Suppose you randomly select a family with three children. Assume that births of boys and girls are equally likely. a. How many birth orders are possible? List them in a probability distribution table. b. What is the probability of two boys and a girl? c. What is the probability of two girls and a boy in that order? d. What is the probability of at least one gir? e. What is the probability of at least two boys? a. How many birth orders are possible?

Answer:

it will take 6 minutes, just keep adding 1.4 to -8.4 until you reach 0

Step-by-step explanation:

Answer: It will take 6 minutes because all you need is to divide 8.4 and 1.4 (don't put the negative sign or ignore it)!

Answer:

35.1

Step-by-step explanation:

There's a formula that i've linked as an image

Basically, substitute all 3 sides and the length into that formula, chuck it into the calculator and viola.

Or... we can use pythagoras' theorem and get the height of the triangle Height = \(3^{2}\) - \(1.5^{2}\) = 2.6

Area of triangle = (3 * 2.6) / 2 = 3.9

Volume = 3.9 * 9

Volume of prism = 35.1

Answer:

For the book standing on the left you have a choice out of all

6

, for the next one you choose from the

5

left, and so on.

Explanation:

So the total number of arrangements you have:

6

×

5

×

4

×

3

×

2

×

1

=

720

Usually this is written as

6

!

, pronounced "6 factorial"

(factorial meaning the product of all whole numbers from

1

up to and including the one before the

!

)

Step-by-step explanation:

CORRECT ME IF IM WRONG

The expected utility of the outcome Heads by its respective probability is $1.

To calculate the expected utility, we need to multiply the value of each outcome by its respective probability and sum them up.

In this case, if the coin comes up Heads, you win $2. Since there are two possible outcomes (Heads or Tails), and assuming the coin is fair, the probability of getting Heads is 0.5.

So, the expected utility of the outcome Heads can be calculated as follows:

Expected Utility (Heads) = Value (Heads) * Probability (Heads)

= $2 * 0.5

= $1

Therefore, the expected utility of the outcome Heads is $1.

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Answer:

The sum of squares is the sum of the squares of variation, where variation is defined as the separate between individual value and the mean. to determine the sum of squares, the distance between each data point and the line of best fit is a squared and then summed up. the line of best fit will minimise dis value.

An isometry transformation preserves the size of the shape that is being transformed.

The transformation does not appear to be a rigid motion because (d) the angle measures and the distances between the vertices are the same as the corresponding angle measures and distances of the  preimage

From the figure, we have the following highlights

Because of the first highlight, we can conclude that: the transformation is not a rigid transformation.

Hence, the true statement is (d)

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The slope intercept form of the equation is B)y=2x-6.

What is slope intercept form of the equation?

When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b).   It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.

Here let us take any two points \((x_1,y_1)=(0,-6)\) and \((x_2,y_2) =(1,-4)\) .

Now using slope formula slope m = \(\frac{y_2-y_1}{x_2-x_1}\)

=> slope m = \(\frac{-4+6}{1-0}\) = 2

Now using equation formula \(y-y_1=m(x-x_1)\) then,

=> y-(-6)=2(x-0)

=> y+6=2x

=> y=2x-6

Hence the slope intercept form of the equation is B)y=2x-6.

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Jack has a total of 35 different combinations of fruits to choose from at the store.

To calculate the number of combinations Jack can choose, we need to use the concept of combinations in mathematics. Since Jack can buy any three fruits out of the seven available options, we need to calculate the number of combinations of 7 fruits taken 3 at a time.

The formula to calculate combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of options and r is the number of options to be chosen.

In this case, n = 7 (total number of fruits) and r = 3 (fruits to be chosen). Plugging these values into the formula, we get:

C(7, 3) = 7! / (3! * (7 - 3)!)

        = (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)

        = (7 * 6 * 5) / (3 * 2 * 1)

        = 35

Jack has a total of 35 different combinations of fruits to choose from at the store. He can select any three fruits out of the available options, which include apples, oranges, pears, bananas, plums, grapefruit, and kiwis.

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Answer:

3 1/3

Step-by-step explanation:

The given series is of the form Σn^(-5), so we have p = 5. Since p > 1, the series converges. The series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

We can use the integral test to determine whether the series ∑(n=5 to infinity) 4/((n-1)^5) converges or diverges. According to the integral test, if the integral of the function f(x) = 4/((x-1)^5) from 4 to infinity converges, then the series converges. If the integral diverges, then the series diverges.

Let's evaluate the integral:

∫(4 to infinity) 4/((x-1)^5) dx = [-1/4(x-1)^4] (4 to infinity)

= [-1/4((infinity-1)^4 - (4-1)^4)]

= [-1/4(infinity^4 - 81)]

= infinity

Since the integral of f(x) diverges, we conclude that the series ∑(n=5 to infinity) 4/((n-1)^5) also diverges. Therefore, the series is not convergent.

To further illustrate this, let's consider the limit comparison test. We can compare the series to a known divergent p-series, such as the series ∑(n=1 to infinity) 1/n^2. We can then take the limit as n approaches infinity of the ratio of the two series:

lim(n→∞) (4/((n-1)^5)) / (1/n^2)

= lim(n→∞) (4n^2/(n-1)^5)

Applying L'Hopital's rule, we get:

= lim(n→∞) (8n/(n-1)^6)

= 8/lim(n→∞) (n-1)^(-6)

Since the limit of (n-1)^(-6) is zero, the limit comparison test tells us that the series ∑(n=5 to infinity) 4/((n-1)^5) diverges, since it can be compared to the divergent series ∑(n=1 to infinity) 1/n^2.

In conclusion, the series ∑(n=5 to infinity) 4/((n-1)^5) diverges.

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Making assumptions about the marginal pmf fx(x) and the conditional pmf h(y|x), probability P(X+Y>4) is 0.35.

To compute P(X+Y>4), we need to consider the possible values of X and Y and calculate the probabilities accordingly.

Let's analyze the scenario step by step:

Randomly choosing X from the interval [0, 4]:

The possible values for X are 0, 1, 2, 3, and 4. We assume a uniform distribution for X, meaning each value has an equal probability of being chosen. Therefore, the marginal pmf fx(x) is given by:

fx(0) = 1/5

fx(1) = 1/5

fx(2) = 1/5

fx(3) = 1/5

fx(4) = 1/5

Choosing Y from the interval [0, x]:

Since the value of X is observed, the range for Y will depend on the chosen value of X. For each value of X, Y can take on values from 0 up to X. We assume a uniform distribution for Y given X, meaning each value of Y in the allowed range has an equal probability. Therefore, the conditional pmf h(y|x) is given by:

For X = 0: h(y|0) = 1/1 = 1

For X = 1: h(y|1) = 1/2

For X = 2: h(y|2) = 1/3

For X = 3: h(y|3) = 1/4

For X = 4: h(y|4) = 1/5

Computing P(X+Y>4):

We want to find the probability that the sum of X and Y is greater than 4. Since X and Y are independent, we can calculate the probability using the law of total probability:

P(X+Y>4) = Σ P(X+Y>4 | X=x) * P(X=x)

= Σ P(Y>4-X | X=x) * P(X=x)

Let's calculate the probabilities for each value of X:

For X = 0: P(Y>4-0 | X=0) * P(X=0) = 0 * 1/5 = 0

For X = 1: P(Y>4-1 | X=1) * P(X=1) = 1/2 * 1/5 = 1/10

For X = 2: P(Y>4-2 | X=2) * P(X=2) = 1/3 * 1/5 = 1/15

For X = 3: P(Y>4-3 | X=3) * P(X=3) = 1/4 * 1/5 = 1/20

For X = 4: P(Y>4-4 | X=4) * P(X=4) = 1/5 * 1/5 = 1/25

Summing up the probabilities:

P(X+Y>4) = 0 + 1/10 + 1/15 + 1/20 + 1/25

= 0.35

Therefore, the probability P(X+Y>4) is 0.35.

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Answer:

i know im late but its 42

Step-by-step explanation:

:/ i think

The total number of visitors to the zoo that day=3980.

Given:

cost of each ticket for an adult=$25

cost of each ticket for an adult=$10

Total ticket sales one day=$47,750.

⇒$25+$10=47,750

⇒25+10=47,750-----(1)

Also,

c=6a+270

6a-c=-270------(2)

multiplying eq(2) with 10 we get:

60a-10c=-2700----(3)

Adding eq(1) and eq(3) we get

25a+10c=47,750

60a-10c=-2700

--------------------------

85a=45050

--------------------

To calculate a value just divide 45050 by 85 we get

a=45050/85

a=530

Now to get the value of c substitutes a value.

c=60(530)+270

c=3450

Number of Adult visitors=530

Number of children visitors=3450

Total Number of visitors=3980.

Therefore, the total number of visitors to the zoo that day=3980.

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The given statement "For any sampled population, the population of all sample means is approximately normally distributed" is true. This is a result of the Central Limit Theorem, which states that when sample sizes are large enough, the means of all samples will be approximately normally distributed.

A sample is a smaller portion of the population that has been taken to draw conclusions about the characteristics of the population as a whole. The sample needs to be representative of the population for the data analysis to be valid.

A sample mean is a statistical analysis in which the sum of all data points in a sample is divided by the number of observations. It gives an idea of the average value of the data points in the sample population.

For any sampled population, the population of all sample means is approximately normally distributed. The central limit theorem states that when the sample size is sufficiently large, the distribution of the sample means will be approximately normal, regardless of the underlying distribution of the population.

The central limit theorem is an important concept in inferential statistics because it provides a theoretical foundation for the use of statistical inference methods to draw conclusions about population parameters based on sample statistics.

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If Binita is going to buy 450 envelopes. The amount in pounds (£), it will cost Binita to buy the envelopes from Value World is 0.72 pounds.

First step is to calculate the cost for letter2go

Cost =  450 / 25 × 3.29

Cost = 59.22

Second step is to calculate the cost for value world

Cost = 450 /30 × (1.95 ×2)

Cost = 58.50

Now let calculate the cost of buying the envelopes from value world

Cost = 59.22 - 58.50

Cost = 0.72 pounds

Therefore the cost is 0.72 pounds.

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Answer:

The answer would most likely be the second one because that one makes the most sense here.

Step-by-step explanation:

When a triangle is dilated, the size of the triangle changes.

The coordinate of G' after dilation is: (a) \(\mathbf{(-\frac 23,\frac 43)}\)

The vertices are given as:

\(\mathbf{G = (-2,4)}\)

\(\mathbf{H = (3,6)}\)

\(\mathbf{J = (3,-2)}\)

The scale factor (k) is given as:

\(\mathbf{k =\frac 13}\)

So, the image of G is calculated as:

\(\mathbf{G' = k \times G}\)

This gives:

\(\mathbf{G' = \frac 13 \times (-2,4)}\)

\(\mathbf{G' = (-\frac 23,\frac 43)}\)

Hence, the coordinate of G' after dilation is: (a) \(\mathbf{(-\frac 23,\frac 43)}\)

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A sample statistic is is any quantity from the sample of a population.

We can see in the last option, that from the population (total of subjects of study) Kaisa, selected 84 of the total students. This fits in to the definition of sample statistic.

Thus, the correct option is the last one.

Answer: 4.64%

\(\dfrac{\text{female research scientist}}{\text{female total}}=\dfrac{103}{2219}=0.0464\quad =\large\boxed{4.64\%}\)

True/False question cannot be answered with a "main answer". However, the archaeologists do believe that the cities of Sodom and Gomorrah were near the Dead Sea.

The location of Sodom and Gomorrah is a subject of debate among archaeologists and scholars. Some believe that they were located near the Dead Sea, while others propose different locations. However, the prevailing theory is that they were situated near the Dead Sea, which is a salt lake bordered by Jordan to the east and Israel and Palestine to the west.

The true/false question you have posed cannot be answered with a long answer as it is a binary question. However, if you want to know more about the archaeology and history of Sodom and Gomorrah, there is a wealth of information available online and in scholarly articles and books. The story of Sodom and Gomorrah is a biblical tale that recounts the destruction of two cities by God due to their wickedness. The story appears in both the Book of Genesis in the Hebrew Bible and in the Quran. Archaeological evidence suggests that there were settlements in the area of the Dead Sea around the time the story of Sodom and Gomorrah is said to have occurred, but there is no conclusive proof that these were the cities referred to in the Bible. Some scholars argue that the story is a myth, while others believe that there is a historical basis for it. Regardless of the veracity of the tale, the story of Sodom and Gomorrah has captured the imagination of people for centuries and continues to be a subject of scholarly inquiry.

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Find the area of the actual property by diving the sale price by the price per square foot:

1,800,000 / 1,000 = 1,800 square feet

Divide actual are by the scale:

1800 / 900 = 2

The scale drawing is 2 square inches.

The area of the square draw will be 2 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The scale factor is a way to compare figures with similar appearances but differing scales or measurements. Consider two circles that resemble one another but may have different radii.

Given that area is 900 ft. the developer hopes to sell the commercial space for $1,800,000, which would be equivalent to $1000 per 1 square foot (ft?) of the property's area.

The area of the actual property by diving the sale price by the price per square foot:

1,800,000 / 1,000 = 1,800 square feet

Divide actual are by the scale:

1800 / 900 = 2

Therefore, the area of the square draw will be 2 square inches.

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Answer:

The distance between their tops is 130 feet

Step-by-step explanation:

The given parameters are;

The height of A, \(h_A\) = 2 × The height of B - 10

The distance between the two buildings, d = 120 feet

The height of B, \(h_B\) = 60 feet

Therefore, we have;

The height of A, \(h_A\)  = 2 × The height of B - 10 = 2 × 60 - 10 = 110 feet

The height of A, \(h_A\) = 110 feet

By Pythagoras theorem, the distance between their tops = √((\(h_A\) - \(h_B\))² + d²)

Substituting the values gives;

The distance between their tops = √((110 - 60)² + 120²) = 130

The distance between their tops = 130 feet.

Answer:

I think it is 4 to 3

Step-by-step explanation:

if I am wrong I'm sorry

Answer:

4-3

Step-by-step explanation:

Distance cycled on Monday = p km

Distance cycled of Tuesday

= 8 km less than the distance cycled on Monday

= p km - 8 km

= (p - 8) km

So, distance cycled of Tuesday is (p - 8) km.