Question 7
Subtract-2x2 + 5xy + 4y2 from the sum
of x² - 2xy + y² and 3x² + 4xy - y²

Answer:

Using the banker's method, we can use the following formula to find the interest:

Interest = (Principal x Rate x Days) / 360

Where,

Principal = $16,400

Amount = $16,851

Days = 180

We know that the interest plus the principal equals the amount, so we can set up the following equation:

Interest + Principal = Amount

Substituting the values:

(16,400 x Rate x 180) / 360 + 16,400 = 16,851

Multiplying both sides by 360:

16,400 x Rate x 180 + 5,904,000 = 6,066,360

16,400 x Rate x 180 = 162,360

Rate = 162,360 / (16,400 x 180)

Rate = 0.055 or 5.5%

Therefore, the interest rate of the loan is 5.5%.

If m = 3/2, the two equations in the system are dependent and have an infinite number of solutions.

To do this, we can set the coefficients of x and y in the two equations equal to each other:

6 - 4m = 2k(2m - 1)

2n - 7 = 3k

Simplifying these equations, we get:

8m - 6 = 4km

2n - 7 = 3k

We can solve the first equation for k:

k = (8m - 6)/(4m)

Substituting this into the second equation and solving for n, we get:

n = (16m - 29)/(8m - 12)

Now we need to check if there are any values of m for which the equations are proportional. We can do this by checking if the expressions for k and n are the same for all values of m.

We find that the expressions for k and n are the same for m = 3/2.

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Complete Question:

Determine the values of m and n so that the following system of linear equations have infinite number of solutions:

(2m−1)x+3y−5=0

3x+(n−1)y−2=0

The equation for the area of a rectangle is A = lw, where l is the length and w is the width. We are given the area (2x² - 3x - 2) and the length (2x + 1). To solve for the width, we can rearrange the equation to w = A/l.

Therefore, the expression to represent the width of the desk is w = (2x² - 3x - 2)/(2x +1).

The correct answer is the triangle

Triangle : 239 yards

Square : 224 yards

555 centigrams = 55.5 GRAMS

The metric system is based on multiples of 10, where each unit is 10 times larger or smaller than the previous one. In this system, "centi-" means one hundredth, so 1 centigram is one hundredth of a gram. Therefore, 555 centigrams is equal to 5.55 grams (since there are 100 centigrams in 1 gram).

On the other hand, "deci-" means one-tenth, so 1 decigram is one-tenth of a gram. Therefore, 555 centigrams is also equal to 55.5 decigrams (since there are 10 decigrams in 1 gram).

In summary, 555 centigrams is equal to:

55.5 decigrams

5.55 grams

555 centigrams is equal to = 55.5 decigrams

1 cg is equal to 10 dg, therefore 555 cg is equivalent to 55.5 dg.

1 Centigram = 1 x 10 = 10 Milligrams

555 Centigrams = 555 / 10 = 55.5 Decigrams

3.25x + 59 = 205.25 is an equation which can be used to determine x, the cost of the labor per hour.

Let's assume that the cost of labor per hour is x dollars.

The technician worked on the computer for 3.25 hours, so the cost of labor is 3.25x dollars.

In addition, Zoey was charged $59 for parts.

The total cost, including labor and parts, was $205.25.

Therefore, we can write the equation:

3.25x + 59 = 205.25

To solve for x, we need to isolate x on one side of the equation.

We can do this by subtracting 59 from both sides:

3.25x = 146.25

Finally, we can solve for x by dividing both sides by 3.25:

x = 45

Therefore, the cost of labor per hour is $45.

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Answer:

We are given two similar triangles, triangle ABC and triangle DEF, and some measurements of triangle ABC. We are also given that DF, one of the sides of triangle DEF, is equal to 15 units. Using this information, we are asked to find the difference between the lengths of sides AB and EF.

To solve the problem, we can first use the angle-angle similarity theorem to determine that the corresponding angles of the two triangles are equal. Therefore, angle DEF is equal to angle BCA, and angle ABE is equal to angle DFE.

Next, we can use the law of sines to find the length of side AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides and angles in the triangle. Applying this to triangle ABC, we have:

AB/sin(73) = BC/sin(48)

Substituting the value of BC as 19 units, we can solve for AB to get:

AB = 22.78 units

Similarly, we can use the law of sines to find the length of side EF. Since angle DFE is equal to angle ABE, we can use the same ratio as above to get:

EF/sin(73) = DF/sin(48)

Substituting the value of DF as 15 units, we can solve for EF to get:

EF = 18.20 units

Finally, we can subtract EF from AB to get:

AB - EF = 22.78 - 18.20 = 4.58 units

Therefore, the difference between the lengths of sides AB and EF is 4.58 units.

The factorizations of these integers above represent their factorizations into their respective prime numbers.

(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.

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Answer:

Step-by-step explanation:

5,9.8,0,4

To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.

The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.

The volume of the box can be calculated by multiplying the width, height, and length:

16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.

Two-thirds of this volume can be found by multiplying the total volume by 2/3:

5,376 cubic inches x 2/3 = 3,584 cubic inches.

Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.

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As per the given metrics, the P/E ratio for Flexsteel Company is 6.9.

The capitalization rate of Flexsteel Company = 12%

Plowback ratio of Flexsteel Company = 75% = 0.75

Return on equity of Flexsteel Company = 13% = 0.13

Expected EPS of Flexsteel Company = Rs. 3.60

Calculating the growth rate -

Growth rate = Plowback ratio x Return on equity

Growth rate = 0.75 x 0.13

= 0.0975

Calculating the price-to-earnings (P/E) ratio -

P/E ratio = (Market capitalization rate - Growth rate) / (Return on equity - Growth rate)

= (0.12 - 0.0975) / (0.13 - 0.0975)

= 0.0225/0.0325

= 0.69 or 6.9

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The required correct answers are [tex]$$H_0: p = 0.08$$[/tex] , [tex]$$H_a: p < 0.08$$[/tex].

Let p be the proportion of residents in the town who are unemployed. The null hypothesis [tex]$H_0$[/tex] is that the proportion of unemployed residents in the town is the same as the national unemployment rate of 8%. The alternative hypothesis [tex]$H_a$[/tex] is that the proportion of unemployed residents in the town is significantly lower than the national unemployment rate.

Using the appropriate notation, the hypotheses can be expressed as:

$H_0: p = 0.08$

$H_a: p < 0.08$

Therefore, the appropriate set of hypotheses for the mayor's significance test are:

[tex]$$H_0: p = 0.08$$[/tex]

[tex]$$H_a: p < 0.08$$[/tex]

Note that this is a one-tailed test since the alternative hypothesis is only considering the possibility of the proportion being lower than the national unemployment rate

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Answer:

We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To do this, we can rearrange the terms as follows:y = 9 - xy = -1x + 9

This gives us a slope of -1 and a y-intercept of 9. We can plot the y-intercept at (0, 9) and use the slope to find another point on the line. The slope tells us that for every increase of 1 in x, the value of y decreases by 1. So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8). We can continue this process to find more points or connect the two points we already have to draw a line.

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The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.

Here, we have,

We can rewrite the equation in slope-intercept form,

y = mx + b,

where m is the slope and b is the y-intercept.

To do this, we can rearrange the terms as follows:

y = 9 - x

y = -1x + 9

This gives us a slope of -1 and a y-intercept of 9.

We can plot the y-intercept at (0, 9) and use the slope to find another point on the line.

The slope tells us that for every increase of 1 in x, the value of y decreases by 1.

So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8).

We can continue this process to find more points or connect the two points we already have to draw a line.

To graph the equation y = 9 - x, you can follow these steps:

Step 1: Create a table of values. Choose some x-values and substitute them into the equation to find the corresponding y-values. For simplicity, let's choose three values for x:

x | y = 9 - x

0 | 9 - 0 = 9

3 | 9 - 3 = 6

6 | 9 - 6 = 3

Step 2: Plot the points. Use the x-values from the table and their corresponding y-values to plot the points on the graph. The points are (0, 9), (3, 6), and (6, 3).

Step 3: Draw the line. Connect the plotted points with a straight line. The line should pass through all the plotted points.

The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.

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He bought 4.29 Kilos of fruit.

4+0.29=4.29

Luke bought 4.29 kilograms of fruit in all

Step-by-step explanation:

Simple addition will be used to find the total fruit Luke bought.

Given

Amount of apples he bought  = 4 kilograms

Amount of oranges he bought = 0.29 kilograms

so the total fruit will be:

[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]

[tex]=4+0.29[/tex]

[tex]=4.29[/tex]

So,

Luke bought 4.29 kilograms of fruit in all

Keywords: Measurement, addition

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The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

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It pays to purchase the information for any value of c less than $13.25 then we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.

To calculate it Let C1 be the event that the first coin is selected and C2 be the event that the second coin is selected. Then, we have:

P(C1) = P(C2) = 1/2 (since one of the two coins is randomly chosen)

P(H|C1) = 0.6 (probability of getting heads when the first coin is flipped)

P(H|C2) = 0.3 (probability of getting heads when the second coin is flipped)

Let's consider the case when we do not buy the insider's information. Then, our expected payoff can be calculated as follows:

E(X) = P(C1) * P(H|C1) * (10) + P(C1) * P(T|C1) * (-10) + P(C2) * P(H|C2) * (10) + P(C2) * P(T|C2) * (-10)

= (1/2) * (0.610 - 0.410 + 0.310 - 0.710)

= -1

Therefore, if we do not buy the insider's information, our expected payoff is a loss of $1.

Now, let's consider the case when we buy the insider's information for an amount c.

If we buy the information, we will know which coin was selected and we can bet accordingly to maximize our expected payoff.

If we know that the first coin was selected, we should bet on heads since it has a higher probability of occurring. If we know that the second coin was selected, we should bet on tails since it has a higher probability of occurring.

Therefore, if we buy the insider's information, our expected payoff can be calculated as follows:

E(X|buying information) = P(C1) * P(H|C1) * (10-c) + P(C1) * P(T|C1) * (-c) + P(C2) * P(H|C2) * (-c) + P(C2) * P(T|C2) * (10-c)

= (1/2) * (0.6*(10-c) - 0.4c + 0.3(-c) - 0.7*(10-c))

= -0.2c + 1.5

To find the values of c for which it pays to purchase the information, we need to solve the inequality:

E(X|buying information) > E(X)

-0.2c + 1.5 > -1

Solving for c, we get:

c < 13.25

Therefore, it pays to purchase the information for any value of c less than $13.25. If we buy the information for a price less than $13.25, we can increase our expected payoff above a loss of $1.

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The probability of the following parts is: a. 0.33 b. 1.925 c. 0.176 d. 0.67 e. 0.99955416 f. 0.018318006 g. 0.4489

a. To find out the probability that none of the first three people is concerned about their credit scores, we need to find: P(none of the first three is concerned about their credit scores)we have been given the probability that a teenager is concerned about his/her credit score is 0.67. So the probability that a teenager is not concerned about his/her credit score is 0.33. Now we can say that this is a binomial distribution since we are repeating a procedure until success is achieved. So we can use the binomial distribution to find the above probability: P(none of the first three are concerned about their credit scores) = (0.33)^3 = 0.0359375

b. The expected value of X is given by: E(X) = 1/p = 1/0.67 = 1.4925

c. Variance of X is given by: Var(X) = (1-p)/p^2 = (0.33)/(0.67)^2 = 0.176

d. Since X is the number of teenagers we select who are not concerned about their credit scores before we find the first teenager who is concerned. The probability that X = 0 is the probability that the first teenager we select is concerned about his/her credit score, which is given by: P(X = 0) = p = 0.67

e. To find out the probability that X ≤ 4, we can use the complement rule: P(X ≤ 4) = 1 - P(X > 4) = 1 - [P(X = 5) + P(X = 6) + ....... to ∞] = 1 - (1 - p)^5 = 1 - (0.33)^5 = 0.99955416

f. To find out the probability that Y = 6, we need to find: P(Y = 6)We know that for Y = 6, we need to select 7 teenagers such that the first and the second teenager we select are not concerned about their credit scores, and the third to the seventh teenager we select are concerned about their credit scores. The probability that the first and the second teenager we select are not concerned about their credit scores is given by: P(selecting 2 teenagers not concerned about their credit scores) = (0.33)^2 = 0.1089 And the probability that the third to the seventh teenager we select are concerned about their credit scores is:

P(selecting 5 teenagers concerned about their credit scores) = (0.67)^5 = 0.16806957Therefore, P(Y = 6) = P(selecting 2 teenagers not concerned about their credit scores) * P(selecting 5 teenagers concerned about their credit scores) = 0.018318006

g. To find out the probability that Y = 0, we need to select the first two teenagers who are concerned about their credit scores. P(Y = 0) = P(selecting the first two teenagers who are concerned about their credit scores) = (0.67)^2 = 0.4489.

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The wοrd "unabated" is used in Narrative οf the Life οf Frederick Dοuglass, An American Slave.

The wοrd "unabated" in this cοntext can be interpreted tο mean "cοntinuing withοut any reductiοn in intensity οr strength." "That cheerful eye, under the influence οf slavery, swοre red with rage; that vice, made all οf sweet accοutrement, changed tο a οne οf harsh and hοrrid discοrd; and that angelic face gave way tο that οf a demοn."

The authοr is describing hοw the slavehοlder's pοwer οver the slaves cοrrupts the wοman's character, turning her previοusly kind demeanοur intο οne οf rage and discοntent. The wοrd "unabated" emphasises hοw persistent and unyielding this transfοrmatiοn is and hοw unlikely it is that it will diminish.

By examining the surrοunding text and cοmmοn usage, I was able tο determine the definitiοn οf the wοrd "unabated." In this sentence, the authοr's descriptiοn οf the slavehοlder's transfοrmatiοn is well-suited tο the wοrd "unabated," which is generally used tο describe sοmething that cοntinues withοut any lοss οf intensity οr strength.

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The p values that would reject the null hypothesis are (f) 0.0500 and (e) 0.0900

To reject the null hypothesis for a two-sided test at the 90% confidence level, we would compare the p-value to the significance level (alpha), which is equal to 1 - confidence level.

In this case, the confidence level is 90%, so alpha is 1 - 0.9 = 0.1.

Any p-value that is less than or equal to the significance level of 0.1 would lead to rejection of the null hypothesis.

So the p-values at which we would reject the null hypothesis are: 0.0500 and 0.0900

Therefore, the correct answers are options, (e), and (f).

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Answer:

1) y=-2, y=-8

2a) v=35

b) u=12

c) t=7

3) c=50.3

4) s=50

1 ]

Given:-

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To find:-

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Solution:-

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now , put the value of x = -3 in equation

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or

[tex] \: [/tex]

[tex] \texttt{The value of \boxed{ \tt \red{ y = ( -8 ) ( -2 )} } \: or \boxed{ \tt \red{ 16}} !}[/tex]

[tex] \: [/tex]

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2 ]

[tex] \texttt{v = u + at} \: - - - \texttt{given \: formula \: or \: eqn}[/tex]

a ) ----»

Given:-

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To find:-

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Solution:-

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now , put the given value in equation

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b )

Given:-

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To find:-

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Solution:-

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put the given value in equation

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c )

Given:-

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To find:-

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Solution:-

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now , put the given value in equation

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3 ]

Given:-

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To find:-

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By using given formula:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \texttt{The Circumference of the circle is { \blue{50.24}} !}[/tex]

[tex] \: [/tex]

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4 ]

Given:-

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To find:-

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By using formula:-

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Solution:-

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \texttt{The Speed of the car is \color{green}50.}[/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps⸙

Step-by-step explanation:

40 Years is the right answer

Answer:

son is 10 , father is 40

Step-by-step explanation:

let x be the sons age then father is x + 30

in 5 years

son is x + 5 and father is x + 30 + 5 = x + 35

at this time the father is three times as old as his son , then

x + 35 = 3(x + 5)

x + 35 = 3x + 15 ( subtract x from both sides )

35 = x + 15 ( subtract 15 from both sides )

20 = x

then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40

The solution to the inequality is for the statement is x > -1/10.

A mathematical statement known as an inequality compares two values and illustrates their connection using symbols like (less than), > (greater than), (less than or equal to), or (greater than or equal to). When two quantities are not equal or one is greater or smaller than the other, this is expressed as an inequality. A set of values that fulfil the inequality is the answer to an inequality.

The statement can be translated into an inequality as follows:

10x + 27 > 26

10x > -1

x > -1/10

where x represents the unknown number.

Hence, the solution to the inequality is x > -1/10.

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The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.

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The value of the given expressions are as follows: a. 25 b. 4 c. 1/4 d. 1/3.

In mathematics, an expression is a combination of symbols and/or numbers that represents a mathematical object or quantity. Expressions can be written using variables, operations, functions, and mathematical symbols such as parentheses, exponents, and radicals. An expression can represent a value, an equation, or a formula, and can be evaluated or simplified using mathematical rules and properties. Examples of expressions include 2x + 5, sin(θ), and (a + b)².

Here,

a. [tex]125^{2/3}[/tex]

radical form:

[tex]\sqrt{ (125^2)} = 125^{1/2}[/tex]

[tex]125^{1/2}[/tex] = √125

= 5√5

Therefore, [tex]125^{2/3} = (125x^{1/3})^{2}[/tex]

= [tex](5^3)x^{2/3}[/tex]

= [tex]5x^{3*2/3}[/tex]

= 5²

= 25

b. √16

In radical form:

√16 = 4

Therefore, [tex]16x^{-1/2} = \sqrt{16}[/tex]

= 4

c. [tex]16^{1/2}[/tex]

In radical form:

1/√16 = 1/4

Therefore, [tex]16^{-1/2} = 1/\sqrt{16}[/tex]

= 1/4

d.[tex]\sqrt[4]{81}[/tex]

In radical form:

[tex]\sqrt[4]{81}[/tex] = √(√81)

= √9

= 3

Therefore, [tex]\sqrt[4]{81} = 1/\sqrt[4]{81}[/tex]

= 1/3

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Assumptions of the error terms in the simple linear regression model except (D) Error terms have a constant variance.

Linear Regression Model:

A linear regression model states that the relationship between a dependent variable y and one or more independent variables X. The dependent variable is also known as a response variable. Independent variables are also called explanatory variable. In statistics, linear regression is a linear method of modeling the relationship between a scalar response and one or more explanatory variables (also called dependent and independent variables). The case of one explanatory variable is called simple linear regression for more than one, the procedure is called multiple linear regression.

The term differs from multiple linear regression, which predicts multiple correlated dependent variables rather than a single scalar variable.

Error Term:

The error term represents the margin of error in a statistical model; it is the sum of the deviations inside the regression line and it provides an explanation of the difference between the theoretical value of the model and the actual observations.

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Answer: To determine if Marco has made a mistake, we would need to know the expected mass of the contents of the beaker before the reaction took place. If the expected mass was 247 g or close to it, then Marco may not have made a mistake.

However, if the expected mass was significantly different from 247 g, then it is possible that Marco made a mistake in his experiment. It could be a measurement error, a calculation error, or a procedural error.

There are several reasons why Marco may have obtained a mass of 247 g at the end of the reaction. One possibility is that the reaction produced a product that was relatively volatile, and some of it was lost during the experiment. Another possibility is that Marco did not completely dry the product before weighing it, which could result in a higher measured mass due to the presence of residual moisture.

To determine the exact reason why Marco obtained a mass of 247 g, further investigation and experimentation would be needed.

Step-by-step explanation:

X = 22

Y = 15

youre  welcome! Brainliest would be appreciated :)

Answer:

x=4/7

Step-by-step explanation:

To start, use the distributive property and multiply 2 by what is in the parenthesis. Do 2x3x as well as 2x-1. This will get you 6x-2 on the left side. On the right side, since there is a minus sign, change the x to -x and 3 to -3. You will ultimately get 6x-2=5-x-3. To solve this, you must isolate the variable by using inverse operations. The final answer is 4/7.

the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)

Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt

Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C

a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt

Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.

Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,

we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:

S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)

dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change

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It is important to be aware that the distribution of sample means x may not match the distribution of the original x values exactly, due to sampling variability.

if the original distribution of x values is known to be normalize size needs to be large, then the sample size does not need to be restricted in order to claim that the distribution of sample means x taken from random samples of a given size is normal. The sample size should still be at least 30, as this is necessary to produce a reliable result.

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