The awnser for this question

Answer:

0.64 = 64% probability that the student passes both subjects.

0.86 = 86% probability that the student passes at least one of the two subjects

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Passing subject A

Event B: Passing subject B

The probability of passing subject A is 0.8.

This means that [tex]P(A) = 0.8[/tex]

If you have passed subject A, the probability of passing subject B is 0.8.

This means that [tex]P(B|A) = 0.8[/tex]

Find the probability that the student passes both subjects?

This is [tex]P(A \cap B)[/tex]. So

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

[tex]P(A \cap B) = P(B|A)P(A) = 0.8*0.8 = 0.64[/tex]

0.64 = 64% probability that the student passes both subjects.

Find the probability that the student passes at least one of the two subjects

This is:

[tex]p = P(A) + P(B) - P(A \cap B)[/tex]

Considering [tex]P(B) = 0.7[/tex], we have that:

[tex]p = P(A) + P(B) - P(A \cap B) = 0.8 + 0.7 - 0.64 = 0.86[/tex]

0.86 = 86% probability that the student passes at least one of the two subjects

===============================================

Work Shown:

A = P*e^(r*t)

A = 47000*e^(0.0526*17)

A = 114,932.799077198

A = 114,932.80

Notes:

Mark's account balance after 17 years would be $114,932.8

[tex]A=Pe^{rt}[/tex]

where,

A = Accrued amount

P = Principal amount

r = interest rate as a decimal

R = interest rate as a percent

r = R/100

t = time in years

For given question,

P = $47000, t = 17 years

R = 5.26%

[tex]\Rightarrow r =\frac{5.26}{100}\\\\\Rightarrow r = 0.0526[/tex]

Using the Continuous Compounding Formula,

[tex]\Rightarrow A=Pe^{rt}\\\\\Rightarrow A=47000\times e^{0.0526\times 17}\\\\\Rightarrow A=114932.8[/tex]

Therefore, Mark's account balance after 17 years would be $114,932.8

Learn more about the Continuous Compounding here:

https://brainly.com/question/24246899

#SPJ2

Answer:

Step-by-step explanation:

[tex]\frac{34-40}{8}= -.75[/tex]

Answer: (f-g)(x) = - 5^x + 3x - 2

Step-by-step explanation:

if f(x) = -5^x - 4 and g(x)= - 3x - 2,find (f-g)(x)

(f-g)(x) = -5^x - 4 - (-3x - 2)

(f-g)(x) = -5^x - 4 + 3x + 2

(f-g)(x) = - 5^x + 3x - 2

Answer:

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

[tex]Competitors = 4[/tex]

[tex]Population = 12000[/tex]

See comment for complete question

Required

The sales

We have:

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

Substitute values for competitors and population

[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]

[tex]Sales = 3.38 + 69.48 + 13.889[/tex]

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

true

9514 1404 393

Answer:

  $4000

Step-by-step explanation:

The problem tells you the relation between commission (c) and stock value (v) is ...

  c = 10 + 0.025v . . . . $10 + .025 of the value traded

We want to find the value (v) for the given commission (c=110). We can put these numbers into the formula and solve for v:

  110 = 10 + 0.025v

  100 = 0.025v . . . . . . . subtract 10

  100/0.025 = v = 4000 . . . . divide by the coefficient of v

The value of stock traded was $4000.

_____

Additional comment

As always, you start by reading and comprehending the problem. You look for what is being asked for, what is being given, and any information that relates one to the other.

Here, the value of stock traded is asked for, the amount of commission is given, and a description of the relation of one to the other is provided. Translate that description to an equation, fill in the given value, and solve for the unknown. (That's what we did above.)

__

You can also work this in your head. The commission is $10 more than some fraction of the amount traded. Since the commission is $110, only $100 of that is the fraction of the amount traded. With a little experience, you can recognize the fraction 0.025 as being 1/40. That means $100 is 1/40 of the value traded, or the value traded is 40 × $100 = $4000.

If z ⁷ = 128i, then there are 7 complex numbers z that satisfy this equation.

[tex]z^7 = 128i = 2^7i = 2^7e^{i\frac\pi2}[/tex]

[tex]\implies z=\sqrt[7]{2^7} e^{i\frac17\left(\frac\pi2+2n\pi\right)}[/tex]

(where n = 0, 1, 2, …, 6)

[tex]\implies z = 2 e^{i\left(\frac\pi{14}+\frac{2n\pi}7\right)}[/tex]

[tex]\displaystyle\implies z = 2 \left(\cos\left(\frac\pi{14}+\frac{2n\pi}7\right)+i\sin\left(\frac\pi{14}+\frac{2n\pi}7\right)\right)[/tex]

Hi there!

[tex]\large\boxed{(x + 2)}[/tex]

x² + 3x + 2

We know that x + 1 is a factor, so:

We must find another number that adds up to 3 when added to 1 and multiplies into 2 with 1. We get:

x + 2

(x + 1)(x + 2)

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

[tex]x(t) = (v_0\cos{\alpha})t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]

In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that [tex]v_0 = 2048, \alpha = 30[/tex].

So

[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]

[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]

(a) After how many seconds will the bullet hit the ground?

It hits the ground when [tex]y(t) = 0[/tex]. So

[tex]1024t - 16t^2 = 0[/tex]

[tex]16t^2 - 1024t = 0[/tex]

[tex]16t(t - 64) = 0[/tex]

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

[tex]x(64) = 1773.62(64) = 113511.7[/tex]

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

[tex]y^{\prime}(t) = 1024 - 32t[/tex]

[tex]1024 - 32t = 0[/tex]

[tex]32t = 1024[/tex]

[tex]t = \frac{1024}{32} = 32[/tex]

At this instant, the height is:

[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]

The maximum height attained by the bullet is of 16,384 feet.

⭕ 17.3

#CARRYONLEARNING

[tex]{hope it helps}}[/tex]

Answer:

c. 5.5 years, 0.51 years

Step-by-step explanation:

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]

Mean of 5.5 years and a standard deviation of 2.1 years.

This means that, for the population, [tex]\mu = 5.5, \sigma = 2.1[/tex]

Random samples of size 17.

This means that [tex]n = 17[/tex]

Use the Central Limit Theorem to find the mean and standard error of the mean of the indicated sampling distribution.

The mean is the same as the mean for the population, that is, 5.5 years.

The standard deviation is:

[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{2.1}{\sqrt{17}} = 0.51[/tex]

This means that the correct answer is given by option c.

Answer:

-6x+15 < 10-5x

x>5

third equation, first graph

Step-by-step explanation:

Answer:

C. 2 and 3 opens down

Step-by-step explanation:

see graph

Answer:

20.76%

Step-by-step explanation:

[tex]33000=8000(1+\frac{i}{4})^{4*7}\\4.125=(1+\frac{i}{4})^{28}\\\sqrt[28]{4.125}=1+\frac{i}{4} \\i= .207648169[/tex]

which rounds to 20.76%

Answer:

About 0.2076 or 20.76%.

Step-by-step explanation:

Recall that compound interest is given by the formula:

[tex]\displaystyle A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]

Where A is the final amount, P is the principal, r is the interest rate, n is the number of times the interest is applied per year, and t is the number of years.

Since Hannah wants to turn an $8,000 investment into $33,000 in seven years compounded quarterly, we want to solve for r given that P = 8000, A = 33000, n = 4, and t = 7. Substitute:

[tex]\displaystyle \left(33000\right)=\left(8000\right)\left(1+\frac{r}{4}\right)^{(4)(7)}[/tex]

Simplify and divide both sides by 8000:

[tex]\displaystyle \frac{33}{8}=\left(1+\frac{r}{4}\right)^{28}[/tex]

Raise both sides to the 1/28th power:

[tex]\displaystyle \left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}= 1+\frac{r}{4}[/tex]

Solve for r. Hence:

[tex]\displaystyle r= 4\left(\left(\frac{33}{8}\right)^{{}^{1}\! / \! {}_{28}}-1\right)[/tex]

Use a calculator. Hence:

[tex]r=0.2076...\approx 0.2076[/tex]

So, the quarterly rate of interest must be 0.2076, or about 20.76%.

Answer: A

Step-by-step explanation:

The main parent functions are x, and x raised to the power of something (examples: [tex]x^2, x^3, x^4[/tex], etc)

Answer:

4,a

5.d

6.c

plz mark me as brainliest

Step-by-step explanation:

Answer:

1. A

2. C

3. A

Step-by-step explanation:

all the explanations are In the image above

Answer:

One larger, more stable nucleus

Answer:

You would expect 807 babies  to weigh between 3 and 6 pounds.

Step-by-step explanation:

We are given that

Mean,[tex]\mu=5.4[/tex]pounds

Standard deviation,[tex]\sigma=1.8[/tex]pounds

n=1500

We have to find how  many would you expect to weigh between 3 and 6 pounds.

The weights for newborn babies is approximately normally distributed.

Now,

[tex]P(3<x<6)=P(\frac{3-5.4}{1.8}<\frac{x-\mu}{\sigma}<\frac{6-5.4}{1.8})[/tex]

[tex]=P(-1.33<Z<0.33)[/tex]

[tex]P(3<x<6)=P(Z<0.33)-P(Z<-1.33)[/tex]

[tex]P(3<x<6)=0.62930-0.09176[/tex]

[tex]P(3<x<6)=0.538[/tex]

Number of newborn  babies expect to weigh between 3 and 6 pounds

=[tex]1500\times 0.538=807[/tex]

Answer:

3x² + 13x + 4

Step-by-step explanation:

I did the steps in my book

Answer:

15

Hope this helped ^^

2[30          5[45

 3[15           3[9

  5[5             3[3

     [1               [1

    30=2*3*5*1

     45=5*3*3*1    HCF= 3*1=3

hope its helps you

keep smiling be happy stay safe

Division yields

[tex]\dfrac{x^4+7}{x^3+2x} = x-\dfrac{2x^2-7}{x^3+2x}[/tex]

Now for partial fractions: you're looking for constants a, b, and c such that

[tex]\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}[/tex]

[tex]\implies 2x^2 - 7 = a(x^2+2) + (bx+c)x = (a+b)x^2+cx + 2a[/tex]

which gives a + b = 2, c = 0, and 2a = -7, so that a = -7/2 and b = 11/2. Then

[tex]\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}[/tex]

Now, in the integral we get

[tex]\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx[/tex]

The first two terms are trivial to integrate. For the third, substitute y = x ² + 2 and dy = 2x dx to get

[tex]\displaystyle \int x\,\mathrm dx + \frac72\int\frac{\mathrm dx}x - \frac{11}4 \int\frac{\mathrm dy}y \\\\ =\displaystyle \frac{x^2}2+\frac72\ln|x|-\frac{11}4\ln|y| + C \\\\ =\displaystyle \boxed{\frac{x^2}2 + \frac72\ln|x| - \frac{11}4 \ln(x^2+2) + C}[/tex]

Step 1: Find the circumference of the circle

Formula for circumference: C = 2 * pi * r

C = 2 * pi * 27

C = 54pi

Step 2: Find the length of the desired arc

We are only looking for 20 degrees out of 360 degrees, therefore we can multiply our circumference by 20/360.

20/360 * 54pi = 3pi units

Hope this helps!

Answer:

15

Step-by-step explanation:

3+7+5

PLEASE BRAINLIESTTTTTTTTT

Answer:

hope it will be helpful to you.....

Answer:

maybe 10000

Step-by-step explanation:

Answer:

9007.35

Step-by-step explanation:

First find the effective rate: .06/12= .005

let x= amount

[tex]x=100\frac{1-(1+.005)^{-12*10}}{.005}\\100*\frac{1-.549632733}{.005}\\9007.345333[/tex]

Answer:

a=27.807

Step-by-step explanation:

Its simple, set it up for law of sine which is sinA/a = sinB/b

Sin108/a = Sin20/10

9514 1404 393

Answer:

  see below

Step-by-step explanation:

Put the x-value in the equation and do the arithmetic.

For example, ...

  for x = -5,

  y = -10(-5) +3 = 50 +3 = 53

Answer:

1. 766,536cm^3

2. 29,680,948cm^3

3. 41,620.8cm^3

Step-by-step explanation:

1. 123×82 = 10,086 10,086×76 = 766,536

2. 422×278 = 117,316 117,316×253 = 29,680,948

3. 87×2.3 = 200.1 200.1×208 = 41,620.8

Hope this helps! :)