Solve 2(x - 1) + 3 = x - 3(x + 1) (make sure to type the number only)

Answer: a = 9, b = 48, c = -1

Step-by-step explanation:

"a" represents the points you receive if an Ace is picked.  It is given that you get 9 points ----> a = 9

"b" represents the number of cards that are Not an Ace.  4 cards in the deck are Aces so 52 - 4 = 48 cards are Not an Ace -----> b = 48

"c" represents the points you receive if Not an Ace is picked.  It is given that you lose 1 point ----> c = -1

Answer:

Here is the rest of the page

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]

[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;

[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]

Hence, the value of the logarithm expression is 24

Answer:

see below

Step-by-step explanation:

Scientific notation is a * 10 ^b

a must be a number between 1 ( including 1 ) and less than 10

12 is greater than 10 so it is not scientific notation

Answer:

25 : 63 and 63 : 25

Step-by-step explanation:

This is a complete question

The table shows the educational attainment of the population of Country X, ages 25 and over. Use the data in the table, expressed in millions, to solve the problem. of 10 questions ge 1: Ages 25 and Over, in Miltions 4 Years igh College 4 Years High School (Less than College School Only 4years) Cor Moce) Total Male 29 19 25 89 Female 11 28 23 Total 2 57 42 50 [176 Find the odds in favor and the odds against a randomty selected person from Country X.age 25 and over, with the stated amount of education. four years (or more) of college 21:67, 67:21 63:88, 88:63 25:63, 63:25 25:88, 88:25

According to the question, the relevant data provided in the question for the solution is as follows

Four years or more of college

Number of students = 50

Total = 176 students

Number of students does not belong = 126

So odds in favor is

= 50 : 126

= 25 : 63

And automatically out against the favor is 63 : 25

Answer:

z = 83/( -c+6-t)

Step-by-step explanation:

-cz + 6z = tz + 83

Subtract tz from each side

-cz + 6z -tz= tz-tz + 83

-cz + 6z - tz = 83

Factor out z

z( -c+6-t) = 83

Divide each side by ( -c+6-t)

z( -c+6-t)/( -c+6-t)  = 83/( -c+6-t)

z = 83/( -c+6-t)

Answer:

1/8

Step-by-step explanation:

3/8-1/8-1/8=1/8

Answer:

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

Step-by-step explanation:

Given that :

Mean  = 265

standard deviation = 14

The formula for calculating the z score is [tex]z = \dfrac{x -\mu}{\sigma}[/tex]

x = μ + σz

At middle of 50% i.e 0.50

The critical value for [tex]z_{\alpha/2} = z_{0.50/2}[/tex]

From standard normal table

[tex]z_{0.25}=[/tex] + 0.67  or -0.67  

So; when z = -0.67

x = μ + σz

x = 265 + 14(-0.67)

x = 265 -9.38

x = 255.62

when z = +0.67

x = μ + σz

x = 265 + 14 (0.67)

x = 265 + 9.38

x = 274.38

the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days

(a) Take the Laplace transform of both sides:

[tex]2y''(t)+ty'(t)-2y(t)=14[/tex]

[tex]\implies 2(s^2Y(s)-sy(0)-y'(0))-(Y(s)+sY'(s))-2Y(s)=\dfrac{14}s[/tex]

where the transform of [tex]ty'(t)[/tex] comes from

[tex]L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)[/tex]

This yields the linear ODE,

[tex]-sY'(s)+(2s^2-3)Y(s)=\dfrac{14}s[/tex]

Divides both sides by [tex]-s[/tex]:

[tex]Y'(s)+\dfrac{3-2s^2}sY(s)=-\dfrac{14}{s^2}[/tex]

Find the integrating factor:

[tex]\displaystyle\int\frac{3-2s^2}s\,\mathrm ds=3\ln|s|-s^2+C[/tex]

Multiply both sides of the ODE by [tex]e^{3\ln|s|-s^2}=s^3e^{-s^2}[/tex]:

[tex]s^3e^{-s^2}Y'(s)+(3s^2-2s^4)e^{-s^2}Y(s)=-14se^{-s^2}[/tex]

The left side condenses into the derivative of a product:

[tex]\left(s^3e^{-s^2}Y(s)\right)'=-14se^{-s^2}[/tex]

Integrate both sides and solve for [tex]Y(s)[/tex]:

[tex]s^3e^{-s^2}Y(s)=7e^{-s^2}+C[/tex]

[tex]Y(s)=\dfrac{7+Ce^{s^2}}{s^3}[/tex]

(b) Taking the inverse transform of both sides gives

[tex]y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right][/tex]

I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that [tex]\frac{7t^2}2[/tex] is one solution to the original ODE.

[tex]y(t)=\dfrac{7t^2}2\implies y'(t)=7t\implies y''(t)=7[/tex]

Substitute these into the ODE to see everything checks out:

[tex]2\cdot7+t\cdot7t-2\cdot\dfrac{7t^2}2=14[/tex]

Answer:

6.02

six point zero two

Step-by-step explanation:

Answer:

602 / 100= 6,02

Step-by-step explanation:

602 to divide 100 = 6,02

Step-by-step explanation:

Using Sine Rule

[tex] \frac{ \sin(a) }{ |a| } = \frac{ \sin(b) }{ |b| } = \frac{ \sin(c) }{ |c| } [/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(38) }{a} [/tex]

[tex]a = \frac{5( \sin(38))}{ \sin(42) } [/tex]

[tex]a = 4.6[/tex]

[tex] \frac{ \sin(42) }{5} = \frac{ \sin(100) }{b} [/tex]

[tex]b= \frac{5( \sin(100))}{ \sin(42) } [/tex]

[tex]b = 7.4[/tex]

Answer:

87; 2%

Step-by-step explanation:

An exponential growth model is defined as :

F(x) = A( 1 + r)^x

Where;

A = Initial amount,

r = rate of increase

x = time

Comparing the exponential growth function with the exponential growth model given;

f(x)=87(1.02)^x

A = 87 = Initial amount

The growth rate of the model expressed as a percentage :

Taking :

(1 + r) = 1.02

1 + r = 1.02

r = 1.02 - 1

r = 0.02

Expressing r as a percentage :

0.02 * 100% = 2%

Answer: 669

Step-by-step explanation:

Given, In a Gallup poll of randomly selected​ adults, 66% said that they worry about identity theft.

i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66

Sample size : n= 1013

Then , Mean for the sampling distribution of sample proportion  = np

= (1013) × (0.66)

= 668.58 ≈ 669  [Round to the nearest whole number]

Hence, the mean of those who do not worry about identify theft is closest to​ 669 .

Answer:

The first picture's answer would be (6, 21)

Step-by-step explanation:

You have to find the points on the 8th and the 9th day, and then you would add them together, and then divide by two finding the average, which would be 24 and 18, so when added, you get 42, divided by 2 you get 21. You look on the graph for the point with 21, and you find it is on 6.

Answer:

Step-by-step explanation:

(f/g) = (3 - 2x ) / (1/x + 5) You could go to the trouble to simplify all of this, but the easiest way is to just put in the 8 where you see an x

(f/g)8 = (3 - 2*8) / (1/8 + 5)

(f/g)/8 = (3 - 16 / (5 1/8)          1/8 = 0.125

(f/g) 8 = - 13 / ( 5.125)

(f/g)8 = - 2.54

Answer:

  his path

Step-by-step explanation:

In order to determine the total distance driven from one place to another, you need to know the path taken.

Answer:

In this question, we shall be accepting the null hypothesis H0 since the critical value is greater than the test statistic value

Step-by-step explanation:

Here in this question, we want to make a conclusion about the null hypothesis H0.

To make or give the correct conclusion about the null hypothesis in this case, we shall need to compare the absolute value of the test statistic used against the value of the critical value.

Hence, we draw a conclusion if the test statistic is larger or smaller than the critical value.

From the value given in the question, we can see that the test statistic given as 1.68 is lesser in value compared to the critical value given as 1.96.

In this kind of case, the conclusion that we shall be drawing is that we will accept the null hypothesis H0 and reject the alternative hypothesis

Answer:

  no

Step-by-step explanation:

If any x-value is repeated, the relation is not a function. Both x=4 and x=9 are repeated values, so this relation is not a function.

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▹ Answer

(-39/35, 9/7)

▹ Step-by-Step Explanation

5y + 2y = 9

-5x - 2y = 3

Solve the equation:

y = 9/7

-5x - 2y = 3

Substitute the value of y:

-5x - 2 * 9/7 = 3

x = -39/35

(x, y) = (-39/35, 9/7)

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

To solve this system by addition, we start by adding both of our equations together but notice that the x terms and the y terms cancel out.

This leaves us with 0 on the left side and on the right side,

9 + 13 = 12 so we are left with the equation 0 = 12.

Since 0 = 12 is a false statement, this means that

there is no solution to our system of equations.

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

Answer:

108.

Step-by-step explanation:

-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d)  = 5.

The 24th term = a1 + (24 - 1)d

=  -7 + 23 * 5

= -7 + 115

= 108.

Answer:

Change due is 3.50

Step-by-step explanation:

20.00-16.50 is 3.50

Answer: $3.50

Step-by-step explanation:

You subtract 20 from 16.50.

Answer:

claire has to leave at 3:50 from her house.

Answer:

She needs to leave by 3:50 to get there on time.

Step-by-step explanation:

4:15 - 0:25 = 3:50.

Answer:

ST, RS, RT

Step-by-step explanation:

Angles of a triangle add up to 180°.

2x + 11° + 3x + 23° + x + 42° = 180°

6x + 76° = 180°

x = 17⅓

m∠R = 2x+11° = 45⅔°

m∠S = 3x+23° = 75°

m∠T = x+42° = 59⅓°

The shortest side is opposite the smallest angle, and the longest side is opposite the largest angle.

ST, RS, RT

We have 26 letters and 3 slots to fill. We can reuse a letter if it has been picked, so we have 26^3 = 26*26*26 = 17,576 different three letter "words". I put that in quotes because a lot of the words aren't actual words, but more just a sequence of letters.

Answer:

Step-by-step explanation:

Hello, please consider the following.

For x > 1, we can apply Pythagoras theorem as below.

[tex]\text{Let's estimate this sum of two squares.} \\\\(2x)^2+(x^2-1)^2=4x^2+x^4-2x^2+1=x^4+2x^2+1\\\\\text{Let's estimate this square, now.} \\\\(x^2+1)^2=x^4+2x^2+1\\\\\text{The two expressions are equal, meaning.} \\\\(2x)^2+(x^2-1)^2=(x^2+1)^2\\\\\text{Using Pythagoras' theorem, we can say that this is a right triangle.}[/tex]

Thank you

the graph has 12 segments so angle enclosed by each segment is [tex] {2\pi\over 12}=\frac{\pi}6[/tex]

anti-clockwise is taken as positive, so if you want positive q, you need to rotate 8 segments [tex] q=8\frac,{\pi}6=\frac{4\pi}3 [/tex] , and and 8 circles or units so r=8

and for a negative angle, you need to rotate clockwise

Which is 4 segments from the horizontal line. so [tex]q=-\frac{2\pi}3[/tex] and r will be same, 8 units.

[not sure about -r so I won't include it in answer]

Answer:

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Step-by-step explanation:

For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.

So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,

( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.

( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120

Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.

( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )

_________________________________

So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,

Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )

Answer:

csctheta= [tex]\frac{\sqrt{13} }{3}[/tex]

Step-by-step explanation:

answer is provided on top

The value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]. Cosec is found as the ratio of the hypotenuse and the perpendicular.

The field of mathematics is concerned with the relationships between triangles' sides and angles, as well as the related functions of any angle

The given data in the problem is;

[tex]\rm cot \theta = \frac{2}{3}[/tex]

The [tex]cot \theta[/tex] is found as;

[tex]\rm cot \theta = \frac{B}{P} \\\\ \rm cot \theta = \frac{2}{3} \\\\ B=2 \\\\ P=3 \\\\[/tex]

From the phythogorous theorem;

[tex]\rm H=\sqrt{P^2+B^2} \\\\ \rm H=\sqrt{2^2+3^2} \\\\ H=\sqrt{13} \\\\[/tex]

The value of the cosec is found as;

[tex]\rm cosec \theta = \frac{H}{P} \\\ \rm cosec \theta = \frac{\sqrt{13} }{3}[/tex]

Hence the value of the [tex]\rm cosec \theta = \frac{\sqrt{13} }{3}[/tex].

To learn more about the trigonometry refer to the link;

https://brainly.com/question/26719838

Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

Answer:

a) 0.36

b) 0.3

c) Yes

Step-by-step explanation:

Given:

Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9

Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6

Period considered = 30 minutes

a)

Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:

As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.

So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is

P(A) = P(Delay) * P(Delay) =  0.6 * 0.6 = 0.36

b)

Let B be the probability that in the long run the traffic will not be in the delay state.

This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.

Let C be the probability of one period in Delay state given that preceding period in No-delay state :

P(C) =  1 - P(No_Delay)

        = 1 - 0.9

P(C) = 0.1

Now using P(C) and P(Delay) we can compute P(B) as:

P(B) = 1 - (P(Delay) + P(C))

      = 1 - ( 0.6 + 0.10 )

      = 1 - 0.7

P(B) = 0.3

c)

Yes this assumption should be questioned for this traffic problem because it implies that  traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).