The numbers 5, 6, 7, and 8 are randomly arranged to create a four-digit number. What is the probability that the number formed is not divisible by 4?

Answer:

Step-by-step explanation:

Given f(x) = 2x³ +x² +ax +b has a factor (x -2) and a remainder of 18 when divided by (x -1), you want to know a, b, and the factored form of f(x).

If (x -2) is a factor, then the value of f(2) is zero:

  f(2) = 2·2³ +2² +2a +b = 0

  2a +b = -20 . . . . . . . subtract 20

If the remainder from division by (x +1) is 18, then f(-1) is 18:

  f(-1) = 2·(-1)³ +(-1)² +a·(-1) +b = 18

  -a +b = 19 . . . . . . . . . . add 1

Subtracting the second equation from the first gives ...

  (2a +b) -(-a +b) = (-20) -(19)

  3a = -39

  a = -13

  b = 19 +a = 6

The values of 'a' and 'b' are -13 and 6, respectively.

We can find the quadratic factor using synthetic division, given one root is x=2. The tableau for that is ...

  \(\begin{array}{c|cccc}2&2&1&-13&6\\&&4&10&-6\\\cline{1-5}&2&5&-3&0\end{array}\)

The remainder is 0, as expected, and the quadratic factor of f(x) is 2x² +5x -3. Now, we know f(x) = (x -2)(2x² +5x -3).

To factor the quadratic, we need to find factors of (2)(-3) = -6 that have a sum of 5. Those would be 6 and -1. This lets us factor the quadratic as ...

  2x² +5x -3 = (2x +6)(2x -1)/2 = (x +3)(2x -1)

The factored form of f(x) is ...

  f(x) = (2x -1)(x -2)(x +3)

Answer:

71

Step-by-step explanation:

Answer:

3: အားနည်းချက်ကို YC တလျှောက်တွင် XYZ Translate ။ ထောင့် X'YA ဖြင့် C ပတ်လည် X'YZ ကိုလှည့်ပါ။ CB ရှိ“ X” Y“ Z” ကိုရောင်ပြန်ဟပ်ပါ။

Answer:

Translate XYZ using directed line segment YC. Rotate X'Y'Z' using C as the center so that X' coincides with B. Reflect X"Y"Z" across line CB.

Step-by-step explanation:

Its correct because I just got the answer right on the assignment

Hope this helps! :)

Answer:

x = 6

y = -9

Step-by-step explanation:

Answer:

x=10 and y=-10

Step-by-step explanation:

-8x-9y=10

4x-5y=14

put each equation in brackets and get the coefficient of y in the first equation , multiply it with everything in the second equation .Get also the coefficient of y in the second equation and multiply it with everything in the first equation.

-5(-8x-9y=10)

-9(4x-5y=14)

the subtract the first equation from the second equation after multiplying.

40x+45y=-50

-

-36x+45y=-90

4x=40

x=10

Now get any equation from the two equations and find the value of y.

-8x-9y=10

-8*10-9y=10

-9y=10+80

-9y=90

y= -10

The sum between angles a° and c° gives 300°.

Here we want to find the sum of the two angles a° and c°.

First, we can see that a is a plane angle, then:

a° = 180°

We also can see that c° plus the angle at its left which is 60° should be a plane angle, then we can write:

60° + c° = 180°

c° = 180° - 60°

c° = 120°

Now we know the values of c°  and a°, then the sum will give:

a° + c° = 120° + 180° = 300°

That is the answer.

Learn more about adding angles at:

https://brainly.com/question/25716982

#SPJ1

Answer:

I = 4 × 0.25 × 5.5 = 5.5

I = $ 5.50

Step-by-step explanation:

Answer:

You would pay $3.17 (rounded since this is money)

The first derivative of the function `g(u) = u(2u - 3)^3` is `g'(u) = 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u) = 12(u - 1)(2u - 3)^2`.

Given function: `g(u)

= u(2u - 3)^3`

To find the first derivative of the given function, we use the product rule of differentiation.`g(u)

= u(2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g'(u)

= u * d/dx[(2u - 3)^3] + (2u - 3)^3 * d/dx[u]`

Using the chain rule of differentiation, we have:

`g'(u)

= u * 3(2u - 3)^2 * 2 + (2u - 3)^3 * 1`

Simplifying:

`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

To find the second derivative, we differentiate the obtained expression for

`g'(u)`:`g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`

Differentiating both sides with respect to u, we get:

`g''(u)

= d/dx[6u(2u - 3)^2] + d/dx[(2u - 3)^3]`

Using the product rule and chain rule of differentiation, we have:

`g''(u)

= 6[(2u - 3)^2] + 12u(2u - 3)(2) + 3[(2u - 3)^2]`

Simplifying:

`g''(u)

= 12(u - 1)(2u - 3)^2`.

The first derivative of the function `g(u)

= u(2u - 3)^3` is `g'(u)

= 6u(2u - 3)^2 + (2u - 3)^3`. The second derivative of the function is `g''(u)

= 12(u - 1)(2u - 3)^2`.

To know more about derivative visit:

https://brainly.com/question/29144258

#SPJ11

The first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

First, let's find the first derivative:

g'(u) = (2u - 3)³ * d(u)/du + u * d/dx[(2u - 3)³]

Using the chain rule, we can differentiate (2u - 3)³ and u as follows:

d(u)/du = 1

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

Plugging these values back into the equation for g'(u), we have:

g'(u) = (2u - 3)² + u * 3(2u - 3)² * 2

= (2u - 3)³ + 6u(2u - 3)²

Simplifying the expression, we have:

g'(u) = (2u - 3)³ + 6u(2u - 3)²

Now, let's find the second derivative:

g''(u) = d/dx[(2u - 3)³ + 6u(2u - 3)²]

Using the chain rule and product rule, we can differentiate each term:

d/dx[(2u - 3)³] = 3(2u - 3)² * d(2u - 3)/du

= 3(2u - 3)² * 2

d/dx[6u(2u - 3)²] = 6(2u - 3)² + 6u * d/dx[(2u - 3)²]

= 6(2u - 3)² + 6u * 2(2u - 3)

Plugging these values back into the equation for g''(u), we have:

g''(u) = 3(2u - 3)² * 2 + 6(2u - 3)² + 6u * 2(2u - 3)

= 6(2u - 3)² + 6(2u - 3)² + 12u(2u - 3)

= 12(2u - 3)² + 12u(2u - 3)

Simplifying the expression further, we have:

g''(u) = 12(2u - 3)² + 12u(2u - 3)

Therefore, the first derivative of g(u) is g'(u) = (2u - 3)³ + 6u(2u - 3)², and the second derivative is g''(u) = 12(2u - 3)² + 12u(2u - 3).

Learn more on differentiation : https://brainly.com/question/25081524

#SPJ4

The possible number of cupcakes is less than or equal to 23

let

The inequality:

2k ≤ 46

divide both sides by 2

k ≤ 46 / 2

k ≤ 23

Therefore, the possible number of cupcakes is less than or equal to 23

Learn more about inequality:

https://brainly.com/question/25275758

\(( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2=\cfrac{1-\cos(\theta )}{1+\cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ \csc(\theta )-\cot(\theta ) ~~ )^2\implies \csc^2(\theta )-2\csc(\theta )\cot(\theta )+\cot^2(\theta ) \\\\\\ \cfrac{1^2}{\sin^2(\theta )}-2\cdot \cfrac{1}{\sin(\theta )}\cdot \cfrac{\cos(\theta )}{\sin(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\implies \cfrac{1}{\sin^2(\theta )}-\cfrac{2\cos(\theta )}{\sin^2(\theta )}+\cfrac{\cos^2(\theta )}{\sin^2(\theta )}\)

\(\cfrac{\cos^2(\theta )-2\cos(\theta )+1}{\sin^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{\sin^2(\theta )} \\\\\\ \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{1-\cos^2(\theta )}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1]}\)

\(\cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos^2(\theta )-1^2]}\implies \cfrac{[\cos(\theta )-1][\cos(\theta )-1]}{-[\cos(\theta )-1][\cos(\theta )+1]} \\\\\\ \cfrac{\cos(\theta )-1}{-[\cos(\theta )+1]}\implies \cfrac{-[\cos(\theta )-1]}{\cos(\theta )+1}\implies \cfrac{1-\cos(\theta )}{1+\cos(\theta )}\)

The percent increase in the population over the initial population after 7 hours is approximately 40.7%.

To solve this problem, we can use the formula for exponential growth:

P(t) = P0(1 + r)^t

Where P(t) is the population after t hours, P0 is the initial population, r is the growth rate as a decimal (in this case, 0.05), and t is the time in hours.

Plugging in the given values, we get:

P(7) = P0(1 + 0.05)^7

To find the percent increase in population over the initial population, we can subtract the initial population from the final population, divide by the initial population, and then multiply by 100:

Percent increase = [(P(7) - P0)/P0] x 100

Simplifying this expression using the formula for exponential growth, we get:

Percent increase = [(1 + 0.05)^7 - 1] x 100

Calculating this expression using a calculator or spreadsheet, we get:

Percent increase ≈ 40.7%

Therefore, the percent increase in the population over the initial population after 7 hours is approximately 40.7%.

To know more about expression problems, visit:

https://brainly.com/question/15583484

#SPJ11

\(y = -\dfrac 25 x +1~~~......(i)\\\\\\y = 3x-2~~~......(ii)\\\\\\\text{Substitute}~ y = 3x -2~ \text{in equation (i):}\\\\\\3x -2 = -\dfrac 25 x +1\\\\\implies 3x + \dfrac{2x}{5} = 1 +2\\\\\implies \dfrac{17x}{5} = 3\\\\\implies 17x = 15\\\\\implies x = \dfrac{15}{17}\\\\\\\text{Substitute}~ x = \dfrac{15}{17}~ \text{in equation (ii):}\\\\\\y = 3\cdot \dfrac{15}{17} -2 = \dfrac{45}{17} - 2 =\dfrac{11}{17}\\\\\\\text{Hence,}~~ (x,y)= \left(\dfrac{15}{17}, \dfrac{11}{17} \right)\)

This can be derived using Chebyshev's inequality, as Chebyshev's inequality and the law of large numbers are different in nature.

Let M_n be the maximum of n independent U(0, 1) random variables.

To derive the exact expression for P(|M_n − 1| > ε), we need to follow the below steps:

First, we determine P(M_n ≤ 1-ε). The probability that all of the n variables are less than 1-ε is (1-ε)^n

So, P(M_n ≤ 1-ε) = (1-ε)^n

Similarly, we determine P(M_n ≥ 1+ε), which is equal to the probability that all the n variables are greater than 1+\epsilon

Hence, P(M_n ≥ 1+ε) = (1-ε)^n

Now we can write P(|M_n-1|>ε)=1-P(M_n≤1-ε)-P(M_n≥1+ε)

P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n.

Thus we have derived the exact expression for P(|M_n − 1| > ε) as P(|M_n-1|>ε) = 1 - (1-ε)^n - (1+ε)^n

Now, to show that $lim_{n\to\∞}$ P(|M_n - 1| > ε) = 0 , we can use Chebyshev's inequality which states that P(|X-\mu|>ε)≤{Var(X)/ε^2}

Chebyshev's inequality and the law of large numbers are different in nature as Chebyshev's inequality gives the upper bound for the probability of deviation of a random variable from its expected value. On the other hand, the law of large numbers provides information about how the sample mean approaches the population mean as the sample size increases.

Learn more about Chebyshev's inequality:

https://brainly.com/question/32750368

#SPJ11

Answer:

O I, II & III

Step-by-step explanation:

(2, 3) and (1, 1)

m = (3 - 1)/(2 - 1) = 2

y = 2x + b

1 = 2(1) + b

b = -1

The equation of the line is

y = 2x - 1

I) y = 2(x - 2) + 3 = 2x - 4 + 3 = 2x - 1   Yes

II) y = 2x - 1   Yes

III) y = 2(x - 1) + 1 = 2x - 2 + 1 = 2x - 1   Yes

Answer: O I, II & III

Answer:

13 lawns

Step-by-step explanation:

Find out how much money Melinda earns for 1 lawn mowed (variable x represents money earned):

3x = 48

Isolate the variable by dividing both sides by 3

3x ÷ 3 = 48 ÷ 3

1x = 16

x = 16

She earns $16 per mowed lawn

Set up equation to find out how many lawns she needs to mow to earn $208 (variable y represents lawns mowed):

16y = 208

Isolate the variable by dividing both sides by 16

16y ÷ 16 = 208 ÷ 16

1y = 13

y = 13

She needs to mow 13 lawns to earn $208

Answer: The answer is 13 lawns... Have a great day!

The assertion is untrue.

The amount that will be received annually must be multiplied by the present value of an annuity factor in order to get the annuity's present value. A mathematical formula known as the present value of an annuity factor is used to determine the current value of a series of future payments, such as an annuity.

It considers the amount owed, the frequency of payments, and the interest rate.

The equation for calculating an annuity's present value is: PV = PMT * (1 - (1 + r)(-n)) / r

where PV is the annuity's present value

Payment amount = PMT

interest rate, r

There have been n payments.

The denominator of this equation, (1 - (1 + r)(-n)), is the present value of an annuity component. By dividing the payment amount (PMT) by the present value of the annuity factor, it is utilised to determine the annuity's present value.

To know more about annuity refer here:

https://brainly.com/question/32006236?#

#SPJ11

Answer:download cameramath it helped me a lot!

Step-by-step explanation:when I have hard questions i just go to

Cameramath!

Answer:

Length of each side of the square = 8 cm

Step-by-step explanation:

In the figure attached, diagrams of a right triangle and a square have been given.

"Area of the square is twice the area of the triangle."

Let one side of the square = x cm

Therefore, area of the square = x²

Area of the given triangle = \(\frac{1}{2}(\text{Base})(\text{Height})\)

                                           = \(\frac{1}{2}(16)(4)\)

                                           = 32 cm²

Therefore, x² = 2 × 32

x² = 64

x = 8 cm

Therefore, length of each side of the square will be 8 cm.

Answer:

GCF= 16

Step-by-step explanation:

factors of 32= 32, 16, 8, 4, 2, 1

factors of 16= 16, 8, 4, 2, 1

16 is the largest factor both numbers have in common

Answer: 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

To know more about Laplace visit:

https://brainly.com/question/30759963

#SPJ11

Step-by-step explanation:

what do you have to find

Measures of∠QTR, ∠RQS, m arcTS and m arcQT are 55°, 47°, 102° and 54° respectively.

An angle is formed when two straight lines intersect at a point. The amount of "spread" between these two rays is called the "angle". It is represented by the symbol ∠. Angles are usually measured in degrees and radians. This is a measure of roundness or rotation.

Given,

In circle P,

m arcQR = 110°

m arcRS = 94°

∠QRT = 27°

Measure of arc is twice to the angle made by arc on boundary of the circle.

m arcQR = 2∠QTR

110° = 2∠QTR

∠QTR = 110/2

∠QTR = 55°

m arcRS = 2∠RQS

94° = 2∠RQS

∠RQS = 94°/2

∠RQS = 46°

m arcQT = 2∠QRT

m arcQT = 2(27°)

m arcQT = 54°

sum of all arcs made on a circle is 360°

m arcQT + m arcTS + m arcRS + m arcQR = 360°

54° + 94° + 110° + m arcTS = 360°

m arcTS = 360° - 258°

m arcTS = 102°

Hence, 55°, 47°, 102° and 54° are measures of∠QTR, ∠RQS, m arcTS and m arcQT respectively.

Learn more about angle here:

https://brainly.com/question/30147425

#SPJ7

the area of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8 is 9, using the concept of area under the curve.

The region between a curve and the -axis is referred to as the "area under a curve." This region may be wholly above the -axis, entirely below the -axis, or somewhere in between. The area under a curve in calculus is a picture of an integral.

The region enclosed by the curve, the axis, and the boundary points is referred to as the "area under the curve." Using the coordinate axes and the integration formula, the area under the curve has been determined as a two-dimensional area. The area of the asymmetric plane form in a two-dimensional array is provided by the region beneath the curve.

The region bounded by the lines y = 5 and 2y + 4x = 8 and the curve

2y = 4√x

Now, finding the intersecting point between 2y + 4x = 8 and 2y = 4√x

so, 4√x + 4x = 8

or,  √x + x = 2

or, √x = (2 - x)

or, x = (2 - x)²

or, x = x² - 4x + 4

or, x² - 5x + 4 = 0

or, ( x - 4) ( x - 1) = 0

or, x = 4, 1

when x = 4 then y = 2√4 = 4

when x = 1 then y = 2 √1 = 2

when y = 4 and x = 4 then equation 2y + 4x = 8 is not satisfied.

Thus, only intersection point is: (1,2)

This is the type (II) region.

So, integrate the region with respect to y.

Now, area =

= \(\int\limits^5_2 {(y/2)^2 - ((8-2y) / 4)} \, dy\)

= \(\int\limits^5_2 {[(y^2/4) -2 + (y/2)]} \, dy\)

= \(\frac{1}{4} [y^3/3]^5_2 - 2 [y]^5_2 + \frac{1}{2} [y^2/2]^5_2\)

= \(\frac{117}{12} - 6 + \frac{21}{4}\)

= \(\frac{108}{12}\)

= 9

Thus, area = 9 of the region. 2y =4√x ; y = 5 ; and 2y+4x = 8.

To now more about area under the curve refer to:

brainly.com/question/25022620

#SPJ4

Answer:

-6.34

Step-by-step explanation:

the answer is -6.34

Answer:

73in to the nearest inch

Step-by-step explanation:

r=d/2

r=25.3/2

r=11.6cm

C=2πr

C=πd

C=22/7×25.3

C=72.51

C=73 to the nearest inch

Answer:

-0.8x+4.8y+16

Step-by-step explanation:

\(4(0.5x+2.5y-0.7x-1.3y+4)\\4(-0.2x+1.2y+4)\\4(-0.2x)+4(1.2y)+4(4)\\-0.8x+4.8y+16\)

Answer: 1.106D

Step-by-step explanation: 7.830=3.915(1.106)D and 2 = 1.106D

The number of days it takes the water lily population to double will be 3.915.

The equation is written as Y= a + bX, where Y is the dependent variable and X is the independent variable.

This is an algebraic idea; imagine the initial number was x and the new number is 2x. If the constant rate of growth is r and the time is D, the function expressing growth will be:

\(2x=x(r)D\\\\ 7.830=3.915(1.106)D\\\\ 7.830=3.915(2)D\)

Hence the number of days it takes the water lily population to double will be 3.915.

To learn more about the regression equation refer to the link;

https://brainly.com/question/7656407

Answer:

8x - 15

Step-by-step explanation:

Aera of rectangule is: length * width