Triangle ABC is folded along the line AD. The area of the new figure is 7/12 the area of triangle ABC. The area of triangle ADE is 65 cm2. Find the area of triangle ABC.

The mean of samples 10, 10, 10, 10, 10, and 16 will be 11.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

In a sample of n = 6, five individuals all have scores of x = 10 and the sixth person has a score of x = 16.

Then the data set will be given below.

10, 10, 10, 10, 10, 16

Then the mean of the data set will be

Mean = (10 + 10 + 10 + 10 + 10 + 16) / 6

Mean = 66/6

Mean = 11

Thus, the mean of the sample will be 11.

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In programming, an "enclose" statement refers to placing a block of code within a specific construct, such as a loop or function, to control its execution and ensure proper behavior.

When writing code, it's common to encounter exceptions, which are unexpected errors or events that can cause the program to crash or behave in unexpected ways. To handle exceptions, programmers use a construct called a "try-catch" statement, which encloses the code that may throw an exception within a "try" block. If an exception is thrown, the "catch" block will execute, allowing the programmer to handle the exception and take appropriate action.

Using a try-catch statement is essential for writing robust and reliable code, as it ensures that unexpected errors are caught and handled gracefully. By enclosing code that may contain an exception within a try block, programmers can prevent their program from crashing or malfunctioning in the event of an unexpected error. Additionally, by handling exceptions appropriately, programmers can provide a better user experience and prevent their users from encountering cryptic error messages or unexpected behavior. Overall, the try-catch statement is a fundamental tool for any programmer, and mastering its use is crucial for writing high-quality code.

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Answer:

62,144

Step-by-step explanation:

60,000 x (1 + 2%)^2 : growth in 2 years

+ 750: in migrants

- 410: out migrants

- 620: died

Answer:

62,144

Step-by-step explanation:

\(60,000 \times (1 + 2\%)^{2} \)

➡️ \( = 62,424\)

In-migrants:

➡️ \(750 - 410 = 340\)

now:

\(62,424 + 340 - 620\)

➡️ \( = 62,144\)

So, the present of the municipality is 62,144

The midpoint between \(-3,5 and 1,6 is (-1,5.5)\)

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between \(-3,5 and 1,6\).

The coordinates of the two points are:

Point 1: (\(-3,5\))

Point 2: (\(1,6\))

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point \(1\) + x-coordinate of Point \(2\)) / \(2\)

Midpoint's y-coordinate = (y-coordinate of Point \(1\) + y-coordinate of Point \(2\)) / \(2\)

According to the problem

Midpoint's x-coordinate = \((-3+1)/2= -2/2= -1\)

Midpoint's y-coordinate = \((5+6)/2= 11/2 = 5.5\)

So, the midpoint between \(-3,5\) and \(1,6\) is \((-1,5.5)\).

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\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-5}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-5}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-5)}}}\implies \cfrac{-6}{5+5}\implies \cfrac{-6}{10}\implies -\cfrac{3}{5}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{-\cfrac{3}{5}}(x-\stackrel{x_1}{(-5)}) \implies y-1=-\cfrac{3}{5}(x+5) \\\\\\ y-1=-\cfrac{3}{5}x-3\implies y=-\cfrac{3}{5}x-2\)

Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we can use either sine or cosine

\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

Hope this helps you

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer

The inequality to solve this is

(330/Time) ≤ 55

The solution of this inequality is

Time ≥ 6 hours

Explanation

We are told that the car's maximum speed is 55 miles per hour.

To solve this, we should note that

Speed = (distance/time)

But for this question, we are told that the car has a maximum speed of 55 miles per hour.

So,

(Distance/Time) ≤ 55

If the distance covered is 330 miles

(Distance/Time) ≤ 55

(330/Time) ≤ 55

55 (Time) ≥ 330

Divide both sides by 55

Time ≥ (330/55)

Time ≥ 6 hours

Hope this Helps!!!

If the polynomial \(f(x) = a0 + a1x + a2x^2 + ... + anx^n\) is a zero divisor in the polynomial ring R[x], and a is not equal to 0R, then the coefficient an is a zero divisor in the commutative ring R.

To prove that if \(f(x) = a0 + a1x + a2x^2 + ... + anx^n\) is a zero divisor in the polynomial ring R[x] where R is a commutative ring and a is not equal to 0R, then an is a zero divisor in R, we can use a proof by contradiction.

Assume that an is not a zero divisor in R. This means that for any element b in R, if anb = 0, then b must be equal to 0.

Now, suppose f(x) is a zero divisor in R[x]. This means that there exists a nonzero polynomial g(x) in R[x] such that f(x) * g(x) = 0.

Expanding the product, we have:

\((a0 + a1x + a2x^2 + ... + anx^n) * g(x) = 0.\)

Looking at the highest degree terms in this expression, we find that the coefficient of x^(n + deg(g(x))) is equal to an * leading coefficient of g(x), which we'll denote as bg.

Since f(x) * g(x) = 0, we have that an * bg = 0.

Since an is not a zero divisor in R, this implies that bg must be equal to 0. However, this contradicts our assumption that g(x) is a nonzero polynomial, as it would imply that bg = 0 for some nonzero b in R.

Therefore, our assumption that an is not a zero divisor in R leads to a contradiction, and thus, an must be a zero divisor in R.

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Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

Last option: 5/8

Step-by-step explanation:

sin(angle) = opposite / hypotenuse

So, sin(B) = 4/6.4 = 20/32 = 10/16 = 5/8

Hope this helps!

Answer:

the vertex is (6,2) i am sorry for not finding all of them

Step-by-step explanation:

Answer:

6*3= 18

Jeff packed 18 pairs of socks

Step-by-step explanation:

Jeff has 6 packs of new socks. Each pack contains 3 pairs of socks. How many pairs of new socks does Jeff have?

3

6

15

18

Answer:

7mm

Step-by-step explanation:

Area=l*b

35cm²=l*50mm

350mm²/50mm=l

7mm=l

Answer:

0.522

0.063

Step-by-step explanation:

6 x 8.7 = 52.2

6 x 1.05 = 6.3

If we move them both two decimal places then...

0.522

0.063

The f(z)/(z - z0) is analytic at z0 and its limit is f’ 0 (z0). This completes the proof of l'Hôpital's rule

To prove l'Hôpital's rule, we can use the Cauchy integral formula. Let D be a small disk centered at z0 and with radius r. Then we have:

f(z) = (1/2πi) ∫γ f(ζ)/(ζ - z) dζ,

where γ is the boundary of D oriented counterclockwise. Similarly, we have:

g(z) = (1/2πi) ∫γ g(ζ)/(ζ - z) dζ.

Since f(z0) = g(z0) = 0 and g' 0 (z0) ≠ 0, we can expand g(z) as:

g(z) = g’ 0 (z0) (z - z0) + O((z - z0)²).

Then, for z in D, we have:

f(z) g(z) = f(z) [g’ 0 (z0) (z - z0) + O((z - z0)²)]

= g’ 0 (z0) [f(z)/(z - z0)] (z - z0) + O((z - z0)³).

Note that the O((z - z0)²) and O((z - z0)³) terms are bounded by Cr² and Cr³, respectively, where C is a constant depending on f and g but independent of r. Using the Cauchy integral formula again, we have:

f(z)/(z - z0) = (1/2πi) ∫γ f(ζ)/(ζ - z) dζ

= (1/2πi) ∫γ [f(ζ) - f(z0)]/(ζ - z0) dζ.

Since f(z0) = 0, the integrand is bounded by M/r for some constant M depending on f but independent of r. Therefore, we have:

|f(z)/(z - z0)| ≤ M/r

for all z in D except z0. Thus, the term (z - z0) cancels out in the limit as z approaches z0, and we get:

limz→z0 f(z) g(z) = limz→z0 g’ 0 (z0) [f(z)/(z - z0)] (z - z0)

= g’ 0 (z0) f’ 0 (z0),

where we used the fact that f(z)/(z - z0) is analytic at z0 and its limit is f’ 0 (z0). This completes the proof of l'Hôpital's rule.

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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If to renew the policy the insurance company charges an extra 40% to her premium rate: b. Even with the extra charge for renewal, Eva’s plan is the least expensive.

Premium rate can be defined as the additional money a person pay  instalmentally for an insurance policy.

Based on the given scenario Eva plan is the least expensive plan due to the fact that despite the  insurance company  charge her  the   additional 40% to her premium rate before they can renew her insurance policy,  her plan will be the  least expensive plan which inturn means that she can often renew the plan because it will cost her less.

Therefore If to renew the policy the insurance company charges an extra 40% to her premium rate: b. Even with the extra charge for renewal, Eva’s plan is the least expensive.

The missing option are:

a.Eva would have been better off selecting the 20-year term policy.

b.Even with the extra charge for renewal, Eva’s plan is the least expensive.

c.Given that Eva plans to renew, she should have selected the whole life policy.

d.Eva ends up paying the same amount for each policy.

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Answer: B

Step-by-step explanation:

Answer:

3,072m

Step-by-step explanation:

32 × 12× 8= 3,072 (This is only you are multiplying them all)

If you are trying to find the area then its: 384m

Answer:

69

Step-by-step explanation:

Answer:

1: (B)

2: (C)

3: (D)

4: (D)

5: (A)

Step-by-step explanation:

Question 1:

Answer choice B is the only set of ordered pairs where there is only possible ouput for each input.

Question 2:

The y-intercept represented on the graph is (0, -3) and only answer choice C & D have it. Next, we're going to find the slope by using the rise/run method. From point (0, -3) to point (2, 0), it rises 3 and runs 2, so the slope is 3/2. Answer choice C is the only one with a y-intercept of -3 and a slope of 3/2.

Question 3:

From point (0, 0) to point (1, 3), it rises 3 and runs 1, so the slope is 3/1 or 3.

Question 4:

It is nonlinear because linear functions increase/decrease at the same rate. In the question, it says that the function decreases quickly at first, but then decreases more slowly as time passes. This function is not decreasing at the same rate the entire time.

Question 5:

The $5 fee is the initial fee, or the y-intercept, and the $2.25 per pound is the rate, or slope, so answer choice A is correct.

Hope this helps (●'◡'●)

Answer:

Thursday's mark is 3/4 inch below Monday's mark.

Explanation

Step 1

Let x represents the number of hours

Let y represents the rate of the company

and

cost per hour = $3

so, the total cost per time is

cost per time= 3* number of hours

cost per time==3x

now, the company charges a $5 boarding rate

so, the rate is

I hope this helps you

There is a change of 1/2 for Adam to get strictly more heads than Ben.

The likelihood that Ben will get more heads than Adam is equal to the likelihood that Ben will get more tails than Adam. (by symmetry)

If Ben and Adam each have n+1 (101) coins, then Ben will receive more heads or even more tails than B, but never both.

Considering (1) and (2), we find that there is a 50% chance that Adam will get more heads than Ben.

Thus, there is a change of 1/2 for Adam to get strictly more heads than Ben.

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Answer:

Let x = number of additional credits the student needs to get 4.0 GPA on. 52 credits with a GPA of 2.8 means a total of 52 * 2.8 = 145.6 145.6+4x52+x=3.2 Solve the equation for x

Step-by-step explanation:

Because i said so

The question asks you to create a confidence interval for the percentage of American households that plan to buy a new automobile next year. A survey of 1400 American homes revealed that 34% expected to purchase a new automobile in the coming year. The aim is to create a 98% confidence interval for the population share of households planning to purchase a new automobile in the coming year. The solution will be one of the offered possibilities, which are all a range of numbers that may or may not include the population proportion.

We can use the following formula to construct the confidence interval:

CI = (proportion ± z*(√(proportion*(1-proportion)/n)))

Where z is the critical value for the given confidence level, the proportion is the proportion of those who indicated they plan to buy a new car next year, and n is the sample size.

For a 98% confidence level, the critical value, z, is 2.326. Therefore, the confidence interval is (0.3074, 0.3726).

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Answer:

2.05 inches

Step-by-step explanation:

V = 4/3 x πr³

36=4πr³/3

36x3= 4πr³

108= 4πr³

108/4 = πr³

27= πr^3

27/π =r³

r=

\( \sqrt[3]{27 \div \pi} \)

r= 2.048in

round off to 2.05in

PROOF

V = 4÷3 x πr³

V= 4/3 x π(2.05)³

V=4/3 x π8.6

V=4×π×8.6/3

V=108/3

V=36in³

Therefore: radius= 2.05 inches

Answer:

146⁰ + x = 180

x = 34⁰ is AC ..a..a.