Two rainstorms occurred in one week. First storm 15 mL of rain fell per hour. Second storm 30 mL of rain fell per hour. The rain lasted for a total of 70 hours with a total of 1500 mL. What was the duration of each storm?

Answer:  The required probability is [tex]\dfrac{14}{15}.[/tex]

Step-by-step explanation:  Given that the probabilities that A, B and C can solve a particular problem are [tex]\dfrac{3}{5},~ \dfrac{2}{3},~\dfrac{1}{2}[/tex] respectively.

We are to determine the probability that at least one of the group solves the problem , if they all try.

Let E, F and G represents the probabilities that the problem is solved by A, B and C respectively.

Then, according to the given information, we have

[tex]P(E)=\dfrac{3}{5},~~~P(F)=\dfrac{2}{3},~~P(G)=\dfrac{1}{2}.[/tex]

So, the probabilities that the problem is not solved by A, not solved by B and not solved by C are given by

[tex]P\bar{(A)}=1-P(A)=1-\dfrac{3}{5}=\dfrac{2}{5},\\\\\\P\bar{(B)}=1-P(B)=1-\dfrac{2}{3}=\dfrac{1}{3},\\\\\\P\bar{(C)}=1-P(C)=1-\dfrac{1}{2}=\dfrac{1}{2}.[/tex]

Since A, B and C try to solve the problem independently, so the probability that the problem is not solved by all of them is

[tex]P(\bar{A}\cap \bar{B}\cap \bar{C})=P(\bar{A})\times P(\bar{B})\times P(\bar{C})=\dfrac{2}{5}\times\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{15}.[/tex]

Therefore, the probability that at least one of the group solves the problem is

[tex]P(A\cup B\cup C)\\\\=1-P(\bar{A\cup B\cup C})\\\\=1-P(\bar{A}\cap \bar{B}\cap \bar{C})\\\\=1-\dfrac{1}{15}\\\\=\dfrac{14}{15}.[/tex]

Thus, the required probability is [tex]\dfrac{14}{15}.[/tex]

Final answer:

To find the probability that at least one of A, B, or C solves the problem, calculate 1 minus the probability that none solve it. The individual non-solving probabilities are multiplied together and subtracted from 1, resulting in a final answer of 14/15.

Explanation:

To determine the probability that at least one person out of A, B, and C solves a problem, we must first understand that the probability of at least one event occurring equals 1 minus the probability that none of the events occur (in this case, that none of the people solve the problem).

We have the individual probabilities as follows:

Probability A solves the problem: 3/5

Probability B solves the problem: 2/3

Probability C solves the problem: 1/2

The probabilities that A, B, or C do not solve the problem are then 1 - (3/5), 1 - (2/3), and 1 - (1/2), respectively. To find the probability that none of them solve the problem, we multiply these probabilities:

P(none solve) = (1 - 3/5) × (1 - 2/3) × (1 - 1/2)

Calculating this gives us P(none solve) = (2/5) × (1/3) × (1/2) = 2/30 = 1/15. Thus, the probability that at least one person solves the problem is:

P(at least one solves) = 1 - P(none solve) = 1 - 1/15 = 14/15.

Answer:

72/4=18 so she could make their lunch for 18 days

Step-by-step explanation:

so it would be 6x12 for the bagels which would be 72

for the apples it would be 8x9 which is 72

the cookies would be 12x6 to get 72

and the juice boxes would be 9x8 to get 72

divide that by 4 to get 18

Answer:

each paid $2.45

Step-by-step explanation:

9.80/4 = 2.45

Answer:

Step-by-step explanation:

We want to determine 95% confidence interval of the population proportion of republican voters who feel that the federal government has too much power.

43% of 300 randomly selected republican voters feel that the federal government has too much power. This means that

p = 43/100 = 0.43

q = 1 - p = 1 - 0.43 = 0.57

n = 300

mean, u = np = 300 × 0.43 = 129

Standard deviation, s = √npq = √129×0.57 = 8.575

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

129 +/- 1.96 × 8.575/√300

= 129 +/- 0.9704

= 129 +/- 0.9704

The lower end of the confidence interval is 129 - 0.9704 =128.0296

The upper end of the confidence interval is 129 + 0.9704 =129.9704

Therefore, with 95% confidence interval, the mean of the population proportion of republican voters who feel that the federal government has too much power is between 128.0296 and 129.9704

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, use the formula CI = p ± Z * √((p*(1-p))/n), where p is the sample proportion, Z is the Z-score for the desired confidence level, and n is the sample size. Given the sample proportion of 0.43, sample size of 300, and desired confidence level of 95%, the confidence interval is approximately 0.381 to 0.479.

To find the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power, we can use the formula:

CI = p ± Z * √((p*(1-p))/n)

Where:

Given that the sample proportion is 0.43, the sample size is 300, and the desired confidence level is 95%, we can calculate the 95% confidence interval:

CI = 0.43 ± 1.96 * √((0.43*(1-0.43))/300)

Simplifying the equation, we get:

CI = 0.43 ± 0.049

Therefore, the 95% confidence interval of the population proportion of Republican voters who feel that the federal government has too much power is approximately 0.381 to 0.479.

Answer:

(d.) 45, 54

Step-by-step explanation:

Let the first digit = y

Let the second digit = z

y +z = 9 ------------------------------------------ (1)

y²- yz +z² = 21------------------------------------(2)

From equation (2),

z = 9-y-------------------------------------------------(3)

Substitute equation (3) into (2):

y²- y(9-y) +(9-y)² = 21

y²-9y+y²+y²-18y+81 = 21

3y²-27y+ 81 = 21

3y²-27y+ 81-21= 0

3y²-27y+ 60= 0

y²- 9y +20= 0

(y -5) (y-4) =0

y= 5 or y =4

z = 4 or 5 (substituting into (3))

So the numbers are  54  or 45.

Answer:

volume of cone = 12.56 cubic units

Step-by-step explanation:

Volume of cone = 1/3  π r² h

            r = 2

            h = 3

then

V= 1/3 3.14 * (2) ² 3

 = 12.56 cubic units

Answer:

12.56 cubic units

Step-by-step explanation:

Right on Edge 2022

Answer:

C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Step-by-step explanation:

The equation of a straight line through a point [tex](x_{1}, y_{1})[/tex] with slope m is given by

                  [tex]y - y_{1} = m(x - x_{1})\\y - 9 = \frac{4}{5}(x - (-7))\\y - 9 = \frac{4}{5} (x + 7)[/tex]

Therefore the answer is C. [tex]y - 9 = \frac{4}{5}(x + 7)[/tex]

Answer:

  3 gallons

Step-by-step explanation:

He will make 8×(6 cups) = 48 cups of soup. There are 16 cups in a gallon, so 3·16 = 48 cups in 3 gallons.

Ariq will make 3 gallons of soup this year.

Answer:

Null hypothesis:[tex]p=0.25[/tex]  

Alternative hypothesis:[tex]p \neq 0.25[/tex]

z=2.53

pv=0.0114

So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .  

Step-by-step explanation:

1) Data given and notation

n=3010 represent the random sample taken

X represent the people who says that said that they use the Internet.

[tex]\hat p=\frac{X}{106}=0.27[/tex] estimated proportion of people who says that said that they use the Internet.

[tex]p_o=0.25[/tex] is the value that we want to test

[tex]\alpha[/tex] represent the significance level  

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that 50% of people who says that  they would watch one of the television shows.:  

Null hypothesis:[tex]p=0.25[/tex]  

Alternative hypothesis:[tex]p \neq 0.25[/tex]  

When we conduct a proportion test we need to use the z statisitc, and the is given by:  

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.27 -0.25}{\sqrt{\frac{0.25(1-0.25)}{3010}}}=2.53[/tex]

4) Statistical decision  

P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

We have the significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z>2.53)=2*(0.0057)=0.0114[/tex]  

So based on the p value obtained and using the significance given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they use the Internet differs from 0.25 or 25% .  

Answer:

option B)[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

According to the given conditions, the total number of outcomes are 24.

The probability that of drawing hearts card is

P=[tex]\frac{(total number of hearts cases)}{(total number of cases)}[/tex]

total number of hearts cases= 6

thus P= [tex]\frac{6}{24} = \frac{1}{4}[/tex]

now the probability of 4 or 6 is,

P=[tex]\frac{(total number of 4 or 6 cases)}{(total number of cases)}[/tex]

thus P= [tex]\frac{8}{24} = \frac{1}{3}[/tex]

thus, by multiplication law,

final probality is P= [tex](\frac{1}{4})(\frac{1}{3})[/tex]

P= [tex]\frac{1}{12}[/tex]

There are 3 individual instances of each of the 'x' and 'y' members, while there's only one instance of static member 'z'. The value of 'x' and 'y' members in each object is 0.

The subject of this question pertains to class declarations in the field of programming, with a focus on how variables are instantiated among objects of a class. Specifically, the interest is on the number of instances and values of private and static member variables in the class Thing which includes private int x, private int y and static int z.

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Final answer:

There are three separate instances each of the non-static members x and y, one instance of the static member z, and since the constructor initializes x and y to z's value, they will both have the value 0.

Explanation:

The question involves understanding the concept of members and static members in the C++ programming language, specifically within the context of class instances. When considering the provided class declaration and the creation of three instances of the Thing class, we are dealing with object-oriented programming principles.

A) Each instance of a class has its own separate set of non-static members. Since x is a non-static member and we have three instances, there are three separate instances of the x member.

B) Similarly, y is a non-static member. Thus, there are also three separate instances of the y member.

C) The z member is declared as static, meaning that it is shared across all instances of the class. Therefore, there is only one instance of the z member that exists across all instances of the class.

D) Because the constructor initializes x and y with the value of z, and z is initially set to 0, the value stored in the x and y members of each object will be 0.

The question is flawed due to its opinion-based and leading nature. It presupposes information, leads the participant, and doesn't provide a full range of response options.

This question, as posed by the 1995 Corporation for Public Broadcasting poll, is opinion-based and leading. There are several factors that make this question flawed. Firstly, it presupposes information by referencing a psychological study that potentially not all participants may be aware of, providing an initial bias. Secondly, it leads the participant in the direction of agreeing with the study, providing no neutral or mixed opinion option. Lastly, the question does not allow for participants to disagree somewhat, only strongly, which may influence the responses to be more in line with the premise of the study. In reliable polling, questions should offer sufficient options for the participant to choose from that captures the range of potential opinions and should avoid leading language or assumptions to obtain an accurate representation of the participants' views.

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Final answer:

The distance from Seattle to the rugged wilderness, calculated using the average speeds and total travel time, is found to be 7424 miles.

Explanation:

Given that a private plane traveled to and from a rugged wilderness, with average speeds of 312 mph on the way to the wilderness and 364 mph on the return trip to Seattle, and the total flying time for round trip was 44 hours, we can calculate the distance by using the formula for average speed, which is average speed = total distance/total time.

Let's denote the distance between Seattle and the wilderness as x miles. The time taken to fly to the wilderness is then x/312 and the time taken to fly back is x/364.

The total flying time of 44 hours can be split into the sum of the time going to the wilderness and coming back, which gives us:
(x/312) + (x/364) = 44.

To solve for x, we need to find a common denominator and solve the equation.

Common denominator for 312 and 364 is 114,048.

Convert the equation: (364x + 312x) / 114048 = 44.

Multiply both sides by 114048: 676x = 5018112.

Divide both sides by 676: x = 7424.

Therefore, the distance from Seattle to the rugged wilderness is 7424 miles.

Step-by-step explanation:

24. A

B' ( t ) = 10 [ 20 CDS ( t/10) ] = 2 COS ( t/10 )

B' ( 7 ) = 1.5

After 7 days the number of beds in use is increasing at the rate of 1 1/2 beds per day.

24.B

2 COS ( t/10) =0

using calculator t = 15.7

B (12) = 20 Sin (1.2) + 50 = 68.6 = 69

B (15.7) = 20 Sin (1.57) + 50 = 70

B (20) = 20 SIn (20) + 50 = 68.25 = 68

Maximum number of beds in use occurs in afternoon of 15th day and is 70 beds.

I hope that helps and I hope  it's right  

Answer: -1.17522136 hertz

there you go :) just to let you know I’m in 7th

Answer:

The answer to your question is r = 2x

Step-by-step explanation:

Volume of a cylinder = V = π r² h

r = radius

h = height = x

Volume = 4x³

Then

                  r² = [tex]\frac{volume}{\pi h}[/tex]

                  r² = [tex]\frac{4x^{3} }{\pi x}[/tex]

                  r² = 4x²

                  r = 2x

Answer:

  H = 30

Step-by-step explanation:

The value of a fraction is zero when its numerator is zero. The value of h that makes the numerator zero is 20.

  h = 20

Answer:

  A.  0

Step-by-step explanation:

The value of the discriminant is ...

  b² -4ac = (-3)² -4(1)(4) = 9 - 16 = -7

The negative discriminant means the roots will be complex.

There are 0 real solutions.

Answer: The weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.

Step-by-step explanation:

Since we have given that

Percentage of seed mixture X for ryegrass = 40%

Percentage of seed mixture Y for ryegrass = 25%

If a mixture of X and Y contains 30 percent ryegrass,

Let total seed mixture be 100

So, for seed X = x

For seed Y = 100-x

So, According to question,

[tex]0.4x+0.25(100-x)=30\\\\0.4x+25-0.25x=30\\\\0.15x=30-25\\\\0.15x=5\\\\x=\dfrac{5}{0.15}\\\\x=\dfrac{100}{3}[/tex]

So, weight of mixture X is given by

[tex]\dfrac{\text{Weight of X}}{\text{Weight of mixture}}\times 100\\\\=\dfrac{\dfrac{100}{3}}{100}\times 100\\\\=\dfrac{100}{3}\%\\\\=33\dfrac{1}{3}\%[/tex]

Hence, the weight of X is [tex]33\dfrac{1}{3}\%[/tex] of weight of mixture.

Answer:

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

Answer:

The answer to your question is below

Step-by-step explanation:

[tex]\frac{x^{6}- 1 }{x -1} = \frac{x^{6}+ 0x^{5} + 0x^{4} + 0x^{3} + 0x^{2} + 0x - 1 }{x - 1}[/tex]

Synthetic division

                             1    0   0   0   0   0   -1    1

                                   1    1    1    1    1     1                                                

                             1    1     1    1    1    1    0              

Quotioent =    x⁵ + x⁴ + x³ + x² + x

Remainder = 0

Answer:

Gina's pay rate next month will be =$9.9 per hour

Step-by-step explanation:

Gina was initial earnings was = $10 per hour

She received an increase by = 10%

Increase in amount received = [tex]10\%\ of\ \$10= 0.1\times\$10 =\$1 [/tex]

New earnings = [tex]\$10+\$1=\$11[/tex] per hour

Next month her pay rate will decrease by = 10%

Decrease in pay rate next month will be = [tex]10\%\ of\ \$11= 0.1\times\$11 =\$1.1 [/tex]

Thus, Gina's pay rate next month will be = [tex]\$11-\$1.1=\$9.9[/tex] per hour

Answer:

C. straight

Step-by-step explanation:

 A Linear Pair is two adjacent angles whose non-common sides form opposite rays.

If two angles form a linear pair, the angles are supplementary.

A linear pair forms a straight angle which contains 180º, so you have 2 angles whose measures add to 180, which means they are supplementary.

In the figure given in attachment, AB and BC are two non common sides of ∠ABD and ∠DBC.

∠1 and ∠2 form a linear pair.

The line through points A, B and C is a straight line.

∠1 and ∠2 are supplementary.

Thus two non-common sides of adjacent supplementary angles form a straight angle.

Answer: the price of an adult ticket is $11

the price of a child ticket is $11

Step-by-step explanation:

Let x represent the price of an adult ticket.

Let y represent the price of a student ticket.

On the first day of ticket sales the school sold 7 adult tickets and 6 student tickets for a total of $143. This means that

7x + 6y = 143 - - - - - - - - - -1

The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets. This means that

4x + 13y = 187 - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 7, it becomes

28x + 24y = 572

28x + 91y = 1309

Subtracting

-67y = -737

y = -737/-67 = 11

Substituting y = 11 into equation 1, it becomes

7x + 6×11 = 143

7x + 66 = 143

7x = 143 - 66 = 77

x = 77/7 = 11

Answer:

A. 0.0021

Step-by-step explanation:

Given that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1inches.

Sample size = 36

Std dev of sample = [tex]\frac{2.1}{\sqrt{36} } =0.35[/tex]

The sample entries X the heights are normal with mean= 66.9 inches and std deviation = 0.35 inches

Or we have

Z = [tex]\frac{x-66.9}{0.35}[/tex]

Hence the probability that they have a mean height greater than 67.9 inches

=[tex]P(X>67.9)\\=P(Z>\frac{1}{0.35)} \\=0.00214[/tex]

So option A is right answer.

Final answer:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, calculate the z-score and find the corresponding area under the standard normal distribution curve.

Explanation:

To find the probability that the mean height of 36 randomly selected men is greater than 67.9 inches, we need to calculate the z-score and find the corresponding area under the standard normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / (σ / √n)

Where x is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the given values into the formula, we have:

z = (67.9 - 66.9) / (2.1 / √36) = 1.71

Using a standard normal distribution table or a calculator, we can find that the area to the right of a z-score of 1.71 is approximately 0.0436.

Since we want the probability of having a mean height greater than 67.9 inches, we need to calculate the area to the right of the z-score. Therefore, the probability is approximately 1 - 0.0436 = 0.9564.

12 CDs ............... 2 %

x CDs .............100 %

x = 12×100/2 = 1200/2 = 600 Cds/month

The required number of CD that was sold last month is 600 CD's.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the number of total CDs sold be x,

The music department of a department store sold 12 jazz CDs last month.
Jazz sales during that month made up 2% of the music department's total sales.

2% of x = 12
x = 12 / 2%
x = 12 / 0.02
x = 600

Thus, the required number of CD that was sold last month is 60 CD's.

Learn more about percentages here:

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Answer: number of people that had allergic reactions is 0.7%

Step-by-step explanation:

The total number of people that came to try the company's product is 3000

21 out of the 3,000 people had an allergic reaction. We want to determine how many percent of the total number of 3000 people that tried the product is 21 people that had reaction

Percentage of people that had allergic reactions = number of people that had allergic reactions / total number of people that tried the products × 100

Percentage of people that had an allergic reaction

= 21/3000× 100

= 0.007 × 100 = 0.7%

Answer:

40

Step-by-step explanation:

Since your only buying stickers you divide 10 by 0.25 to see how many you can purchase.

Answer:

It means a sticker costs $0.25 and a charm costs $0.5

Therefore without buying any charm

You can use $10 to buy 10/0.25

40 stickers

Step-by-step explanation:

I think the answer would be -$5.17 because you would have to find the unexpected value.

I think the answer to this picture is 0.122

Game:

1/36(94) + 35/36(-8) = 94/36 -280/36 = -186/36 = -5.17

4. Add the probabilities together for 5 and under:

0.122 + 0.061 + 0.022 + 0.006 + 0.001 = 0.212

Airline :

Given: P = 70, P = 97% = 0.97, q = 1-0.97 = 0.03

Probability of being greater than 68:

(70 * 0.97^69 * 0.03^1) + (1*0.97^70*1)

= 0.2567 + 0.1185

= 0.375

Answer:

Easy, it is C) $136,800

Step-by-step explanation:

All you need to do is multiply $3,800 by 12 to get the yearly rent. To get $45,600 per year. You now multiply $45,600 by 3 to get the total price of the 3 year lease. You now have a total cost of $136,800 over the 3 year time period of the lease.