i have to write equations in standard form using integer coefficients for A,B, and, C Example: y= -8/15x + 1/20

Answer:  K = ¹/₃, V = 32in³

Step-by-step explanation:

Volume of s cylinder (V) = πr²h where πr² is the base area.

Now from the question,

V ∞ πr²h

V = kπr²h where k is the constant of proportionality which is also the variation constant.

40 = 6 x 20 x k

40 = 120k and

k   = ⁴⁰/₁₂₀

     = ¹/₃.

Now to find the volume when base area is 8in² and h is 12,

V = 8 x 12 x ¹/₃

V = 32in³

Looks like the given function is

[tex]f(x)=\dfrac1{9-x}[/tex]

Recall that for |x| < 1, we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

We want the series to be centered around [tex]x=4[/tex], so first we rearrange f(x) :

[tex]\dfrac1{9-x}=\dfrac1{5-(x-4)}=\dfrac15\dfrac1{1-\frac{x-4}5}[/tex]

Then

[tex]\dfrac1{9-x}=\displaystyle\frac15\sum_{n=0}^\infty\left(\frac{x-4}5\right)^n[/tex]

which converges for |(x - 4)/5| < 1, or -1 < x < 9.

Answer:

Step-by-step explanation:

∆ BCD ~ ∆ DCA

[tex] \frac{bc}{dc} = \frac{dc}{ac} [/tex]

Plug the values:

[tex] \frac{5}{y} = \frac{y}{6 + 5} [/tex]

[tex] \frac{5}{y} = \frac{ y}{11} [/tex]

Apply cross product property

[tex]y \times y = 11 \times 5[/tex]

Calculate the product

[tex] {y}^{2} = 55[/tex]

[tex]y = \sqrt{55} [/tex]

Hope this helps...

Good luck on your assignment..

Answer: 3. 0.287

Step-by-step explanation:

Let p be the true proportion of BB fans who favor that song.

As per given, Sample size for survey of Beach Boys fans = 394

Number of Beach Boys fans said that California girls was their fav song = 113

Then, the sample proportion of BB fans who favor that song: [tex]\hat{p}=\dfrac{113}{394}[/tex]

[tex]=0.286802030457\approx0.287[/tex]

Since sample proportion is the best estimate for the true proportion.

Hence, a point estimate for the true proportion of BB fans who favor that song is 0.287.

So, the correct option is 3. 0.287 .

Answer:

Campaign Finance Reform

Gender Gap among Voters in the District

There is a gender gap among women and men who favor campaign finance reform.

Step-by-step explanation:

In issues such as the above, a gender gap always exist between women and men who think that there is the need to reform the campaign finance.  Women ordinarily favor a reduction in the campaign finance.  On the other hand, men do not mind so much about the candidate expenditure in campaigns.  Reducing the huge campaign finance will ensure that political campaigns and aspiration to political offices are not left to money bags.  Many women would like to get involved, but they are limited by funding.  So, anytime the issue of reforming the whole electoral system, especially with respect to campaigns, women favor the reforms more than men.  The gap is always there.  The main issue is how would this gap be measured?

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

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

Explanation:

The angle 945 degrees is not between 0 and 360. We need to adjust it so that we find a coterminal angle in this range. To do this, subtract off 360 repeatedly until we get into the right range

945 - 360 = 585, not in range, so subtract again

585 - 350 = 225, we're in range now

Since 945 and 225 are coterminal angles, this means cos(945) = cos(225)

From here, we use the unit circle. Your unit circle should show the angle 225 in quadrant 3, which is the lower left quadrant. The terminal point here at this angle is [tex]\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)[/tex]

The x coordinate of this terminal point is the value of cos(theta). Therefore  [tex]\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}[/tex] and this is also the value of cos(945) as well

Using the periodic property of cos function, you can evaluate the value of cos(945°).

The value of cos(945°) is given by:

[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

A function returning to same value at regular intervals of specific length(called period of that function).

It is [tex]2\pi[/tex]

Thus, we have:

[tex]cos(x) = cos(2\pi +x) \: \forall \: x \in \mathbb R[/tex]

[tex]cos(945^\circ) = cos(2 \times 360^\circ + 225^\circ) = cos(2\pi + 2\pi + 225)\\ cos(945^\circ) = cos(2\pi) + 225) = cos(225^\circ)[/tex]

[tex]cos(\pi + \theta) = -cos(\theta)[/tex]

Thus:

[tex]cos(945^\circ) = cos(225^\circ) = cos(180^\circ + 45^\circ) = -cos(45^\circ) = -\dfrac{1}{\sqrt{2}}\\ cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

Note that wherever i have used [tex]\pi[/tex], it refers to [tex]\pi ^ \circ[/tex] (in degrees).

Thus, the value of cos(945°) is given by:

[tex]cos(945^\circ) = -\dfrac{1}{\sqrt{2}}[/tex]

Learn more about periodicity of trigonometric functions here:

https://brainly.com/question/12502943

In general, if we have [tex]x^a=x^b,[/tex] then [tex]a=b.[/tex] Thus, the first answer choice is correct.

Answer:

[tex]\boxed{\red{2x - 1 = 5x - 14}}[/tex]

First answer is correct.

Step-by-step explanation:

we know that,

[tex] {x}^{a} = {x}^{b} [/tex]

[tex]a = b[/tex]

So, according to that,

[tex] {5}^{(2x - 1)} = {5}^{(5x - 14)} [/tex]

Therefore,

[tex]2x - 1 = 5x - 14[/tex]

Answer:

1. Y= 7t^5 +C

2. Y= 35/12x^(12/7)+C

Step-by-step explanation:

The general solution will be determined by integrating the equations as the integration is a simple integration.

For dy/dt = 35t^4

The general solution y

= integral (35t^4)dt

The general solution y

=( 35/(4+1))*t^(4+1)

= 35/5t^5

= 7t^5 +C

To prove by differentiating the above.

Y= 7t^5 +C

Dy/Dt= (5*7)t^(5-1) +0

Dy/Dt= 35t^4

For dy/dx = 5x^(5/7)

Y=integral 5x^(5/7)Dx

Y= 5/(5/7 +1)*x^(5/7+1)

Y= 5/(12/7) *x^(12/7)

Y= 35/12x^(12/7)+C

To prove by differentiating

Y= 35/12x^(12/7)+C

Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0

Dy/Dx=(35/7)x^(5/7)

Dy/Dx= 5x^(5/7)

Answer:

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

Step-by-step explanation:

You can understand the statement from many perspectives, but in terms of proposition logic it is best to understand it as   "negation of a" or "  b" in mathematical terms is written like this

[tex]a => b \equiv ( \neg a \ \lor \ b )[/tex]

You can show that they are logically equivalent because they have the same truth table.

Steps to solve:

1 = -4 + 3/8x

~Add 4 to both sides

1 + 4 = -4 + 4 + 3/8x

~Simplify

5 = 3/8x

~Multiply 8/3 to both sides

5 * 8/3 = 3/8x * 8/3

~Simplify

13 1/3 = x

As we look through the answer choices, we can see that none resembles any of the steps I did above but by looking at the answers for each one, the only logical answer is B since it has a final answer of x = 40/3 or 13 1/3.

Best of Luck!

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

44 degrees

Step-by-step explanation:

4 multiplied by 7 is 28.

28 + 2 = 30

angle ABC = 30 degrees

3 multiplied by 7 is 21

21 - 7 = 14.

angle CBD = 14 degrees.

30 + 14 = 44.

The answer is ABD = 44 degrees

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Steb by step explanation:

The condition for the line is (7,3) and (4,4).

Point slope form of equation is in this format below.

(Y-y1)= m(x-x1)

We have the given parameters in the above format except the m

M = gradient

Gradient= (y2-y1)/(x2-x1)

Gradient=(4-3)/(4-7)

Gradient= 1/-3

Gradient= -1/3

So

(Y-y1)= m(x-x1)

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Answer:

16 hours

Step-by-step explanation:

From the above question, we are given the following information

For one wall, working alone,

Amy can paint for 12 hours

Which means, in

1 hour , Amy would have painted = 1/12 of the wall

Bob can paint for 18 hours

Which means ,

in 1 hour, Bob would have painted = 1/18 of the wall.

We are told Amy painted the wall for 4 hours and then Bob took over and completed the wall.

Step 1

Find the portion of the wall Amy painted before Bob took over.

Amy painted the wall for 4 hours before Bob took over.

If:

1 hour = 1/12 of the wall for Amy

4 hours =

Cross multiply

4 × 1/12 ÷ 1

= 4/12 = 1/3

Amy painted one third(1/3) of the wall

Step 2

Find the number of hours left that Bob used in painting the remaining part of the wall

Let the entire wall = 1

If Amy painted 1/3 of the wall

Bob took over and painted = 1 - 1/3

= 2/3 of the wall

If,

Bob painted 1/18 of the wall = 1 hour

2/3 of the wall = ?? = Y

Cross multiply

2/3 × 1 = 1/18 × Y

Y = 2/3 ÷ 1/18

Y = 2/3 × 18/1

Y = 36/3

Y = 12 hours.

This means, the number of hours Bob worked when he took over from Amy = 12 hours.

Step 3

The third and final step is to calculate how many hours it took them to paint the wall

Number of hours painted by Amy + Number of hours painted by Bob

= 4 hours + 12 hours

= 16 hours

Therefore, it took them 16 hours to paint the entire wall.

Answer:

x= 45

Step-by-step explanation:

In this diagram, there is an angle that is split into 2 angles.

The angle is a 90 degree angle. We know this because of the little square in the corner that denotes a right angle.

Therefore, the 2 angles inside of the right angle must add to 90 degrees. The 2 angles that make up the right angle are x and 45.

x+45=90

We want to find x. We need to get x by itself. 45 is being added on to x. The inverse of addition is subtraction. Subtract 45 from both sides.

x+45-45=90-45

x= 90-45

x=45

The measure of angle x is 45 degrees.

Answer:

Option C.

Step-by-step explanation:

In the given figure we have two parallel lines AB and CD.

A transversal line FB intersect the parallel lines at point B and C.

We know that the if a transversal line intersect two parallel lines, then corresponding angles are congruent.

[tex]\angle ABC=\anle ECF[/tex]

[tex]x=y[/tex]

To prove this by translation, we need a translation along the directed line segment CB maps ine CD onto line AB and angle y onto angle x.

Therefore, the correct option is C.

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

let us build equation for unknown legs

If we keep the length pf one leg as x

the other leg would be x +3

so we can build a relationship using pythagoras theorem

x^2 + (x+3)^2 = 15^2

x^2 + x^2 + 6x + 9 = 225

2x^2 + 6x + 9 = 225

2x^2 + 6x+ 9-225 = 0

2x^2 + 6x - 216 = 0

x^2 + 3x - 108 = 0 dividing whole equation by 2

x^2 + 12x - 9x - 108 = 0

x ( x + 12 ) - 9 (x + 12) = 0

(x -9) ( x +12) = 0

solutions for x are

x = 9 or x = -12

as lengths cannot be negative

one side length is 9cm

and other which is( x + 3)

9 + 3

12cm

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse² = First Leg² + Second leg²

Let x represent the length of one leg. The other leg is three more = x + 3, hypotenuse = 15 ft. Hence:

15² = x² + (x + 3)²

x² + 6x + 9 + x² = 225

2x² + 6x - 216 = 0

x² + 3x - 108 = 0

x = - 12 or x = 9

Since the length cant the negative hence x= 9, x + 3 = 12

The lengths of the legs of the right angled triangle is 9 feet and 12 feet.

Find out more at: https://brainly.com/question/10040532

Answer:

Step-by-step explanation:

We can solve each inequality apart and then see the possible solution sets.

Consider the inequality 4x+8 < -16. If we divide by 4 on both sides, we get

x+2 < -4. If we substract 2 on both sides we get x<-6. So the solution set for this inequality is the set of real numbers that are less than -6 (lie to the left of the point -6).

Consider 4x+8>4. If we divide by 4 on both sides we get x+2>1. If we substract 2 on both sides we get x>-1. So the solution set for this inequality is the set of real numbers that are bigger than -1 (lie to the right of the point -1).

So, for us to have 4x+8<-16 or 4x+8>4 we must have that either x <-6 or x>-1. So the solution set for the set of inequalities is the union of both sets, that is

[tex](\-infty, -6) \cup (-1,\infty)[/tex]

Answer:

a = 16

b = [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Length of the design 16 inches is represented by the point (0, 16) and length of 12 inches by (1, 12).

That means these points lie on the graph of the function 'f' represented by,

f(x) = a(b)ˣ

For the point (0, 16),

f(0) = a(b)⁰

16 = a(1)

a = 16

For another point (1, 12),

f(1) = a(b)¹

12 = ab

12 = 16(b) [Since a = 16]

b = [tex]\frac{12}{16}[/tex]

b = [tex]\frac{3}{4}[/tex]

Therefore, values of a and b are 16 and [tex]\frac{3}{4}[/tex] respectively.

Answer:

P = 0.0714

Step-by-step explanation:

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

Additionally, from the 28 cubes painted only 4 have exactly two painted faces.

Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:

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

So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:

[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]

Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.

Answer:

See Image Below.

Step-by-step explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer:

Please see attached image

Step-by-step explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)  [tex]\leq[/tex] 3 (3)

0   [tex]\leq[/tex] 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.

Energía cinética = 1 / 2mv²

Donde m es la masa y v es la velocidad

De la pregunta

la masa es de 16 libras

la velocidad es de 30 m / s

16 libras es equivalente a 7.257 kg

Entonces la energía cinética es

1/2(7.257)(30)²

Espero que esto te ayude

Answer: 1/5

Step-by-step explanation:

given data;

chances of winning = 1/3

chances of losing = 1/3

chances of tying in a given round = 1/3

solution:

probability that you would win atleast 2 in any 3 matches without a tied match is

1/3 /  ( 2 - 1/3 )

= 1/3 / 5/3

= 1/5

the probability of winning 2 of 3 games without a tie is 1/5

Answer:

When an obect has rotational symmetry, that means the object will look the same after a certain amount of rotating. When an object has reflection symmetry, it means the object mirrors itself at the midpoint.

Step-by-step explanation:

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

[tex]\boxed{366}[/tex]

Step-by-step explanation:

[tex]2 \times 3+4 \times 100-50+10[/tex]

Multiplication is first.

[tex]6+400-50+10[/tex]

Add or subtract the numbers.

[tex]350+10+6[/tex]

[tex]366[/tex]

Answer

B. 27

firist divide 9÷2=4.5

the formula

=1/2×4.5×6

=13.5

cause there are 2 triangles. let's multiply 13.5 with 2

13.5×2= 27²