A few people gather together to play a game in which one needs to roll 3 six-sided dice. One person notices that the sum of the number of spots on three dice comes up as 11 (the event E1) more often than it does 12 (the event E2) even though it looks like it should be even. This person argues as follows: E1 occurs in just six ways:

{(1,4,6),(2,3,6),(1,5,5),(2,4,5),(3,3,5),(3,4,4)}, and E2 occurs also in just six ways: {(1,5,6),(2,4,6),(3,3,6),(2,5,5),(4,4,4),(3,4,5)}.

Therefore E1 and E2 have the same probability P(E1) = P(E2). Why isn’t it?

9514 1404 393

Answer:

  22

Step-by-step explanation:

For calculators without a cube root key, you can use the 1/3 power. The attached shows the quotient to be about 22.

9514 1404 393

Answer:

  4

Step-by-step explanation:

The function definition tells you its domain is ...

  -6 < x ≤ 4

Values -7, -6, and 5 are not in this domain.

Of the listed values, only 4 is in the domain.

Answer:

Step-by-step explanation:

21,753

at unit place=3 not an even number,not equal to 5 and not equal to 0

so 21,753 is not divisible by 2,5 and 10

again

2+1+7+5+3=18 divisible by 3 and 9.

so 21,753 is divisible by 3 and 9.

Answer:

45 km por galón

60 galones en 2700 Km

Step-by-step explanation:

180 / 4

45 km por galón

900 / 45

20 galones

2700 / 45

60 galones en 2700 Km

sinh(ln(4)) = (exp(ln(4)) - exp(-ln(4)))/2 = (4 - 1/4)/2 = 15/8 = 1.875

sinh(4) = (exp(4) - exp(-4))/2 ≈ 27.28992

Value of the expression in which each variable was swapped out with a number from its corresponding domain sinh⁡ (l5)

sinh (5)

=sinh(1.6094) =2.39990 rad

=sinh⁡(1.6094) =2.3

By doing the following, you may determine the numerical value of an algebraic expression: Replace each variable with the specified number. Then, enter your score in your team's table.

Value of the expression in which each variable was swapped out with a number from its corresponding domain. In the case of a number with only one digit, referring to the numerical value associated with a digit by its "value" is a convenient shorthand.

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Answer:

3cm/s

Step-by-step explanation:

Area of a square is expressed as:

A = L²

Rate of change of area is expressed as:

dA/dt = dA/dL•dL/dt

Given that

dA/dt = 24cm²/s

L = 4cm

Required

dL/dt

Since dA/dl = 2L

dA/dl = 2(4)

dA/dl = 8cm

Subatitute the given values into the formula

24 = 8 dL/dt

dL/dt = 24/8

dL/dt = 3cm/s

Answer: (8x8x9)/3=192

Answer:

x = 69

Step-by-step explanation:

m<M = x

From the triangle we know that

m<M + m<MNQ + m<MQN = 180

From the parallel lines we know that

m<MNQ = m<UQN = x

x + x + 42 = 180

2x + 42 = 180

2x = 138

x = 69

Step-by-step explanation:

here is the answer to your question

Answer:

f(4) = 31

f(0) = 7

f(-1) = 1

Step-by-step explanation:

f(x) = 6x + 7

f(4) = 6(4) + 7

f(4) = 24 + 7

f(4) = 31

f(0) = 6(0) + 7

f(0) = 0 + 7

f(0) = 7

f(-1) = 6(-1) + 7

f(-1) = -6 + 7

f(-1) = 1

Answer:

BC = 28

Step-by-step explanation:

The midsegment DF is half the measure of the third side BC , then

BC = 2 × DF = 2 × 14 = 28

Answer:

The story tells of a plain-looking little bird (the Ugly Duckling) born in a barnyard. His brothers and sisters as well as the other birds and animals on the farm tease him for being plain and ugly, so he runs off to live with a flock of wild ducks and geese until hunters shoot down the flock. Alone again, the Ugly Duckling finds a home with an old woman, but her cat and hen also tease him, so he doesn't stay there long.

In his wanderings, the Ugly Duckling comes across a flock of migrating swans, and he wishes to join them but can't because he's too young and can't fly well enough. When winter sets in, a farmer rescues the Ugly Duckling, but the farmer's children and other animals frighten him with their noise and teasing, so again, he flees. He spends a cold and lonely winter hiding in a cave until springtime, when the flock of swans comes to the lake near his hiding place.

When the Ugly Duckling approaches the swans, he's delighted to find that they accept him and treat him like one of them. When he looks at his reflection in the lake, he realizes, to his astonishment, that he's matured into a beautiful swan himself. When the swans fly off from the lake, he spreads his wings and joins them, finally having found a family who accepts him.

9514 1404 393

Answer:

  3/4

Step-by-step explanation:

It might be easier to start by expressing the ratios with AD as the denominator.

  AD/AC = 2/1   ⇒   AC/AD = 1/2

  AD/AB = 3/1   ⇒   AB/AD = 1/3

From the latter, we have ...

  (AD -AB)/AD = 1 -1/3 = 2/3 = BD/AD

Then the desired ratio is ...

  AC/BD = (AC/AD)/(BD/AD) = (1/2)/(2/3) = (3/6)/(4/6)

  AC/BD = 3/4

Answer:

310/[tex]3^{3}[/tex] = 310/27 =11.48

Step-by-step explanation:

Answer:

310/ = 310/27 =11.48

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

3-(-2) will become positive 5. so number line will go towards positive 5.

Answer:

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose a large shipment of televisions contained 9% defectives

This means that [tex]p = 0.09[/tex]

Sample of size 393

This means that [tex]n = 393[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{393}} = 0.0144[/tex]

What is the probability that the sample proportion will differ from the population proportion by less than 3%?

Proportion between 0.09 - 0.03 = 0.06 and 0.09 + 0.03 = 0.12, which is the p-value of Z when X = 0.12 subtracted by the p-value of Z when X = 0.06.

X = 0.12

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.12 - 0.09}{0.0144}[/tex]

[tex]Z = 2.08[/tex]

[tex]Z = 2.08[/tex] has a p-value of 0.9812

X = 0.06

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0144}[/tex]

[tex]Z = -2.08[/tex]

[tex]Z = -2.08[/tex] has a p-value of 0.0188

0.9812 - 0.0188 = 0.9624

0.9624 = 96.24% probability that the sample proportion will differ from the population proportion by less than 3%

Answer: 5%

Step-by-step explanation:

In 2006, there were 160 teachers in College A, and ¾ of them had their own vehicles, the number of people who had their own vehicles will be:

= 3/4 × 160

= 120

In 2007, 20 new teachers came to the school and 6 of them had own vehicles. This means the number if people with vehicles will be:

= 120 + 6

= 126

The percentage increase will be:

= Increase / Old vehicle owners × 100

= 6/120 × 100

= 1/20 × 100

= 5%

The Percentage increase is 5%.

Answer:

The price elasticity of demand is -10

Step-by-step explanation:

Given

[tex]p_1,p_2 = 50,40[/tex]

[tex]q_1,q_2 = 400,500[/tex]

Solving (a): The coefficient of price elasticity of demand (k)

This is calculated as:

[tex]k = \frac{\triangle q}{\triangle p}[/tex]

So, we have:

[tex]k = \frac{500 - 400}{40 - 50}[/tex]

[tex]k = \frac{100}{-10}[/tex]

[tex]k = -10[/tex]

Because |k| > 0, then we can conclude that the company made a wise decision.

Answer:

$40,000

Step-by-step explanation:

this the workings above

Answer:

Bob had 25 cars

Step-by-step explanation:

10+15=25

Answer:

243.125

Step-by-step explanation:

First do the integral part

11110011

1. From left to right, starting with a zero,

2. add the digit, double, move on to the next digit and repeat step 2 until digits are exhausted.

The successive results are

1

3

7

15

30

60

121

243

For the decimal part, we proceed similarly but

1. From the right-most digit proceed to the left, start with a zero.

2. Add the digit, halve, move on to the next digit and repeat step 2 until the decimal is reached.

Successive results are:

0.5

.25

.125

So the final result is 11110011.001 binary is 243.125 decimal

Answer:

- 3.027

Step-by-step explanation:

First price = 10000 ; second price = 700

Number of tickets sold = 11000

Ticket cost = $4

Probability that a ticket wins grand price = 1 / 11000

Probability that a ticket wins second price = 1 / 11000

X ____ 10000 _____ 700

P(x) ___ 1 / 11000 ___ 1/11000

Expected winning for a ticket buyer :

E(X) = Σx*p(x)

E(X) = (1/11000 * 10000) + (1/11000 * 700) - ticket cost

E(X) = 0.9090909 + 0.0636363 - 4

E(X) = - 3.0272728

E(X) = - 3.027

Answer:

21.4 m

Step-by-step explanation:

Let x represent the sum of the tall metal, medium metal and short metal heights. Since the tall metal has a length of 1.44 m, and the ratio is in 9:8:7, hence:

(9/24) * x = 1.44

x = 3.84 m

For the medium metal pieces:

(8/24) * 3.84 = medium metal height

medium metal height = 1.28 m

For the short metal pieces:

(7/24) * 3.84 = short metal height

short metal height = 1.12 m

Total horizontal metal piece length  = 3 * 1.8 m = 5.4 m

Total tall metal piece length  = 2 * 1.44 m = 2.88 m

Total medium metal piece length  = 5 * 1.28 m = 6.4 m

Total short metal piece length  = 6 * 1.12 m = 6.72 m

Total length of metal = 5.4 + 2.88 + 6.4 + 6.72 = 21.4 m

9514 1404 393

Answer:

  y = 7√2

Step-by-step explanation:

We are given the side opposite the angle, and we want to find the hypotenuse. The relevant trig relation is ...

  Sin = Opposite/Hypotenuse

  sin(45°) = 7/y

  y = 7/sin(45°) = 7/(1/√2)

  y = 7√2

__

Additional comment

In this 45°-45°-90° "special" right triangle, the two legs are the same length. Thus, ...

  x = 7

Answer:

The margin of error for her confdence interval is of 0.3757.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 18 - 1 = 17

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 17 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.8982

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Standard deviation of 0.55 meters.

This means that [tex]s = 0.55[/tex]

What is the margin of error for her 99% confidence interval?

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.8982\frac{0.55}{\sqrt{18}}[/tex]

[tex]M = 0.3757[/tex]

The margin of error for her confdence interval is of 0.3757.

Margin of error is the distance between the mean and the limit of confidence intervals. The margin of error for the given condition is 3.28 approximately.

Suppose that we have:

Sample size n  < 30

Then the margin of error(MOE) is obtained as

Margin of Error = [tex]MOE = T_{c}\dfrac{\sigma}{\sqrt{n}}[/tex]

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}[/tex]

where [tex]T_{c}[/tex] is critical value of the test statistic at level of significance

For the given case, taking the random variable X to be tracking the height of trees in the sample taken of trees from the considered forest.

Then, by the given data, we get:

[tex]\overline{x} = 4.8[/tex], [tex]s = 4.8[/tex], n = 18

The degree of freedom is n-1 = 17

Level of significance = 100% - 99% = 1% = 0.01

The critical value of t at level of significance 0.01 with degree of freedom 17 is obtained as T = 2.90 (from the t critical values table)

Thus, margin of error for 99% confidence interval for considered case is:

[tex]MOE = T_{c}\dfrac{s}{\sqrt{n}}\\\\MOE = 2.9 \times \dfrac{4.8}{\sqrt{18}} \approx 3.28[/tex]

Thus, the margin of error for the given condition is 3.28 approximately.

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Answer:

Step-by-step explanation:

46.327=46 ( neaarest whole number)

-4.801=-5 (nearest whole number)

46-(-5)=46+5=51

Answer:

-3,-1

Step-by-step explanation:

x²+4x+3=0

x²+4x=-3

x²+4x+(2)²=-3+(2)²

(x+2)²=-3+4

(x+2)²=1

Take square root of both sides

x+2=±1

x=-2±1

x=-1 or-3

Answer:

B

Step-by-step explanation:

Let the base of the triangle be b and the height be h.

The sum of the base and height is 14. Thus:

[tex]b+h=14[/tex]

Recall that the area of a triangle is given by:

[tex]\displaystyle A=\frac{1}{2}bh[/tex]

From the first equation, solve for either variable:

[tex]h=14-b[/tex]

Substitute:

[tex]\displaystyle A=\frac{1}{2}b(14-b)[/tex]

Distribute:

[tex]\displaystyle A=\frac{1}{2}(14b-b^2)[/tex]

Distribute:

[tex]\displaystyle A=-0.5b^2+7b[/tex]

Let b = x. Hence:

[tex]A=-0.5x^2+7x[/tex]

Therefore, our answer is B.

Answer:

33.51 cm

Step-by-step explanation:

240/360 = 2/3 (Arc length is 2/3 of the total circumference)

C = 2[tex]\pi[/tex]r             ( Calculate the total circumference)    

C = 2(8)[tex]\pi[/tex]

C = 50.265

2/3(50.265)      (Take 2/3 of the circumference. times 2 divide by 3)

33.51

Use a calculator and leave the answer to C and then multiply and divide. You get a more precise answer.

The exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

The arc length in approximate form is 33.49 radians.

[tex]s = r\times \theta[/tex]

where r is the radius of the circle and [tex]\theta[/tex] is the central angle in radians.

Radians = Degrees ×[tex]\frac{\pi}{180^{\circ}}[/tex]

For given question,

We have been given a circle with a 8-cm radius associated with a central angle of 240 degrees.

[tex]r=8~cm,~\theta=240^{\circ}[/tex]

First we convert angle in radians.

[tex]\theta=240^{\circ}\\\\\theta=240^{\circ} \times \frac{\pi}{180^{\circ}}\\\\ \theta=\frac{4\pi}{3}[/tex]

Using the formula of the arc length,

[tex]s=8\times \frac{4\pi}{3} \\\\s=\frac{32\pi}{3}[/tex]

The exact answer of the arc length is [tex]s=\frac{32\pi}{3}[/tex]

Substitute the value of [tex]\pi = 3.14[/tex]

So, the arc length would be,

[tex]\Rightarrow s=\frac{32\times \pi}{3}\\\\\Rightarrow s=\frac{32\times 3.14}{3}\\\\\Rightarrow s=33.49[/tex]radians

Therefore, the exact arc length is [tex]\frac{32\pi}{3}[/tex] radians.

the arc length in approximate form is 33.49 radians.

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Answer: 30%

Step-by-step explanation:

Let A be the probability of a student opting for mathematics - it consists of either boy opting for mathematics or girl opting for mathematics. As there is "or" we need to sum these probabilities.

[tex]P(A) = P(B)* P(M|G) + P(G)*P(M|G)[/tex]

[tex]P(A) = \frac{1}{2} * \frac{20}{100} + \frac{1}{2} * \frac{40}{100}[/tex]

[tex]P(A) = 3/10 = 0.3[/tex]

=> 30%

Answer:

30% Chance

Step-by-step explanation:

This one is rather simple. If half the class is girls, split 40 into half. Do the same with 20 if half is boys. Add 10 and 20 and you get 30.