A couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child. However, if their first child is a boy, they will try again and have a second child. As it turns out, the probability of having a boy is slightly greater than having a girl. Here is the probability distribution for the number of boys the couple could have. Boys 0 boys 1 boy 2 boys 3 boys Probability 0.490 0.250 0.127 0.133

What is the expected number of boys the couple will have? (Recall: the expected value is the mean). 0.903 1.5 0.228

Answer: \(g(-2)=2a\)

Step-by-step explanation:

\((f \cdot g)(-2)=f(-2)g(-2)\\\\\therefore a \cdot g(-2)=2a^2 \implies g(-2)=2a\)

The function g(-2) from the given functions is 2a.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given functions are f(-2)=a and (f·g)(-2)=2a².

Here, (f·g)(-2)=2a²

f(-2)·g(-2)=2a²

a·g(-2)=2a²

g(-2)=2a²/a

g(-2)=2a

Therefore, the function g(-2) is 2a.

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The solution to the system is x = -8 and y = -8.

The system -3x + 2y = 8 and -6x + 7y = -8 by elimination, we need to eliminate one of the variables by adding or subtracting the two equations.

We can eliminate x by multiplying the first equation by -2 and then adding the two equations:

-2(-3x + 2y = 8) -> 6x - 4y = -16

-6x + 7y = -8

Adding these two equations eliminates the x variable:

6x - 4y = -16

-6x + 7y = -8

0x + 3y = -24

Simplifying the resulting equation gives us:

3y = -24

Dividing both sides by 3, we get:

y = -8

Now, we can substitute this value of y into either of the original equations to solve for x.

Let's use the first equation:

-3x + 2y = 8

-3x + 2(-8) = 8

-3x - 16 = 8

Adding 16 to both sides gives:

-3x = 24

Dividing both sides by -3 gives:

x = -8

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The labeling of bases and height in a trapezium is not fixed and can vary based on the context or problem. It doesn't matter where they are on the trapezium, as long as they are clearly defined and consistent within the given situation.

In a trapezium (or trapezoid), the labeling of the bases and height is not fixed or standardized. It can vary depending on the context or the specific problem being considered. However, there are a few general guidelines to keep in mind when labeling a trapezium.

Bases: The trapezium has two parallel sides, often referred to as the "top base" and the "bottom base." The bases are usually labeled based on their relative lengths or position in the trapezium. The longer parallel side is commonly referred to as the "top base," while the shorter parallel side is referred to as the "bottom base." However, this is not a strict rule and can vary depending on the problem or preference.

Height: The height of a trapezium is the perpendicular distance between the bases. It is generally labeled as a vertical line segment connecting the bases. The placement of the height is not fixed, and it can be drawn from any point on the top base to any point on the bottom base, as long as it forms a perpendicular line. The height is usually labeled with the symbol "h" or sometimes "x" or "y" depending on the context.

It's important to note that the labeling of the bases and height is primarily for communication and clarity. As long as the labeling is consistent and clearly defined within the given problem or context, it does not have to conform to any specific arrangement or be in a rectangular shape. The key is to ensure that the labels are clearly understood and can be used to calculate the desired quantities or solve the problem at hand.

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Answer:

The line y = 1/4x −3 and the half-plane lying above it.

Step-by-step explanation:

I attached the work to your problem. Please see the attachment.

Answer:

The p-value of the test statistic is 0.2019.

Step-by-step explanation:

Test if there is evidence at the 0.02 level that the medicine relieves pain in more than 384 seconds.

At the null hypothesis, we test if it relieves pain in at most 384 seconds, that is:

\(H_0: \mu \leq 384\)

At the alternative hypothesis, we test if it relieves pain in more than 384 seconds, that is:

\(H_1: \mu > 384\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

384 is tested at the null hypothesis:

This means that \(\mu = 384\)

For a sample of 41 patients, the mean time in which the medicine relieved pain was 387 seconds. Assume the population standard deviation is 23.

This means that \(n = 41, X = 387, \sigma = 23\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{387 - 384}{\frac{23}{\sqrt{41}}}\)

\(z = 0.835\)

P-value of the test:

The p-value of the test is the probability of finding a sample mean above 387, which is 1 subtracted by the p-value of z = 0.835.

Looking at the z-table, z = 0.835 has a p-value of 0.7981.

1 - 0.7981 = 0.2019

The p-value of the test statistic is 0.2019.

Answer:

10

Step-by-step explanation:

Change the fraction to a decimal:

2 1/2 = 2 + 1/2 = 2 + 0.5 = 2.5

Multiply:

4 x 2.5 = 10

10 is your answer.

~

The unknown angle in the cyclic quadrilateral is as follows:

∠R = 86 degrees

The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.

The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.

Hence, let's find the unknown angle.

∠R = 1 / 2 (92 + 80)

∠R = 1 / 2 (172)

∠R = 86 degrees

Therefore, the unknown angle is 86 degrees.

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The type of toy the kids enjoyed the most is the doll.

The total number of kids evaluated = 80

The percentage of kids that like train = 30%

The percentage of kids that like doll = 70%

30% of 80 = 30/100×80

= 2400/100

= 24

70% of 80 = 70/100×80

= 5600/100

= 56

Therefore, the type of toy the kids enjoyed the most is the doll.

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Answer:

B. acute, isosceles

Step-by-step explanation:

The two small lines intersecting the two sides stand for congruency.

Two sides are congruent, so this is an isosceles triangle.

None of the angles here are greater or equal to 90 degrees, so it is an acute triangle.

Please mark brainliest!

Answer:

B. Acute, isosceles

Step-by-step explanation:

Angles can be classified by both their sides and angles. There are 3 classification for each measurement, making 6 total classifications. This includes acute, right, and obtuse for angles and isosceles, scalene, and equilateral for sides.

Sides

The tic marks on 2 sides on the side show that they are congruent. Any triangle that has 2 congruent sides is classified as isosceles.

An additional fact is that the angles opposite of the congruent sides are also congruent. This information is not pertinent to this question, but might be useful in the future.

Angles

A triangle's classification for its angles is always based on the largest angle in the triangle. In this case, the largest angle is an acute angle. Remember that an acute angle is less than 90 degrees. This means that the triangle is acute.

Answer:

116,280 ways

Step-by-step explanation:

Because your finish place is mutually exclusive (if you come in first you cant come in second, if you come in second you cant come in third, etc) you have to decrease the amount of runners for each place.

20 runners can get first

19 for second

18 for third

17 for fourth.

To find out the total amount of possibilities you multiply each amount. 20 x 19 x 18 x 17 = 116,280.

I hope this helps!

-TheBusinessMan

Given:

mean, μ = 165

Standard deviation, σ = 13

n = 150

Let's find how many of them she would expect to score less than 149.

Apply the z-score formula:

Thus, we have the z-score:

Here, we are to solve for: P(x < 149).

We have:

P(x < 149) = P(z < -1.23)

Using the standard normal table, we have:

NORMSDIST(-1.23) = 0.10935

Therefore, out of the 150 games, the expected score less than 149 would be:

150 x 0.10934 = 16.4 ≈ 16

The expected number to score le

Answer:

She would make 91

Step-by-step explanation:

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

We have,

The actual dimensions of the island are 3 1/2 feet by 1 3/4 feet.

We need to find the dimensions of the island on the blueprint, given that the scale of the blueprint is 1 inch = 2 feet.

To convert the actual dimensions to the dimensions on the blueprint, we need to use the scale factor of 1 inch = 2 feet.

We can set up a proportion to relate the actual dimensions to the dimensions on the blueprint:

Actual dimension/blueprint dimension = scale factor

Let x be the length of the island on the blueprint.

Then we can set up the following proportion:

3.5 feet / (1.75 feet)

= x inches / 7 inches

Simplifying,

2 = x / 7

Multiplying both sides by 7, we get:

x = 14 inches

The length of the island on the blueprint is 14 inches.

Similarly, we can find the width of the island on the blueprint:

1.75 feet / 3.5 feet

= y inches / 7 inches

Simplifying, we have:

0.5 = y / 7

Multiplying both sides by 7, we get:

y = 3.5 inches

The width of the island on the blueprint is 3.5 inches.

Thus,

The dimensions of the island on the blueprint are 14 inches by 3.5 inches.

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The way the numbers will be placed in the square box will be:

First row = 4 12 14

Second row = 2 10 18

Third row = 6 8 16

It should be noted that the question is simply about adding the numbers and getting 39 in each place.

This will be:

First row = 4 12 14 = 4 + 12 + 14 = 30

Second row = 2 10 18 = 2 + 10 + 18 = 30

Third row = 6 8 16 = 6 + 8 + 16 = 30

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Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Answer:

144mm²

Step-by-step explanation:

48mm / 4 = 12

12 × 12 = 144mm²

Area = 144mm²

Answer:

You would need to show us what terms there are by taking a picture

Answer:

EIGHT divided by EIGHT

Step-by-step explanation:

The 8/8 word form is EIGHT divided by EIGHT

Answer:

eight over eight

Step-by-step explanation:

there can be multiple verbal forms of this such as

eight over eight

one

complte eght over the whole eight

or just plain ol' one because eight over eight equals one

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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The dot isn’t shaded so > or <

From -55, it’s showing small than

From -49, it’s showing greater than

x < -55 or x > -49

Answer:  x < -55 or x > -49

Step-by-step explanation:

x < -55 or x > -49

They both start with an opened circle, and also these two opened circle dots do not connect to each other. On the left side, the number is going from -55 to the smaller side, -57 or less, so we can say that x is smaller than -55. On the right side, the number goes from -49 to the bigger number, we can say that x is greater than -49.

The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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The number of sodas sold at the baseball game was 119, while the number of hot dogs sold was 72.

Let's assume the number of sodas sold as 'x' and the number of hot dogs sold as 'y'.

According to the problem, the total number of sodas and hot dogs sold is 191, so we can write the equation:

x + y = 191   ...(1)

The problem also states that the number of hot dogs sold was 47 less than the number of sodas sold. Mathematically, we can express this as:

y = x - 47   ...(2)

To find the values of x and y, we can solve the system of equations (1) and (2). Substituting equation (2) into equation (1), we have:

x + (x - 47) = 191

Simplifying the equation:

2x - 47 = 191

2x = 191 + 47

2x = 238

Dividing both sides by 2:

x = 238/2

x = 119

Substituting the value of x back into equation (2):

y = 119 - 47

y = 72

As a result, the total amount of sodas sold is 119, and the total amount of hot dogs sold is 72.

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9514 1404 393

Answer:

Step-by-step explanation:

This is to help you learn to take advantage of the distributive property and the fact that multiplication can simplify repeated addition.

The numbers to be added include ...

This means we can add 11 and -7, and multiply the result by 3. It also means we can multiply -8 by 4. The sum of these products will be the same as the sum of the original 10-number set.

  3(11 -7) +4(-8) = 3(4) -32 = 12 -32 = -20

Answer:

I think its false

Step-by-step explanation:

Answer: True i think

Step-by-step explanation: If Nancy is two years older than Mark who is 13, then Nancy would be 15, 15 + 13 equals 28.

Answer: the cost of gas for traveling 1,128.3 miles is $109.73

Step-by-step explanation:

Given:

cost per gallon of gas is $3.89

total miles traveled is 1128.3 miles

the car can travel 40 miles per gallon

gas is required to travel  1128.3 miles= total miles traveled / miles traveled                                            

                                                                per gallon

                                                         =1128.3/40 gallon

                                                         = 28.2075-gallons

we know that the cost per gallon of gas is $3.89

from this, we can find the cost for 28.2075-gallon

the cost for 28.2075 gallons = 28.2075*cost per gallon

                                       = 28.2075*3.89

                                       = $109.727175

                                       ~= $109.73

therefore it takes approximately 109.73 dollars to travel 1,128.3 miles

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The Variables (a) Gender is Categorical , (b) Alcohol can be either Categorical or Quantitative and (c) Height is Quantitative .

We can identify the type of each variable as categorical or quantitative.

(a) Gender: This variable is categorical, as it describes a characteristic that can only take on a limited number of values (e.g., male or female).

(b) Alcohol: Without additional information , it is not clear whether this variable is categorical or quantitative.

If the data set only includes information about whether an individual drinks alcohol or not, then this variable is categorical. If the data set includes information about how much alcohol an individual consumes, then this variable would be quantitative.

(c) Height: This variable is quantitative, as it represents a numerical measurement of a continuous variable.

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The given question is incomplete , the complete question is

Identify and classify the variable(s) you will use. here is the list of variables in the data set.  

(i) identify the variable as either categorical or quantitative.

the variables are (a) Gender , (b) Alcohol , (c) Height .

Answer:

60

Step-by-step explanation:

7/10=35/x

7x=350

x=50

AC=50+10=60

Answer:

\(x = - \frac{1}{56} \)

Step-by-step explanation:

-x/56x = 2

-1/56 = 2

x = -1/56

To find the total length of the two sides of the triangle, we need to add the lengths of side 1 and side 2.

Side 1: 3x^2 - 4x - 1

Side 2: 4x - x^2 + 5

To find the sum, we add the like terms:

Side 1 + Side 2 = (3x^2 - 4x - 1) + (4x - x^2 + 5)

Rearranging the terms and grouping like terms:

= 3x^2 - x^2 - 4x + 4x - 1 + 5

Combining like terms:

= (3x^2 - x^2) + (-4x + 4x) + (-1 + 5)

Simplifying:

= 2x^2 + 4

Therefore, the total length of sides 1 and 2 is 2x^2 + 4.

Part B: To find the length of the third side of the triangle, we subtract the sum of sides 1 and 2 from the perimeter of the triangle.

Perimeter of the triangle: 5x^3 - 2x^2 + 3x - 8

Sum of sides 1 and 2: 2x^2 + 4

Length of the third side = Perimeter - Sum of sides 1 and 2

= (5x^3 - 2x^2 + 3x - 8) - (2x^2 + 4)

Rearranging the terms and grouping like terms:

= 5x^3 - 2x^2 + 3x - 8 - 2x^2 - 4

Combining like terms:

= 5x^3 - 2x^2 - 2x^2 + 3x - 4 - 8

Simplifying:

= 5x^3 - 4x^2 + 3x - 12

Therefore, the length of the third side of the triangle is 5x^3 - 4x^2 + 3x - 12. To justify that polynomials are closed under addition and subtraction, we need to show that when we add or subtract two polynomials, the result is also a polynomial.

A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication, where the exponents on the variables are non-negative integers.

In both part A and part B, we performed addition and subtraction of polynomials, and the resulting expressions were still polynomials. This demonstrates closure under addition and subtraction for polynomials.

Hence, the answers for part A and part B show that the polynomials are closed under addition and subtraction.

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