a series circuit contains an inductor, a resistor, and a capacitor for which l = 1 2 h, r = 10 ω, and c = 0.01 f, respectively. the voltage e(t) = 10, 0 ≤ t < 9 0, t ≥ 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 probability that the chosen adult have high school or some college degree but no college degree is 0.683.

From the definition of probability we know that,

Probability of Event = (Outcomes favorable to that event)/(Total number of outcomes under that event)

Total number of adults in the town is given by = 4286 + 6313 + 3033 + 1886 = 15518.

The number of adults have high school degree only = 4286

The number of adults have some college degree only = 6313

The number of adults have high school or some college degree but no college degree = 4286 + 6313 = 10599.

The probability that the chosen adult have high school or some college degree but no college degree is given by

= 10599/15518 [According to definition of probability]

= 0.683 [Rounding off to nearest thousandth]

Hence, probability that the chosen adult have high school or some college degree but no college degree is 0.683.

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The question is incomplete. The complete question will be -

Answer: 400 : 560

Step-by-step explanation:

add 5 and 7 = 12

960/12 = 80

multiply the numbers again to get the right ratio

(5 x 80) : (7 x 80)

= 400 : 560

Ratio gives the fractional division of a whole into a given portion. Manu's will get 400 while Swapna will get 560.

To divide 960 in the ratio 5 : 7

Therefore, Manu and Swapna's share is 400 and 560 respectively.

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The explanatory variable is whether or not a subject received tea before bedtime.

The theory behind this study is that drinking tea before bedtime may help with falling asleep faster.

Participants were randomly assigned to one group that received tea before bedtime and the other group that did not receive tea before bedtime.

The researcher then monitored the amount of time it took for each person to fall asleep.

The explanatory variable of this study is whether or not a subject received tea before bedtime, and the goal is to compare the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

The results of this study will help determine if drinking tea before bedtime is an effective way to fall asleep faster.

The goal is to test whether or not this is true by comparing the amount of time it takes for each person to fall asleep depending on if they received tea before bedtime.

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Answer:

36-meet

37-feature

38-drag

39-Strength

40-speed

Step-by-step explanation:

The area of the considered trapezoid  PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)

The area of a trapezoid is the half of the product of sum of its parallel sides to the height of that trapezoid (the distance between those parallel sides).

Thus, if we have:

Length of its parallel sides = 'a' and 'b' units respectively

Perpendicular distance between its parallel sides = 'h' units,

Then, we get:

\(A = \dfrac{1}{2}\times(a+b) \times h \: \rm unit^2\)

Consider the figure attached below, which is a bit more labeled figure of the given trapezoid.

We constructed PA perpendicular to the level of SR, and therefore, as SR is parallel to PQ, we have PA perpendicular to PQ too.

Similarly, QB is constructed perpendicular to both PQ and SR.

Thus, for PQBA, all pair of adjacent sides are perpendicular to each other, therefore its a rectangle.

Sum of parallel sides = Length of PQ + Length of SR

= 24 + |SR| = 24 + |SB| + |BR| = 24 + |AS| - |AS| + |SB| |+ |BR|

= 24 + |AS| + |SB| + |BR| - |AS| = 24 + |AB| + |BR| - |AS|

Due to PABQ being a rectangle (its four sides are such that adjacent sides are perpendicular to each other), we have |PQ| = |AB| = 24 units.

Thus, we get:

Sum of parallel sides = 24 + |AB| + |BR| - |AS| = 48 + |BR| - |AS|

Perpendicular distance between its parallel sides = |PA| = |QB|

Thus, we need to find the values of 3 line segments, which are:

|BR|, |AS|, and |PA| (instead of |PA|, we can find |QB| too, since both are of same length).

From the perpective of angle R(interior) in right triangle RBQ, we know the side RQ's length (32 units), and want length of BR.

Thus, its hypotenuse and base from the perspective of angle R (interior).

Thus, we can use cosine ratio or secant ratio. Let we use cosine ratio.

Then, we get:
\(\cos(30^\circ) = \dfrac{|BR|}{|RQ|} \\\\|BR| = 32 \times \cos(30^\circ) = 32 \times \dfrac{\sqrt{3}}{2} = 16\sqrt{3}\: \rm units\)

For the same triangle as in case 1 (ie RBQ), but now taking the sine ratio, we get:

\(\sin(30^\circ) = \dfrac{|BQ|}{|RQ|} \\\\|BQ| = 32 \times \sin(30^\circ) = 16 \: \rm units\)

This is same as |PA| because of PQBA being a rectangle.

The angle PSA is supplement of angle PSR as both joined make a straight line ASR. Thus, we get:
\(m\angle PSA + m\angle PSR = 180^\circ\\m\angle PSA = 180^\circ-135^\circ = 45^\circ\)

Thus, for the triangle PSA, similar to the first case or second case, but now using tangent ratio as we've got |PA| = |QB| = 16 units, we get:

\(\tan(m\angle PSA) = \dfrac{|PA|}{|AS|}\\\tan(45^\circ) = \dfrac{|PA|}{|AS|} \\\\|AS| = 1 \times 16 = 16 \: \rm units\)

Thus, we get:

Sum of parallel sides = 48 + |BR| - |AS| = 48 + 16√3 - 16 = 32 + 16√3 units

Perpendicular distance between its parallel sides = |PA| = |QB| = 16 units.

Thus, Area of the trapezoid PQRS is evaluated as:

\(A = \dfrac{1}{2} \times \text{Sum of parallel sides} \times \text{Distance between those sides}\\A =\dfrac{1}{2} \times (32 + 16\sqrt{3}) \times 16 \\\\A = 256 + 128\sqrt{3} \: \rm unit^2\)

Thus, the area of the considered trapezoid  PQRS in simplest radical form is given by: Option c: 256 + 128√3 (in sq. units)

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Point c is the midpoint of ab and point b is between points a and d. If ad=17 and bd=9 , then cd = 13.

In the given question,

Point c is the midpoint of ab and point b is between points a and d.

If ad=17 and bd=9

We have to find the value of cd.

ac = cb

ad = 17

bd = 9

ad = ab+bd

17 = ab+9

Subtract 9 on both side, we get

ab = 8

cb = ab/2

cb = 8/2

cb = 4

Hence, cd = cb + bd

cd = 4+9

cd = 13

Hence, the value of cd is 13.

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Answer:

12 oranges

Step-by-step explanation:

The ratio is K/L where K = Kudi's oranges and L = Ludi's oranges

K/L = 2/3

To find the number of oranges that Kudi has, divide the numerator by the sum of numerator and denominator.Then multiply by total number of oranges

For Ladi, divide the denominator by the sum of numerator and denominator. Then multiply by total number of oranges

\(K = 20\cdot \dfrac{2}{2+3} = 20 \cdot \dfrac{2}{5} = 8 \; \mathrm {oranges}\\\\L = 20\cdot \dfrac{3}{2+3} = 20 \cdot \dfrac{3}{5} = 12 \; \mathrm {oranges}\)

So answer is Ladi has 12 oranges

Step-by-step explanation:

\( \sqrt{ ( - 8)} = 2 \sqrt{2} i\)

The correct answer is

The expected value for the percent of all US adults who would say they smoked cigarettes is 22%

The expected value is arrived at by finding the product of a possible output and the probability that the output will occur and summing up the results. Expected value can be used for investment management to calculate options and make decisions most likely to bring about the desired gain. The random variable provides categorization of the outcomes of the game while the expected provides the probability of an outcome

In the above, the source of the sample is nationwide whereby 22 % said they smoked therefore it cannot be applied to a different population that has a different expected value for the same survey.

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The given question is not in proper form, The question is:

A recent Harris poll asked a random sample of 1016 adults nation-wide whether or not they smoked cigarettes. 22% said they smoked. Based on this sample, can you conclude that... the expected value for the percent of all adults world-wide who would say they smoked cigarettes is 22%? the expected value for the percent of students at UI who would say they smoked cigarettes is 22%? the expected value for the percent of professors at UI who would say they smoked cigarettes is 22%? the expected value for the percent of all US adults who would say they smoked cigarettes is 22%?

a.) The expected value for the percent of all adults world-wide who would say they smoked cigarettes is 22%?

b). The expected value for the percent of students at UI who would say they smoked cigarettes is 22%?

c). The expected value for the percent of professors at UI who would say they smoked cigarettes is 22%?

d). The expected value for the percent of all US adults who would say they smoked cigarettes is 22%?

These box plots show the basketball scores for two teams Bulldogs & Wolvernies.

Here we have to compare the spread of scores by Interquartile Range.

The interquartile range defines the difference between the third and the first quartile

It express as : Upper Quartile - Lower Quartile

For the Bulldogs :

Upper Quartile is 90

Lower Quartile is 70

So, Interquartile Range = Upper Quartile - Lower Quartile

Interquartile Range = 90 - 70

Interquartile Range = 20

For the Wolveniers :

Upper Quartile is 85

Lower Quartile is 55

So, Interquartile Range = Upper Quartile - Lower Quartile

Interquartile Range = 85 - 55

Interquartile Range = 30

as : 20 < 30

So, The Interquartile Range for bulldogs, 20 is less than the IQR for the Wolveniers, 30.

Answer : B) The Interquartile Range for bulldogs, 20 is less than the IQR for the Wolveniers, 30.

Answer:

∠ Z = 75°

Step-by-step explanation:

• the upper base angles of an isosceles trapezoid are congruent, then

∠ Z = ∠ S = 75°

The correct option regarding the 95% confidence interval for this problem is given as follows:

A. The confidence interval from the first simulation is (0.187, 0.237), and the confidence interval from the second simulation is (0.209, 0.261). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.187 and 0.237. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.209 and 0.261.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameters for the first simulation are given as follows:

\(n = 1000, \pi = \frac{212}{1000} = 0.212\)

Hence the lower bound of the interval is of:

\(0.212 - 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.187\)

The upper bound is of:

\(0.212 + 1.96\sqrt{\frac{0.212(0.788)}{1000}} = 0.237\)

For the second simulation, the parameters are given as follows:

\(n = 1000, \pi = \frac{235}{1000} = 0.235\)

Hence the lower bound of the interval is of:

\(0.235 - 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.209\)

The upper bound is of:

\(0.235 + 1.96\sqrt{\frac{0.235(0.765)}{1000}} = 0.261\)

This means that option A is the correct option.

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When multiplying the same number raised to different powers add the powers together.

3 + 2 + 5 = 10

Because you are also multiplying a value without a power you need to add 1 to the sum of the powers:

10 + 1 = 11

Answer: 6^11

The time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

The Linear equation for a scatter plot y = mx+b has two variables i.e., a Dependent Variable [Y] and an Independent variable [X] .

A student who spends more time on his work and do it nicely will automatically get good exam grade . On the other side, a student who did'nt dedicate much time to the homework and carelessly does it , will obviously score a low exam grade.We can see that the exam grade is dependent on the time spent on the homework which naturally makes exam grade a response variable and time spent on home a independent thus an explanatory variable.

Hence, the time spent on homework will be naturally more an explanatory variable and exam grade a response variable.

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Answer:

some numbers that involve the

a=3

b=4

c=5

Answer:

Step-by-step explanation:

a=0.5

Answer:

No solutions.

Step-by-step explanation:

-10 = 7

No solutions

Answer: 6 guides

Step-by-step explanation:

Question wants to know the number of Guides present on Sunday.

On Saturday there were 120 tourists and 18 guides. The ratio was therefore:

120 : 18

On Sunday, the ratio must be the same and there are 40 tourists. You can solve this using direct proportion and multiplying:

120 : 18

40   :  x

120x = 18 * 40

x = 720/120

x = 6 guides

Answer:

System of equation : 14x+23y = 213 and y = x-2

The cost of regular tickets is $7 and the cost of tickets with donation is $5.

Step-by-step explanation:

Let regular ticket's cost be x and tickets with donation's cost be y.

14x+23y = 213

y = x-2

Now,

14x+23y = 213

or, 14x+23(x-2) = 213

or, 14x + 23x - 46 = 213

or, 37x = 259

so, x = 7

again,

y = x-2

or, y = 7-2

so, y = 5

Answer:

n = 2

Step-by-step explanation:

-1 + 3 = 2

To find the number of integer solutions for x1+x2+x3+x4+x5=31 with the given conditions, we can use the stars and bars formula. Therefore, the number of integer solutions to x1+x2+x3+x4+x5=31 with (a) xi≥0 is 5,814, with (b) xi>0 is 4,755, and with (c) xi≥i (i=1,2,3,4,5) is 8,907.

a) xi≥0: In this case, we can use the formula (n+k-1) choose (k-1) where n is the number of stars (31 in this case) and k is the number of bars (4 in this case since there are 5 variables). Therefore, the number of solutions is (31+4-1) choose (4-1) = 34 choose 3 = 5,814.
b) xi>0: In this case, we can subtract 1 from each variable to get y1+y2+y3+y4+y5=26 with yi≥0. Then, we can use the same formula to get the number of solutions which is (26+4-1) choose (4-1) = 29 choose 3 = 4,755.
c) xi≥i: In this case, we can subtract i from xi to get z1+z2+z3+z4+z5=16 with zi≥0. Then, we can use the same formula to get the number of solutions which is (16+4-1) choose (4-1) = 19 choose 3 = 8,581 for i=1, 13 choose 3 = 286 for i=2, 7 choose 3 = 35 for i=3, 4 choose 3 = 4 for i=4, and 1 for i=5.

Therefore, the total number of solutions is 8,581+286+35+4+1 = 8,907.
Therefore, the number of integer solutions to x1+x2+x3+x4+x5=31 with (a) xi≥0 is 5,814, with (b) xi>0 is 4,755, and with (c) xi≥i(i=1,2,3,4,5) is 8,907.

We need to find the number of integer solutions for the equation x1+x2+x3+x4+x5=31 with given constraints:
(a) xi≥0
(b) xi>0
(c) xi≥i for i=1,2,3,4,5
To solve this, we can use the stars and bars method for each case.
(a) xi≥0: We can treat the variables as stars, and we need to divide these 31 stars into 5 groups using 4 bars. We have 31 stars + 4 bars = 35 objects to arrange. So, the number of ways to arrange them is C(35, 4) = 52,360.
(b) xi>0: To satisfy this condition, we need to subtract 1 from each variable, so we have x1+x2+x3+x4+x5=31-5=26. Now, we need to divide these 26 stars into 5 groups using 4 bars. We have 26 stars + 4 bars = 30 objects to arrange. So, the number of ways to arrange them is C(30, 4) = 27,405.
(c) xi≥i for i=1,2,3,4,5: Here, we subtract the minimum value for each variable: x1+x2+x3+x4+x5=31-1-2-3-4-5=16. Now, we need to divide these 16 stars into 5 groups using 4 bars. We have 16 stars + 4 bars = 20 objects to arrange. So, the number of ways to arrange them is C(20, 4) = 4,845.
In summary, there are:
(a) 52,360 integer solutions for xi≥0,
(b) 27,405 integer solutions for xi>0, and
(c) 4,845 integer solutions for xi≥i for i=1,2,3,4,5.

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Answer:

20160 ways

Step-by-step explanation:

\(8 \times 7 \times 6 \times 5 \times 4 \times 3 \\ 20160\)

a. The equilibrium interest rate,  is determined by the risk-free interest rate, the probability of repayment, and the cost of default.

b. The probability of the government repaying its loan can be calculated using the loan repayment threshold and the distribution of the output.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default.

a. To find the equilibrium interest rate,  we need to consider the risk-free interest rate, the probability of repayment, and the cost of default. The equilibrium interest rate is given by the formula: r = r + (c/p), where r is the risk-free interest rate, c is the cost of default, and p is the probability of repayment.

b. The probability that the government will repay its loan can be calculated by determining the percentage of the output distribution that exceeds the loan repayment threshold. Since 0.5 of the output is required to repay the loan, we need to calculate the probability that the output exceeds L/0.5.

c. If the interest rate, r, is equal to or greater than the equilibrium interest rate, the borrowing country would default. This can be proven by comparing the repayment threshold (L/0.5) with the loan repayment amount (L + Lr). If the repayment threshold is greater than the loan repayment amount, the borrowing country would default.

Calculations and further details would be required to provide specific numerical answers for each part of the question.

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To calculate the cliff's elevation in 10 millennia, we need to use a little bit of math.

Since the cliff is losing elevation at a rate of 5% every millennium, we know that after one millennium, the cliff's elevation will be 95% of its current elevation. Therefore, we can use this formula to calculate the cliff's elevation after three millennia:
1,519 meters * 0.95^10 = 601.83 meters
So, after 10 millennia, the cliff's elevation will be approximately 601.83 meters. This means that the cliff will have lost approximately 917 meters of elevation over the course of 10,000 years due to erosion.

Finally, by applying the formula, we can determine the cliff's elevation in 10 millennia. After doing the calculation, we find that the final elevation will be approximately 744.29 meters.

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Answer:

1st option

Step-by-step explanation:

The translation is as shown in the figure in option B

Translation transformation is a type of geometric transformation that moves every point of a figure the same distance and direction. This transformation does not change the size, shape, or orientation of the figure, but only its position in space.

The transformation required ahs the rule defined as

Applying the rule arrives the image in option B

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