a man walks around a field once.
a runner runs around the field 6 times in the same time
the walker walks at 3m/s
calculate the speed of the runner.

Answer:

16.5 gallons per minute.

Step-by-step explanation:

The given table is:

\(\begin{center}\begin{tabular}{ c c } Time(minutes) & Water(gallons) \\ 1 & 16.50 \\ 1.5 & 24.75 \\ 2 & 33 \\\end{tabular}\end{center}\)

We are given this linear function in the form of table.

Let 't' be the time and W(t) be the function with which the gallons of water are changing with time.

We can use slope intercept form to find the equation.

\(y=mx+c\)

Slope of a function:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

\(x_2 = 1.5\\x_1 = 1\\y_2 = 24.75\\y_1 = 16.50\)

\(m=\dfrac{24.75-16.50}{1.5-1}\\\Rightarrow m =16.5\)

This slope is the constant of proportionality.

i.e. the rate at which the number of gallons are changing per minute.

So, the answer is 16.5 gallons per minute.

Explanation:

Everywhere you see an x, replace it with 5. Then simplify using PEMDAS

f(x) = x^2 - 3x

f(5) = 5^2 - 3(5) ... plug in x = 5

f(5) = 25 - 15

f(5) = 10

Answer:

loss is 91.8%

Step-by-step explanation:

The man made a loss not a gain

%loss = CP - Sp/Cp * 100

%loss = 5500 - 450/5500 * 100

%loss  = 5050/5500 * 100

%loss  = 0.918 * 100

%loss  = 91.8%

Hence the man percentage loss is 91.8%

Answer:6,155.55

Step-by-step explanation: 6.255*1010=6,317.55

1.5*108=162

6,317.55-162=6,155.55

Answer:  X=-4

Step-by-step explanation:

The point e. x = 5, y = 0 satisfies the two linear constraints simultaneously. We have two linear constraints which are given as;

2x + 5y ≤ 10 (Equation 1)

10x + 6y ≤ 42 (Equation 2)

We need to find the point which satisfies both equations. Let us plug in the values one by one to check which one satisfies the two equations simultaneously.

a. x= 6, y = 2

In Equation 1:2x + 5y = 2(6) + 5(2) = 17

In Equation 2:10x + 6y = 10(6) + 6(2) = 66

Thus, this point does not satisfy equations 1 and 2 simultaneously.

b. x=6, y=4

In Equation 1:2x + 5y = 2(6) + 5(4) = 28

In Equation 2:10x + 6y = 10(6) + 6(4) = 72

Thus, this point does not satisfy equations 1 and 2 simultaneously.

c. x=2, y = 1

In Equation 1:2x + 5y = 2(2) + 5(1) = 9

In Equation 2:10x + 6y = 10(2) + 6(1) = 26

Thus, this point does not satisfy equations 1 and 2 simultaneously.

d. x=2, y = 6

In Equation 1:2x + 5y = 2(2) + 5(6) = 32

In Equation 2:10x + 6y = 10(2) + 6(6) = 52

Thus, this point does not satisfy equations 1 and 2 simultaneously.

e. x = 5, y = 0

In Equation 1:2x + 5y = 2(5) + 5(0) = 10

In Equation 2:10x + 6y = 10(5) + 6(0) = 50

Thus, this point satisfies both equations simultaneously.

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Answer

put 1 on top and exo on bottom

Step-by-step explanation:

Answer:

  4n√(3n) +3√n -√(3n)

Step-by-step explanation:

The expression can be simplified, but terms cannot be combined.

  \(\sqrt{48n^3}+\sqrt{9n}-\sqrt{3n}=\sqrt{(4n)^2(3n)}+\sqrt{3^2n}-\sqrt{3n}\\\\=\boxed{4n\sqrt{3n}+3\sqrt{n}-\sqrt{3n}}\)

The steps to condensing the expressions
2loga(4)+3loga(X-4)loga(4)

Log(x+3)+log(x-3) is given below.

To condense the   expressions, we can apply the  properties of logarithms. Here are the condensed forms of the given expressions.

2loga (4) + 3loga(X - 4) - loga 4 )  

By using the product and quotient rules of logarithms, we can simplify this expression as follows

2 loga( 4) + 3 loga( X-4) - log a(4)

= loga(4 ²) + loga((X-4)³) -  loga (4) = loga (16 ) + loga((X-4)³) - loga (4)

Combining the logarithms  using the power rule and quotient rule we have

= loga(16(X-4)³/4)

log(x+3) + log (x-3)

By using the product rule of logarithms, we can combine these logarithms

log (x +3) +log (x - 3) = log ((x +3 )(x -3 ))

Simplifying further, we get

= log (x² - 9 )

So this means that the condensed forms of the given expressions are

2loga( 4) + 3loga(X -4) - loga (4) = loga(16 (X-4) ³/4)

log (x+ 3) + log(x- 3) = log(x² - 9)

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Answer:

-16x-28

Step-by-step explanation:

Break it into little pieces; start with distributing the -7:

-7(5+x)

-35-7x

Now add the rest of the problem: 7-35-7x-9x

Combine like terms: 7-35               7x-9x

7-35=-28             7x-9x=-16x

Rearrange so the coefficient and variable are upfront, giving you:

-16x-28

If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to widen.

This is because the standard deviation is a measure of the spread of the data, so if it increases, the data points are more spread out from the mean. As a result, the range of values that could reasonably contain the true population parameter (i.e., the confidence interval) needs to be wider to account for the increased variability in the sample.
If the population standard deviation of a sample increases without other changes, the confidence interval is most likely to become wider.
When standard deviation increases, it indicates more variability in the data. As a result, the confidence interval, which is a range of values that estimates the true population parameter with a certain level of confidence, needs to be wider to account for the increased variability. This ensures that the true population parameter is still captured within the interval with the same level of confidence.

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Answer:

22 + 2\(\sqrt{2}\)

Step-by-step explanation:

(4 + \(\sqrt{2}\) )(6 - \(\sqrt{2}\) )

each term in the second factor is multiplied by each term in the first factor.

4(6 - \(\sqrt{2}\) ) + \(\sqrt{2}\) (6 - \(\sqrt{2}\) ) ← distribute both parenthesis

= 24 - 4\(\sqrt{2}\) + 6\(\sqrt{2}\) - 2 ← collect like terms

= 22 + 2\(\sqrt{2}\)

Answer/Step-by-step explanation:

43 = (4 * 101) + (3 * 100)

43 = (4 * 10) + (3 * 1)

43 = 40 + 3

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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Answer: 100001

Step-by-step explanation: The trick for binary is that it only uses 1 & 0 for its number system. It goes by a system where you take 1 and multiply by 2, then you multiply 2 by 2, and so forth. So 33 has one 32, and one 1.

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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The random variable is the number of brown MOM's in a package of 50 MOM's. The given numbers are n = 50 and p = 0.13. The probabilities of exactly none, exactly 44, at least 43, and at most 45 MOM's being brown can be calculated using the binomial probability formula.

a) The random variable in this scenario is the number of brown MOM's in a package of 50 MOM's.

b) The given numbers with correct symbols are:

n = 50 (number of MOM's in the package)

p = 0.13 (proportion of brown MEM's)

c) This is a binomial experiment because the following conditions are met:

- There are only two outcomes for each MOM: brown or not brown.

- The number of MOM's is fixed at 50.

- The probability of selecting a brown MOM remains constant at 13% for each randomly selected MOM.

- The selection of one MOM being brown does not affect the probability of another MOM being brown.

d) The probability that exactly none of the MOM's are brown can be calculated using the binomial probability formula as P(X = 0) = C(50, 0) * (0.13)^0 * (1 - 0.13)^(50 - 0).

e) The probability that exactly 44 MOM's are brown can be calculated using the binomial probability formula as P(X = 44) = C(50, 44) * (0.13)^44 * (1 - 0.13)^(50 - 44).

f) The probability that at least 43 MOM's are brown can be calculated by summing the individual probabilities of having 43, 44, 45, ..., 50 MOM's brown. This can be calculated as P(X ≥ 43) = P(X = 43) + P(X = 44) + ... + P(X = 50).

g) The probability that at most 45 MOM's are brown can be calculated by summing the individual probabilities of having 0, 1, 2, ..., 45 MOM's brown. This can be calculated as P(X ≤ 45) = P(X = 0) + P(X = 1) + ... + P(X = 45).

By substituting the appropriate values into the binomial probability formula and performing the calculations, we can find the probabilities (d), (e), (f), and (g) to 4 decimal places.

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Answer:

n-5

 2

Steps:

subtract n ny 5 and then hind half of the difference.

Answer:

a. 35 people participated in the walk.

b. About 16 people traveled more than 14 kilometers.

Step-by-step explanation:

(Warning: This may be wrong)

Answer:

b; |-4|<|-5|

Step-by-step explanation:

Absolute value is the distance from zero, so the absolute value of -5 is greater than the the absolute value of -4.

The equation of the line of h is x2 + y2 + 2 = 0

Lines that are parallel do not intersect or meet at any point in a plane. They are always parallel and equidistant from each other. Parallel lines are non-intersecting lines.

Given that Line p is parallel to h

Line p connects the points (2, 4), (4, 2)

The slope of a given point

m = (y_2-y_1)/(x_2-x_1 )

m = (2-4)/(4-2)

m = -2/2

m = -1

Now line h passes through the point (-1, -1)

m = (y_2-y_1)/(x_2-x_1 )

-1 = (y_2+1)/(x_2+ 1)

-x2 -1 = y2 +1

x2 + y2 + 2 = 0

There the equation of the line of h is x2 + y2 + 2 = 0

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The largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

Explanation:

To find where the function is increasing, we need to find where the first derivative of the function is positive. Taking the derivative of f(x), we get:

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

The denominator of this expression is always positive, so the sign of f'(x) is determined by the numerator. The numerator is negative for x < 0 and positive for x > 0. Therefore, f(x) is decreasing on (-∞, 0) and increasing on (0, ∞).

We also need to check the endpoints of these intervals to make sure that the function is increasing on the entire interval. As x approaches negative infinity, the function approaches 0, and as x approaches positive infinity, the function approaches 0. Therefore, the function is increasing on (-∞, 0) ∪ (0, ∞).

In summary, the largest open interval where the function f(x) = 1/(x^2+1) is increasing is (-∞, 0) ∪ (0, ∞). On this interval, the function is increasing from negative infinity to zero and from zero to positive infinity.

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The value of v is 8.83.

A rational equation is an equation that includes one or more fractions with polynomials. It can be solved by cancelling common factors between the numerator and the denominator, and then solving the resulting equation. It is important to note that when cancelling common factors, one must always check that the original equation is still satisfied.

To solve this rational equation that simplifies to linear, you need to solve for v. To do this, first multiply both sides by the denominator:

6(v-8) = 5

Then add 8 to both sides to get rid of the variable in the denominator:

6v - 48 = 5

Finally, add 48 to both sides to isolate the variable v:

6v = 53

Finally, divide both sides by 6 to solve for v:

v = 53/6 = 8.83

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Answer:

\(a = \frac{a - 12bh}{12a} \)

Answer:40

Step-by-step explanation:

One of Pryor's 10 Laws of shaping is D. Train one behavior at a time is one of Pryor's 10 Laws of shaping. This law emphasizes the importance of focusing on one behavior at a time when shaping behavior.

By doing so, the trainer can avoid confusing the animal and can more effectively reinforce the desired behavior. This law also helps the trainer to break down complex behaviors into smaller, more manageable parts, which can then be shaped individually.

According to Karen Pryor's 10 Laws of Shaping, one of the key principles is to train one behavior at a time. This is important because it helps the learner to focus on mastering a specific behavior without getting overwhelmed or confused by multiple tasks.

By concentrating on one behavior at a time, the trainer can provide clear, consistent reinforcement and feedback, which increases the likelihood of successfully shaping the desired behavior.

Overall, following this law can lead to more successful shaping and training outcomes.

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Among the provided options, Pryor's 10 Laws of Shaping suggests training one behavior at a time. This technique avoids confusion and ensures reliable behavior is established before moving to the next behavior.

According to Pryor's 10 Laws of Shaping, among the given options, the correct answer is: Train one behavior at a time. This rule focuses on the fact that trying to shape multiple behaviors simultaneously can often lead to confusion for the individual or animal being trained. Instead, it's more effective to focus on one behavior at a time, reinforcing each successful approximation towards the target behavior before moving on to the next. The goal is to build a strong, reliable behavior before adding complexity or new behaviors.

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Answer:

the total volume is 0.0157 m³.

Step-by-step explanation:

To calculate the total volume of the four concrete pillars, we need to find the volume of one pillar and then multiply it by four.

The volume of a cylinder can be calculated using the formula:

Volume = π * r^2 * h

Where:

π ≈ 3.14159 (pi, a mathematical constant)

r = radius of the cylinder

h = height of the cylinder

Given:

Diameter of each pillar = 50 cm

Radius (r) = Diameter / 2 = 50 cm / 2 = 25 cm = 0.25 m

Height (h) = 4 cm = 0.04 m

Now we can calculate the volume of one pillar:

Volume of one pillar = π * (0.25 m)^2 * 0.04 m

Calculating the above expression gives us:

Volume of one pillar = 3.14159 * (0.25 m)^2 * 0.04 m

= 3.14159 * 0.0625 m^2 * 0.04 m

= 0.00392699082 m^3

Since we have four pillars, we can multiply the volume of one pillar by four to get the total volume of the four pillars:

Total volume of the four pillars = 4 * 0.00392699082 m^3

Answer: The total volume of the four pillars is 0.251 cubic meters.

Step-by-step explanation: The volume of a cylinder is calculated by multiplying the area of its base by its height. The area of the base of a cylinder is calculated by multiplying the square of its radius by pi (π).

The radius of each pillar is half its diameter, so it’s 25cm.

The height of each pillar is 4m (400cm).

So, the volume of one pillar is π * (25cm)^2 * 400cm = 785398.16 cubic centimeters.

Since there are four pillars, the total volume is 4 * 785398.16 cubic centimeters = 3141592.64 cubic centimeters.

Since 1 cubic meter = 1000000 cubic centimeters, the total volume in cubic meters is 3141592.64 / 1000000 = 0.251 cubic meters.

Hop this helps, and have a great day! =)

Answer:

13.2 g

Step-by-step explanation:

let x = grams sugar in a 200 ml glass

16.5 g sugar / 250 ml = x g sugar / 200 ml

x(250) = (16.5)(200)

x =  (16.5)(200) / (250) = 3300 / 250 = 13.2

Answer:  there are 13.2 g sugar in a 200 ml glass of juice

Given: Mary, Gracie, and Nancy all have little collections of seashells, but Gracie has 5 more than 14 times as many as Mary does. So Mary has 16 shells

To find: Recognize the equation that captures this circumstance and recognize its resolution.

olution:

Let x be mary's shells, so according to question, we get:

gracie = 14x + 5   nancy  = 1 x+ 1

Now we have given that:

          gracie = nancy

So: 14x + 5 = 1 x + 1

  5/4x + 5 = 3/2x + 1

Fractions will be eliminated by multiplying by the common denominator of 4, but this step is optional; you can still work with fractions if you choose.

Now solving further, we get:

        5x + 20 = 6x + 4  5x - 6x = 4 - 20    -x = - 16    x = 16.

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