a. With respect to​ gender, how many different​ three-child families are possible if birth order is taken into​ account? b. What is the probability of a​ three-child family with zero girls​?

Answer: 9.7 seconds

Step-by-step explanation:

\(16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7\)

Hey there! I'm happy to help!

We want to get m all by itself on one side of the equation. To do this, we use inverse operations on both sides of the equation to cancel out variables on one side to isolate m.

am/c=n

We multiply both sides by c.

am=nc

We divide both sides by a.

m=(nc)/a

I hope that this helps! Have a wonderful day! :D

When a line segment is drawn from a point on a circle's circumference, through the center to another point on the circle's circumference, the distance of the line segment is equal to the diameter of the circle.

The diameter is defined as any straight line passing through the center of a circle, connecting two points on the circumference. It is the longest chord of the circle and is also the length of a circle's widest point.

The diameter is an important parameter of a circle, as it determines the circle's size and area. It is related to the circle's radius, which is half the length of the diameter. The diameter is also used in various formulas for calculating the circumference, area, and other properties of circles.

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Answer:

A and C

Step-by-step explanation:

A. The prediction is reasonable.

C. No data is given in the scatterplot for a height of 80 inches, but a shoe size can still be predicted.

__________________________________________________________

Based on the average height-to-shoe size ratio, it is rational to predict that a man who is 80 inches tall would wear a size 16 shoe, even without there being a scatterplot for a height of 80 inches.

The cosine of angle J is given as follows:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the rules presented as follows:

For the angle J in this problem, we have that:

Hence the cosine of angle J is given as follows:

\(\cos{J} = \frac{4}{\sqrt{98}} \times \frac{\sqrt{98}}{\sqrt{98}}\)

\(\cos{J} = \frac{4\sqrt{98}}{98}\)

\(\cos{J} = \frac{2\sqrt{98}}{49}\)

As 98 = 2 x 49, we have that \(\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}\), hence:

\(\cos{J} = \frac{14\sqrt{2}}{49}\)

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Answer:

Step-by-step explanation:

(2 + 3) + 4 = 2 + (3 + 4)This expression can be simplified using the associative property of addition, which states that the grouping of the terms in a sum can be changed without changing its value. By rearranging the terms within the parentheses, we can simplify the expression as follows:2 + (3 + 4) = 2 + 7 = 9

Answer:

Step-by-step explanation: (a+b) +c =a +(b+c)

Answer:

Step-by-step explanation:

Let the third side be x

Triangle inequality theorem: sum of the length of any two sides must be greater than the third side length:

Combined together we have:

The third side must be between 10cm and 14 cm

The percentage of attorneys in given range is approximately 50%.

The boxplot below represents the salaries of attorneys in Los Angeles.

We can estimate the percentage of attorneys who have salaries between $55,000 and $80,000 by counting the number of boxes between the range (called the interquartile range, or IQR), which is from $55,000 to $80,000.

There are two boxes within the range, and two boxes that are not within the range (called the lower and upper outliers).

Thus, the percentage of attorneys with salaries between $55,000 and $80,000 is approximately 50%.

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Step-by-step explanation:

Solve for x

(3x + 94) + (x + 30) + (2x - 4) = 180

(3 + 1 + 2)x = 180 - (94 + 30 - 4)

6x = 60

x = 60/6

x = 10°

Solution → x = 10°

__________

\( \: \)

3x + 94 + x + 30 + 2x - 4 = 180

(3x + 1x + 2x) + (94 + 30 - 4) = 180

6x + 120 = 180

6x = 180 - 120

6x = 60

x = 10

The seamstress can cover a banner of **72 square inches** with the fabric.

The length of the fabric is 2 yards, which is equal to 72 inches. The width of the fabric is 36 inches. To find the size of the banner that the seamstress can cover with the fabric, we need to multiply the length and width.

```

72 inches * 36 inches = 2592 square inches

```

Therefore, the seamstress can cover a banner of 2592 square inches with the fabric.

Here is an explanation of the steps involved in finding the answer:

1. We convert the length of the fabric from yards to inches.

2. We multiply the length and width of the fabric.

3. We simplify the result to get the size of the banner in square inches.

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Answer:

14.7

Step-by-step explanation:

x^2+15^2=21^2

         x^2=216

             x=14.6969...

             x=14.7

Answer:

Mr. A initially paid approximately N8000 for the land.

Step-by-step explanation:

Step 1: Let's assume Mr. A initially purchased the land for a certain amount, which we'll call "x" in currency units.

Step 2: Mr. A sold the land to Mr. B at a profit of 10%. This means Mr. A sold the land for 110% of the amount he paid (1 + 10/100 = 1.10). Therefore, Mr. A received 1.10x currency units from Mr. B.

Step 3: Mr. B sold the land to Mr. C at a gain of 5%. This means Mr. B sold the land for 105% of the amount he paid (1 + 5/100 = 1.05). Therefore, Mr. B received 1.05 * (1.10x) currency units from Mr. C.

Step 4: According to the given information, Mr. C paid N1240 more for the land than Mr. A paid. This means the difference between what Mr. C paid and what Mr. A paid is N1240. So we have the equation: 1.05 * (1.10x) - x = N1240

Step 5: Simplifying the equation: 1.155x - x = N1240

Step 6: Solving for x: 0.155x = N1240

x = N1240 / 0.155

x ≈ N8000

Therefore, in conclusion, Mr. A initially paid approximately N8000 for the land.

Answer:

C

Step-by-step explanation:

Answer:

This one is C

Step-by-step explanation:

The dimensions that minimize the cost are x ≈ 13.42 ft and y ≈ 33.58 ft.

We are given that;

Brick wall costing= $30

Area= 450ft^2

Now,

To find the critical points, we take the derivative of C and set it equal to zero:

C’ = 50 - 9000/x2 C’ = 0 50 - 9000/x2 = 0 9000/x2 = 50 x2 = 9000/50 x2 = 180 x = ±√180 x ≈ ±13.42

Since x must be positive, we only consider x ≈ 13.42 as a critical point. To check if this is a minimum or maximum, we can use the first derivative test or the second derivative test. Using the second derivative test, we find:

C’’ = 18000/x3

Since x ≈ 13.42 is positive, C’’ > 0 at this point, which means C has a local minimum at x ≈ 13.42.

To find the absolute minimum, we also need to evaluate C at the endpoints of its domain:

C(0) = undefined C(450) = 50(450) + 20(1) = 22520

So, C has an absolute minimum at x ≈ 13.42 with a value of:

C(13.42) ≈ 50(13.42) + 20(33.58) ≈ $1,337

To find the dimensions of the garden that minimize the cost, we use y = 450/x and plug in x ≈ 13.42:

y ≈ 450/13.42 y ≈ 33.58

Therefore, by area the answer will be x ≈ 13.42 ft and y ≈ 33.58 ft.

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Answer:

x=66

Step-by-step explanation:

A quadrilateral is 360 degrees

you add all of the other angles and subtract it from 360 to find x

103+133+58 = 294

360-294 = 66

x = 66

Answer:

x = 66

Step-by-step explanation:

The interior angles of a 4 sided shape always add up to 360 degrees. This means that the sum of the angles in the shape = 360. Using this information we can create an equation to solve for x

103 + 133 + 58 + x = 360

==> combine like terms

294 + x = 360

==> subtract both sides by 294

x = 66

Using the slope concept, it is found that the change in elevation was of -699 feet.

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, we have that:

Hence:

tan(-4º) = h/10000

h = 10000 x tan(-4º)

h = -699.

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Answer:

1. 70  2. 85  3. 63  4. 20  5. They are vertical angles

Step-by-step explanation:

a) The probability that 9 out of 30 flowers will bloom early is 0.171.

b) The probability that fewer than 11 out of 30 flowers will bloom early is 0.454.

c) On average, you would expect to observe 3.42 flowers in order to see the first one that blooms early.

d) The probability that more than 9 out of 50 flowers will bloom early is 0.999.

e) The probability that between 11 and 18 (inclusive) out of 50 flowers will bloom early is 0.884.

f) The probability that you will have to observe 4 flowers in order to see the first one that blooms early is 0.219.

g) The probability that you will observe more than 4 flowers to see the first one that blooms early is 0.781.

Explanation for a: This can be calculated using the binomial distribution formula:

P(X=9) = (30 choose 9) * \(0.293^9\) * \(0.707^21\) = 0.171, where (30 choose 9) is the number of ways to choose 9 flowers out of 30 and 0.293 is the probability of a flower blooming early.

Explanation for b: This can be calculated using the cumulative probability function of the binomial distribution: P(X<11) = P(X=0) + P(X=1) + ... + P(X=10) = ∑(10, i=0) (30 choose i) * 0.293^i * 0.707^(30-i) = 0.454.

Explanation for c: This can be calculated using the geometric distribution formula: E(X) = 1/p = 1/0.293 = 3.42, where p is the probability of a flower blooming early.

Explanation for d: This can be calculated using the cumulative probability function of the binomial distribution: P(X>9) = P(X=10) + P(X=11) + ... + P(X=50) = ∑(50, i=10) (50 choose i) * 0.293^i * 0.707^(50-i) = 0.999.

Explanation for e: This can be calculated using the cumulative probability function of the binomial distribution:

P(11<=X<=18) = P(X=11) + P(X=12) + ... + P(X=18) = ∑(18, i=11) (50 choose i) * 0.293^i * 0.707^(50-i) = 0.884.

Explanation for f: This can be calculated using the geometric distribution formula:

P(X=4) = \((1-p)^{(4-1)} * p = 0.707^3 * 0.293\) = 0.219

where p is the probability of a flower blooming early.

Explanation for g: This can be calculated using the cumulative probability function of the geometric distribution:

P(X>4) = 1 - P(X=1) - P(X=2) - P(X=3) - P(X=4) = 1 - p = 0.781

where p is the probability of a flower blooming early.

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Answer:

29.96

Step-by-step explanation:

First find the discount

35 * 20 %

35*.2

7

Subtract the discount from the price

35-7

28

Now find the tax on the new price

28* 7%

28 *.07

1.96

Add the tax to the new price

28+1.96

29.96

Step-by-step explanation:

7.1 + 7.3 = 28 = 7 + 21

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The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the relationship between these different interest rates.

Subtracting the real rate of interest from the money rate of interest gives us the inflation component, which is then added to the real rate of interest to arrive at the nominal rate of interest.

The money rate of interest that lenders pay for borrowed funds minus the real rate of interest equals the nominal rate of interest. This is because the nominal rate of interest reflects both the money rate of interest and the inflation rate.

The real rate of interest, on the other hand, reflects the true return on investment after accounting for inflation.

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The final conclusion is that there is sufficient evidence to warrant the rejection of the claim that the population mean is not equal to 65.2.

What is the mean and standard deviation?

The mean and standard deviation are commonly used in various statistical analyses, such as hypothesis testing, probability distributions, and the characterization of data distributions. They provide valuable insights into the central tendency and variability of a dataset, allowing for comparisons and further statistical calculations.

To find the critical value for this test, we need to determine the z-score corresponding to the significance level of α = 0.05. Since this is a two-tailed test, we divide the significance level by 2 to get α/2 = 0.025 for each tail.

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to α/2 = 0.025 is approximately 1.96.

The critical value for this test is ±1.96.

the formula to calculate the test statistic,

test statistic = (sample mean - population mean) / (standard deviation / √(sample size))

Plugging in the given values:

test statistic = (62 - 65.2) / (6.9 / √(42))

≈ -1.742

The test statistic is approximately -1.742.

Since the test statistic falls outside the critical region (which is defined by the critical values ±1.96), we fail to reject the null hypothesis.

The test statistic is not in the critical region.

Therefore, the final conclusion is that there is sufficient evidence to warrant the rejection of the claim that the population mean is not equal to 65.2.

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Answer:

x = 8

Step-by-step explanation:

1/4 + 1/x = 3/8

LCM: 4 x 8 = 8x

1/4 * 8x + 1/x * 8x = 3/8 * 8x

Simplify

2x + 8 = 3x

Subtract

2x + 8 - 8 = 3x - 8

Simplify

2x = 3x - 8

Subtract

2x - 3x = 3x - 8 - 3x

Simplify

-x = -8

Divide both sides -1

-x/-1 = -8/-1

Simplify

x = 8

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer: Yes, 59 is a prime number

Step-by-step explanation: 59 is a prime number, it has only two factors, such as one and the number itself. Hence, the factors of 59 are 1 and 59.

Yes, 59 is a prime number.

What is a prime number?

Any natural number greater than 1 that is not the sum of two smaller natural numbers is referred to as a prime number. A composite number is a natural number greater than one that is not prime.

In other terms, prime numbers are positive integers greater than one that only has the number itself and 1 as factors. 2, 3, 5, 7, 11, 13, and other prime numbers are just a few examples. Never forget that 1 is neither a prime number nor a composite. Apart from 1, the other numbers can all be categorised as prime and composite numbers. Except for 2, which is the smallest prime number and the only even prime number, all prime numbers are odd.

The number in question, which is 59,  has only two factors: 1 and 59.

Therefore 59 is a prime number.

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