Jermaine lives in Los Angeles and his cousin Brandon lives in San Francisco. The two cities are 381 miles apart. They want to meet somewhere in between the two cities. They start at 8:00 am in the morning. Jermaine drives at 67 miles per hour, and David drives at 60 miles per hour. What time will they meet?

The perimeter of the rectangle, when the area is maximized, is approximately 24.63 units. Therefore, correct option is a.

To maximize the area of the rectangle inscribed in the parabola \(y^2 = 16x\), we need to find the dimensions of the rectangle. Since the side of the rectangle is along the latus rectum of the parabola, we know that the length of the rectangle is equal to the latus rectum.

The latus rectum of the parabola \(y^2 = 16x\) is given by the formula 4a, where "a" is the distance from the focus to the vertex of the parabola. In this case, the focus is located at (4a, 0).

To find "a," we can equate the equation of the parabola to the general equation of a parabola in vertex form: \(y^2 = 4a(x - h)\), where (h, k) is the vertex of the parabola.

Comparing the two equations, we get:

4a = 16

a = 4

Therefore, the latus rectum of the parabola is 4a = 4 * 4 = 16 units.

Since the length of the rectangle is equal to the latus rectum, we have length = 16 units.

Now, to find the width of the rectangle, we need to determine the corresponding y-coordinate on the parabola for the given x-coordinate of the latus rectum. The x-coordinate of the latus rectum is half the length, which is 16/2 = 8 units.

Substituting x = 8 into the equation of the parabola, we get:

\(y^2 = 16(8)\\y^2 = 128\\y = \sqrt{128} = 11.31\)

Therefore, the width of the rectangle is approximately 11.31 units.

The perimeter of the rectangle is given by the formula:

Perimeter = 2(length + width)

Plugging in the values, we have:

Perimeter = 2(16 + 11.31)

Perimeter ≈ 2(27.31)

Perimeter ≈ 54.62

Rounding the perimeter to two decimal places, we get approximately 54.62 units, which is equivalent to 24.63 units.

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Answer:

-23.8 and +23.8

Step-by-step explanation:

Answer:

The 95% confidence interval lies between -23.8 and +23.8

Step-by-step explanation:

I just did it on Edmentum.

In a trapezoid, the height is the perpendicular distance between the two parallel bases. It is usually denoted as "h".

In order to determine the height of a trapezoid, we need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions.

The lengths of the bases of a trapezoid are crucial for calculating the height using various formulas. Without the lengths of the bases or any other relevant information, we cannot determine the height of the trapezoid.

To determine the height of a trapezoid, we need more information. The height of a trapezoid is typically defined as the perpendicular distance between the two parallel bases. In this case, we would need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions. Without that information, we cannot determine the height of the trapezoid.

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Answer: 5 units

Step-by-step explanation:

The equation that is set up correctly using the Pythagorean Theorem for the triangle below is 9^2 + x^2 = 15^2.

The concept that will be used here is Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Pythagoras discovered that the square of the hypotenuse of a right-angled triangle, where one of the angles is 90 degrees, equals the sum of the squares of the other two sides:

According to theorem, the (adjacent)^2 + (opposite)^2 = (hypothenus)^2.

a^2+b^2=c^2

The 9^2 + x^2 = 15^2

Therefore, option C is correct.

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The required arc length of sector VW is 8\(\pi\).

Given that, in a circle U, radius  UV = 9 and  central angle of sector m∠VUW = 160°.

To find the arc length of sector VW, we can use the formula:

Arc length = (central angle / 360) x circumference of the circle.

First,  find the circumference of the circle by the  formula for the circumference of a circle is given by:

Circumference = 2 x \(\pi\) x radius.

Circumference = 2 x \(\pi\) x 9 = 18π.

Now, let's find the arc length of sector VW using the central angle of 160 degrees:

Arc length = (160/360) x 18π

Arc length = (4/9) * 18\(\pi\) = 8\(\pi\).

Therefore, the arc length of sector VW is 8\(\pi\).

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Answer:

3360.

Step-by-step explanation:

That would be the number of permutations of 3 from 16.

= 16P3

= 16!/(16-3)!

= 16*15*14

= 3360

Answer:

3 360 permutations

Step-by-step explanation:

the number of permutations :

16P3 = 16 × 15 × 14 = 3 360

Answer:

Name as a person

Step-by-step explanation:

Answer:

In the name of a person.

Step-by-step explanation:

The seasons are not written with capital letters unless they form part of a name. For example:

I am leaving in the winter.

I live near Winter Mountain River.

Answer:

Yes

Step-by-step explanation:

The reason is all u do is 12 +1=13 aka 1pm then 30 +50=80 making the time 2:20

No, the sample mean or sample proportion will not always be inside a confidence interval for the population mean or population proportion.

The reason is that a confidence interval is constructed based on the observed sample data and provides a range of values within which the true population parameter is likely to fall.

However, there is still a certain level of uncertainty involved.

Confidence intervals are calculated based on the principles of statistical inference, which involve making inferences about a population based on a sample.

The width of a confidence interval depends on several factors, including the sample size, the variability of the data, and the desired level of confidence.

When constructing a confidence interval, we make assumptions about the distribution of the data, such as assuming the data follows a normal distribution.

If these assumptions are violated, or if the sample is not representative of the population, the resulting confidence interval may not accurately capture the true population parameter.

Moreover, confidence intervals are subject to sampling variability. This means that if we were to take multiple samples from the same population and calculate confidence intervals for each sample, the intervals would vary.

In some cases, the sample mean or sample proportion may fall outside the confidence interval, indicating that the estimated parameter based on that particular sample is not within the range of likely values for the population.

In summary, while confidence intervals provide a useful tool for estimating population parameters, they are not infallible.

There is always a margin of error and uncertainty associated with statistical inference, and it is possible for the sample mean or sample proportion to fall outside the calculated confidence interval.

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Answer:

52.5

Step-by-step explanation:

median is where u find the middle number

put them in order first

24,28,51,54,67,70

its between 54 and 51

Answer:

fourteen times six equals eighty-four, eighty-four plus six equals 90

Answer:

slope = - 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 8,6) and (x₂, y₂ ) = (0, - 2) ← 2 points on the line

m = \(\frac{-2-6}{0+8}\) = \(\frac{-8}{8}\) = - 1

Answer:

\( an \: equation \: for \: this \: problem \:i s \: \to : \\ \boxed{ 7200 = 12t}\)

Step-by-step explanation:

\(let \: the \: distance \: be \to \: d \\ \\ let \: the \: speed \: rate \: be \to \: s \\ \\ let \: the \: time \: of \: action \: be \to \: t \\ therefore \to: \\ s = \frac{d}{t} = 12 = \frac{7200}{t} \\ \\ 7200 = 12t \\ \)

**Maximum Area with a given perimeter:**

The rectangle with the maximum area, given the perimeter of 'P' units, the length and width would be 'P / 4' units each.

To find the length and width of a rectangle that has a given perimeter and a maximum area, we can utilize the concept that a square has the maximum area for a given perimeter. This means that if the perimeter is fixed, the maximum area will be achieved when the rectangle is a square.

Let's apply this concept to the given exercises:

11. Perimeter: 80 meters

If the perimeter is 80 meters, and we want to find the dimensions (length and width) of a rectangle with the maximum area, we can consider it as a square.

Since a square has all sides equal, let's assume the length of each side of the square as 's'. The perimeter of a square is given by 4s.

Given that the perimeter is 80 meters, we have:

4s = 80

Simplifying the equation:

s = 80 / 4

s = 20

Therefore, the length and width of the rectangle with the maximum area, given the perimeter of 80 meters, would be 20 meters each.

12. Perimeter: P units

In this case, the perimeter is given as 'P' units. Similarly, we can apply the same concept and assume the length and width of the rectangle as 'x' units.

The perimeter of a rectangle is given by the formula: 2(length + width).

Given that the perimeter is 'P', we have:

2(length + width) = P

Simplifying the equation:

length + width = P / 2

Since we want to find the maximum area, we can consider the length and width to be equal, as in a square.

So, we have:

2x = P / 2

x = P / 4

Therefore, for the rectangle with the maximum area, given the perimeter of 'P' units, the length and width would be 'P / 4' units each.

In both exercises, the maximum area is achieved when the rectangle is a square (for a given perimeter), with all sides equal to one-fourth of the perimeter.

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Quantitative type of variable is the number of robberies reported in your city.

The number of robberies reported in your city is a quantitative variable because it represents a numerical measurement or quantity.

It involves the collection of numeric data that quantifies the frequency or amount of a specific event (in this case, the number of robberies) occurring in your city.

More specifically, it is a continuous variable. Continuous variables are characterized by being able to take on any value within a certain range. In the case of the number of robberies reported, it can have decimal or fractional values.

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Answer:

352cm^3

Step-by-step explanation:

V= whl =

8*5*4 = 160

8*4*6 = 192

192 + 160 = 352

Answer:

-64x^12

Explanation:

Given the expression

m = -4x^4

You are to look for m^3 as shown;

Open the bracket:

THe correct answer is -64x^12

Answer:

47 I believe

Step-by-step explanation:

The formula 2x/(x-7) - (x+7)/x therefore equals (x² + 49) / (x × (x-7)).

Mathematical expressions consist of at least two integers or factors, a minimum of one math procedure, and a sentence. It's possible to multiply, divide, add, or remove with this mathematical procedure.

To simplify the expression 2x/(x-7) - (x+7)/x, we need to find a common denominator.

First, we can rewrite the second term as (x+7)/(x × 1), so the expression becomes:

2x/(x-7) - (x+7)/(x × 1)

To find a common denominator, we need to multiply the first term by x/x and the second term by (x-7)/(x-7):

2x × x / (x × (x-7)) - (x+7) × (x-7) / (x × (x-7))

Simplifying the expression further, we get:

(2x² - (x² - 49)) / (x × (x-7))

Simplifying the numerator, we get:

(2x² - x² + 49) / (x × (x-7))

And finally, we can simplify the expression to:

(x² + 49) / (x × (x-7))

Therefore, the expression 2x/(x-7) - (x+7)/x is equivalent to (x² + 49) / (x × (x-7)).

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Answer:

\(\frac{x^{2}+49 }{x(x-7)}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The resulting test statistic will indicate how many standard errors the sample mean is away from the hypothesized mean. A larger absolute value of the test statistic suggests stronger evidence against the null hypothesis.

To find the test statistic, we can use the formula for the t-statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case, the hypothesized mean is 7 hours, the sample mean is 6.01 hours, the sample standard deviation is 8.96 hours, and the sample size is 617.

Substituting these values into the formula, we get:

t = (6.01 - 7) / (8.96 / sqrt(617))

Calculating this expression will give us the test statistic.t = (6.01 - 7) / (8.96 / sqrt(617))

Calculating the numerator:

(6.01 - 7) = -0.99

Calculating the denominator:

(8.96 / sqrt(617)) ≈ 0.360

Therefore, the test statistic (t) is approximately:

t ≈ -0.99 / 0.360 = -2.75

The test statistic is -2.75.

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Answer:

it’s -93

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

plug y = 6 on to the equation y =x + 5

=> 6 = x +5

=> x = 1

Answer:

38.33

Step-by-step explanation:

Given: Total amount = 120, Amount used = 74

To find: percent that was not spent

Solution: Firstly, find how much is 74 out of 120. To find the percentage of a number when it is in decimal form, you just need to multiply the decimal number by 100. For this case, to convert 74 to a percentage, 74 x 100 = ...61.67%

Then, 100% - 61.67 = 38.33

Answer:

About 16 years

Step-by-step explanation:

The formula for compound interest is

\(P(t)=P_{0}(1+r/n)^n^t\), where P0 is the principal, r is the interest rate, n is the number of compounding periods, and t is the time in years.

For this problem, our n = 12 because there are 12 months in a single year and we must convert our percentage to a decimal (3.60/100 = 0.0360): \(7000=4000(1+0.0360/12)^1^2^t\\7000=4000(1.003)^1^2^t\\1.75=1.003^1^2^t\\log(1.75)=log(1.003)^1^2^t\\log(1.75)=12t*log(1.003)\\\frac{log(1.75)}{log(1.003)} =12t\\1/12*\frac{log(1.75)}{log(1.003)}=t\\ 15.56818868=16=t\)

Answer:

in terms of pi: 112.5pi mm squared

substituting pi for 3.14: 353.25 mm squared

Step-by-step explanation:

Surface area cone equation:

Πr2 + π*r*s

4.5^2 = 20.25pi

400 + 20.25 = 420.25

sqrt(420.25) = 20.5

20.25pi + 92.25pi = 112.5pi

Answer:

\(-2\frac{9}{40}\)

Step-by-step explanation:

\(-\frac{5}{8}+(-\frac{8}{5}) = -\frac{25}{40}-\frac{64}{40}\) (find common denominator)

\(=-\frac{89}{40}\)

\(=-2\frac{9}{40}\) (reduce to simplest form)

Hope this helps :)

The observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

An investigator is studying the association between cell phone use and migraine headaches.

100 cases (migraine patients) and 100 controls (people who don't suffer from migraine), and asks each group how many hours they use their cell phones per day, on average.

To calculate odd ratio ( exposure is cell phone as to check cell phone use on migraine)

Odds of disease in exposed = 60/55= 1.09

Odd of disease in non exposed = 40/45 = 0.88

Thus the odds ratio will be = 1.09:0.88

=> Odds of disease in exposed / odds of disease in non exposed = 1.09/ 0.88 = 1.23

= OR = 1.23

Hence the answer is the observed odds ratio (the observed association between migraine headache and cell phone use) is OR = 1.23.

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