Determine whether the ordered pair is a solution of the given system.
(8,2);
3x-2y \leq 17
0.3x + 4y > 9

The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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The connection test is performed prior to making any ends in view of the tests for the primary impacts. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

Before drawing any conclusions based on the tests for the main effects, the interaction test is carried out. The effect of one factor on the population mean when two factors interact is determined by the specific value or level of the other factor.

There may be an interaction if the plot's lines don't line up in the same direction. A collaboration demonstrates that the method for the Y information at the levels of the main X variable are different at each level of the second X variable. The interaction's strength increases with the number of nonparallel lines.

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Answers:

============================================================

Explanation:

Let's use the slope formula to get

m = (y2-y1)/(x2-x1)

m = (6-4)/(5-2)

m = 2/3

The slope of the line is 2/3.

We can see that the responses for choices 1 and 3 are "no" because they involve a slope of 3/2.

-------------

Recall that y-y1 = m(x-x1) represents the point slope form. The m is the slope and (x1,y1) is the point the line goes through.

If we plugged the point (x1,y1) = (2,4) , along with the slope m = 2/3, then we'll get to what choice 2 is saying

If we tried the other point (5,6), and kept m the same, then we'd get to choice 4.

That makes choices 2 and 4 "yes" responses.

The probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I can be denoted as P(S|C'). The correct option is (a) P(S'|C').

To represent the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I, we need to consider the complement of the events.

The complement of event C (grade of B or better in Calculus I) is C' (grade less than B in Calculus I). Similarly, the complement of event S (grade of A in Statistics I) is S' (grade other than A in Statistics I).

Therefore, the probability that a student received an A in Statistics I given that the student received less than a B grade in Calculus I is denoted as P(S|C'). This notation indicates the conditional probability of event S occurring given that event C' has occurred.

Among the given options, (a) P(S'|C') correctly represents the desired probability. Option (b) P(CIS) represents the joint probability of events C, I, and S, which is not relevant to the given question.

Option (c) P(SIC) represents the joint probability of events S, I, and C, which is also not relevant. Option (d) P(SIC) is a duplicate of option (c) and does not represent the desired probability.

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Answer:

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= 2000π unit³

Volume= 6284 unit³

Step-by-step explanation:

The decimal value of the volume already given= 600π

The decimal value of the volume already given= 600*3.142

The decimal value of the volume already given= 1885.2 unit³

For radius 11 unit height 12 unit

Volume= πr²h/3

Volume= 11²*12/3 *π

Volume= 484π unit³

Volume= 1520.73 unit ³

For radius 4 unit height 6 unit

Volume = πr²h/3

Volume= 4²*6/3(π)

Volume= 32π unit³

Volume= 100.544 unit³

For radius 20 unit height 15 unit

Volume= πr²h/3

Volume= 20²*15/3(π)

Volume= 2000π unit³

Volume= 6284 unit³

Here's the right answer.

Answer:

Third term (5)

Step-by-step explanation:

A(3) is the third term which is 5.

Answer: Tn=2n−1.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since you can't measure such a huge distance, using meters, inches or centimeters will be inappropriate. Only answer is miles, but I'd prefer kilometers

The sample space of the experiment is {(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)}. The probability that there were 13 carrots in total planted over the two days is 0.4 and the probability that an odd number of carrots were planted on the second day is 0.4.

a) Sample space: {(4,5),(4,6),(4,7),(4,8),(4,9),(5,6),(5,7),(5,8),(5,9),(6,7),(6,8),(6,9),(7,8),(7,9),(8,9)}

b) i). There are 6 ways of planting 13 carrots, and there are 15 possible outcomes for planting carrots. Hence,

P(13) = 6/15

P(13) = 0.4

ii). We can have odd total carrots only if we have an odd number of carrots planted on both days or we plant 5 carrots on the first day and 7 carrots on the second day. Therefore, the sample space is {(4,5),(6,5),(4,7),(6,7),(5,5),(5,7)}. There are 6 possible outcomes for planting an odd number of carrots. Hence,

P(odd) = 6/15

P(odd) = 0.4

c) The events are mutually exclusive because if an odd number of carrots are planted on the second day then the total number of carrots planted cannot be 13.

d) We know P(13) = 0.4 and P(odd) = 0.4, and P(13 and odd) = 0, so the events are not statistically independent.

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Swinging an arc on either side of the segment is the correct next step when bisecting a segment using a compass.

We have,

When bisecting a segment using a compass, Jessica's next step after placing the compass on one endpoint and opening it to a width larger than half of the segment is to swing an arc on either side of the segment.

Here's a step-by-step explanation:

- Jessica starts by placing the compass on one endpoint of the segment.

- She opens the compass to a width larger than half of the segment. This ensures that the arcs she will create will intersect on both sides of the segment.

- Keeping the compass width unchanged, Jessica pivots the compass around the endpoint, drawing arcs on both sides of the segment.

- The arcs will intersect at two points.

- Finally, Jessica can connect these two points with a straight line to find the midpoint, which is the point where the segment is bisected.

- By swinging the arcs on either side of the segment, Jessica ensures that the midpoint is accurately determined, as it is the point equidistant from both endpoints.

Therefore,

Swinging an arc on either side of the segment is the correct next step when bisecting a segment using a compass.

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The simplified form of f(x) is:

ak = {

-20 if k = 1,

2(1 - 6(k+1)) / (k+1) if 1 < k < n,

2 if k = n

}

The given expression for f(x) is:

\(f(x) = 2\sum nk=1 x^k / (k) - 3\sum nk=1 4k x^k\)

To simplify this expression, we need to write it in the form ∑nk=1akxk, where ak is the coefficient of xk. To find these coefficients, we can use algebraic manipulation:

Thus, we have:

Therefore, the coefficients are:

ak = {

-20 if k = 1,

2(1 - 6(k+1)) / (k+1) if 1 < k < n,

2 if k = n

}

These coefficients can be used to write the simplified form of f(x) as:

f(x) = ∑nk = 1 ak \(x^k\)

where ak is the coefficient of \(x^k\).

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Answer:

50 years.

Step-by-step explanation:

Hope this helps!

The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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SSR represents the amount of variation in Y that is explained in regression analysis.

It is also known as the sum of squares due to regression, which measures the difference between the predicted values and the actual values of the dependent variable (Y).

The higher the value of SSR, the better the fit of the regression line to the data. This is because a higher SSR indicates that more of the variation in Y is being explained by the independent variable (X).

Therefore, the correct answer to the multiple choice question is "The amount of variation in Y that is explained."

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a) With regard to Edward, single deposit would he need to make now into an account that pays 4.3% interest, compounded daily, to meet his goal  is $32,526.67.

b) The total interest that he would pay on this loan is given as follows: $2,160.

c) The finance charge is $295.84

A) Let the Principle be P

amount here A= $50,000

time n= 10 years n= 10 x 36 5= 3650 days

rate of interest= 4.3% compounded daily= 4.3/365

let us use compound interest formula to calculate the principle

A = P (1 + (r/100)ⁿ

putting all the values we get

50000 = P (1 + (4.3/(100 x 365))⁽¹⁰ ˣ ³⁶⁵)

on solving we get P =  $32,526.67

therefore he need to deposit $32,526.67

B)

The balance of an account after t years, using simple interest, that is, a single compounding per year, is given by the equation shown as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are explained as follows:

P is the value of the initial deposit.

r is the interest rate, as a decimal.

Considering this equation, the interest accrued is given as follows:

I(t) = Prt.

In the context of this problem, the values of these parameters are given as follows:

P = 7500, r = 0.064, t = 4.5.

Hence the interest accrued on the payment is obtained as follows;

I(4.5) = 7500 x 0.064 x 4.5 = $2,160.


C)

We know that,

Finance charge = Total Amount Paid - Original cost

As the original cost of the drum is = $1972

She paid 20% as down payment. So the amount of down payment is,

1972 x 20/100 = $394.40

She has to pay 36 monthly payments of $52.04 each. So the amount to be paid is,

= 36 x 52.04 = $1873.44

So the total amount paid will be,

=  $1873.44 + 394.40 = $2267.84

Therefore, the finance charge is 226.84 - 1972 = $295.84

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The regular expression excludes strings like "1000" or "100000" because they have an even number of 0s following the 1.

The set of all bit strings made up of a 1 followed by an odd number of 0s can be represented by the regular expression:

1(00)*

Breaking down the regular expression:

1: The string must start with a 1.

(00)*: Represents zero or more occurrences of the pattern "00". This ensures that the 1 is followed by an odd number of 0s.

Examples of valid bit strings in this set include:

10

100

10000

1000000

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The probability that a student studied for 4 hours is 0.3.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.

To determine the probability;

The number of students that has 4 hours is 9

The total number of students are 30.

Pr(4 hours) = 9/30

Pr(4 hours) = 0.3

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Answer:

3/8 cups of milk.

Step-by-step explanation:

3/4 * 1/2

= 3/8.

Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

Realicando una division, veremos que necesitan 1,040 barras de pan para alimentar a las 65 personas durante los 80 días

Primero sabemos que para alimentar durante 24 días a 40 trabajadores la empresa necesita 192 barras de pan.

Entonces el numero de barras de pan requerido por día para los 40 trabajores es obtenido con la división:

192/24 = 8

Es decir, se necesitan 8 barras de pan por día.

Esas 8 barras de pan se dividen entre 40 trabajadores, entonces lo que cada trabajador necesita se obtiene con la división:

8/40 = 0.2 barras de pan por día.

Entonces, si tenemos 65 personas, estas necesitaran:

65*0.2 = 13 barras de pan por día.

Y si se las debe alimentar drante 80 días, entonces la cantidad total necesaria será:

13*80 = 1,040

Se necesitan 1,040 barras de pan para alimentar a 65 personas durante 80 días

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The sum of the multiplicities of the roots in a polynomial equation is equal to the degree of the polynomial (the highest power of the variable in the equation).

This is known as the Fundamental Theorem of Algebra. The multiplicity of a root is the number of times a root appears in a polynomial equation, and it can be a whole number, a fraction, or even an irrational number.

For example, if the polynomial equation is x³ + 2x² + 4x - 8 = 0, then the degree of the polynomial is 3 and the multiplicities of the roots are 1, 2, and 1, respectively.

Therefore, the sum of the multiplicities of the roots in this equation is 3. This is true for any polynomial equation: the sum of the multiplicities of the roots will always be equal to the degree of the polynomial.

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Answer:

.045% or about half of one percent

Step-by-step explanation:

P(queen) = 4/52

P(3 queens) = (4/52)³ = 64/140608 = .045%

Answer:

972

Step-by-step explanation:

t/27=36

t=36*27

t=972

Answer:

t=972

Step-by-step explanation:

t = 27 x 36

t = 972

Check:

972/27 = 36

Check!

Hope that helps!

We know that 100paise=1 rupee

=>500 paise = 5 rs

ratio =5/20=1/4=1:4

hope it helps :)

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Answer: 110 yards

Step-by-step explanation:

From the question, the distance from the shovel to the treasure chest is

60 yards while the distance from the treasure chest to the boat is 50 yards. We are to calculate the distance from the boat from the shovel.

The distance from the boat from the shovel will be the addition of the distance from the shovel to the treasure chest which is 60 yards with the distance from the treasure chest to the boat is 50 yards.

= 60 yards + 50 yards

= 110 yards

The percent decrease in meals is 56.6667%.

Just dividing the decreased number by the original value and multiplying the result by 100 will yield the percentage decrease formula.

Percent Decrease = (Decreased Value / Original Value) × 100.

Given:

The change in meals from 120 to 52.

So, the Change in amount

= 120- 52

=  68

And, Percent Decrease

= Change in amount/ Original amount x 100

= 68 / 120 x 100

= 68/12 x 10

= 5.6667 x 10

= 56.667%

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Answers: Angle ABE = 117 And DBE = 27