Four balls are placed in a bowl. one green, one black and two yellow. the bowl is shaken and someone draws two balls from the bowl. he looks at the balls and announces that at least one of them is yellow. what are the chances that the other drawn ball is yellow?

Answer:

1.  16

2.  -4

Step-by-step explanation:

First factor the expression

lim x→1  (x^3 + 5x^2 + 3x-9)/(x-1)

lim x→1  (x-1) (x+3)^2/(x-1)

Canceling the x-1  in the top and bottom

lim x→1   (x+3)^2

Let x=1

lim x→1   (1+3)^2 = 4^2 = 16

2.  lim x→0 (x^2 -6x+8) /(x-2)          

First factor the expression

    lim x→0 (x-4) (x-2) /(x-2)        

Canceling the x-2  in the top and bottom

lim x→0 (x-4)

Let x=0

lim x→0   (0-4) = -4

Filling in the table

x     -.1      -.01       -.001     .001     .01     .1

f(x) -4.1  -4.01    -4.001   -3.999   -3.99  -3.9

I know this isn't helpful, but I REALLY need help on this question...

Given: f(x) = x^2 + 7x + 10. From the Rational Root Theorem, we know p=10 and q=1. List all potential roots using the ratio p/q.

Answer:

In quadrilateral LMNO, LO ∥ MN.

ML ∥ NO

LO ≅ MN

Answer:

1 & 3 is correct on edg.

Answer:

A

Step-by-step explanation:

given that y varies directly with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the given condition y = 2 when x = 10

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

y = [tex]\frac{1}{5}[/tex] x ← equation of variation

when x = 40, then

y = [tex]\frac{1}{5}[/tex] × 40 = 8 → A

The value of y when x = 40 with the same proportion will be 8 thus option (A) is correct.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

As per the given,

If y varies directly with x.

y ∝ x

y = kx

k = y/x

Thus, k will be the same for both conditions.

2/10 = y/40

1/5 = y/40

40/5 = y

8 = y

Hence "The value of y when x = 40 with the same proportion will be 8 ".

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Answer:

P =44 + 4xy

Step-by-step explanation:

To find the perimeter of a triangle, add up the three sides

P = 29+15+4xy

P =44 + 4xy

Answer:

The first one, because the x values are not repeated in a data set.

Answer:g hvt

Step-by-step explanation:

2. CD = CD , Reflexive Prop.

3. BC = DE, Subtraction Prop.

Answer:

Step-by-step explanation:

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Answer:

First I'm not exactly sure what you're asking but the equation for slope is:

Y2-Y1/X2-X1=M

Step-by-step explanation:

M is your slope

X1 and Y1 represent your first point

X2 and Y2 represent your second point

To translate you are finding the rate of change (slope) between two points

Answer: Slope = ∆y/∆x = y2-y1/x2-x1

Step-by-step explanation:

The slope of a line which is also known as the gradient can be gotten by taking the ratio of the change in coordinate of y-axis to the x-axis of the line.

Change in y axis = y2-y1

Where y2 and y1 are final length and initial length respectively on the y axis

Change in x axis = x2-x1

Where x2 and x1 are final length and initial length respectively on the x axis.

The slope of the line therefore gives;

Slope = ∆y/∆x = y2-y1/x2-x1

Answer: Correct Option is "C"

( - ∞ , 3) U (3, ∞ )

Step-by-step explanation:

The function f/g is defined as

( x + 8) / (x -3)

Domain of the function is the set of values which the independent variable can assume.

Clearly in the above function x cannot assume the value 3, otherwise the function would become undefined.

So domain of the function is

( - ∞ , 3) U (3, ∞ )

Hope it helps.

Thank you.

Answer:

<T = 83

Step-by-step explanation:

In a parallelogram  <M = < P   and < N = <T  (opposite angles are congruent)

We also know that <M + <N = 180  ( consecutive angles are supplementary)

<M + <N = 180

6x+10  + 5x+10.5 = 180

Combine like terms

11x+20.5 = 180

Subtract 20.5 from each side

11x +20.5-20.5 = 180-20.5

11x = 159.5

Divide each side by 11

11x/11 = 159.5/11

x=14.5

We can find <N

<N = 5x+10.5

    = 5(14.5)+105

   =72.5 +10.5

   = 83

<N = <T = 83

Answer:

The experimental probability is 7/12 or 58.3%

Step-by-step explanation:

In order to find the experimental probability, we just look at the amount of times it happened in our test. The fact that the actual probability is 50% does not matter when looking at experimental numbers.

Answer:

251

Step-by-step explanation:

2008/8

Answer:

16064

Step-by-step explanation:

2,008 x 8= 16064

Answer:

7x + 9

Yes they are equivalent

Step-by-step explanation:

The first expression given to us is

2x + 3 + 5x + 6

Let us call it equation (i)

Now we have to find equivalent expression to it

the given equation is 2x + 3 + 5x +6

similar terms are terms involving x and not involving x

so solving the equation gives

2x + 5x + 3 +6

= 7x + 9

Now we have two equations one is

2x + 3 +5x + 6              ...............(i)

Other is

7x + 9                            ..............(ii)

To check they are equivalent or not

Put x = 3 in equation (i)

2(3)+3+5(3)+6= 6 + 3 + 15 + 6

                      =30

Now put x=3 in second equation

7(3)+9=21 + 9

          =30

As the answer of both the equations are 30 so they are equivalent

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, the expression can be simplified to 7x + 9. Substituting x with 3 in both expressions shows that they have the same value, which is 30.

To write an equivalent expression to 2x + 3 + 5x + 6 by combining like terms, we add the coefficients of the like terms. In this case, the like terms are the terms with the same variable, which is x. So, 2x + 3 + 5x + 6 simplifies to 7x + 9. To show that this expression is equivalent to the original expression, we can substitute x with 3. So, when we replace x with 3, both expressions 2x + 3 + 5x + 6 and 7x + 9 result in the same value, which is 30.

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Answer:

(f + g)(x) = 5x^2 + 4x + 6

Step-by-step explanation:

The given functions are f(x) = 4x + 6 and g(x) = 5x^2

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

= 4x + 6 + 5x^2

= 5x^2 + 4x + 6

Thank you.

For [tex]f[/tex] to be differentiable, it must be continuous, so we need to have

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3^+}f(x)=f(3)[/tex]

By its definition, [tex]f(3)=3^2=9[/tex]. The one-sided limits are

[tex]\displaystyle\lim_{x\to3^-}f(x)=\lim_{x\to3}x^2=9[/tex]

[tex]\displaystyle\lim_{x\to3^+}f(x)=\lim_{x\to3}mx+b=3m+b[/tex]

so we require [tex]3m+b=9[/tex].

In order for [tex]f[/tex] to be differentiable at [tex]x=3[/tex], we also need to have [tex]f'(3)[/tex] exist, which requires that [tex]f'[/tex] also be continuous at [tex]x=3[/tex]. First, compute the derivatives of all pieces of [tex]f[/tex]:

[tex]f'(x)=\begin{cases}2x&\text{for }x<3\\?&\text{for }x=3\\m&\text{for }x>3\end{cases}[/tex]

[tex]f'[/tex] is continuous at [tex]x=3[/tex] if

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3^+}f'(x)=f'(3)[/tex]

The one-side limits are

[tex]\displaystyle\lim_{x\to3^-}f'(x)=\lim_{x\to3}2x=6[/tex]

[tex]\displaystyle\lim_{x\to3^+}f'(x)=\lim_{x\to3}m=m[/tex]

so we need to have [tex]m=6[/tex], and moreover [tex]f[/tex] will be differentiable if we set [tex]f'(3)=6[/tex].

So with [tex]m=6[/tex], we must have [tex]3m+b=9\implies b=-9[/tex].

For the piecewise function f(x) = x^2 when x <= 3 and mx + b when x > 3, values m = 6 and b = -9 ensure differentiability at x = 3.

To make the piecewise function f(x) differentiable at x = 3, we need the two pieces, x^2 and mx + b, to smoothly connect at x = 3. This requires the values of m and b to ensure continuity of both function values and derivatives.

First, evaluate both pieces at x = 3:

x^2 when x <= 3 and mx + b when x > 3

For continuity, set these expressions equal to each other:

3^2 = m * 3 + b

This yields 9 = 3m + b. To ensure differentiability, the derivatives of both pieces must also match at x = 3:

f'(x) = 2x when x <= 3 and f'(x) = m when x > 3

For continuity of derivatives, set the derivatives equal to each other at x = 3:

2 * 3 = m

This gives m = 6. Substituting m = 6 into the continuity equation 9 = 3m + b gives b = -9.

Therefore, the values m = 6 and b = -9 make the piecewise function f(x) differentiable at x = 3.

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Answer: A

Step-by-step explanation:

[tex]\overline{AB}[/tex] has a length of 6

[tex]\overline{A'B'}[/tex] has a length of 6 + 12 = 18, which is 3 times the length of [tex]\overline{AB}[/tex]

B = B' so this will be the center point

⇒ center B and a scale factor of 3

Answer:

Option A is the answer.

Step-by-step explanation:

Triangle A'B'C' is a dilation of triangle ABC.

We can apply the formula to get the scale factor as

Scale factor = [tex]\frac{\text{One side of triangle A'B'C'}}{\text{Corresponding side of triangle ABC}}[/tex]

= [tex]\frac{A'B'}{AB}[/tex]

= [tex]\frac{AB'+AA'}{AB}[/tex]

= [tex]\frac{6+12}{6}[/tex]

= [tex]\frac{18}{6}[/tex]

= 3

Therefore, ΔABC has been dilated with a scale factor of 3 about the point B as the center.

Option A is the answer.

Answer:

A

Step-by-step explanation:

Your first step is to figure out what f(x) is. You should start with x = 0. f(x) has a value of - 4.  That only tells you that whatever x is or what it is coupled with, the constant term is - 4.

What you know so far is that y = x something - 4

Now go to work on some of the other numbers. It really doesn't look linear so don't try it.

What happens when x = 16? Somehow f(x) winds up being 0. What can cause that?

First of all it can't be y = ax - 4. We've already establish the constant must be  - 4

What about y = ax^2 - 4

That cannot be either. y = 16^2*a - 4  ?? y = 256ax  - 4. No other value will fit the bill.

By looking at g(x) you get the idea that y = a*sqrt(x) - 4 might have something to do with f(x). The most obvious value for a = 1, so try it first.

Now try some of the other values.

And that's what the table says.

The red graph is y = sqrt(x) - 4

The blue graph is y = 4*sqrt(x) - 8

Answer

It looks like A is the answer.

g(x) has a y intercept of - 8

f(x) has a y intercept of - 4

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

The two intercepts are not equal. If they were they would start from the same point.   B is incorrect

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

C is wrong. the x intercepts are distinct points. One is 4 and the other is 16 I think.

0 = sqrt(x) - 4

4 =  sqrt(x)                Square both sides.

16 = x                         This is the x intercept of the red line

The other intercept = 4 (Blue line). I'll leave you to work it out. Leave a not if you can't.

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

A and D can't  both be true. Since A is true, D can't be.

C it the answer because since heads hit 14 times it haves a higher percent of hitting heads again.

Answer:

1) Her final bill: 334,5+ the tax

the tax = 334,5*8/100= 26,76 $

Her final bill = 334,5+ 26,76= 361,26 $

2) The gift card only has 350$ and the bill is 361,26

therefore she doesn't have enough money to pay for the sound bar

Step-by-step explanation:

Answer:

$1808263    

Step-by-step explanation:

We're given with the below information:-

Initial price of the building = Principal amount (P) = $590000

Rate of interest (r) = 14% = 0.14

Time in years (t) = 2020 - 2012 = 8

The formula to calculate the final amount where interest is continuously  compounded each year is :-

[tex]A = Pe^{rt}[/tex]                              [e is the mathematical const = 2.71828]

Plugging in the values of P, e, r, and t in the above formula, we get

[tex]A = 590000*2.71828^{0.14*8}[/tex]

=> A= 1808262.6

=> A = $1808263     (rounded off to the nearest whole dollar)

So, she expect to sell the building in 2020 for an amount of $1808263

Answer:\

180000

Step-by-step explanatii took

Answer:

The period is [tex]\pi[/tex].

Step-by-step explanation:

The answer is determined by finding the length of 1 cycle of the function. Trig functions sine and cosine have a wavy form. One starts and ends int he middle - sine. The other starts above and stops above- cosine. Regardless of the function, the period will be the same because the period asks "how fast does this function complete 1 wave?"

If cosine we start at one of the top points, trace the graph till we reach the same y-value again. The period is the time or difference in x-values. For instance if I started at the x-value [tex]\frac{\pi }{2}[/tex] and ended at [tex]\frac{3\pi }{2}[/tex] then I'd subtract them.

[tex]\frac{3\pi }{2}[/tex]-[tex]\frac{\pi }{2}[/tex]=[tex]\frac{2\pi }{2}[/tex]=[tex]\pi[/tex]

The period is [tex]\pi[/tex].

Adam has 6,000 points.

Let's use algebra to solve this problem. Let's assume that Adam's points are represented by 'x'. According to the problem, Nick has 20% more points than Adam, so Nick's points can be represented as 'x + 20% of x' or '1.2x'. Given that Nick has 7,200 points, we can set up the equation 1.2x = 7,200 and solve for 'x'. Divide both sides of the equation by 1.2 to isolate 'x' and find that Adam has 6,000 points.

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Answer:

7.15x + 3.55y + 20 = weekly income

Step-by-step explanation:

7.15x + 3.55y + 20 = weekly income

Answer:

Option d is correct.

Domain = all real number

range = positive real numbers

Step-by-step explanation:

Given the function: [tex]y=f(x) = a^x[/tex]

Domain of the function is all real numbers except where the expression is undefined.

In this case, there is no real number that makes the expression undefined.

Domain of f(x) = [tex](-\infty , \infty)[/tex] = {a | a∈R}

Range is the set of all valid  f(x) values.

[tex](0,1) \cup (1, \infty)[/tex]

[tex]\{y | y\neq 1 , y>0\}[/tex]

Therefore, Domain is all real number and the range of function is positive real number