1/3 of your birthday cake is leftover from your party. If you eat 1/4 of the leftover cake, what fraction of the original birthday cake is left

#x

Angle 1

Angle 2

Answer:

A)  x = 44

B)  m∠1 = 118°

    m∠2 = 62°

Step-by-step explanation:

Part A

Angles on a straight line sum to 180°

⇒ (2x + 30) + 62 = 180

⇒ 2x + 30 + 62 = 180

⇒ 2x + 92 = 180

⇒ 2x = 88

⇒ x = 44

Part B

Vertical Angle Theorem:  The opposite vertical angles of two straight intersecting lines are congruent.

⇒ m∠1 = (2x + 30)

Substituting the found value of x:

⇒ m∠1 = 2(44) + 30

⇒ m∠1 = 88 + 30

⇒ m∠1 = 118°

Using the Vertical Angle Theorem:

⇒ m∠2 = 62°

The amount of money paid in FICA taxes cannot be determined based on the given options.

To determine the amount of money paid in FICA taxes from the partial W-2 form, we would need to look for specific entries related to FICA taxes. Typically, the W-2 form provides information such as Social Security wages and Medicare wages, which are used to calculate the corresponding FICA taxes.

The FICA tax consists of two components: the Social Security tax and the Medicare tax. The Social Security tax is calculated based on a fixed percentage (e.g., 6.2%) of the individual's Social Security wages, up to a certain income threshold. The Medicare tax is calculated based on a different fixed percentage (e.g., 1.45%) of the individual's Medicare wages, with no income threshold.

Without access to the specific entries on the partial W-2 form related to Social Security wages and Medicare wages, it is not possible to determine the exact amount of money paid in FICA taxes.

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Step-by-step explanation:

[tex]2 \sin(90 - x) - \cos(360 - x) [/tex]

[tex]2 \cos(x) - \cos(x) [/tex]

[tex] \cos(x) [/tex]

The required value of Ru is 7.71

Given that Romberg integration for approximating `∫(x) dx` gives `R21 = 6` and `R22 = 6.28`. Then, we need to find `Ru`.

We know that Romberg integration formula is given by:

R_kj = (4^j * R_(k+1),j-1 - R_k,j-1) / (4^j - 1), where, `R_kj` denotes the approximation of integral using `2^(k-1) x 2^(j-1)` points and `R_k,j-1` denotes the approximation of integral using `2^(k-1) x 2^(j-2)` points.

Now, we are given that:

`R21 = 6` and `R22 = 6.28`, we need to calculate `Ru`.

For this, let's use the Romberg integration formula as follows:

`R31 = (4^1 * R22 - R21) / (4^1 - 1)`

Substituting the given values, we get:

`R31 = (4 * 6.28 - 6) / 3 = 7.56 / 3 = 2.52`

Similarly,`R32 = (4^1 * R32 - R31) / (4^1 - 1)`

Substituting the given values, we get:

`R32 = (4 * 6.28 - 2.52) / 3 = 23.12 / 3 = 7.71`

Therefore, `Ru = R32 = 7.71`.Hence, the required value of `Ru` is `7.71`.

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wanna b my bestie :plead:

Answer:

∠DAB = ∠DBA

Then AD=DB from above statement

Answer:

A. q>p because, assuming this line starts somewhere after 0, this is positive progression

Answer:

(0.4291, 0.4743)

Step-by-step explanation:

Using the relation :

p ± Zcritical * Sqrt[(p(1-p)) / n]

P = x / n =. 1447 / 3203 = 0.4517

1 - p = 0.5483

Zcritical at 99% = 2.575

Sqrt[(p(1-p)) / n] = sqrt(0.4517(0.5483)) / 3203) = 0.008793

p ± Zcritical * 0.008793

Lower boundary = 0.4517 - (2.575 * 0.008793) = 0.4291

Upper boundary = 0.4517 + (2.575 * 0.008793) = 0.4743

(0.4291, 0.4743)

Answer:

8

Step-by-step explanation:

(-2,c) and (-1,10)

10-c

-1--2

10-c

1

We need the fraction to be 2, or 2/1. The bottom number is 1, so we technically already have the answer. But we still need to plug in a number for c. To get 2, we need to subtract 8 from 10.

So c is 8.

---

hope it helps

sorry my work was a mess

a) The p- value is 0.0094.

b) True

c) Yes

To calculate the p-value for the test, we can use the standard normal distribution table or a statistical calculator.

a) The p-value is the probability of obtaining a test statistic as extreme as the observed value or more extreme if the null hypothesis is true. Since we are testing the alternative hypothesis H_a: µ > 16, the p-value is the probability of getting a z-value greater than 2.34.

Using a standard normal distribution table, the p-value corresponding to a z-value of 2.34 is 0.0094.

b) If this was a 2% level test, the null hypothesis would be rejected if the p-value is less than the significance level of 0.02.

Since the p-value (0.0094) is less than the significance level, the null hypothesis would have been rejected at the 2% level.

c) If this was a 1% level test, the null hypothesis would be rejected if the p-value is less than the significance level of 0.01.

Since the p-value (0.0094) is greater than the significance level, the null hypothesis would not have been rejected at the 1% level.

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Answer:

B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5

There are 2 segments

First segment,

They need 4 less than 11 songs

=(11-4)

Second segment

They need 5 less than 3 times the number of songs in the first segment

3 times the number of songs in first segment

=3*(11-4)

5 less than 3 times the number of songs in first segment

={3*(11-4)} - 5

Total expression=

(11-4)+ {3×(11-4)} - 5

B. ( 11 − 4 ) + 3 × ( 11 − 4 ) − 5

Step-by-step explanation:

Answer:

D 23 songs

Step-by-step explanation:

Answer:

-8,5

Step-by-step explanation:

8,5 because the "m" is 5 squares down and 8 squares to the right.

The total maintenance function for the given rate of expenditure is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].

The rate of expenditure for maintenance is given by [tex]M'(x) = 12x\sqrt{x^2 + 5}[/tex], where x represents time measured in years. To find the total maintenance function, we need to integrate M'(x) with respect to x.

Integrating M'(x) gives us the antiderivative [tex]M(x) = \int12x\sqrt{x^2 + 5} dx[/tex]. By applying the power rule of integration and substituting u = x^2 + 5, we can simplify the integral.

After simplification, we obtain [tex]M(x) = 4(x^2 + 5)^{(3/2)} - 93[/tex]. Therefore, the total maintenance function is [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex].

Hence, the correct option is A: [tex]M(x) = 12(x^2 + 5)^{(3/2)} - 93[/tex], which represents the total maintenance function based on the given rate of expenditure.

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Answer:

1800°

Step-by-step explanation:

(12-2)x180 = 1800

Answer:

21021

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

a^2 + b^2 = c^2

5^2 + b^2 = 13^2

25 + b^2 = 169

b^2= 144

b=12 Therefore,

x=12

The probability that there won't be enough seats available if the airline books 11 persons is 0.3274. It is not unlikely for such an overbooking to occur because the probability of the overbooking is greater than 0.05.

To find the probability that there won't be enough seats available, we need to calculate the probability that more than 10 persons show up out of the 11 booked. This can be done using the binomial distribution.

The probability of a person showing up for the flight is given as 86.0%, which means the probability of not showing up is 14.0%. Since the events of individuals showing up or not showing up are independent, we can use the binomial distribution to calculate the probability.

Using the binomial distribution formula, we can calculate the probability of 11 or more persons showing up out of 11 bookings. This gives us a probability of 0.3274.

To determine if it is unlikely for such an overbooking to occur, we compare the probability to a significance level of 0.05. If the probability is less than or equal to 0.05, we can consider it unlikely. However, in this case, the probability of 0.3274 is greater than 0.05, indicating that it is not unlikely for such an overbooking to occur.

Therefore, the correct answer is OD. It is not unlikely for such an overbooking to occur, because the probability of the overbooking is greater than 0.05.

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(a) The upper bound for P(X ∈ (µX − 1, µX + 1)) using Chebyshev's inequality is 0.75.

(b) The lower bound for P(X ∈ (µX − 3, µX + 3)) using Chebyshev's inequality is 0.55.

(a) The upper bound for \(P(X \notin (\mu_X - 1, \mu_X + 1))\) using Chebyshev's inequality can be found as follows:

Chebyshev's inequality states that for any random variable \(X\) with mean \(\mu_X\) and standard deviation \(\sigma_X\), the probability that \(X\) deviates from its mean by more than \(k\) standard deviations is at most \(1/k^2\).

In this case, we have the random variable \(X\) with the probability density function (pdf) \(f_X(x) = 2e^{-2x}\) for \(x \geq 0\). The mean \(\mu_X\) of this distribution can be calculated as \(\mu_X = \int_0^\infty xf_X(x) dx\). By integrating, we find \(\mu_X = \frac{1}{2}\).

To calculate the standard deviation \(\sigma_X\), we need to find the variance first. The variance \(\text{Var}(X)\) is given by \(\text{Var}(X) = E[X^2] - (E[X])^2\). Evaluating the integral, we find \(E[X^2] = \frac{3}{4}\).

Thus, the variance is \(\text{Var}(X) = \frac{3}{4} - \left(\frac{1}{2}\right)^2 = \frac{1}{4}\). Taking the square root of the variance gives us the standard deviation \(\sigma_X = \frac{1}{2}\).

Now, applying Chebyshev's inequality with \(k = 1\), we have \(P(X \notin (\mu_X - 1, \mu_X + 1)) \leq \frac{1}{1^2} = 1\).

Therefore, the upper bound for \(P(X \notin (\mu_X - 1, \mu_X + 1))\) is 1.

Chebyshev's inequality is a probabilistic bound that gives us an estimate of how likely a random variable is to deviate from its mean by a certain number of standard deviations. In this case, we used Chebyshev's inequality to find an upper bound for the probability that \(X\) falls outside the interval \((\mu_X - 1, \mu_X + 1)\).

By calculating the mean and standard deviation of the random variable \(X\), we were able to apply Chebyshev's inequality and determine that the probability is bounded above by 1. This means that it is guaranteed that \(X\) will be within the interval \((\mu_X - 1, \mu_X + 1)\) at least 0% of the time.

(b) The lower bound for \(P(X \in (\mu_X - 3, \mu_X + 3))\) using Chebyshev's inequality can be obtained as follows:

By the same reasoning as in part (a), we have the mean \(\mu_X = \frac{1}{2}\) and the standard deviation \(\sigma_X = \frac{1}{2}\) for the random variable \(X\) with pdf \(f_X(x) = 2e^{-2x}\) for \(x \geq 0\).

Applying Chebyshev's inequality with \(k = 3\), we have \(P(X \notin (\mu_X - 3, \mu_X + 3)) \leq \frac{1}{3^2} = \frac{1}{9}\).

To find the lower bound

for \(P(X \in (\mu_X - 3, \mu_X + 3))\), we subtract the upper bound from 1: \(P(X \in (\mu_X - 3, \mu_X + 3)) \geq 1 - \frac{1}{9} = \frac{8}{9}\).

Therefore, the lower bound for \(P(X \in (\mu_X - 3, \mu_X + 3))\) is \(\frac{8}{9}\).

Chebyshev's inequality allows us to establish a lower bound for the probability that a random variable falls within a certain range around its mean. In this case, we used Chebyshev's inequality to find a lower bound for the probability that \(X\) falls within the interval \((\mu_X - 3, \mu_X + 3)\).

By calculating the mean and standard deviation of the random variable \(X\), we applied Chebyshev's inequality with \(k = 3\) to obtain an upper bound for the probability of being outside the interval.

Subtracting this upper bound from 1 gives us the lower bound for the desired probability, which is \(\frac{8}{9}\). This means that at least 88.9% of the time, \(X\) will fall within the interval \((\mu_X - 3, \mu_X + 3)\).

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Answer:

60°

Step-by-step explanation:

∠B=(240-120)/2=120/2=60°

Answer:

x=8

Step-by-step explanation:

The ratio of the sides is 7:14=1:2. So, the ratio of DF:XZ is 1:2. DF=2x-5, and XZ=22. This makes the ratio. 2x-5:22=1:2. That means 2x-5 is half of 22, which is 11. We can solve from there.

Check your work:

The correct formula to find the nth term in a geometric sequence with a first term (a₁) of 3 and a common ratio (r) of 2 is aₙ = 3.2^(n-1).The correct answer is option D.

In a geometric sequence, each term is obtained by multiplying the previous term by a constant ratio. In this case, the first term (a₁) is 3, and the common ratio (r) is 2.

To find the nth term (aₙ), we can use the formula aₙ = a₁ * r^(n-1), where a₁ is the first term and r is the common ratio.

Plugging in the given values, we get aₙ = 3 * 2^(n-1), which simplifies to aₙ = 3.2^(n-1). Therefore, option D is the correct formula.

It is important to provide a plagiarism-free answer and properly attribute any sources used. The explanation provided above is a common mathematical formula for finding the nth term in a geometric sequence and does not require external sources.

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The probable question may be:

Which formula can be used to find the nth term in a geometric sequence where a_{1} = 3 and r=2?

A. a_{n} - 3 + 2(n - 1)

B. a_{2} - 3(n - 1) + 2

C. a_{3} = 3 ^ (n - 1) * 0.2

D. a_{n} = 3.2 ^ (n - 1)

Answer:

B

Step-by-step explanation:

The function reaches the y-axis at the point (0,5).

The asymptote is the line that the function follows but never quite reaches. In this case, the function follows the path of y = 2. However, it never exactly fits the line.

The y-intercept is (0,5) and the asymptote is y = 2. The answer, then, is B.

Good luck ^^

The equation of the asymptote is y = 2 and the coordinate of the y-intercept will be (0, 5). Then the correct option is B.

An asymptote is a line that constantly reaches a given curve, but does not touch at any infinite distance.

The equation of the function is given below.

[tex]\rm f(x) = 3(0.2)^x + 2[/tex]

The asymptote of the function is given as by substituting x as infinity, then the equation of the asymptote will be

[tex]\rm y = 3(0.2)^{\infty} + 2\\\\y = 2[/tex]

Then the y-intercept of the function will be given by substituting y = 0, then the y-intercept will be

y = 3(0.2)⁰ + 2

y = 3 + 2

y = 5

The coordinate of the y-intercept will be (0, 5).

Then the correct option is B.

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Answer:

c. 4

Step-by-step explanation:

yan sagot

Answer:

Step-by-step explanation: