Assuming boys and girls are equally likely, find the probability of a couple's last child being a baby boy. They have a total of 3 children not including the last child in question and all were boys before the last child was born.
Express your answer as a percentage rounded to the nearest hundredth without the % sign.

The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.

The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.

Expanding the left side of the equation we have:

[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)

= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12

= [tex]e^2[/tex] - 4e√3 + 12

Substituting back in the function

[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3

[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0

Using the quadratic formula:

e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2

e = [4√3 ± √(4f - 64√3)] / 2

e = 2√3 ± √(f - 16√3)

Now for,

(e - 2√3)² = f - 20√3

(2√3 + √(f - 16√3) - 2√3)² = f - 20√3

f - 20√3 = f - 16√3

f = 4√3

Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.

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Answer:

The maximum number of students to whom 48 apples, 60 bananas, and 96 guavas can be distributed equally is 20. Each student will receive 2 apples, 3 bananas, and 4 guavas.

Answer:

What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←​

Step-by-step explanation:

To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.

We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.

To do this, we need to find the angle between these two vectors. Using the dot product, we have:

<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0

Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.

To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:

[0 -1]

[1 0]

Multiplying this matrix by the vector <4, -7>, we get:

[0 -1] [4] = [-7]

[1 0] [-7] [ 4]

which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.

Answer:

90° counterclockwise

Step-by-step explanation:

I am not sure if the picture helps or not.  I am trying to show that I traced the point (4,-7).  Then I have a plus sign at (0,0).  I start rotating the tracing paper counterclockwise until  I get to the point (7,4).  I needed to turn one turn of the plus sign.  That would be 90°

Helping in the name of Jesus.

The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

What is gravitational force?

Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.

The gravitational force that the moon produces on the Earth can be calculated using the formula:

[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]

where:

[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]

[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]

[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]

[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]

Substituting these values into the formula, we get:

[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]

Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]

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The function for the value of the account after t years can be written as:

V(t) = 93000(1.08900365)t

The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.

The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.

the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

How to solve and what is graph?

The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.

In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.

A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.

Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.

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There are 81 potential outcomes in Andy's sample space.

Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.

The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.

We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.

For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.

9 × 9 = 81.

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Answer:

15.8823% error

Step-by-step explanation:

Percent Error Formula

abs([tex]\frac{(a-x)}{x}[/tex]) * 100%

abs:  absolute value

a:  actual value

x:  expected value

Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%

                       = abs(-0.158823) * 100%

                       15.8823% error

Answer:

................................

Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)

Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:

g(1) = 18

g(6) = 11

If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.

So the correct optionis the last one.

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The probability that the sum of the numbers on the dice will be a square number is 1/6.

The area of mathematics known as probability explores potential outcomes of events as well as their relative probabilities and distributions.

We can first make a list of every conceivable result when rolling two dice in order to determine the likelihood that the sum of the numbers on the two dice will be a square number:

[tex](1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6[/tex])

[tex](2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]

[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)[/tex]

[tex](4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]

[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)[/tex]

[tex](6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)[/tex]

The sums can then be listed, and the square numbers can be identified:

2, 3, 4, 5, 6, 7

3, 4, 5, 6, 7, 8

4, 5, 6, 7, 8, 9

5, 6, 7, 8, 9, 10

6, 7, 8, 9, 10, 11

7, 8, 9, 10, 11, 12

The likelihood that the sum of the numbers on the dice will be a square number is 6 out of a total of 36 potential outcomes.

P(square sum) = 6/36 = 1/6.

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Answer:

10 metres

Step-by-step explanation:

All sides are equal in Rhombus

So, the length of one side= 40m÷4

=10 metres

Answer:

D. y = -2x

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

y-intercept = (0,0)

y = mx + b

y = -2x + 0

y = -2x

The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.

Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.

The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.

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Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.

In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.

Here,

To develop a confidence interval, we need to use the following formula:

Confidence Interval = sample mean ± margin of error

where the margin of error is calculated as:

Margin of Error = z* (sample standard deviation/ √n)

where z* is the critical value from the standard normal distribution table based on the chosen confidence level.

a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:

Margin of Error = 1.645 * (4 / √25) = 1.317

So, the 90% confidence interval for the population mean is:

30 ± 1.317, or (28.683, 31.317)

b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:

Margin of Error = 1.96 * (4 / √25) = 1.568

So, the 95% confidence interval for the population mean is:

30 ± 1.568, or (28.432, 31.568)

c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:

Margin of Error = 2.576 * (4 / √25) = 2.0656

So, the 99% confidence interval for the population mean is:

30 ± 2.0656, or (27.9344, 32.0656)

d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.

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Answer:

38%

Step-by-step explanation:

I learned in class on Friday.

Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.

[tex]0.38\times \dfrac{100}{100}[/tex]

[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]

Write in percentage notation: 38%

The correct options are:

The data contain a sample of multiple individuals.

The data are collected  are approximately at  the same point in time.

Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.

One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.

Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.

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The midline equation of the function is y = 1.5.

The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.

Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.

Using the definition of the amplitude the midline is the given amplitude.

Hence, the midline equation of the function is y = 1.5.

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Answer:

3

Step-by-step explanation:

Khan Academy

Answer:

Step-by-step explanation:

The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:

Protein: 1x + 1y ≥ 8 (at least 8 units of protein)

Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)

Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)

The inequalities that x and y must satisfy because they cannot be negative are:

x ≥ 0

y ≥ 0

Step-by-step explanation:

To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:

1. 1x + 1y ≥ 8 (At least 8 units of protein)

2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)

3. 1x + 1y ≤ 10 (No more than 10 units of fat)

To ensure that x and y are non-negative, the following inequalities must be satisfied:

x ≥ 0y ≥ 0

Therefore, the complete set of inequalities for x and y are:

x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0

Here's a graph of the cost function C = 25000p / (100 - p), using graphing utility. The graph shows that the cost function is continuous and defined for all values in its domain.

The domain of the function is restricted to 0 ≤ p ≤ 100, since it doesn't make sense to supply recycling bins to more than 100% of the population, or to a negative percentage of the population.

As p approaches 100%, the cost of supplying recycling bins becomes very large, since it becomes increasingly expensive to provide bins to a large portion of the population. As p approaches 0%, the cost also approaches 0, since there are fewer bins needed for a smaller population.

The function has a vertical asymptote at p = 100, since the denominator of the fraction approaches 0 as p approaches 100 from the left. This means that the cost becomes infinitely large as the percentage of the population approaches 100%.

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3, 6, 11, 18, 27, 38, 51  , Next term 51 in the sequence is nth term .

What does math sequence mean?

An arrangement of numbers in a specific order is referred to as a sequence. The sum of the components of a sequence, on the other hand, is what is referred to as a series.

SEQUENCE    3,6,11,18,27...

  the series follows the odd counting.

for example:

we have odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, etc.

now

    3 + 3 = 6

    6 + 5 = 11

we can see adding odd numbers in a series results in the solution of the proceeding number of series.

similarly,

    11 + 7 = 18

     18 + 9 = 27

      27 + 11 = 38

now adding 13 to 38 according to the series will result in the next number.

     38 + 13  = 51

hence, 51 is the next number in the series.

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Answer:

  (a)  0.413

  (b)  0.400

  (c)  1 — ... the difference should be small

Step-by-step explanation:

Given a table of experimental results from 1000 spins and a diagram of a spinner, you want the experimental and theoretical probabilities of landing on Red. You also want a statement comparing them.

The table tells you 1000 experiments resulted in 413 reds. The experimental probability of landing on red is ...

  413/1000 = 0.413

The diagram of the spinner shows 10 equal segments, of which 4 are red. The theoretical probability of landing on red is ...

  4/10 = 0.400

The presumption in statistics is that any experiment repeated a sufficient number of times should see experimental results approaching theoretical results. We expect a small difference between experimental and theoretical results for a large number of trials.

The volume of the solid is given by the equation V = 36π (√2 - 1) using the triple integral.

A three-dimensional object's volume in three-dimensional space may be determined using the triple integral. The three-variable function is represented by the triple integral. If in space is a closed region, the region's entire volume may be expressed as V = Ddv, which is equivalent to V = D d x d y d z.

Cone: z = [tex]\sqrt{x^2+y^2}[/tex]

sphere: x² + y² + z² = 18

Here, we will use cylindrical coordinates to evaluate volume:

x = rcosθ , y = rsinθ, z = z

so, z = [tex]\sqrt{r^2cos^2\theta+r^2sin^2\theta} =r[/tex]

z = [tex]\sqrt{18-(x^2+y^2)} =\sqrt{18-r^2}[/tex]

r = [tex]\sqrt{18-r^2}[/tex]

r = 3

Finding limits,

[tex]Volume = \int\limits^2_0 \int\limits^3_0\int\limits^a_r {rdzdrd\theta} \, \\\\= \int\limits^2_0 \int\limits^3_0rz \ drd\theta\\\\= \int\limits^2_0 \int\limits^3_0 r(\sqrt{18-r^2}-r ) \ drd\theta\\\\[/tex]

Now, we have

[tex]\int\limits^3_0 {r\sqrt{18-r^2} } \, dr = -(9-18\sqrt{2} ) = 18\sqrt{2} -9[/tex]

Now the integral becomes,

Volume = 2π [(18√2-9) - 9]

= 2π x 18√2 - 18

V = 36π (√2 - 1)

Therefore, the volume of the solid is given by V = 36π (√2 - 1).

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In this case, we'll have to carry out several steps to find the solution.

Step 1:

Data:

camera:

list price (before tax) = $459.99

sales tax = 7.25%

Step 2:

percentage:

[tex]sales \ tax = 7.25\% = 7/100 = 0.07[/tex]

[tex]total \ cost = \$459.99 + \$459.99 \times (0.07) = \$459.99 + \$32.1993 = \$492.1893[/tex]

The answer is:

$492.19

Answer:

g(x)

=6x−4

=3x

2

−2x−10

Escribe (g∘f)(x) como una expresión en términos de x.

Step-by-step explanation:

Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).

Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:

f(x) = x^2 - 2x + 1

Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:

g(f(x)) = 6f(x) - 4

= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))

= 6x^2 - 12x + 2

Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.

Answer:

The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.

The total number of students in the survey is:

50 + 75 + 125 + 50 = 300

The number of students who voted for the Republican party is:

75 + 50 = 125

Therefore, the probability of selecting a student who voted for the Republican party is:

125/300 = 0.4167 (rounded to four decimal places)

So, the answer is option D: 125/300

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Answer:

It means the point x = 5 and y = 10

Answer: The place 5 units right and 10 units up from the center of the graph (the origin).

Step-by-step explanation:

Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.

Answer:

A≈1.83m²

Step-by-step explanation:

Using the formulas

A=πr2C=2πr

Solving forAA=C24π=4.824·π≈1.83346m²

Answer:

1.83 (approximate)

Step-by-step explanation:

First, we need to find the radius of the circle.

Using the formula:

[tex]C=2 \pi r[/tex]

We have to reorganize terms:

[tex]r=\frac{C}{2\pi}[/tex]

[tex]\frac{4.8}{2 \times \pi}[/tex]

r ≈ 0.76

Now we have the radius and the circumference in order to find the area.

Use the formulas:

[tex]A= \pi r^2[/tex]

[tex]C=2 \pi r[/tex]

A = C^2/4[tex]\pi[/tex]  = 4.8^2 / 4 * pi = 1.83

The slope of the function is 12. Because of the slope, Jennifer will require 12 extra meters of tape for each additional office she needs to tape the baseboards in.

A line's slope on a graph is its steepness or inclination. It may be derived from any two locations on a line by dividing the vertical change (rise) by the horizontal change (run). Positive, negative, zero, or undefinable slopes are all possible for lines. A line on a graph with a positive slope is growing as you travel from left to right, while one with a negative slope is declining. A line has a slope of zero when it is horizontal and a slope of infinity when it is vertical.

The given function is y = 12x + 25.

The standard equation of the line is given as:

y = mx + b

where, m is the slope.

Comparing the equation with the given equation the slope of the function is 12.

Because of the slope, Jennifer will require 12 extra metres of tape for each additional office she needs to tape the baseboards in. In other words, if more offices need to be painted, the amount of sellotape required also grows linearly.

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The Length of arcXY is 4π/3

The Circle identities refer to a set of fundamental identities in trigonometry that relate the six trigonometric functions of an angle in a right-angled triangle.

Given, (radius) WX =3, it means, r = 3

given, m∠XWY = 80°

So, the length of arc XY;

arcXY = [tex]\frac{80}{360}* 2\pi r[/tex]        (by formula: length of arc)

arcXY = [tex]\frac{2}{9}* 2\pi *3[/tex]

arcXY = [tex]\frac{4}{3}\pi[/tex]

Therefore, the Length of arcXY is 4π/3

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Complete question-