Billy made 2 gallons of juice for a picnic. He said that he made
2
4
quarts of juice.

a. The probability of all girls in a family with four children is 1/16 or 0.0625.

b. The probability of all girls given there is at least one girl is 1/15 or 0.0667.

c. The probability of having at least one boy and one girl in a family with four children is 15/16 or 0.9375.

a. To calculate the probability of all girls, we need to consider the possible outcomes of each child being a girl. Since each child has an independent probability of being a girl or a boy, the probability of all girls is (1/2) * (1/2) * (1/2) * (1/2) = 1/16 or 0.0625.

b. Given that there is at least one girl, we have three remaining children. The probability of all girls among the three remaining children is (1/2) * (1/2) * (1/2) = 1/8. Therefore, the probability of all girls given there is at least one girl is 1/8 divided by the probability of having at least one girl, which is 1 - (1/2)⁴ = 15/16, resulting in a probability of 1/15 or approximately 0.0667.

c. The probability of having at least one boy and one girl can be calculated by subtracting the probability of having all boys from the total probability space. The probability of having all boys is (1/2)⁴ = 1/16. Therefore, the probability of having at least one boy and one girl is 1 - 1/16 = 15/16 or approximately 0.9375. This probability accounts for all possible combinations of boys and girls in a family with four children, excluding the scenario of having all boys.

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Answer:

150a

Step-by-step explanation:

Answer:

115.552 or 116 inches.

Step-by-step explanation:

Use the circumference of a circle formula which is C= 2piR. Where C is circumference and R is radius. So you get C=2(3.14×18.4) which gives you 115.552.

Answer:

[tex]y=-|x|+2[/tex]

Step-by-step explanation:

The y-intercept is 2 and the line of symmetry is the y-axis.

Answer:

b = 6.1 ft

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here A = 10.98 and h = 3.6 , then

[tex]\frac{1}{2}[/tex] × b × 3.6 = 10.98

1.8b = 10.98 ( divide both sides by 1.8 )

b = 6.1

By using iteration, we can guess the explicit formula for the given sequence. It is found that the sequence follows a quadratic pattern, and the explicit formula is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.

Let's start by analyzing the given sequence: dx = 2dx-1 + 3[tex]k^2[/tex]. We are given that d1 = 3. We can use this initial value to find d2, d3, and so on.

Substituting k = 2 into the given equation, we get d2 = 2d1 + 3([tex]2^2[/tex]) = 2(3) + 3(4) = 6 + 12 = 18.

Similarly, substituting k = 3, we get d3 = 2d2 + 3[tex](3^2)[/tex] = 2(18) + 3(9) = 36 + 27 = 63.

Based on these calculations, we observe that each term in the sequence is related to the previous term by multiplying it by 2 and adding 3[tex]k^2[/tex]. Moreover, we notice a quadratic pattern in the sequence.

To find the explicit formula, we can express dx in terms of k:

dx = 2dx-1 + 3[tex]k^2[/tex]

  = 2(2dx-2 + 3[tex](k-1)^2[/tex]) + 3[tex]k^2[/tex]

  = 4dx-2 + 6[tex](k-1)^2[/tex][tex](k-1)^2[/tex] + 3[tex]k^2[/tex].

We can continue this iteration process, expanding dx-2 in terms of dx-3, and so on. By continuing this process and simplifying the equation, we find that the explicit formula for the sequence is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.

In conclusion, by using iteration, we have determined that the explicit formula for the given sequence dx = 2dx-1 + 3[tex]k^2[/tex], with d1 = 3, is dx = 3([tex]2^{k-1}[/tex]) + 3[tex]k^2[/tex] - 6k + 3.

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The given values are: Ksp of CaSO4 = 4.93 × 10⁻⁵, Molarity of Na2SO4 = 0.250(m). Molar mass of CaSO4 = 136.14 g/mol. We can write the equation for the dissolution of CaSO4 in water as:CaSO4(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq). Let's consider that "x" grams of CaSO4 dissolves in "1 L" of 0.250 M Na2SO4. Since the CaSO4 dissolves according to the following equation:CaSO4(s) ⇌ Ca²⁺(aq) + SO₄²⁻(aq). The concentration of Ca²⁺ ions in the solution will be "x" moles / 1 L. The concentration of SO₄²⁻ ions in the solution will be "x" moles / 1 L. Since the concentration of Na2SO4 in the solution is 0.250 M or 0.250 moles / L, the concentration of SO₄²⁻ ions contributed by Na2SO4 will be (2 × 0.250) M or 0.500 M. In order to determine the value of "x" or the amount of CaSO4 that dissolves, we need to consider the equilibrium of the solution. The Ksp expression for the dissolution of CaSO4 can be written as: Ksp = [Ca²⁺][SO₄²⁻], Ksp = (x)(x) = x². As the dissociation is very small compared to the concentration of Na2SO4, we can consider "0.250" moles of Na2SO4 in "1 L" of the solution completely dissociated. Thus, the final concentrations of Ca²⁺ and SO₄²⁻ ions in the solution will be:[Ca²⁺] = x moles / L[SO₄²⁻] = (x + 0.500) moles /L. Therefore, we can write the expression for the ion product: IP = [Ca²⁺][SO₄²⁻]IP = (x)(x + 0.500)As the value of Ksp is equal to the IP, we can write the expression for Ksp as: Ksp = x² + 0.500xWe can substitute the value of Ksp as 4.93 × 10⁻⁵M:4.93 × 10⁻⁵ = x² + 0.500x. Solving for "x", we get the following quadratic equation: x² + 0.500x - 4.93 × 10⁻⁵ = 0. Solving for "x" using the quadratic formula: x = 0.00796 g/L. Therefore, the solubility of CaSO4(s) in 0.250 M Na2SO4 solution at 25°C is 0.00796 g/L.

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Answer:

The answer is B, have a wonderful day!

Step-by-step explanation:

There insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.

Step 1: State the hypotheses:

- Null hypothesis (H0): The mean amount spent by a customer is equal to or greater than last year's mean ($52).

- Alternative hypothesis (H1): The mean amount spent by a customer is significantly less than last year's mean ($52).

Step 2: Set the significance level:

The significance level (α) is given as 0.10. This represents a 10% chance of rejecting the null hypothesis when it is true.

Step 3: Formulate the decision rule:

Since the alternative hypothesis is stating a decrease in the mean amount spent, we will conduct a one-tailed t-test and reject the null hypothesis if the test statistic falls in the critical region corresponding to the left tail of the t-distribution.

Step 4: Calculate the test statistic:

We need to calculate the t-statistic using the formula:

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

Given data:

Population mean (μ) = $52

Sample mean (X) = $50

Sample standard deviation (s) = $11

Sample size (n) = 36

Plugging in the values:

t = ($50 - $52) / ($11 / √(36))

t = -2 / ($11 / 6)

t ≈ -1.0909

Step 5: Determine the critical value and make a decision:

Since the significance level is 0.10 and the test is one-tailed to the left, we need to find the critical t-value at a 0.10 significance level with degrees of freedom equal to (n - 1) = (36 - 1) = 35.

so, the critical t-value is -1.3104.

Since the calculated t-statistic (-1.0909) does not fall in the critical region (t < -1.3104), we do not have enough evidence to reject the null hypothesis.

Step 6: State the conclusion:

Based on the data and the hypothesis test, at the 0.10 significance level, there is insufficient evidence to support the claim that the mean amount spent by a customer has significantly decreased since last year.

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Answer: Y less than -3x – 3

Step-by-step explanation:

The correct answer should be 32.

To simplify the expression (4 + 3i)(2 - 8i), we can use the distributive property of multiplication.

First, we multiply the real parts of the two complex numbers:

(4)(2) = 8.

Next, we multiply the imaginary parts of the two complex numbers:

(3i)(-8i) = -24i^2.

Remember that i^2 is defined as -1, so we can substitute -1 for i^2:

-24i^2 = -24(-1) = 24.

Now, we combine the real and imaginary parts:

8 + 24 = 32.

Therefore, the simplified expression is 32.

Since none of the given answer choices match the simplified expression, it appears that there may be an error in the options provided. The correct answer should be 32.

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Answer:

Answer:

1/3 or 33%

Step-by-step explanation:

15 + 15 + 20 +25 is equal to 75

25/75 is 1/3

Answer:

1 by 3

Step-by-step explanation:

15 + 15 + 20 + 25 = 75

so,

again,

Answer:

2(x plus 20)

Step-by-step explanation:

this is the highest common factor

Answer: 11x + 20y ≥ 220

x + y ≤ 15

Hope this helps

9514 1404 393

Answer:

Step-by-step explanation:

The two inequalities represent the two relations described in the problem statement.

  x + y ≤ 15 . . . . . . . Mia works a maximum of 15 hours

  11x + 20y ≥ 220 . . . . Mia makes at least $220

These are graphed in the attachment. The solution area is the doubly-shaded area with vertices at (9, 6), (0, 11) and (0, 15). One possible solution is shown at (3, 11), which represents ...

  3 hours babysitting

  11 hours lifeguarding . . . . . . . . total 14 hours for $253

Answer:

5%

Step-by-step explanation:

Answer:

5% increase

Step-by-step explanation:

30/600 equals .05 or 5%

Answer:

its 77 1/3

just do the math with a calculator

Answer: 48 1/3

Step-by-step explanation:

Answer:

10, 12 and 11

Step-by-step explanation:

On each median , the distance from the vertex to the centroid is twice as long as the distance from the centroid to the midpoint.

TZ = 2 × ZX = 2 × 5 = 10

UY = UZ + ZY = 8 + 4 = 12

ZW = [tex]\frac{1}{3}[/tex] × VW = [tex]\frac{1}{3}[/tex] × 33 = 11

Answer:

106

Step-by-step explanation:

reflection

Answer:

0.1666...

Step by step explanation:

By using long division (with 6 as the divisor) the number sentence would keep on going with 40-36.

0.166666666

1.000000000

− 0                  

 10                

−  6                

  40              

 −36              

   40            

   −36            

       40          

     − 36          

         40        

       − 36        

           40      

         − 36      

             40    

           − 36    

               40  

             − 36  

                 40

               − 36

A. Does mean blood pressure differ for three different age groups?

This is a research question that could be addressed using a one-way analysis of variance.

A one-way analysis of variance (ANOVA) is a statistical test used to determine whether there are any significant differences between the means of three or more groups. In the given research question, we are interested in examining whether the mean blood pressure differs across three different age groups.

To address this question using a one-way ANOVA, we would collect blood pressure measurements from individuals belonging to three different age groups. We would then calculate the mean blood pressure for each group and compare these means statistically. The one-way ANOVA test would allow us to determine if there is enough evidence to suggest that the mean blood pressure differs significantly between the age groups.

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There is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

Therefore, the correct answer is A.

To construct a confidence interval for the difference in proportions, we can use the following formula:

CI = (p1 - p2) ± Z ×√[(p1×(1 - p1) / n1) + (p2 × (1 - p2) / n2)]

Where:

p1 and p2 are the sample proportions for males and females, respectively.

n1 and n2 are the sample sizes for males and females, respectively.

Z is the critical value corresponding to the desired confidence level.

From the given information, we have:

p1 = 190/1233

n1 = 1233

p2 = 128/1033

n2 = 1033

Confidence level = 99% (which corresponds to a critical value of Z)

Calculating the confidence interval:

CI = (190/1233 - 128/1033) ± Z× √[(190/1233× (1 - 190/1233) / 1233) + (128/1033 ×(1 - 128/1033) / 1033)]

Now, let's find the critical value Z for a 99% confidence level. Since the sample sizes are large, we can use the standard normal distribution. The critical value for a 99% confidence level is approximately 2.576.

CI = (0.154 - 0.124) ± 2.576× √[(0.154× (1 - 0.154) / 1233) + (0.124 × (1 - 0.124) / 1033)]

CI = 0.030 ± 2.576×√[0.000118 + 0.000124]

CI = 0.030 ± 2.576×√(0.000242)

CI = 0.030 ± 2.576×0.015556

CI = 0.030 ± 0.040085

CI ≈ (-0.010, 0.070)

The lower bound of the 99% confidence interval is approximately -0.010, and the upper bound is approximately 0.070.

Interpreting the interval, we can say:

A. There is 99% confidence that the difference of the proportions is in the interval. Conclude that there is insufficient evidence of a significant difference in the proportion of males and females that have at least one tattoo.

Therefore, the correct answer is A.

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The mass flow rate is 0.56 kg/s

The formula for calculating the mass flow rate is expressed as;

m = W / (hf - hg)

Such that the parameters are expressed as;

Substitute the values, we get;

m = 90 MW / (2418 - 2257)

Subtract the values, we have;

m = 90/161

Divide the values, we get;

m=  0.56 kg/s

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Answer:

el numero 1

Step-by-step explanation:

Answer:

1733.33

Step-by-step explanation:

The volume of a pyramid is (length*width*height) divided by 3

Answer:

1733.33

Step-by-step explanation:

v = (lwh)/3

v = (20 x 20 x 13)/3 = 5200/3 = 1733.33

(a) If plurality voting is used, Plan E will be chosen.

b It has the most first-place votes, with 2 each from voters 1 and 5. No other plan has more than 1 first-place vote.

c If the Borda Count method is used, Plan C will be chosen.

a The best part of this project was learning about different voting methods and how they can be used to choose a winner. The worst part of the project was the difficulty of calculating the Borda Count.

b If Instant Runoff Voting is used, Plan C will be chosen. In the first round of counting, Plan E is eliminated, as it has the fewest first-place votes. In the second round, Plan C is eliminated, as it has the fewest second-place votes. In the third round, Plan B is eliminated, as it has the fewest third-place votes. In the fourth round, Plan D is eliminated, as it has the fewest fourth-place votes. This leaves Plan A as the winner, as it has the most votes remaining.

c If the Borda Count method is used, Plan C will be chosen. Each voter's ballot is assigned a number of points equal to the number of candidates ranked lower than that candidate. For example, voter 1's ballot gives Plan E 5 points, Plan C 4 points, Plan A 3 points, Plan B 2 points, and Plan D 1 point. The total number of points for each candidate is then calculated. Plan C has the most points, with 16, so it is the winner.

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Answer:

They a similar because they both had zero as their final answer. Andre decided to do 3 x 200 while Jada  decided to do 3 x 50. Andre work is more complicated and uses big number while Jada's work uses small numbers and are more easier to do.

Step-by-step explanation:

Answer:

yes.

Step-by-step explanation:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional.

6/9 divided by 3/3= 2/3

proportional

Answer:

x²=20² -14²

x²=400-196

x²=204

x=√204