In a survey of 1002 people, 701 (which is 70%) said that they voted in the most recent presidentia l election (based on data from ICR Research Group). The margin of error for the survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this necessarily imply

The probability that exactly one tank in the sample contains high-viscosity material is P(A) = 0,4607 or P(A) = 46,07 %

P(A) = Number of favorable events/ Total number of events FE/TE

If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

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Averagely, Ana practiced for a greater amount of time each day.

Mean for ana= (20 + 20 + 30 + 60 + 60 + 60 + 70 + 70 + 100 + 100 + 100 + 115 + 115 + 115)/14 = 69.6

Mean for tara= (20 + 20 + 30 + 30 + 45 + 45 + 45 + 70 + 70 + 70 + 75 + 90 + 90 + 120)/14 = 58.6

Median for ana= 70

Median for tara= (45 + 70)/2 = 57.5

Ana has the greater median and also has the greater mean.

Averagely, we can conclude that ana practiced for a greater amount of time each day.

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The statement that is true about Sheila's savings plan is that; C.

Sheila must save $60 per month to achieve her goal.

The price of bathroom remodeling is $ 810.

After 13 months , she has saved $ 510

This means that she has a $300 shortage to cover in 5 months.

This means that she need to save :

$300/5  = $60 / month in order to achieve her goal

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Answer: C

Step-by-step explanation: edge

I think you mean in terms of [tex]\sin(x)[/tex]?

Recall Euler's identity

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

and de Moivre's theorem

[tex]\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}[/tex]

where [tex]i=\sqrt{-1}[/tex].

It follows that

[tex]\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4[/tex]

By the binomial theorem, expanding the right side gives

[tex]\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)[/tex]

and so

[tex]\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)[/tex]

We can factorize this as

[tex]\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)[/tex]

and using the Pythagorean identity

[tex]\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}[/tex]

this reduces to

[tex]\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))[/tex]

Answer:

300

Step-by-step explanation:

25 choose 2 (exactly how it sounds like)

= (25*24)/(2*1)=600/2=300

According to my calculation the answer is 188.

Answer:

Step-by-step explanation:

Solving    3x2-5x-1 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x, the solution for   Ax2+Bx+C  = 0, where  A, B, and  C number, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -5

                     C   =   -1

 B2  -  4AC   =

      25 - (-12) =

             37

Applying the quadratic formula :

              5 ± √ 37

  x  =    —————

                   6

 √ 37, rounded to 4 decimal digits, is   6.0828

So now we are looking at:

          x  =  ( 5 ±  6.083 ) / 6

Two solutions:

x =(5+√37)/6= 1.847

x =(5-√37)/6=-0.180

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

An equation is an expression that shows the relationship between two or more variables and numbers.

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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Answer:

The correct answer is A:3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a)

      1 - Simplify 4 - 9 to -5.

         ⇒ | - 5 |

      2 - Simplify.

       ⇒ 5

  (b)  

   1 -  Simplify

 ⇒ -5

[tex] \frac{5}{6} \: of \: a \: number \: is \: 180[/tex]

[tex] \frac{1}{6} \: is \: 5 \: times \: less \: than \: \frac{5}{6} \\ \frac{1}{6} = \frac{180}{5} = 36[/tex]

Answer,

Leaves from home=22:15hour

get to destination=4:00hour

time taken on a journey,

from time 22:15hour to 24:00hour=2:45hour and,

time is taken form 22:00hour to 4:00hour=4:00hour
So, the total time taken to reach the destination is 2:45+4:00=6:45hour

Answer:

see image

Step-by-step explanation:

The two circles will represent "starter" or "pudding" people and the overlap are both, but also don't forget people who chose neither. There must be 3-neither people. Because 6+7+8 only add to 21 and the question said there were 24 people.

Answer:

m= -1/5

Step-by-step explanation:

slope formula to find it ^^

The number of ways pets can be arranged in group according to the species is  in a row 288 ways.

Pets can be grouped by permutation concept as follows.

Total number of pets = 10

Number of dogs = 4

Number of cats = 3

Number of alpacas = 2

Number of bunny = 1

The number of ways pets can be arranged in group according to the species in a row as,

⇒ (4!)(3!)(2!)(1!)

⇒ (24)(6)(2)(1)

⇒ 288

Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.

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Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given by:

[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]

Hence the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]

M = 0.0486 = 4.86%.

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Answer:

99% - 0.06

95% - 0.05

90% - 0.04

Step-by-step explanation: i got it right

Answer:

Step-by-step explanation:

150 kilometers

60 kph

tank is 20 liters

6 km/l

150/6 = 25 liters needed

$60/l

5 more liters of fuel

total cost 25 x .60 =  $15

Answer:

$29.75

Step-by-step explanation:

If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757

Answer:

30

Step-by-step explanation:

Let's start by multiplying the equation through bt the least common denominator so that we can clear the denominator:

[tex]\frac{2}{5}x+\frac{1}{3}y=1[/tex]

The least common of 3 and 5 is 15, so we can multiply through by 15:

[tex]15(\frac{2}{5}x+\frac{1}{3}y)=15(1)\\6x+5y=15[/tex]

We want the left side of the equation to be 12x + 10y. We can get this if we multiply the expression we currently have (6x + 5y) by 2. However, if we multiply the left side by 2, we must also multiply the right side by 2 to balance out the equation. If we do this, we will get our answer:

[tex]2(6x+5y)=2(15)\\12x+10y=30[/tex]

On the right side, we get 30. Therefore, the answer is 30

[tex]\tan 45^{\circ}=\frac{x}{2\sqrt{10}}\\\\1=\frac{x}{2\sqrt{10}}\\\\\boxed{x=2\sqrt{10}}\\\\\\\\\sin 45^{\circ}=\frac{2\sqrt{10}}{y}\\\\\frac{1}{\sqrt{2}}=\frac{2\sqrt{10}}{y}\\\\y=2\sqrt[20}\\\\\boxed{y=4\sqrt{5}}[/tex]

If the domain of the function y=-2/3 x+7 is {-12,-6,3,15} then the range of the function is {15,11,5,-3}.

Given that the domain of the sunction y=-2/3 x+7 is {-12,-6,3,15}.

We have to find the range of the function and complete the table.

Function is relationship between two or more variables expressed in equalto form. In a function each value of x has some value of y.

To complete the table we need to find the value of the function at different values of x.Domain is basically value of  x which satisfies the function.

We have to first put the value of x=-12 in y=-2/3+7

y--2/3*-12+7

=15

Now put x=-6 in the function.

y=-2/3 *-6+7

=3

Put the value of x=3 in the function.

y=-2/3*3+7

=5

Put the value of x=15.

y=-2/3*15+7

=-41/3.

Hence the range of function is {15,11,-41/2,5}.

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The Surface area of the triangular prism with the net shown below is 106 cm²

An equation is an expression that shows the relationship between two or more variables and numbers.

Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²

The Surface area of the triangular prism with the net shown below is 106 cm²

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The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

According to the question,

Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.

In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.

Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.

s = {(x, y) /1≤x≤2 and 1≤y≤2}

In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.

Formula for Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]

= 1/2

Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

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Answer:

62,500

Step-by-step explanation:

250,000 ÷ 4 = 62,500

∴ Each member would receive 62,500.

Answer:

[tex]y = -3x+4[/tex]

I hope this helps and that you can give a brainliest!

Step-by-step explanation:

A linear equation means that the y value changes at a constant rate as x increases by 1.

To find the rate of change you need to plug 2 ordered pairs into the formula:
[tex]\frac{y1-y2}{x1-x2}[/tex]

(x1,y1) can be any data point on this table. To make it easy, we will make it (2,-2).

(x2,y2) can be any data point other than the previously chosen point. So, we will choose (-1,7).

If we substitute this into the formula, previously mentioned, we get:

[tex]\frac{-2-7}{2-(-1)}[/tex]

When we solve this, we get the rate of change as -3.

This will be the "m" value in the linear equation format:
"y = mx+b"

The b value is the y-value of the data when x = 0.

So to get the b-value, you need to plug in one ordered pair into the "y=mx +b" equation.

"m" was the rate of change, which we found in the previous step.

Let's use (2,-2) as the chosen ordered pair.

By substitution, we end up with:
[tex]-2=-3(2)+b[/tex]

If we solve this out, we get:
[tex]b = 4[/tex]

m was -3 and b is now 4.

So, putting this into the equation "y = mx+b"
We get our answer as [tex]y=-3x+4[/tex].

Answer:

large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la

or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues

Identify the root tissues. Record your answer under "Slide 5" on your lab report.

8  is the largest possible value of the median of all nine numbers in this list.

Lets simplify it,

⇒  The given six numbers are 7,8,3,5,9 and 5.

⇒  Arrange the six numbers in order 3,5,5,7,8,9.

⇒  We have three more numbers to insert into the list, and the median will be the  highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.

∴  The median is the 5th item of data which is 8.

∴  Median=8

Hence 8  is the largest possible value of the median of all nine numbers in this list.

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The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

The given figure is a kite with two intersecting lines that are perpendicular to each other.

Since the lines are perpendicular to each other, hence;

m<1 = 90 degrees

For the measure of m<2

m<2 + 90 + 27 =180

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63degrees

Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees

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