Can someone just check my answers please? Please let me know which questions are wrong. Thank you for your time.

Answer:

Yes, P(E1)=P(E2)

Step-by-step explanation:

We are given that

Number of dice=3

Total outcomes of 1 die=6

Therefore,

Total number of outcomes =[tex]6^3=216[/tex]

E1={{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}

E2={(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}

We have to show that E1 and E2 have the same probability P(E1) = P(E2).

Probability, [tex]P(E)=\frac{Favorable\;outcomes}{Total\;outcomes}[/tex]

Using the formula

[tex]P(E_1)=\frac{6}{216}[/tex]

[tex]P(E_1)=0.0278[/tex]

[tex]P(E_2)=\frac{6}{216}[/tex]

[tex]P(E_2)=0.0278[/tex]

Hence, P(E1)=P(E2)

Answer:

8x +15

Step-by-step explanation:

f(x) = 10 + 2x and g(x) = 6x + 5

(f+ g)(x) =  10 + 2x + 6x + 5

Combine like terms

              = 8x +15

Answer:

8x+15

Step-by-step explanation:

(f+g)(x) = f(x)+g(x)

= (10+2x) + (6x+5)

= 8x+15

hope it helped, please mark me brainliest.

Answer:

The probability that Swallows will win the trophy is 0.8064

The probability that Rucks will win the trophy is 0.1936

Step-by-step explanation:

For each game, there are only two possible outcomes. Either the Swallows win, or they do not. The probability of them winning a game is independent of any other game, which means that the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Probability the Swallows wins is 0.56

This means that [tex]p = 0.56[/tex]

2 games:

This means that [tex]n = 2[/tex]

The probability that Swallows will win the trophy is

Probability they win at least one game, so:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.56)^{0}.(0.44)^{2} = 0.1936[/tex]

Then

[tex]P(X \geq 1) = 1 - 0.1936 = 0.8064[/tex]

0.8064 = 80.64% probability the Swallows win the trophy and 0.1936 probability that the Rucks win the trophy.

You do X2 + 15 and that will be your answer.

By the way, the 2 is a power and is meant to be smaller on top of the X.

Answer:

2x + 2y = 4 and 4x + 4y = 16

Step-by-step explanation:

For two lines to be parallel, they must have the same slope.

To determine the correct answer to the question, we shall determine the slope of each equation in the given options to see which have the same slope. This can be obtained as follow:

1st option:

3x + 2y = 45 and 8x + 4y = 135

We shall rearrange the above equations to look like y = mx + c

NOTE: m is the slope.

3x + 2y = 45

rearrange

2y = –3x + 45

Divide both side by 2

y = –3x/2 + 45/2

Slope (m) = –3/2

8x + 4y = 135

Rearrange

4y = –8x + 135

Divide both side by 4

y = –8x/4 + 135/4

Slope (m) = –8/4 = –2

The two equation has different slopes. Thus, they are not parallel.

2nd option:

x + y = 25 and 2x + y = 15

x + y = 25

Rearrange

y = –x + 25

Slope (m) = –1

2x + y = 15

Rearrange

y = –2x + 15

Slope (m) = –2

The two equations has different slopes. Thus, they are not parallel.

3rd option:

2x + 2y = 50 and 4x + 2y = 90

2x + 2y = 50

Rearrange

2y = –2x + 50

Divide both side by 2

y = –2x/2 + 50/2

Slope (m) = –2/2 = –1

4x + 2y = 90

Rearrange

2y = –4x + 90

Divide both side by 2

y = –4x/2 + 90/2

Slope (m) = –4/2 = –2

The two equations has different slopes. Thus, they are not parallel.

4th option:

2x + 2y = 4 and 4x + 4y = 16

2x + 2y = 4

Rearrange

2y = –2x + 4

Divide both side by 2

y = –2x/2 + 4/2

Slope (m) = –2/2 = –1

4x + 4y = 16

Rearrange

4y = –4x + 16

Divide both side by 4

y = –4x/4 + 16/4

Slope (m) = –4/4 = –1

The two equations have the same slopes. Thus, they are parallel.

Given: Given that for 16 brownies we need

Butter- [tex]\frac{2}{3}[/tex] cups

unsweetened chocolate-5 ounces

sugar-1-1/2 cup

vanilla-2 teaspoons

eggs-2

flour- 1 cup

To find: The amount of ingredients to make 6 brownies.

Solution: The amount we need to make 6 brownies is,

Butter

[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]

unsweetened chocolate

[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces

sugar-0.5625 cup

vanilla-[tex]\frac{12}{16}[/tex]teaspoons

eggs-[tex]\frac{12}{16}[/tex]

flour- [tex]\frac{6}{16}[/tex] cup

Answer:

a=1, b=9, c=-2, d=4

Step-by-step explanation:

Answer:

ok so if she gets paid 372 we just multiply this by 4 since there's 4 weeks in a month then we multiply by 4 so

372*4*12=17856

now we just multiply 831.33 by 2 since she is paid semimonthly and we multiply by 12

831.33*2*12=19951.92

now we just subtract

19951.92-17856=2095.92

so she gets paid 2095.92 more dollars per year

Hope This Helps!!!

Answer:

D. y =

Step-by-step explanation:

The solutions to this graph (meaning when y equals 0 or when the graph crosses the x-axis) are 4 and 5.

The only answer choice that has the solutions 4 and 5 when you factor it out is D.

Here's the proof:

[tex]x^{2} -9x + 20[/tex]

Factors of 20: - 5 & -4

Sums that add up to -9: -5 + (-4)

[tex]x^{2} -4x-5x+20[/tex]

(factor the first two terms and the last two terms separately)

[tex](x^{2}-4x)(-5x+20)[/tex]

[tex]x(x-4) -5(x-4)[/tex]

(x - 5) (x - 4)

Hope it helps (●'◡'●)

Answer:

I don't really understand the question

Step-by-step explanation:

c

Answer:

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex] --- set builder

[tex][-21,\infty)[/tex] --- interval notation

Step-by-step explanation:

Given

[tex]-3a - 15 \le -2a + 6[/tex]

Required

Solve

Collect like terms

[tex]-3a + 2a \le 15 + 6[/tex]

[tex]-a \le 21[/tex]

Divide by -1

[tex]a \ge - 21[/tex]

Rewrite as:

[tex]-21 \le a[/tex]

Using set builder

[tex]\{a[/tex] ∈ [tex]R\ -21 \le a \le \infty \}[/tex]

Using interval notation, we have:

[tex][-21,\infty)[/tex]

Step-by-step explanation:

each point should be at a 2. the center is 0,0

Answer:

It will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

Step-by-step explanation:

Given that a crew clears brush from 1/3 acre of land in 2 days, to determine how long will it take the same crew to clear the entire plot of 2 1/2 acres, the following calculation must be performed:

1/3 = 0.333

1/2 = 0.5

0.333 = 2

2.5 = X

2.5 x 2 / 0.333 = X

15 = X

Therefore, it will take 15 days for the same crew to clear the entire plot of 2 1/2 acres.

Answer:

i think that $19980 is the answer

Step-by-step explanation:

i hope it will help u

9514 1404 393

Answer:

  P' = (3, -5)

Step-by-step explanation:

Rotation 180° about the origin is the same as reflection across the origin. The transformation is given by ...

  (x, y) ⇒ (-x, -y) . . . . . . the signs of the coordinates are both changed

  P(-3, 5) ⇒ P'(3, -5)

Answer:

26244π in³

Step-by-step explanation:

Applying,

Voluem of a sphere

V = 4/3(πr³).......... Equation 1

Where r = radius of the sphere, π = pie

From the diagram,

Given: r = 54/2  = 27 in

Substitute these value in equation 1

V = 4/3(27³)(π)

V = 26244π in³

Hence the volume of the figure expressed in terms of π is 26244π in³

Answer:

45°

Step-by-step explanation:

<lmk=90°

angles in a triangle add up to 180

45+90+<o=180

<o=180-135

<o=45

Answer:

∠ O = 45°

Step-by-step explanation:

The angle between the tangent and the radius at the point of contact is 90°

The sum of the 3 angles in Δ OML is 180° , then

∠ O = 180° - (90 + 45)° = 180° - 135° = 45°

Answer:

B. -infinity < x < infinity

Step-by-step explanation:

Since it's linear and kind of horizontal, it stretches to infinity on both sides (indicated by arrows on both sides of the line.

9514 1404 393

Answer:

   C.  y = 1/2x +2

Step-by-step explanation:

The magnitude of the slope is the measure of "steepness." The slope is the coefficient of x in these equations. Here those values are ...

  4, 3/4, 1/2, 10

Of these, 1/2 is the smallest (least steep). 1/2 is the slope in the equation ...

  y = 1/2x +2

Answer:

hi, see mate the third angle is not in the photo, please upload another one

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

[tex]a = 2i + j -3k[/tex]

[tex]b = 3i - 2j -k[/tex]

Required

The angle between them

The cosine of the angle between them is:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

First, calculate a.b

[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]

Multiply the coefficients of like terms

[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]

[tex]a \cdot b =7[/tex]

Next, calculate |a| and |b|

[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]

[tex]|a| = \sqrt{14[/tex]

[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]

[tex]|b| = \sqrt{14}[/tex]

Recall that:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

This gives:

[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]

[tex]\cos(\theta) = \frac{7}{14}[/tex]

[tex]\cos(\theta) = 0.5[/tex]

Take arccos of both sides

[tex]\theta =\cos^{-1}(0.5)[/tex]

[tex]\theta =60^o[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

One way to write the relationship between time, speed, and distance is ...

  time = distance/speed

For the first part of the trip, the time is ...

  t1 = 240/r

For the second part of the trip, the time is ...

  t2 = 72/(r+10)

The total time is 6 hours, so we have ...

  t1 +t2 = 6

  240/r +72/(r+10) = 6

We can simplify this a bit by multiplying by (r)(r+10)/6 to get ...

   40(r+10) +12(r) = r(r+10)

  r² -42r -400 = 0 . . . . . . . . subtract the left side and collect terms

  (r -50)(r +8) = 0 . . . . . . . . factor

  r = 50 . . . . . the positive solution of interest.

The two average speeds were 50 mph and 60 mph.

Answer:

upper bound for the error, | Error |  ≤ 0.0032

Step-by-step explanation:

Given the data in the question;

[tex]e^{0.4[/tex] < e < 3

Using Taylor's Error bound formula

| Error | ≤ ( m / ( N + 1 )! ) [tex]| x-a |^{N+1[/tex]

where m = [tex]| f^{N+1 }(x) |[/tex]

so we have

| Error |  ≤ ( 3 / ( 3 + 1 )! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 4! ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 3 / 24 ) [tex]|[/tex] -0.4 [tex]|[/tex]⁴

| Error |  ≤ ( 0.125 ) [tex]|[/tex] -0.0256 [tex]|[/tex]

| Error |  ≤ ( 0.125 ) 0.0256

| Error |  ≤ 0.0032

Therefore, upper bound for the error, | Error |  ≤ 0.0032

NUE is 30° LUN is 60° EUS is 30° LUE is 90° LUS is 120°

Step-by-step explanation:

NUE is given

LUN was from the 90° angle LUE but just minus 30°

EUS is honestly a guess :/

LUE is obviously 90° as we used it earlier

LUS was the 90° plus the EUS

Step-by-step explanation:

[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]

Answer:

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 49% of American singers are Grammy award winners.

This means that [tex]p = 0.49[/tex]

Sample of size 502

This means that [tex]n = 502[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.49[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.49*0.51}{502}} = 0.0223[/tex]

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%?

Proportion below 49% - 4% = 45% or above 49% + 4% = 53%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 45%

p-value of Z when X = 0.45. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.45 - 0.49}{0.0223}[/tex]

[tex]Z = -1.79[/tex]

[tex]Z = -1.79[/tex] has a p-value of 0.0363.

2*0.0363 = 0.0726

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Answer:

what is the question

pls mark me as brainlist

Thank you for the points

Answer:

212.06

Step-by-step explanation:

can't really explain since the formula is fricking long but trust me that's uts 212.06 in²