Find 3/7 of 1/5. A 4/12. B 3/35 C 8/35 D 22/35

Answer:

B) R - 52 = 208

Step-by-step explanation:

Robert has 52 more cards than Jason, who has 208, so Robert has 208 + 52 cards. This can be turned into:

R = 208 + 52

then subtract 52 from both sides:

R - 52 = 208 + 52 - 52

R - 52 = 208

and that's the answer

Probability that a randomly selected driver uses seat belt,

P(S)=0.56 P(S)= 0.44

The probability that a driver is stopped for a moving violation and using a seat belt is,

P(VIS)=0.002

The probability that a driver is stopped for a moving violation and not using a seat belt is,

P(VS')=0.004

(a)

The required probability is,

P(S|V)= P(VIS).P(S) P(VIS) P(S)+P(V | S').P(S') 0.002×0.56 (0.002x0.56)+(0.004×0.44)

0.00112 0.00288

0.389

(b)

The required probability is P(SV)= P(V S'). P(S) P(VS) P(S)+P(V|S') · P(S') . 0.004×0.44 (0.002x0.56)+(0.004 x 0.44)

0.00176

0.00288

≈ 0.611

Probability is a branch of mathematics that quantifies the likelihood of an event occurring or the likelihood of a statement being true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty.

Probability = number of paths to success. Total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

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The more variable the data, the less accurate the sample mean will be as an estimate of the population mean. In statistical analysis, accuracy is important. Statistical analysis is a method of gathering and examining data to uncover useful information.

A sample mean is a numerical estimate that represents a data set's central tendency. The population mean, on the other hand, is a statistical measure that represents the mean value of the entire population. The difference between the two lies in the fact that sample mean is computed on a subset of the population whereas population mean is calculated for the entire population. If the variability of the sample data is large, the sample mean becomes less accurate as an estimate of the population mean.

As a result, the more variable the data, the less accurate the sample mean will be as an estimate of the population mean.Therefore, it is essential to examine the variability of the data in order to better estimate the population mean. The greater the variability in the data, the more difficult it becomes to identify the true population mean and the less accurate the sample mean is as an estimator of the population mean.

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Answer:

31 yards

Step-by-step explanation:

If she has $12.83 left, that means she spent $2.17 out of the $15

15 - 12.83 = 2.17

One cent is .01 of a dollar

So that would be $0.07 per yard

To find the number of yards, we need to divide the total amount she spent by the price per yard.

2.17 ÷ 0.07 = 31

Each number should be classified as follows:

In Mathematics, there are six (6) common types of numbers and these include the following:

A rational number simply refers to a type of number which consist of integers, fractions, terminating or repeating decimals such as -3, 3, 1/2, -3 3/4, etc.

Additionally, an integer is a whole number that may either be positive, negative, or zero such as, -3, -2, -1, 0, 1, 2, 3, 4 etc.

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Answer:

1. 100        1. 150           1. 1

2.45          2. 800

Step-by-step explanation:

1. 25% * 400 = 0.25 * 400 = \(\frac{1}{4}\) * 400 = 100

2. 50% * 90 = 45

1. 75% * 200 = 0.75 * 200 = 3/4 * 200 = 150

2. 10% * 8000 = 0.1 * 8000 = 800

1. 5% * 20 = 0.05 * 20 = 1

Answer:

10,000+750x=25,000

Step-by-step explanation:

This is because shes starts with 10,000 and gets 750 per month so she needs x months to get to 25,000 you can also do 25,000-10,000/750 = x

The rate constant of inactivation is -0.6538 \(s^{-1}\).

To determine the rate constant of inactivation using the Chick-Watson model, we need to plot the natural logarithm of the surviving fraction of the virus (N/N₀) against time (t) and fit a linear regression to the data. The Chick-Watson model is given by the equation:

ln(N/N₀) = -kt

Where:

N₀ is the initial number of viruses (\(10^{6}\))

N is the number of viruses at time t

k is the rate constant of inactivation

Let's calculate the surviving fraction (N/N₀) and perform the linear regression:

Time (s) | N/N₀ | ln(N/N₀)

0 | 1.0 | 0.0

2 | 0.2 | -1.61

4 | 0.01 | -4.60

6 | 0.0015 | -6.50

8 | 0.0001 | -9.21

Using the given data, we can perform linear regression on the ln(N/N₀) values against time (t) values to determine the rate constant (k).

Let's calculate the rate constant (k) using linear regression:

Sum of ln(N/N₀) = -21.92

Sum of t = 20

Sum of (\(t^{2}\)) = 120

Mean of ln(N/N₀) = (-21.92) / 5 = -4.384

Mean of t = 20 / 5 = 4

Mean of (\(t^{2}\)) = 120 / 5 = 24

Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))] = -52.304

Sum of \((t-mean(t))^{2}\) = 80

Using the linear regression formula:

k = [Sum of [(t - mean(t)) * (ln(N/N₀) - mean(ln(N/N₀)))]] / [Sum of  \((t-mean(t))^{2}\) ]

k = -52.304 / 80 = -0.6538

Therefore, the rate constant of inactivation for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is approximately -0.6538 \(s^{-1}\).

Correct Question :

The data for NH2Cl disinfection of MS2 bacteriophage at a concentration of 2 mg/L is shown below. The temperature was 20 °C, the pH was 6.0. Determine the rate constant of inactivation assuming the Chick-Watson model applies with an n value of 1.0.

Time (s) 0 2 4 6 8

Number of virus \(10^{6}\) 0.2*\(10^{6}\) 0.1*\(10^{5}\) 0.15*\(10^{4}\) 0.1*\(10^{3}\)

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a. If the account pays simple interest at a rate of 4% per annum, Andrew would earn $500 in interest over 5 years. b. If the interest is compounded quarterly, Andrew would earn $530.64 in interest over 5 years.

a. Simple interest is calculated by multiplying the principal amount (initial deposit) by the interest rate and the time period. In this case, Andrew deposited $2500 and the interest rate is 4% per annum. So, the interest earned would be $2500 * 0.04 * 5 = $500.

b. When interest is compounded quarterly, the interest is added to the principal at the end of each quarter. The formula to calculate compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the interest rate, n is the number of times interest is compounded per year, and t is the time in years. In this case, the principal is $2500, the interest rate is 4% per annum (or 0.04), the number of times interest is compounded per year is 4 (quarterly), and the time period is 5 years. Plugging these values into the formula, we get A = 2500(1 + 0.04/4)^(4*5) ≈ $3030.64. The interest earned would be the difference between the final amount and the principal, which is $3030.64 - $2500 = $530.64.

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Answer:

Step-by-step explanation:

b

-5 and 7

Step-by-step explanation

lets try putting -5 and 7

-5 +7=2

and the difference is 8

i am not smart sorry

Answer:

2.94

Step-by-step explanation:

3.29 - 35/100 = 2.94

The region bounded by the parabolas r=t,4t2 and r=t,45−t2​, for −3≤t≤3 question content area bottom part 1 set up the line integral for the boundary

the combined parameterization of the boundary curves, f(x, y) represents the function being integrated, and ds represents the differential arc length.

To set up the line integral for the boundary of the region bounded by the parabolas, we need to parameterize the curves. Let's go through the process step by step.

1. Parameterize the curves:

For the curve r = t, 4t^2, we can parameterize it as:

x = t

y = 4t^2

For the curve r = t, 45 - t^2, we can parameterize it as:

x = t

y = 45 - t^2

2. Determine the limits of the parameter:

In this case, the parameter t ranges from -3 to 3 as given in the question: -3 ≤ t ≤ 3.

3. Combine the parameterizations:

Since both curves use the same parameter range, we can combine them into a single parameterization.

Let's call the combined parameterization (x(t), y(t)):

x(t) = t

y(t) = 4t^2 for -3 ≤ t ≤ 3

y(t) = 45 - t^2 for -3 ≤ t ≤ 3

4. Set up the line integral:

The line integral for the boundary of the region can be represented as:

∮C f(x, y) ds

where C represents the combined parameterization of the boundary curves, f(x, y) represents the function being integrated, and ds represents the differential arc length.

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♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

\(0 \leqslant y \leqslant 8\)

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Thus the correct answer is (( D )) .

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Answer: x = ∛5. This is even. If the answer is wrong I'm sorry.

Step-by-step explanation:

Let, speed of car B is -x.

So, speed of car A is x + 10.

Relative speed of A w.r.t B is ,

\(v_{ab}=(x+10)-(-x)\\\\v_{ab}=2x+10\ mph\)

So, time taken by A to travel 300 miles relative to B given by 3 hours .

\(v_{ab}=2x+10\\\\\dfrac{300}{3}=2x+10\\\\x = 45 \ mph\)

Therefore, speed of car A is 45 + 10 = 55 mph.

Hence, this is the required solution.

Answer:

Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99

Step-by-step explanation:

Cost of k key chain=$2.49

Cost of p photo frames=$2.49

Cost of a T-shirt=$5.99

Total cost of all items=cost of k key chain + cost of p photo frame + cost of The shirt

=2.49k + 2.49p + 5.99

Factorise

2.49 is common to both k and p

=2.49(k + p) + 5.99

Total cost of Theo's purchases in terms of k and p=2.49(k + p) + 5.99

Answer:

1. 36

2. 90

3. 9

4. 6

Step-by-step explanation:

x= 4  is a number and five is at least half the difference of six and the same number.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

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Answer: 36

Step-by-step explanation:

1.) You divide 180 by 20 to find out how many gallons their are

180÷20= 9

2.) Now you multiply the 9 by the cost of each gallon, which is $3.98

9×3.98= 35.82

3.) 35.82 is rounded to $36

The estimates of tolerance intervals, we first need to calculate the mean and standard deviation of the breaking strengths of the trash bags.

To calculate estimates of tolerance intervals using the empirical rule, we need to know the mean and standard deviation of the data. In this case, we are looking for the breaking strengths of trash bags.

The empirical rule states that for a normal distribution:
- Approximately 68.26% of the data falls within one standard deviation of the mean
- Approximately 95.44% of the data falls within two standard deviations of the mean
- Approximately 99.73% of the data falls within three standard deviations of the mean

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 Based on the given information, the ordered pairs formed to be plotted on graph are: (1,34) ; (2,68) ; (3,102) ; (4,136) ; (5,170) ; (6,204) and (7,238).

1.According to the values, k=34

2.Total revenue for 86 tickets=$2924

3.If venue has maximum of 200 people,total revenue earned=$6800

4.As the ratio of all the ordered pairs is same/equal to 1:34, it is proportional.

5.The pair (0,0) represents zero tickets sold & zero revenue earned.

6.The pair (6,204) indicates that for 6 tickets sold, $204 revenue earned.

What is graph?

Graph is a two or three dimensional axes or plane representing the location of any point from the reference point. This reference point is called origin which has coordinates (0,0) in 2-D plane and (0,0,0) in3-D plane.

Here, given that the cost of each ticket earns revenue of $34.

Similarly, revenue earned will be proportional to 34t, where t is the number of tickets.

2 tickets=2 x $34 =$68

3 tickets=3 x $34 =$102

4 tickets=4 x $34 =$136

5 tickets=5 x $34 =$170

6 tickets=6 x $34 =$204

7 tickets=7 x $34 =$238

The ordered pairs formed are:  (1,34) ; (2,68) ; (3,102) ; (4,136) ; (5,170) ; (6,204) and (7,238)

1.The value of constant K=$34

2.If tickets sold are 86:

86 tickets=86 x $34 =$2924

Total revenue for 86 tickets=$2924

3.If maximun capacity is 200 & all tickets are sold:

200 tickets=200 x $34 =$6800

If venue has maximum of 200 people,total revenue earned=$6800

4.As the ratio between number of tickets & total revenue at any point is 1:34, it is proportional.

5.The pair (0,0) represents zero tickets sold & zero revenue earned.

6.The pair (6,204) indicates that for 6 tickets sold, $204 revenue earned.

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Refer to the attachments for complete question,chart & graph.

Yes, it is valid to use the Central Limit Theorem (CLT) to describe the sampling distribution of the sample mean, even for a random sample of five households. Although a sample size of five is relatively small, the CLT still applies as long as the sample is random and independent.

  The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

While a sample size of five may be considered small, the CLT still holds for this case. The key consideration is that the sample is selected randomly and each observation is independent of the others. As long as these conditions are met, the CLT can be applied, even for small sample sizes.

In practice, larger sample sizes are generally preferred to ensure better approximation to the normal distribution. However, the CLT provides a theoretical foundation for the validity of using the normal distribution as an approximation for the sampling distribution of the sample mean, even with relatively small sample sizes like five households.

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Answer:

She can buy 5 bowls of noodles

Step-by-step explanation:

she has $10

each bowl cost $2

so then you divide 2÷10 which = 5

Answer:

The ratio at its simplest form it 4:1

Step-by-step explanation:

That means they type 4 letters in 1 second

Answer:

she types 4 letters in one second so its a 4:1 ratio of letters to seconds.

Step-by-step explanation:

The equation is 7x+11y+14z=33.

So,

The family of planes equation passing through the intersection of the planes x+2y+3z4=0 and 2x+yz+5=0 is:

It is assumed that the required plane's x-intercept is twice its z-intercept.

Substitute k = 4/5 in equation (1) as follows:

As a result, the required plane's equation is 7x+11y+14z=15.

Also,

7x+11y+14z=15 is the equation of the plane passing through the point (2,3,1) and parallel to the plane.

Therefore, the equation is 7x+11y+14z=33.

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the complete question is given below;
Find the equation of the plane which contains the line of intersection of the planes x+2y+3z−4=0 and 2x+y−z+5=0 and whose x−intercept is twice its z−intercept. Hence, write the equation of the plane passing through the point (2,3,−1) and parallel to the plane obtained above.

Answer:

1. y= -2/5x+3

2. y= 3x-2

3. y= -1/2+0

Step-by-step explanation:

The formula for a linear equation is y=mx+b with

m=slope

and b= the y-intercept.

We conclude that less than 30% of teen girls smoke to stay thin.

Let p be the percentage of teen girls who smoke to stay thin.

So, the Null Hypothesis,(\(H_{0}\)):

p≥ 30%

This means that at least 30% of teen girls smoke to stay thin

Alternate Hypothesis,(\(H_{A}\)) :

p < 30%

This means that less than 30% of teen girls smoke to stay thin.

The test statistics that would be used here

One sample z proportion statistics:

T.S = p' - p/ \(\sqrt{p'(1-p')/n}\) ≈N( 0,1)

Here p'= sample percent of teen girls who smoke to stay thin = 63/ 273 = 0.231

n = number of sample of teen girls = 273

Now putting these values we have:

Test statistics = 0.231 - 0.30/ \(\sqrt{0.231( 1- 0.231)/ 273}\)

                      = -2.705

So we get the value of z-test statistics as - 2.705.

As there is not provided in the question that the level of significance so we assume it to be 5%. Now at a 5% significance level, the z table gives the critical value of -1.645 for left- the tailed test.

As test statistics is less than the critical value of z that is -2.705< -1.645. So we reject our null hypothesis as will fall in reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore we get that less than 30% of teen girls smoke to stay thin.

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The lower bound for the number of minutes that it takes for all people to leave is of:

70 minutes.

At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:

29,750.

(as 29749 would be rounded to 29,700).

At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:

424 people per minute.

(as 425 people would be rounded to 450).

Hence the time it would take is obtained applying the proportion as follows:

29750/424 = 70 minutes.

(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).

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