find x - special right triangles

Answer: step 1:

wickets 2 and 9, (16,18) and (15,43) = 25.02ft

wickets 9 and 8, (15, 43) and (37,65) = 31.11 ft

wickets 8 and 5, (37, 65) and (63,39) = 36.7 ft

wickets 5 and 3, (63, 39) and (41, 17) = 31.11 ft

wickets 3 and 2, (41, 17) and (16, 18) = 25.02 ft

The seasonal index (ST), based on the Ratio-to-Moving average data, is 1.35.

To find the seasonal index (ST) for using the Ratio-to-Moving average data, we need to calculate the average ratio across the three years.

Let's calculate the seasonal index (ST) step by step:

Ratio-to-Moving average for 2019: 1.32

Ratio-to-Moving average for 2020: 1.28

Ratio-to-Moving average for 2021: 1.44

Sum of Ratio-to-Moving averages: 1.32 + 1.28 + 1.44 = 4.04

Number of years: 3

Seasonal index (ST) = (Sum of Ratio-to-Moving averages) / (Number of years)

= 4.04 / 3

= 1.35 (rounded to 2 decimal places)

Therefore, the seasonal index (ST) is 1.35.

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Answer:

Angle 8 = 84 degrees

Angle 5 = 96 degrees

Step-by-step explanation:

Angle 8 = 84 degrees because Angle 2 and Angle 8 are inside opposite which makes them equivalent.

Angle 5 = 96 degrees because 180-84=96

The function given is a graph of a trigonometric function.

The amplitude is the distance between the peak and the midline of the wavelengths. The midline of this graph is at -4 while the peak is at -2 and -6. The amplitude therefore, is the distance between -4 ans -2 (or -4 and -6.

The distance in absolute value is 2. The amplitude therefore is 2.

The period is the distance covered by one revolution. The period in this graph

Answer:

2n-1

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

The graph given is of inequality x ≤ -7.

In Algebra, inequality is a mathematical statement that shows the relation between two expressions using the inequality symbol.

Given is a graph of an inequality, we need to determine the inequality,

So, the graph is cutting the x-axis at -7 and all the numbers less than -7 is covered by the graph,

so the inequality will be x ≤ -7

Hence, the graph given is of inequality x ≤ -7.

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(a) To find the inverse Laplace transform of 1/(s^2 + 4), we can recognize that this is the Laplace transform of the function sin(2t). Therefore, the inverse Laplace transform is given by: L^(-1){1/(s^2 + 4)} = sin(2t)

(b) To find the inverse Laplace transform of (s - 1)^2 - 1, we can expand and simplify: (s - 1)^2 - 1 = s^2 - 2s + 1 - 1 = s^2 - 2s. The inverse Laplace transform is then: L^(-1){(s - 1)^2 - 1} = t^2 - 2t.  (c) To find the inverse Laplace transform of (s + 3)/(s^2 + 4s + 7), we can use partial fraction decomposition. The denominator can be factored as (s + 2)^2 + 3. Therefore, we have: (s + 3)/(s^2 + 4s + 7) = A/(s + 2) + B/(s + 2)^2.

Multiplying through by the denominator and equating coefficients, we find A = -1/3 and B = 2/9. The inverse Laplace transform is then: L^(-1){(s + 3)/(s^2 + 4s + 7)} = (-1/3)e^(-2t) + (2/9)te^(-2t).

(d) To find the inverse Laplace transform of (s^3 + 35s^2 + 2s)/(s^2 + 4s + 7), we again use partial fraction decomposition. The denominator can be factored as (s + 2)^2 + 3. Therefore, we have: (s^3 + 35s^2 + 2s)/(s^2 + 4s + 7) = A/(s + 2) + B/(s + 2)^2 + C/(s + 2)^2.  Multiplying through by the denominator and equating coefficients, we find A = 2, B = -1, and C = 2.The inverse Laplace transform is then: L^(-1){(s^3 + 35s^2 + 2s)/(s^2 + 4s + 7)} = 2e^(-2t) - te^(-2t) + 2t^2e^(-2t).  (e) To find the inverse Laplace transform of (s + 1)/(s^2 + 4s + 4), we can again use partial fraction decomposition. The denominator can be factored as (s + 2)^2. Therefore, we have: (s + 1)/(s^2 + 4s + 4) = A/(s + 2) + B/(s + 2). Multiplying through by the denominator and equating coefficients, we find A = 1/2 and B = 1/2.

The inverse Laplace transform is then: L^(-1){(s + 1)/(s^2 + 4s + 4)} = (1/2)e^(-2t) + (1/2)te^(-2t)

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Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

9)  17 miles/hr

10)  7.14 miles

Step-by-step explanation:

See the attached worksheet.  Note the use of conversion factors.  In question 9 we want to convert minutes to hours.  We know there are 60 minutes/hr.  So we can set up a conversion factor in one of 2 ways:  (60 minutes/1 hr) or (1 hr/60 minutes).  Both are valid, and both are = 1, since the numerator and denominator are both equivalent.  This means we can invert a conversion factor and it is still = 1.  Since conversion facots are equal to 1, we can multiply them times anything, and the result is numerically the same (anything times 1 = anything) and only the units have changed.  For question 9, we want to convert miles/min to miles/hr.  I'll choose the conversion factor (60 min/1 hr), mostly because I like multiplication over division.  Note how the units cancel in the attachment, resulting in 17 miles/hr.  One may also use the factor (1hr/60min), but then a division is required.  Perfectly fine, but not my preferred route.

The same approach is used to answer question 10.  Again, note how he units cancel, leaving a number wth just the units desired,

The family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P) on an appropriate interval of definition.

In the first paragraph, we summarize that the family of functions P = C1e^t / (1 + C1e^t) is a solution to the differential equation dP/dt = P(1 - P). This equation represents the rate of change of the variable P with respect to time t, and the solution provides a relationship between P and t. In the second paragraph, we explain why this family of functions satisfies the given differential equation.

To verify the solution, we can substitute P = C1e^t / (1 + C1e^t) into the differential equation dP/dt = P(1 - P) and see if both sides are equal. Taking the derivative of P with respect to t, we have:

dP/dt = [d/dt (C1e^t / (1 + C1e^t))] = C1e^t(1 + C1e^t) - C1e^t(1 - C1e^t) / (1 + C1e^t)^2

      = C1e^t + C1e^(2t) - C1e^t + C1e^(2t) / (1 + C1e^t)^2

      = 2C1e^(2t) / (1 + C1e^t)^2.

On the other hand, evaluating P(1 - P), we get:

P(1 - P) = (C1e^t / (1 + C1e^t)) * (1 - C1e^t / (1 + C1e^t))

        = (C1e^t / (1 + C1e^t)) * (1 - C1e^t + C1e^t / (1 + C1e^t))

        = (C1e^t - C1e^(2t) + C1e^t) / (1 + C1e^t)

        = (2C1e^t - C1e^(2t)) / (1 + C1e^t)

        = 2C1e^t / (1 + C1e^t) - C1e^(2t) / (1 + C1e^t).

Comparing the two sides, we see that dP/dt = P(1 - P), which means the family of functions P = C1e^t / (1 + C1e^t) is indeed a solution to the given differential equation.

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Answer:the width is 5 1/4 ft

Step-by-step explanation:

Step 1

The area of a rectangle is given as  Length x width

Therefore the area of the rectangular board = Length x width

The length of the first board =6ft  

The length of the second board =5 1/2 ft  (5.5ft) with both having a total area of 60 3/8 (60.375ft²). To find the width of the boards since both have equal width, we use the equation

Length x width of board A +  Length x width of board B= area of board A and Board B

6w + 5.5w =60.375

Step 2---- Solving the equation

 6w + 5.5w =60.375

       11.5w = 60.375

               w = 60.375/11.5

                  w= 5.25

Therefore  the width of the two boards are  5.25 ft / 5 and 1/4 ft each

Answer:

Pythagoras was the Greek geometer .

Please mark me as the brainliest.

Considering the perimeter concept, we have that:

The perimeter of a polygon is given by the sum of all the lengths of the outside edges of the polygon.

For this problem, the outside edges are given as follows:

Danielle's mistake is that she did not consider two outside edges, one of length 6x - 4 and the other of length 12x + 3. Considering all the edges, the perimeter is given by:

P = 2(6x - 4) + 2(12x + 3) + 14x + 13

P = 12x - 8 + 24x + 6 + 14x + 13

P = 12x + 24x + 14x + 8 + 6 + 13

P = 50x + 27.

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according to question the values of i0, ω, and ϕ are:

i0 = ±0.08 A

ω = 8000π rad/s

ϕ = -90 degrees

We are given:

vs(t) = 20sin(4000t)V

io(t) = i0cos(ωt + ϕ)

We need to find i0, ω, and ϕ.

To find i0, we can use the fact that the maximum value of io(t) occurs when sin(ωt + ϕ) = 1. Therefore, i0 is the maximum value of io(t). We can find the maximum value of io(t) by taking the amplitude of the cosine function, which is |i0|. We know that vs(t) = 20V is the maximum value of the voltage source, and io(t) is the current flowing through it. Therefore, |i0| = |vs(t)/Zc|, where Zc is the impedance of the capacitor.

The impedance of a capacitor is given by Zc = 1/(jωC), where j is the imaginary unit and C is the capacitance. Substituting the values, we get:

Zc = 1/(j400010^-6) = -j250

|i0| = |vs(t)/Zc| = |20/(−j250)| = 0.08 A

Therefore, i0 = ±0.08 A.

To find ω and ϕ, we can use the fact that io(t) lags vs(t) by 90 degrees. Therefore, ϕ = -90 degrees.

We also know that the angular frequency ω is related to the frequency f by ω = 2πf. In this case, the frequency is 4000 Hz. Substituting the value, we get:

ω = 2π(4000) = 8000π rad/s

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If you received a gift of $10,000 3 years ago and you want to spend it in 3 years with interest rate is 4%, it will be worth $12,653.19. Option b is correct.

To calculate the future value of a present sum after a specified period, we can use the formula for compound interest:

Future Value = Present Value * (1 + Interest Rate)ᴺ

In this case, the present value is $10,000, the interest rate is 4% or 0.04, and the number of periods is 6 years because you received the gift 3 years ago and want to spend it in 3 years.

Using the formula:

Future Value = \(\$10,000 * (1 + 0.04)^6\)

Future Value = \(\$10,000 * (1.04)^6\)

Future Value = $10,000 * 1.1265319

Future Value ≈ $12,653.19

Therefore, the amount will be approximately $12,653.19. Option b is correct.

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Answer: the first one is (-9,-12) the second one is 13 or 25 i'm not sure

Step-by-step explanation:

Answer:

slope =2

Step-by-step explanation:

use math-way it helps

Slope or Gradient = y

\( \frac{y2 - y1}{x2 - x1} = \frac{2 - 0}{1 - 0} = 2\)

Answer:

Amdjss

Step-by-step explanation:

1. For the triple integral ∫∫∫ f(x, y, z) dV with f(x, y, z) = x and Σ being the part of the plane x + 4y + z = 10 in the first octant, the limits of integration are 0 ≤ x ≤ 10, 0 ≤ y ≤ (10 - x)/4, and 0 ≤ z ≤ 10 - x - 4y.

2. For the triple integral ∫∫∫ f(x, y, z) dV with f(x, y, z) = y² and Σ being the part of the plane z = x for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4, the limits of integration are 0 ≤ x ≤ 2, 0 ≤ y ≤ 4, and 0 ≤ z ≤ x.

1. To evaluate ∫∫∫ f(x, y, z) dV, where f(x, y, z) = x and Σ is the part of the plane x + 4y + z = 10 in the first octant:

We need to find the limits of integration for x, y, and z within the given region Σ. In the first octant, the region is bounded by the planes x = 0, y = 0, and z = 0. Additionally, the plane x + 4y + z = 10 intersects the first octant, giving us the limits: 0 ≤ x ≤ 10, 0 ≤ y ≤ (10 - x)/4, and 0 ≤ z ≤ 10 - x - 4y. Integrating f(x, y, z) = x over these limits will yield the desired result.

2. For ∫∫∫ f(x, y, z) dV, where f(x, y, z) = y² and Σ is the part of the plane z = x for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4:

The given region Σ lies between the planes z = 0 and z = x. To evaluate the triple integral, we need to determine the limits of integration for x, y, and z. In this case, the limits are: 0 ≤ x ≤ 2, 0 ≤ y ≤ 4, and 0 ≤ z ≤ x. Integrating f(x, y, z) = y² over these limits will give us the final result.

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Answer:

Step-by-step explanation:

The required inequality x + m ≤ 510, and the distance is 316 miles.

Inequity occurs when two phrases are joined by a sign such as "not equal to," "more than," or "less than." The inequality illustrates the larger than and less than the relationship between variables and numbers.

Given that Mr. Estrada's car can only drive 510 miles on a full tank of petrol. He drove the car 194 miles after filling up the tank with gasoline.

Let,

x miles = distance already traveled

m miles = distance miles can travel with remaining gas

510 = max. miles can travel on a full tank

As per the given question,

The inequality will be written as,

x + m ≤ 510

194 + m ≤ 510

m ≤ 510 - 194

Apply the subtraction operation, and we get

m ≤ 316

Therefore, the required inequality x + m ≤ 510, and the distance is 316 miles.

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Answer:

1 = B, 2 = B, 3 = C

Step-by-step explanation:

1) When there are same digits with exponents being multiplied, you add the exponents

2) When an exponent is being distributed through a parenthesis, you multiply

3) When there are same digits with exponents being divided, you subtract the exponents

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Answer:

x²- √3 x +1/2

Step-by-step explanation:

To write a quadratic equation with roots only:

x² -(sum of the roots)x+(product of roots)

x²-((√3-1/2)+(√3+1/2)x + ((√3-1/2)(√3+1/2)

x² -(2√3)/2 + ( 9-1)/4

x²- √3 x +1/2

Answer:

the answer is 0,1

Step-by-step explanation:

the diragram of 42 is like a rice of age 92 hope this helps

sine's rule

\(\tt \dfrac{A}{sin~a}=\dfrac{B}{sin~b}\)

1. 27/sin 61 = BC sin 54

BC = 25

2. ∠A=180 -(17+111)=52

27/sin 52 = AB sin 17

AB = 10

3. AC/sin 65 = 27/sin 61

AC = 28

4. ∠C = 180 -(61+30)=89

24/sin 89=AC/sin 61

AC=21

Its better to choose the simple random samples, if the defect is in every other cake, a systematic random sample could miss it completely depending on what Sergio chooses for k.

Here he is  taking a random sample of cakes to get a better idea of how many cakes might have this defect.

The random sample is defined as the method of choose a sample from the group of sample and each of the sample has same probability of being chosen

The systematic sample is the method of choosing the sample from the group of sample with a periodic interval.

Here Sergio noticed a potential defect that seems to be showing in every other cake, so there will be chance of missing the defect completely

Hence, to choose the defect items, the simple random sample is better than systematic random sample.

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Answer:

2L+2W

Step-by-step explanation:

U JUST MOVE THE 2 TO THE L AND MOVE THE 2W TO THE OTHER SIDE. I THINK MY ANSWER IS RIGHT BUT MAYBE WAIT FOR ANOTHER PERSON

Confirmed Solution:

\(p=2l+2w\)

Hope this helps!

Answer:

Step-by-step explanation:

150 - total budget (150)

25 out of total budget (150 - 25)

solve 150 - 25 for (125)

125/10 = 12.5

the 150-25 is in parentheses so using PEMDAS, it will be completed first for an answer of (125). then 125 x .10 to divide.

the equation would be  -  (150-25).10  (OR)   (150-25)/10

(you can either choose to divide by a whole or multiply by a fraction.

Answer:

12 people

Step-by-step explanation:

25+10x=150

subtract 25 each side

10x=125

divide both sides by 10

x = 12.5

can't have half a body at a party.

hope this helps :)

a. To estimate the fraction of all likely voters who preferred the incumbent (p), we can use the fraction of survey respondents who preferred the incumbent (p^​). In this case, 215 out of 400 respondents preferred the incumbent. So, the estimate for p would be 215/400 = 0.5375, or 53.75%.

b. The estimator of the variance is np^​(1−p^​), where n is the sample size (400) and p^​ is the fraction of survey respondents who preferred the incumbent (0.5375). Plugging these values into the formula, we get the variance estimate as 400 * 0.5375 * (1 - 0.5375) = 86.4.

To calculate the standard error of the estimator, we take the square root of the variance estimate. So, the standard error would be √86.4 ≈ 9.29.

c. The p-value for the test of H0​:p=0.5 vs. H1​:p≠0.5 can be calculated by conducting a two-tailed test. We compare the estimated p value (0.5375) to the assumed value (0.5) and use the standard error (9.29) to calculate the test statistic. Based on the test statistic, we can determine the p-value. Without the specific values for the test statistic, we cannot calculate the exact p-value.

d. The p-value for the test of H0​:p=0.5 vs. H1​:p>0.5 can be calculated by conducting a one-tailed test. We compare the estimated p value (0.5375) to the assumed value (0.5) and use the standard error (9.29) to calculate the test statistic. Based on the test statistic, we can determine the p-value. Without the specific values for the test statistic, we cannot calculate the exact p-value.

e. To determine if the survey contains statistically significant evidence that the incumbent was ahead of the challenger at the time of the survey, we need to compare the p-value obtained from the test to a significance level (such as 0.05). If the p-value is less than the significance level, we can conclude that there is statistically significant evidence that the incumbent was ahead of the challenger.

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