = 24 is the hypotenuse, so:

cosβ = 22/24 {adjacent/hypotenuse}

cosβ = 11/12

cosβ = 0.9167

Therefore, the cosine of the angle β is equal to 0.9167 using the trigonometric ratio.

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Answer:

A and C : cones and pyramids

Step-by-step explanation:

only cones, pyramids and isosceles triangles have apexes

The shapes that have at least 1 apex are:

Right circular cone

Right pyramid

Therefore, the answer is C and D.

After answering the given query, we can state that Expression: A group variable of words, divided by signs for addition or subtraction.

In the context of a mathematical idea or experiment, a variable is something that can be altered. Frequently, a single symbol is used to symbolize a variable. Variables are frequently represented by the letters x, y, and z as abstract symbols. A wide variety of values can be assigned to characteristics known as variables. These factors include, among others, your size, age, wealth, place of birth, scholastic standing, and type of residence. Both numerical and categorical methods can be used to divide variables into two primary groups.

Here are where the labels should be placed based on the illustration:

Coefficient, label one

2nd label: variable

Label 4: the equals symbol Label 3: constant

5th label: term

Expression 6th label

The definition of each term is broken down as follows:

A integer multiplied by a variable in a term of an algebraic expression is referred to as a coefficient.

Variable: A symbol for a quantity that is subject to shift or variation.

A fixed, unchanging number is referred to as a constant.

The equals sign: Shows that the expressions on the left and right are equivalent.

Term: A grouping of variables multiplied by a coefficient and denoted by addition or subtraction marks.

Expression: A group of words, divided by signs for addition or subtraction.

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The variance of 3a+2,3b+2, 3c+2,3d+2,3c+2, is 3657.6.

What is Variance?

Variance is a statistical measurement of the variation in numbers within a data set. Variance, in more precise terms, indicates how far apart any number in the set is from both the mean (average) and, consequently, from every other number in the set.

First, we can calculate the mean of the original dataset:

Mean = (a + b + c + ta + e) / 5

Then, we can calculate the variance using the formula:

Variance = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Given that the variance of the original dataset is 2032, we can substitute this value in the formula and solve for the mean:

2032 = ((a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)²) / 5

Simplifying this equation, we get:

(a - Mean)² + (b - Mean)² + (c - Mean)² + (ta - Mean)² + (e - Mean)² = 10160

Now, we can apply the transformation to the dataset by adding 2 and multiplying by 3:

New dataset: 3a + 2, 3b + 2, 3c + 2, 3d + 2, 3e + 2

To find the variance of the new dataset, we follow the same steps as before:

Mean = (3a + 2 + 3b + 2 + 3c + 2 + 3d + 2 + 3e + 2) / 5 = 3Mean + 2

Variance = ((3a + 2 - Mean)² + (3b + 2 - Mean)² + (3c + 2 - Mean)² + (3d + 2 - Mean)² + (3e + 2 - Mean)²) / 5

Simplifying this equation, we get:

Variance = ((3a - 3Mean)² + (3b - 3Mean)² + (3c - 3Mean)² + (3d - 3Mean)² + (3e - 3Mean)²) / 5

Variance = 9((a - Mean)² + (b - Mean)² + (c - Mean)² + (d - Mean)² + (e - Mean)²) / 5

Variance = 9(2032) / 5

Variance = 3657.6

Therefore, the variance of the new dataset is 3657.6.

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The probability that this whole shipment will be accepted is 0.000133. The probability that this whole shipment will be accepted can be found using the binomial probability formula, where n is the number of trials, x is the number of successes, p is the probability of success, and q is the probability of failure.[tex]P(x) = (n! / (x! * (n - x)!)) * (p^x) * (q^(n - x))[/tex]


In this case, n = 17, p = 0.97 (the probability of a tablet meeting the required specifications), and q = 0.03 (the probability of a tablet not meeting the required specifications).

We want to find the probability of either 0 or 1 defects, so we will calculate the probabilities for both and add them together.
[tex]P(0) = (17! / (0! * (17 - 0)!)) * (0.97^0) * (0.03^(17 - 0)) = 0.00000497P(1) = (17! / (1! * (17 - 1)!)) * (0.97^1) * (0.03^(17 - 1)) = 0.000128P(0 or 1) = P(0) + P(1) = 0.00000497 + 0.000128 = 0.000133[/tex]

Therefore, the probability that this whole shipment will be accepted is 0.000133.

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