when the function f(x) is divided by x-1, the quotient is 3x^2-9x+7 and the remainder is 5. Find the function f(x) and write the result in standard form?​

Answer:

∠ MON = 51°

Step-by-step explanation:

∠ LON is composed of the 2 angles LOM and MON , that is

∠ LOM + ∠ MON = ∠ LON

42° + ∠ MON = 93° ( subtract 42° from both sides )

∠ MON = 51°

Answer:

<MON= 51°

Step-by-step explanation:

Look at the diagram and locate LON. You can see that LON is the angle of the complete line. Now LOM is given which is the angle of a part of the lines. So that means that to find MON we can minus LON with LOM.

<MON= <LON - <LOM

= 93-42

<MON= 51°

Feel free to ask any doubt you have!

Reason:

0.5% = 0.5/100 = 5/1000

or you could say

5/100 = 0.05 = 5%

Answer:

Bottom graph

Step-by-step explanation:

[tex]|4x+5|-7 > 12\\|4x+5| > 19\\\\4x+5 > 19\\4x > 14\\x > \frac{7}{2}\\\\4x+5 < -19\\4x < -24\\x < -6[/tex]

Therefore, the last graph is the correct answer

hmmm let's reword it

what is the Decay equation for sunlight, decaying at 69% at every interval of 10 mm of thickness for "t"?

[tex]\textit{Periodic/Cyclical Exponential Decay} \\\\ A=(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{current amount}\\ r=rate\to 69\%\to \frac{69}{100}\dotfill &0.69\\ t=thickness\\ c=period\dotfill &10 \end{cases} \\\\\\ A=(1 - 0.69)^{\frac{t}{10}}\implies A=0.31^{\frac{t}{10}}\hspace{5em}\boxed{S=0.31^{\frac{t}{10}}}[/tex]

The key differences between the graphs of a nonmember's and a member's yearly cost lie in the slope, y-intercept, and the overall rate of increase in cost as the number of game tokens purchased increases.

The given equations represent the yearly cost in dollars for a member and a nonmember at a video game arcade based on the total game tokens purchased.

For a member:

y = (1/10)x + 60x + 60

For a nonmember:

y = (1/5)x

To understand how the graph of a nonmember's yearly cost differs from a member's yearly cost, let's analyze the equations and their characteristics.

Slopes:

The slope of the member's equation is (1/10), indicating that for every unit increase in the number of game tokens purchased (x), the yearly cost (y) for a member increases by 1/10 of a dollar. This means that the member's yearly cost increases at a slower rate compared to the nonmember's yearly cost.

The slope of the nonmember's equation is (1/5), which means that for every unit increase in the number of game tokens purchased, the yearly cost for a nonmember increases by 1/5 of a dollar. Therefore, the nonmember's yearly cost increases at a faster rate compared to the member's yearly cost.

y-intercepts:

For the member's equation, the y-intercept is 60, which represents the fixed cost component for being a member of the arcade. This means that even without purchasing any game tokens (x = 0), a member incurs a yearly cost of $60.

For the nonmember's equation, there is no additional fixed cost component. The y-intercept is 0, indicating that a nonmember has zero yearly cost if no game tokens are purchased (x = 0).

Overall cost:

The member's equation includes both a fixed cost component and a variable cost component, whereas the nonmember's equation only includes the variable cost component. This means that for any given number of game tokens purchased, the member's yearly cost will be higher than the nonmember's yearly cost.

Graphically, the member's equation will result in a line with a positive slope that intersects the y-axis at 60. The nonmember's equation will yield a line with a steeper positive slope that intersects the origin (0,0). The graph of the nonmember's yearly cost will rise more quickly than the graph of the member's yearly cost.

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The probability of choosing a different type of animal as the second toy is $\frac{7}{18}.

The problem is to draw a tree diagram to determine the probability of choosing a different type of toy animal when two toys are randomly selected. Imogen has two toy elephants and seven toy bears in a box.

It should be noted that a tree diagram is a visual tool that can be used to show the possible outcomes of a particular event. Each branch represents a possible outcome and the probabilities associated with each branch are assigned in the diagram. The steps involved in solving the problem are:

Step 1: Construct the tree diagram.

Step 2: Calculate the probability of choosing a different type of animal as the second toy. Step 3: Simplify the fraction. Solution:

Step 1: Construct the tree diagram. The tree diagram for the given problem is shown below. [asy] size(200); defaultpen(linewidth(0.7));   draw((0,0)--(2,-2),MidArcArrow(size=10)); draw((0,0)--(2,2),MidArcArrow(size=10)); draw((2,2)--(4,2),MidArcArrow(size=10)); draw((2,-2)--(4,-2),MidArcArrow(size=10)); draw((2,2)--(4,0),MidArcArrow(size=10)); draw((2,-2)--(4,0),MidArcArrow(size=10)); draw((4,2)--(6,2),MidArcArrow(size=10)); draw((4,0)--(6,0),MidArcArrow(size=10)); draw((4,-2)--(6,-2),MidArcArrow(size=10));  label("Elephant",(-1,0)); label("Bear",(-1,2)); label("Bear",(3,2)); label("Bear",(3,0)); label("Bear",(3,-2)); label("Elephant",(3,0)); label("Bear",(5,2)); label("Elephant",(5,0)); label("Bear",(5,-2));  [/asy] Step 2: Calculate the probability of choosing a different type of animal as the second toy. The total number of outcomes is 9, as there are 2 elephants and 7 bears. There are four possible ways in which Imogen can pick two different types of animal:

Elephant followed by bear, Bear followed by elephant, Elephant followed by elephant, and Bear followed by bear. The probability of choosing a different type of animal as the second toy is the sum of the probabilities of the first two outcomes, which is: $P(\text{different animal}) = \frac{2}{9}\times\frac{7}{8}+\frac{7}{9}\times\frac{2}{8}$ $=\frac{14}{72}+\frac{14}{72}$ $=\frac{28}{72}$

Step 3: Simplify the fraction. The fraction can be simplified by dividing the numerator and denominator by the highest common factor. The highest common factor of 28 and 72 is 4. Hence, $\frac{28}{72} = \frac{7}{18}$

Therefore, the probability of choosing a different type of animal as the second toy is $\frac{7}{18}$.

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The probability that the second toy Imogen chooses will be a different type of animal to the first toy is 7/18. This is calculated by determining the probability of picking an elephant then a bear, and the probability of picking a bear then an elephant, and adding these two probabilities.

Firstly, let's define the event: Picking an elephant (E) and picking a bear (B). At the beginning, Imogen has 2 elephants and 7 bears in the box, making a total of 9 toys.

When Imogen picks the first toy, the probabilities are: P(E) = 2/9 and P(B) = 7/9. Then, Imogen picks the second toy, not replacing the first one.

So, we have two scenarios for the second pick: Given that the first pick was an elephant, the probabilities for the second pick are: P(E) = 1/8 (because one elephant left) and P(B) = 7/8 (there are still 7 bears). If the first pick was a bear, the probabilities for the second pick are: P(E) = 2/8 (still 2 elephants) and P(B) = 6/8 (one bear left).

Now, we're interested in the probability of picking two different types of animal toys. That will be the sum of the probabilities of picking an elephant then a bear, and the probability of picking a bear then an elephant. So it's (P(E) * P(B|E)) + (P(B) * P(E|B)) = (2/9 * 7/8) + (7/9 * 2/8) = 14/72 + 14/72 = 28/72 which reduces to 7/18.

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Answer:

30: 100

31: -13

32: -45

33: 14

34: -32

35: -22

36: 17

Answer:

the value of c is 50°.

Step-by-step explanation:

To solve for the value of c in the equation (2c - 3)° = 97°, we can start by isolating the term with c.

First, we add 3 to both sides of the equation to get rid of the -3:

(2c - 3)° + 3 = 97° + 3

Simplifying the equation, we have:

2c° = 100°

Next, we divide both sides of the equation by 2 to solve for c:

(2c°)/2 = (100°)/2

Simplifying further, we have:

c° = 50°

Answer:

x^2-5x-25 doesnt factorise im very sorry, maybe check ur question

The sum  in scientific notation is  2.88 × 10⁰

To add numbers in scientific notation, we need to make sure the exponents are the same. Let's add 5.8 × 10⁴ and 2.3 × 10⁵.

First, we need to adjust the numbers so that they have the same exponent. We can do this by moving the decimal point.

5.8 × 10⁴ can be written as 0.58 × 10⁵ (moving the decimal point one place to the right).

Now, we have 0.58 × 10⁵ + 2.3 × 10⁵. Since the exponents are the same, we can add the coefficients:

0.58 + 2.3 = 2.88

The sum of the coefficients is 2.88. To express this in scientific notation, we need to adjust the decimal point and exponent.

Since we moved the decimal point one place to the right in 0.58 × 10⁵, we need to move it one place to the left in 2.88.

2.88 can be written as 0.288 × 10¹.

Therefore, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 0.288 × 10¹.

In scientific notation, this can also be expressed as 2.88 × 10⁰ or simply 2.88.

So, the sum of 5.8 × 10⁴ and 2.3 × 10⁵ is 2.88.

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The domain and the range of the function are (-∝, ∝) and (-∝, -1), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an quadratic function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (-∝, -1)

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As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`. Therefore, the value of `k` is `2`.

The correct answer to the given question is option d.

We have the function `g(x) = k⋅f(x)`. The values of `f(x)` and `g(x)` are given as follows:

Line `f(x)` passes through points `(-4,0)` and `(-3,1)`.

Line `g(x)` passes through points `(-4,0)` and `(-3,-2)`.

Now, we have to determine the value of `k`.

Formula to find slope of a line is given by:(y2 - y1)/(x2 - x1)

Here, (x1, y1) = (-4, 0) and (x2, y2) = (-3, 1) for line f(x).

So, slope of line `f(x)` is given by:(1 - 0)/(-3 - (-4)) = 1

So, equation of line `f(x)` is given by:

y - y1 = m(x - x1) ⇒ y - 0 = 1(x - (-4)) ⇒ y = x + 4

Also, (x1, y1) = (-4, 0) and (x2, y2) = (-3, -2) for line g(x).

So, slope of line `g(x)` is given by:(-2 - 0)/(-3 - (-4)) = 2

So, equation of line `g(x)` is given by: y - y1 = m(x - x1) ⇒ y - 0 = 2(x - (-4)) ⇒ y = 2x + 8

Now, we can substitute the value of `k` and the equation of line `f(x)` to find the equation of line `g(x)`.

Let `k = 2`.

Then, `g(x) = k⋅f(x) = 2(x + 4) = 2x + 8`.

As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`.

Therefore, the value of `k` is `2`. Hence, option (d) is the correct answer: `2`.

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that is physics ...

but yes, applied math. we need to know the formulas though.

(1)

in general, since there are 2 cables supporting in an equal way.

that means each cable is responsible for 600/2 = 300 pounds to bring and hold up.

a cable or rope at an angle has to handle a combined tension force : horizontally (Fx) and vertically (Fy).

the tension force (Ftens) on the rope is a combination of both.

we know

Fx = Ftens × cos(theta)

Fy = Ftens × sin(theta)

from the problem we do know Fy (the vertical = up/down force), as this is the force needed to lift and keep the 300 pound weight up there.

and that is Fgravity, the force needed to counteract gravity.

Fgravity = mass × g

g being the constant gravitational acceleration of Earth = 9.8 m/s²

forces are described in Newton.

1 N ≈ 0.225 pounds (lifting on Earth)

so, to lift 1 pound requires 1/0.225 ≈ 4.44822 N

to lift 300 pounds requires

4.44822 × 300 ≈ 1334.47 N

that is what Fy is for one of the 2 cables.

the tension on one of the cables is then given by

Fy = Ftens × sin(60)

Ftens = Fy / sin(60) = 1334.47 / sin(60) =

= 1,540.913227... N = 346.41107515867... pounds

≈ 346 pounds per cable.

(2)

3cos(t) + 4 = 2

3cos(t) = -2

cos(t) = -2/3

cosine is negative in the 2nd and 3rd quadrant.

so, for t > pi/2 and t < 3pi/2.

because the given interval is [0, pi), we are only looking at the 2nd quadrant (pi/2, pi).

t = 131.8103149...° = 2.300523983... rad

(3)

well, that are the numbers

1/2

sqrt(2)/2 = 1/sqrt(2)

sqrt(3)/2

1

they are getting bigger and bigger, all positive, so they indicate larger and larger angles

1/2 is :

sin(30° or pi/6 or 150° or 5pi/6)

cos(60° or pi/3 or 300° or 5pi/3)

1/sqrt(2) is :

sin(45° or pi/4 or 135° or 5pi/4)

cos(45° or pi/4 or 315° or 7pi/4)

sqrt(3)/2 is :

sin(60° or pi/3 or 120° or 2pi/3)

cos(30° or pi/6 or 330° or 11pi/6)

1 is :

sin and csc(90° or pi/2)

cos and sec(0° or 0pi or 360° or 2pi)

tan and cot(45° or pi/4 or 225° or 5pi/4)

(4)

the height moves between 4 meters and 70 meters in a circle.

the circumference of the circle is 2pi×r or pi×d, so in our case : 66pi meters.

it takes 5 minutes to move along these 66pi meters.

let's say, when the height is 4 meters (starting position), the angle is 0 and the arc is 0.

after a quarter trip the angle is 90° or 66pi/4, and the height is 4 + 66/2 = 37 meters

and at 70 meters the angle is 180° or 66pi/2.

the function of the height based on the current angle is then for the first half-circle

height(theta) = 4 + (theta/360)×2×66

or

height(theta) = 4 + (theta/(2pi))×2×66

now we need to find the angle theta for which we reach the height of 47 meters :

47 = 4 + (theta/360)×132

43 = (theta/360)×132

theta/360 = 43/132

theta = 360×43/132 = 117.2727272...°

= 2.046795214... rad

so, after starting at the lowest position at 4 meters we reach the height of 47 meters at an angle of about 117°.

then we get and stay above 47 meters until we get to

360 - theta = 242.7272727...°

= 4.236390093... rad

when going down again on the second half-circle of the trip.

that means we are at and above 47 meters for

(360 - theta) - theta = 360 - 2×theta = 125.4545455...°

= 2.18959488... rad

of the whole trip of 360° or 2pi. which takes 5 minutes.

the time we spend there is then

5 × (360 - 2×theta)/360 = 1.742424242... minutes

= 1 minute 44.54545454... seconds

Answer:

A:(-1,0)

B:(0,5)

C:(2,9)

D:(5,0)

Step-by-step explanation:

count the x axis to get x and y axis to get y

(x,y)

Answer:

See below

Step-by-step explanation:

A is located at (-1,0) which is an x-intercept

B is located at (0,5) which is the y-intercept

C is located at (2,9) which is the vertex

D is located at (5,0) which is an x-intercept

The solution to the equation is x = 61

From the question, we have the following parameters that can be used in our computation:

-3 + √(2x - 1) = 8

Add 3 to both sides of the equation

So, we have

√(2x - 1) = 11

Take the square of both sides

2x - 1 = 121

So, we have

2x = 122

Divide through by 3

x = 61

Hence, the solution is x = 61

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We know that the sum of the angles in triangle MLK is 180 degrees. Therefore, we can find the measure of angle KLM as follows:

m∠MLK + m∠KLM + m∠LMK = 180

130 + m∠KLM + m∠LMZ = 180

We also know that angles ZLK and MLZ are vertical angles, so they are congruent. Therefore:

m∠ZLK = m∠MLZ

x + 86 = x + 66

86 = 66

This is a contradiction, so there is no value of x that satisfies the given conditions. Therefore, we cannot find the measure of angle ZLK.

Answer:

2.4 yd

Step-by-step explanation:

Let the width of the walkway = x.

total length = x + 7.5

total width = x + 4.5

total area = (x + 7.5)(x + 4.5)

total area = 68.31 yd²

(x + 7.5)(x + 4.5) = 68.31

x² + 4.5x + 7.5x + 33.75 - 68.31 = 0

x² + 12x - 34.56 = 0

x = [-12 ± √(12² - 4(1)(-34.56)]/(2 × 1)

x = [-12 ± √(144 + 138.24)]/(2 × 1)

x = [-12 ± 16.8]/2

x = 2.4 or x = -14.4

Answer: 2.4 yd

The correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, using Excel, the correlation coefficient is approximately 0.83.

To calculate the correlation coefficient (r) between the number of plays and the number of passes completed by the top 30 college quarterbacks, you can use Excel. Here's a step-by-step guide:

Open Excel and enter the data for the number of plays in one column and the number of passes completed in another column. Ensure that the data is entered consistently, with the same row representing the same quarterback's data in both columns.

Select an empty cell where you want to display the correlation coefficient.

Use the CORREL function in Excel to calculate the correlation coefficient. The syntax for the CORREL function is: =CORREL(array1, array2). In this case, array1 represents the range of cells containing the number of plays, and array2 represents the range of cells containing the number of passes completed. For example, if the number of plays is in column A (A2:A31) and the number of passes completed is in column B (B2:B31), the formula would be: =CORREL(A2:A31, B2:B31).

Press Enter to calculate the correlation coefficient. The result will be displayed in the cell you selected.

Round the correlation coefficient to two decimal places using the ROUND function. The syntax for the ROUND function is: =ROUND(number, num_digits). In this case, number represents the correlation coefficient, and num_digits represents the number of decimal places to round to. For example, if the correlation coefficient is in cell C1, the formula would be: =ROUND(C1, 2).

By following these steps, you can use Excel to calculate the correlation coefficient (r) between the two data sets for the top 30 college quarterbacks.

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Trey must pay $2420 in income tax for last year.

Based on the tax rates, we'll divide his taxable income into two halves.

The first portion is the minimal amount of Trey's taxable income between $9500 and $20,000 that is subject to a 10% tax rate. Consequently, the first component is $9500.

The second portion is the amount over $9500, which is $20,000 - $9500 = $10,500.

Now, let's calculate the tax for each portion:

Tax on the first portion (10% rate) = $9500 * 0.10 = $950.

Tax on the second portion (14% rate) = $10,500 * 0.14 = $1470.

We sum up the taxes on both portions to find Trey's total income tax:

Total income tax = Tax on the first portion + Tax on the second portion = $950 + $1470 = $2420.

So, Trey must pay $2420 in income tax for last year.

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Answer: the correct answer would option (C).

Step-by-step explanation:7x²+16x+25  is corresponds to the equivalent expression of (x²+15x+65) + (2x - 5) (3x +8).

7x²-3x+8 is corresponds to the equivalent expression of (4x + 1)(3x - 4) - (5x²-10x-12)

11x²+6x-6 is corresponds to the equivalent expression of (8x²+19x+4) + (3x + 2)(x - 5).

11x²-5x+13 is corresponds to the equivalent expression of (6x + 1)(3x - 7) - (7x²-34x-20)

What is expression?

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Given expression no. 1 as :

⇒ (x²+15x+65) + (2x - 5) (3x +8).

⇒ x²+15x+65 + 6x²-15x+16x-40

⇒ 7x²+16x+25

Hence, the correct answer would be option (B).

Given expression no. 2 as :

⇒ (4x + 1)(3x - 4) - (5x²-10x-12)

⇒ 12x²+3x-16x-4 - 5x²+10x+12

⇒ 12x²-13x-4 - 5x²+10x+12

⇒ 7x²-3x+8

Hence, the correct answer would be option (D).

Given expression no. 3 as :

⇒ (8x²+19x+4) + (3x + 2)(x - 5).

⇒ (8x²+19x+4) + 3x²+2x-15x-10

⇒ 8x²+19x+4 + 3x²-13x-10

⇒ 11x²+6x-6

Hence, the correct answer would be option (A).

Given expression no. 4 as :

⇒ (6x + 1)(3x - 7) - (7x²-34x-20)

⇒ 18x²+3x-42x-7- 7x²+34x+20)

⇒ 11x²-5x+13

Hence, the correct answer would be option (C).

The ordered pair which is not a solution to the inequality y - 3x < 10 is (-6,0).

Given the inequality in the question:

y - 3x < 10

Given the ordered pairs: (0,-4), (0,-1), and (-6,0). To determine which ordered pair is not a solution, we need to plug the values into the inequality and check.

For (0,-4):

y - 3x < 10

Plug in x = 0 and y = -4

-4 - 3(0) < 10

-4 < 10

True: -4 is less than 10.

For (0,-1):

y - 3x < 10

Plug in x = 0 and y = -1

-1 - 3(0) < 10

-1 < 10

True: -1 is less than 10.

For (-6,0):

y - 3x < 10

Plug in x = -6 and y = 0

0 - 3(-6) < 10

18 < 10

False: 18 is Not less than 10.

Therefore, (-6,0) is not a solution to the inequality.

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Let [tex]x[/tex] be the number of pounds of Nigerian coffee and [tex]y[/tex] be the number of pounds of Bolivian coffee.

We can set up a system of equations to represent the given information:

So we have the following system of equations:

[tex]\qquad\quad\begin{aligned} 17x + 18y &= 437.50 \\ x + y &= 50 \end{aligned}[/tex]

Solving this system of equations, we get:

[tex]\qquad\qquad\quad\begin{aligned} x &= 12.5 \\ y &= 37.5 \end{aligned}[/tex]

[tex]\therefore[/tex] We need 12.5 pounds of Nigerian coffee and 37.5 pounds of Bolivian coffee for the mixture.

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

(ノ^_^)ノ [tex]\large\qquad\qquad\qquad\rm 06/21/2023[/tex]

The probability that both events B and C will occur is:

P(B and C) = 9/20

Probability is the likelihood of an event to occur. It is expressed as a number in the range from 0 to 1.

The probability of an impossible event is 0, that of an event that is certain to occur is 1.

We have:

The probability that event B will occur, P(B) = 3/4

The probability that event C will occur, P(C) = 3/5

The probability that both events B and C will occur is:

P(B and C) = P(B) × P(C)

P(B and C) = 3/4 × 3/5

P(B and C) = 9/20

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The median cost of a home in 2014 is $480

First, we need to know that the median of a given set of data is expressed as the middle number determined with the data set is arranged in an order from least to greatest or in an ascending order.

Also, note that the median is one of the measures of central tendency.

From the information given, we have that;

The median cost of a home in 2014 traced from the point year to the cost on the graph is;

$480

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We can conclude that the function f(x) = x² is increasing when x > 1.The given function is f(x) = x². You need to determine whether this function is increasing or decreasing when x > 1.

To do this, we can find the derivative of the function and evaluate it for x > 1.If the derivative is positive, then the function is increasing, and if it is negative, then the function is decreasing.

The derivative of the function f(x) = x² is given by:f '(x) = 2x

We can see that the derivative is always positive when x > 1, as 2x is always positive for x > 0.Therefore, we can conclude that the function f(x) = x² is increasing when x > 1.

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Since the probability of success is 0.74, the probability of failure is 1 - 0.74 = 0.26. This means that there is a 26% chance of failure in the given binomial trial. Option C

In a binomial trial, the probability of success, denoted by "p," represents the likelihood of the desired outcome occurring. The probability of failure, denoted by "q," represents the complement of the probability of success, i.e., the likelihood of the desired outcome not occurring.

In this case, the probability of success is given as 0.74. To find the probability of failure, we subtract the probability of success from 1, since the sum of the probabilities of success and failure must equal 1.

Probability of failure = 1 - Probability of success

Therefore, the probability of failure = 1 - 0.74 = 0.26.

Hence, the correct answer is C. 0.26.

It's important to understand that in a binomial distribution, there are only two possible outcomes: success and failure. The probabilities of these outcomes must add up to 1. Therefore, if the probability of success is known, the probability of failure can be obtained by subtracting the probability of success from 1.

Option C

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a. From the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.

The number of members who catch fish per day is equal to the number of members who catch fish per day, which means that half of the tribe has a higher opportunity cost than the other half.

The expected cost can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
b. When members are selected based on opportunity cost, the minimum cost that the boat could be built for is 450 fish. The cost of building the boat is equal to the opportunity cost of the members who build it, which is the value of their next best alternative.

Since the boat builders are drawn from the tribe with half the members catching fish per day and the other half catching fish per day, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Therefore, the minimum cost would be 450 fish.

Half of the members catch fish per day, and half of the members catch fish per day. Hence the total cost of building the boat would be the summation of the costs of the members in the group.

For instance, the expected cost of building the boat can be calculated by multiplying the number of workers who catch fish per day by the daily cost of their fishing and adding this to the number of workers who catch fish per day multiplied by their daily cost of fishing.
In this case, the expected cost would be the cost of ten members who build the boat. Since each member is expected to contribute to the building of the boat, the total cost will be calculated as the summation of the cost of the members, which equals 975 fish.

Therefore, from the tribe's perspective, the expected cost of building the boat when the boat builders are drawn at random from the tribe is 975 fish.
The opportunity cost of building the boat is the value of the next best alternative.

When members are selected based on opportunity cost, the minimum cost that the boat could be built for is the opportunity cost of the members who build it. In this case, the members are drawn based on their fishing cost, meaning members with the lowest opportunity cost would be selected to build the boat.

Therefore, the minimum cost would be equal to the opportunity cost of the members who catch fish per day since their cost is higher than the other half of the tribe who catch fish per day. Hence the minimum cost of building the boat would be 450 fish.

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[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{+6}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (5) \pm \sqrt { (5)^2 -4(1)(6)}}{2(1)} \implies x = \cfrac{ -5 \pm \sqrt { 25 -24}}{ 2 } \\\\\\ x= \cfrac{ -5 \pm \sqrt { 1 }}{ 2 }\implies x=\cfrac{-5\pm 1}{2}\implies x= \begin{cases} -2\\ -3 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{-2}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x= \cfrac{ - (-3) \pm \sqrt { (-3)^2 -4(2)(-2)}}{2(2)} \implies x = \cfrac{ 3 \pm \sqrt { 9 +16}}{ 4 } \\\\\\ x= \cfrac{ 3 \pm \sqrt { 25 }}{ 4 }\implies x=\cfrac{3\pm 5}{4}\implies x= \begin{cases} 2\\ -\frac{1}{2} \end{cases}[/tex]

The expression (sinx + cosx)^2 + (sinx - cosx)^2 simplifies to

To simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2 using trigonometric identities, we can expand and simplify the expression.

Expanding the squared terms

(sin^2x + 2sinxcosx + cos^2x) + (sin^2x - 2sinxcosx + cos^2x)

Using the trigonometric identity sin^2x + cos^2x = 1, we can simplify further:

(1 + 2sinxcosx + 1) + (1 - 2sinxcosx + 1)

Simplifying the expression, we have:

2 + 2sinxcosx + 2

Combining like terms, we get:

4 + 2sinxcosx

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The inequality shown by the graph is m ≤ 1. This means that the values of m are less than or equal to 1. Any value of m that is equal to or smaller than 1 satisfies the inequality. However, any value of m that is greater than 1 does not satisfy the inequality.

Inequalities can be represented graphically using number lines.

The inequality m ≤ 1 means that all values of m that are less than or equal to 1 are solutions to the inequality.

The solution set is represented by a closed circle on the number line at the point where m = 1, and a line segment extending to the left of this point.
If we choose a value of m from the shaded region on the graph, such as m = 0, the inequality m ≤ 1 is satisfied because 0 is less than 1.

If we choose a value of m from the unshaded region, such as m = 2, the inequality is not satisfied because 2 is greater than 1. Therefore, the inequality shown by the graph is m ≤ 1.

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