The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 6. If there were 4508 no votes, what was the total
number of votes

Answer:

3/11

Step-by-step explanation:

From the above question, we have the following information

Total number of balls = 12

Number of white balls = 4

Number of blue balls = 3

Number of red balls = 5

We solve this question using combination formula

C(n, r) = nCr = n!/r!(n - r)!

We are told that 3 balls are drawn out at random.

The chance/probability of drawing out 3 balls = 12C3 = 12!/3! × (12 - 3)! = 12!/3! × 9!

= 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1/(3 × 2 × 1) × (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)

= 220 ways

The chance of selecting 3 balls at random = 220

To find the chance that all the three balls are selected,

= [Chance of selecting (white ball) × Chance of selecting(blue ball) × Chance of selecting(red balls)]/ The chance/probability of drawing out 3 balls

Chance of selecting (white ball)= 4C1

Chance of selecting(blue ball) = 3C1 Chance of selecting(red balls) = 5C1

Hence,

= [4C1 × 3C1 × 5C1]/ 220

= 60/220

= 6/22

= 3/11

The chance that all three are selected is = 3/11

Answer:

11.422

Step-by-step explanation:

[tex]78.2 - 66.778 \\ = 11.422[/tex]

Answer:

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Step-by-step explanation:

The other addend is determined by subtracting [tex]-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b-5[/tex] from [tex]10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a\cdot b^{2}-4\cdot a \cdot b + 2[/tex]:

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b + 2 - (-5\cdot a^{2}\cdot b^{2}+12\cdot a^{2}\cdot b -5)[/tex]

[tex]x = 10\cdot a^{2}\cdot b^{2}-8\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +2 +5\cdot a^{2}\cdot b^{2}-12\cdot a^{2}\cdot b+5[/tex]

[tex]x = (10\cdot a^{2}\cdot b^{2}+5\cdot a^{2}\cdot b^{2})-(8\cdot a^{2}\cdot b+12\cdot a^{2}\cdot b)+6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

[tex]x = 15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex]

The other addend is [tex]15\cdot a^{2}\cdot b^{2}-20\cdot a^{2}\cdot b + 6\cdot a \cdot b^{2}-4\cdot a \cdot b +7[/tex].

Answer:

A

Step-by-step explanation:

Answer:

69

Step-by-step explanation:

90-21=69

Answer:

69 degrees

Step-by-step explanation:

The full angle = 90 degrees.

One part of the full angle = 21 degrees

The other part of the full angle = x

Other angle = 90 - 21

=> the other angle = 69 degrees

Answer: [tex]\dfrac{8}{\pi}[/tex] .

Step-by-step explanation:

We know that the rate of change of function f(x) from x=a to x= b is given by :-

[tex]k=\dfrac{f(b)-f(a)}{b-a}[/tex]

The given points on graph  :  (0, -4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, -4).

The rate of change from x = 0 to x = pi over 2 will be :-

[tex]\dfrac{0-(-4)}{\dfrac{\pi}{2}-0}=\dfrac{4}{\dfrac{\pi}{2}}[/tex]     [By using points (0, -4) and (pi over 2, 0) ]

[tex]=\dfrac{8}{\pi}[/tex]

Hence, the rate of change from x = 0 to x = pi over 2 is [tex]\dfrac{8}{\pi}[/tex] .

Answer:

hi Ghana how are you doing I am fine here. I really miss u and my friends in the old.U know what in Nigeria this school is really awesome and fantastic we have a swimming pool here and we can go to trip and we can have many things here I really loved this school.

at starting I was not have any friends and know I have many friends. But I really miss u this is what about our . Come to my house I can show you my school it is very near to my house .

Ur friend

writ ur name

Answer:

y > 1

Step-by-step explanation:

-2(7 + y) > -8(y + 1)

-14 -2y > -8y -8

-2y +8y > -8 +14

6y > 6

6y/6 > 6/6

y > 1

Answer:

No solution

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Step 1: Write out systems of equations

-x + 3y = 3

x - 3y = 3

Step 2: Rewrite equations into slope-intercept form

3y = 3 + x

y = 1 + x/3

-3y = 3 - x

y = -1 + x/3

Step 3: Rewrite systems of equations

y = x/3 + 1

y = x/3 - 1

Since we have the same slope for both equations but different y-intercepts, we know that both lines are parallel. If that is the case, they will never touch or intersect each other. Therefore, we have no solution.

Answer:

(A) A 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval would increase.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval would decrease.

(D) A 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

Step-by-step explanation:

We are given that 19 students are randomly selected the sample mean was $390 and the standard deviation was $120.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                             P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean = $390

            s = sample standard deviation = $120

            n = sample of students = 19

            [tex]\mu[/tex] = population mean

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.101 < [tex]t_1_8[/tex] < 2.101) = 0.95  {As the critical value of t at 18 degrees of

                                               freedom are -2.101 & 2.101 with P = 2.5%}  

P(-2.101 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.101) = 0.95

P( [tex]-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                        = [ [tex]\$390-2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] , [tex]\$390+2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] ]

                        = [$332.16, $447.84]

(A)  Therefore, a 95% confidence for the population mean is [$332.16, $447.84] .

(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex] would increase because of an increase in the z value.

(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex]  would decrease because as denominator increases; the whole fraction decreases.

(D) We are given that to estimate the proportion of students who purchase their textbooks used, 500 students were sampled. 210 of these students purchased used textbooks.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                             P.Q.  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion students who purchase their used textbooks = [tex]\frac{210}{500}[/tex] = 0.42    

            n = sample of students = 500

            p = population proportion

Here for constructing a 99% confidence interval we have used a One-sample z-test statistics for proportions

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5%

                                               level of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

= [ [tex]0.42 -2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] , [tex]0.42 +2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] ]

= [0.363, 0.477]

Therefore, a 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477]  .

First find the critical points of f :

[tex]f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7[/tex]

[tex]\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1[/tex]

[tex]\dfrac{\partial f}{\partial y}=6y=0\implies y=0[/tex]

so the point (1, 0) is the only critical point, at which we have

[tex]f(1,0)=-7[/tex]

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

[tex]f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t[/tex]

Find the critical points of g :

[tex]\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0[/tex]

[tex]\implies\sin t=0\text{ OR }1+5\cos t=0[/tex]

[tex]\implies t=n\pi\text{ OR }t=\cos^{-1}\left(-\dfrac15\right)+2n\pi\text{ OR }t=-\cos^{-1}\left(-\dfrac15\right)+2n\pi[/tex]

where n is any integer. We get 4 critical points in the interval [0, 2π) at

[tex]t=0\implies f(10,0)=155[/tex]

[tex]t=\cos^{-1}\left(-\dfrac15\right)\implies f(-2,4\sqrt6)=299[/tex]

[tex]t=\pi\implies f(-10,0)=235[/tex]

[tex]t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299[/tex]

So f has a minimum of -7 and a maximum of 299.

Answer:

(3x-5)(4x+7) / 4x + 17

Step-by-step explanation:

Rewrite the division as a fraction

12 x ^2 + x-35 / 4x+17

Factor by grouping

(3x-5)(4x+7) / 4x + 17

Hope this was the answer you were looking for

Answer:

Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true. You can use the equation to check if events are independent; multiply the probabilities of the two events together to see if they equal the probability of them both happening together.

Answer:

Events are independent if the outcome of one effect does not effect the outcome

Step-by-step explanation:

Answer:

[tex]\boxed{\boxed{ x=\frac{C-By}{A}; A\neq 0}}[/tex]

Step-by-step explanation:

[tex]Ax+By=C\\\\Ax+By-By=C-By\\\\Ax=C-By\\\\\frac{Ax=C-By}{A}\\\\\boxed{ x=\frac{C-By}{A}; A\neq 0}[/tex]

Hope this helps.

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

Answer:

-50

Step-by-step explanation:

Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)

-50(0)+100 (0,100)  Y₂-Y₁/X₂-X₁ 50-100/1-0

Rate of change per month = -$50

Answer:

The probability that a particular firm selected has $1 million or more in income after taxes is 49%.

Step-by-step explanation:

We are given a study of 200 computer service firms revealed these incomes after taxes below;

         Income After Taxes                  Number of Firms

           Under $1 million                              102

      $1 million up to $20 million                    61

           $20 million or more                          37      

                 Total                                           200    

Now, the probability that a particular firm selected has $1 million or more in income after taxes is given by;

Total number of firms = 102 + 61 + 37 = 200

Number of firms having $1 million or more in income after taxes = 61 + 37 = 98  {here under $1 million data is not include}

So, the required probability =  [tex]\frac{\text{Firms with \$1 million or more in income after taxes}}{\text{Total number of firms}}[/tex]

                                           =  [tex]\frac{98}{200}[/tex]

                                           =  0.49 or 49%

The probability that a particular firm selected has $1 million or more in income after taxes is 0.49 or 49%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

A study of 200 computer service firms revealed these incomes after taxes:

Income After Taxes Number of Firms Under

$1 million 102

$1 million up to $20 million 61

$20 million or more 37.

Then the total event will be

Total event = 102 + 37 +61 = 200

The probability that a particular firm selected has $1 million or more in income after taxes will be

Favorable event = 37 + 61 = 98

Then the probability will be

[tex]\rm P = \dfrac{98}{200} \\\\P = 0.49 \ or \ 49 \%[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

at least one solution

Step-by-step explanation:

Consistent solutions have at least one solution, but may have more than one solution.  Intersecting lines and  Lines that are the same are consistent solutions

Answer:

[tex]\boxed{Atleast\ one \ Solution}[/tex]

Step-by-step explanation:

A consistent system of equations have at least one solution. It can be more than that. There are no compulsions.

Answer:

see below

Step-by-step explanation:

Difference is subtract

(8-2)

Then add this to x

(8-2) +x

6+x

Answer: -3

Step-by-step explanation: 2x = -2 then you subtract 1 from that which is the same as adding negative one so -2 - 1 or -2 + -1 = -3

Answer:

The answer is 36

Step-by-step explanation:

Let the number be x

7 less than the quotient of a number and 3 is written as

The result is 5

So we have

Move - 7 to the right side of the equation

That's

Multiply both sides by 3 to make x stand alone

We have

We have the final answer as

Hope this helps you

Answer: 7 mi

Step-by-step explanation: since the distance from bluepoint to Manchester is 12 9/10 mi and you know that bluepoint to Silverstone is 5 9/10 subtract that and you get 7 mi as your answer

Answer:

7 miles

Step-by-step explanation:

Hey there!

Well given BM and BS, we need to subtract them.

12 9 /10 - 5 9/10

9/10 - 9/10 = 0

12 - 5 = 7

Silvergrove to Manchester is 7 miles.

Hope this helps :)

Answer:

x = 2 and x = -2

Step-by-step explanation:

To find the vertical asymptotes, set the denominator equal to zero and solve for x:

vertical asymptotes are x = 2 and x = -2

Answer:

50%

Step-by-step explanation:

Girls                                            Boys

total:                 59                     total:                              41

- Chemistry       35                   - Physics                           2

                       = 24                                    =                     39

                                                 - Chemistry ( 30 - 6 )      24

                                                                   =                     15

Total boys and girls for Biology = 35 + 15 = 50

% = 50/100*100

   = 50%

Answer:

D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]

Step-by-step explanation:

Any parabola is modelled by a second-order polynomial, whose standard form is:

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]

Where:

[tex]x[/tex] - Independent variable, dimensionless.

[tex]y[/tex] - Dependent variable, dimensionless.

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.

In addition, a system of three linear equations is constructed by using all known inputs:

(-2, 0)

[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)

(4, 0)

[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)

(0,-16)

[tex]c = -16[/tex] (Eq. 3)

Then,

[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)

[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)

(Eq. 3 in Eqs. 1 - 2)

[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)

[tex]a = 4 + 0.5\cdot b[/tex]

Then,

[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)

[tex]64 + 12\cdot b = 16[/tex]

[tex]12\cdot b = -48[/tex]

[tex]b = -4[/tex]

The remaining coeffcient is:

[tex]a = 4 + 0.5\cdot b[/tex]

[tex]a = 4 + 0.5\cdot (-4)[/tex]

[tex]a = 2[/tex]

The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.

Answer:

D ƒ(x) = 2x2 – 4x – 16

Step-by-step explanation:

Answer:

Option (D)

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}[/tex]

[tex]\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}[/tex]

      = 1.1489

XW : XY ≈ 1.15 : 1

[tex]\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }[/tex]

[tex]\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}[/tex]

XY : WY = 1 : 0.7342

XW : XY : WY = 1.15 : 1 : 0.7342

Therefore, WX > XY > WY

Option (D). will be the correct option.

Answer:

First convert them which will be

-7/5 - (-4/5)

so when you subtract a negative number from negative number they actually subtract ex = -4-(-2) = -2

so its simply 7/5-4/5 then add a negative sign

so

3/5

now add negative sign so

-3/5

Answer:

  subtracting 56 instead of adding (or adding wrong)

Step-by-step explanation:

She wrote ...

  x - 56 = 230

  x - 56 - 56 = 230 -56 . . . . correct application of the addition property*

  x = 230 -56 . . . . . . . . . . . . incorrect simplification

Correctly done, the third line would be ...

  x -112 = 174

This would have made Sherina realize that the error was in subtracting 56 instead of adding it. The correct solution would be ...

  x - 56 + 56 = 230 + 56 . . . using the addition property of equality

  x = 286 . . . . . . . . . . . . . . . . correct simplification on both sides

__

There were two errors:

  1) incorrect strategy --- subtracting 56 instead of adding

  2) incorrect simplification --- simplifying -56 -56 to zero instead of -112

We don't know whether you want to count the error in thinking as the first error, or the error in execution where the mechanics of addition were incorrectly done.

_____

* The addition property of equality requires the same number be added to both sides of the equation. Sherina did that correctly. However, the number chosen to be added was the opposite of the number that would usefully work toward a solution.

Answer:

D: Sherina should have added 56 to both sides of the equation.

Step-by-step explanation:

I got a 100% on my test.

I hope this helps.

Answer:

The mean age is 48

The standard deviation is 4

Step-by-step explanation:

The answer is, (a) mean age is 48.

                          (b)  standard deviation is 4.

Learn more about mean age and standard deviation here:

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Answer:

Step-by-step explanation:

First we start with 12 pounds

On Monday, she and her friends eat 4 pounds. So we have 8 now.

On Tuesday, she and her friends eat another 3 pounds. So we gave 5 now.

On Wednesday, her friend Mark gives her some more cheesecake so that she has 3 times as much as she had at the end of Tuesday. 5 * 3 = 15

On Thursday, some of her cheesecake goes bad, so she has the amount that she had at the end of Wednesday, but divided by 5. She had 15 at the end of Wednesday. 15/5 = 3.

On Friday, she gives 3 pounds to her dog. 5 - 3 = 2.

On Saturday, her mom gives her one more pound. 2 + 1 = 3.

On Sunday, she finally has 3 pounds.

Answer:

nnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

Step-by-step explanation:

Answer:

Apllying cos on the triangle

cos(angle)= Base/ Hyp

cos(34)= 29/ AB

AB= 29/0.8290

AB=34.98

Step-by-step explanation:

The length of AB is 34.98 units which the correct answer would be an option (D).

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

Given that ΔABC

∠C = 90°

Here base = BC = 29 units and hypotenuse = AB

To determine the length of AB

Apply the cosine on the given right triangle

⇒ cos(θ) = Base/hypotenuse

⇒ cos(34) = 29/ AB

∴ cos(34°) = 0.8290

⇒ 0.8290 = 29/ AB

⇒ AB= 29/0.8290

⇒ AB = 34.98 units

Hence, the length of AB is  34.98 units

Learn more about Trigonometric functions here:

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