A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if the total perimeter is 22 feet.

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

step by step and the dog got 10 fire wood

The number of solutions in nonnegative integers of the inequality x1 x2 ··· xn ≤ m is c(m n, n), where c(a,b) denotes the binomial coefficient.

Let's define a new variable y_i = m - x_i for each i in {1, 2, ..., n}. Then we have the following equivalence:

x1 x2 ··· xn ≤ m <==> y1 y2 ··· yn ≥ (m+1)^n / (x1 x2 ··· xn)

Note that the right-hand side is a positive integer, since x1 x2 ··· xn divides (m+1)^n. Therefore, we are counting the number of solutions in positive integers y1, y2, ..., yn of the inequality y1 y2 ··· yn ≥ (m+1)^n / (x1 x2 ··· xn).

Now, using the stars and bars argument, we can count the number of solutions of the equation y1 y2 ··· yn = k, where k is a positive integer. The number of solutions is c(k-1, n-1), since we can place n-1 dividers among k-1 identical objects to partition them into n nonempty groups.

Therefore, the number of solutions of y1 y2 ··· yn ≥ (m+1)^n / (x1 x2 ··· xn) is:

sum(c(k-1, n-1), k=(m+1)^n / (x1 x2 ··· xn), infinity)

This sum can be simplified using the following identity:

sum(c(k-1, n-1), k=a, b) = c(b, n) - c(a-1, n)

Therefore, the number of solutions of x1 x2 ··· xn ≤ m is:

c((m+1)^n, n) - sum(c((m+1)^n / x1 x2 ··· xn - 1, n), x1, x2, ..., xn >= 1)

The second sum can be seen as a summation over all divisors of (m+1)^n. Therefore, we have:

c((m+1)^n, n) - sum(c(d-1, n), d| (m+1)^n)

Using the multiplicativity of the divisor function and the binomial coefficient, we can simplify this to:

c(m n, n)

We have shown that the number of solutions in nonnegative integers of the inequality x1 x2 ··· xn ≤ m is c(m n, n).

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Answer:

5

Step-by-step explanation:

Distance formula is \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

now you plug in your numbers. \(\sqrt{(-6-(-9))^2+(-4-(-8))^2}\)

\(\sqrt{3^2+4^2}\)

\(\sqrt{9+16}\)

\(\sqrt{25}\)

=5

:)

Answer:

cosA = AB/ AD = AC/BC is the correct one.

Answer:

Brian had 4 jeans

Step-by-step explanation:

Together Cam and Brian had 24 pair of jeans. Cam had 4 less the Brian. Which inequality of equation could be used to find the number of jeans that Brian had?

Let the number of jeans

Cam had = x

Brian had = y

Hence: x + y= 24 Jeans

Cam had 4 less the Brian.

= x = y - 4

Hence:

x > y

The number of jeans Brian had is calculated as:

x + y= 24

y - 4 + y= 24

2y = 24+ 4

2y = 28

y = 28/2

y = 14 jeans

This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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Answer:

87.92 m

Step-by-step explanation:

Circumference = pi*diameter

3.14*28m = 87.92 m

Answer:

B. Approximately 0.3159

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution, and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallon.

This means that \(\mu = 1, \sigma = 0.1\)

Sample of 9:

This means that \(n = 9, s = \frac{0.1}{\sqrt{9}}\)

If the sample mean is less than 0.97 gallons, the department will fine the dairy. Based on this information, what is the probability that the dairy will get fined even when its filling process is working correctly?

This is the pvalue of Z when X = 0.97. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.97 - 1}{\frac{0.1}{\sqrt{9}}}\)

\(Z = -0.9\)

\(Z = -0.9\) has a pvalue of 0.1841.

The correct answer is given by option B.

Answer:

Option C

Step-by-step explanation:

Given  

Probability of Mean value less than 0.97  

= Mean value -1/(0.1/sqrt (9))

Substituting the given values, we get -

Probability of Mean value less than 0.97  

= 0.97 -1/(0.1/sqrt (9))

= 0.97-1/(0.1/3)

= 0.1841

Hence, option C is correct

Answer:

22.77 miles

Step-by-step explanation:

1.65 multiplied by 13.8

Answer:

408.7 mi

Step-by-step explanation:

Answer:

-4 and 10

Step-by-step explanation:

let me know if this is incorrect

The velocity at t = 4 seconds is 210.4 m/s.

To find the equation for the velocity v at time t, we need to integrate the given acceleration function a(t) with respect to time.

Given: a(t) = 9.3\(t^2\) + 3

To find v(t), we integrate a(t) with respect to t:

v(t) = ∫ (9.3\(t^2\) + 3) dt

Integrating each term separately:

∫ 9.3\(t^2\) dt = 9.3 * (\(t^3\) / 3) = 3.1\(t^3\)

∫ 3 dt = 3t

Combining the results:

v(t) = 3.1\(t^3\) + 3t

Therefore, the equation for the velocity v at time t is v(t) = 3.1\(t^3\) + 3t.

To find the velocity at t = 4 seconds, we substitute t = 4 into the equation for v(t):

v(4) = \(3.1(4)^3\) + 3(4)

    = 3.1(64) + 12

    = 198.4 + 12

    = 210.4 m/s

Therefore, the velocity at t = 4 seconds is 210.4 m/s.

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The equation for the plane through P0(8,1,−4) perpendicular to the following line is x + 4y + 5z - 8 = 0

The slope of the perpendicular line should be a/b, and if one line is perpendicular to this line, the product of slopes should be -1. The equation of a line perpendicular to a given line ax + by + c = 0 is bx - ay + = 0, where is a constant.

The given parameters are

x=8−t​, y=1−2t​, z=3t​,

P0(- 9, 6, - 5).

Direction vector of line is < -1, 4, 5>,

This vector is normal vector for unknown plane.

So, equation of plane: -1(x - (-9)) + 4(y - 6) + 5(z - (-5)) = 0; - x - 9 + 4y - 24 + 5z + 25 = 0;

In conclusion the equation is given as  -x + 4y + 5z - 8 = 0

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If buses arrive at stop at "15-minute" intervals, then the probability that he waits more than 10 minutes for a bus is "1/3".

Let us denote the arrival-time of the passenger by X, where X is uniformly distributed between 7am and 7:30am. hence, the probability-density-function (pdf) of "X" is written as :

f(x) = 1/30, for 7am ≤ x ≤ 7:30am

f(x) = 0, otherwise

We observe that, the passenger will wait for more than 10 minutes for a bus only if he arrives between 7:00 a.m. and 7:05 a.m. , or between 7:15 a.m. and 7:20 a.m.

So, the probability for waiting time can be written as ;

⇒ \(\int\limits^5_0 {\frac{1}{30} } \, dx\) + \(\int\limits^{20}_{15} {\frac{1}{30} } \, dx\),

⇒ (1/30)(5 - 0) + (1/30)(20 - 15);

⇒ 1/3.

Therefore, the required probability is 1/3.

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The given question is incomplete, the complete question is

Buses arrive at a specified stop at 15-minute intervals starting at 7am. If a passenger arrives at the stop at a time that is uniformly distributed between 7am and 7:30am, find the probability that he waits more than 10 minutes.

Step-by-step explanation:

take 48 and divide it by 5/6 on a calculator

Answer: the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Step-by-step explanation:

Let's assume the price of one senior citizen ticket is 's' dollars and the price of one student ticket is 't' dollars.

According to the given information, on the first day, the school sold 7 senior citizen tickets and 11 student tickets, totaling $125. This can be expressed as the equation:

7s + 11t = 125 ---(1)

On the second day, the school sold 14 senior citizen tickets and 8 student tickets, totaling $180. This can be expressed as the equation:

14s + 8t = 180 ---(2)

We now have a system of two equations with two variables. We can solve this system to find the values of 's' and 't'.

Multiplying equation (1) by 8 and equation (2) by 11, we get:

56s + 88t = 1000 ---(3)

154s + 88t = 1980 ---(4)

Subtracting equation (3) from equation (4) eliminates 't':

(154s + 88t) - (56s + 88t) = 1980 - 1000

98s = 980

s = 980 / 98

s = 10

Substituting the value of 's' back into equation (1), we can solve for 't':

7s + 11t = 125

7(10) + 11t = 125

70 + 11t = 125

11t = 125 - 70

11t = 55

t = 55 / 11

t = 5

Therefore, the price of one senior citizen ticket is $10, and the price of one student ticket is $5.

Given:

A line passes through the point (-6,2) and has a slope of \(-\dfrac{3}{2}\).

To find:

The equation of line.

Solution:

If a line passes though a point \((x_1,y_1)\) and has a slope m, then the equation of line is

\(y-y_1=m(x-x_1)\)

The line passes through the point (-6,2) and has a slope of \(-\dfrac{3}{2}\). So, the equation of line is

\(y-2=-\dfrac{3}{2}(x-(-6))\)

\(y-2=-\dfrac{3}{2}(x+6)\)

\(y-2=-\dfrac{3}{2}(x)-\dfrac{3}{2}(6)\)

\(y-2=-\dfrac{3}{2}(x)-9\)

Add 2 on both sides.

\(y=-\dfrac{3}{2}(x)-9+2\)

\(y=-\dfrac{3}{2}x-7\)

Therefore, the equation of line is \(y=-\dfrac{3}{2}x-7\).

Answer:  approximately 24 square units in the shaded areas

Step-by-step explanation:  

The area of the entire dark circles will be for each πr², then divided by 2 to get the area of the semicircles created on the sides of the triangles:

16π + 9π = 25π   Half that times value for pi

≈ 39.2699  is the area of the dark semicircles. Round to 39.27

Now the fun! Find the area of the parts subtracted by the light semicircle:

The area of the entire circle is 25π  or about 78.54. The triangle is half of an inscribed rectangle, 6×8, so 48.  Subtracted from the circle leaves about 30.54 in the four slices between the arcs of the circumference and the perimeter of the rectangle. We are concerned with only half of the slices, so we will subtract 15.27

Area of the dark semicircles minus the area of the light slices will leave the area of the shaded crescents:

The following is how to determine a worker's percentile score if their completion time is 0.4 standard deviations above the mean. To determine a worker's percentile score, we will use the standard normal distribution table.

The formula for converting an X-value into a Z-score is: X - μ / σ = Z Where: X is the observed value of a variable.μ is the mean of the variable.σ is the standard deviation of the variable. Z is the z-score. To calculate the z-score, we'll use the formula: X - μ / σ = 0.4 standard deviations above the mean Z = (X - μ) / σ = 0.4 .The percentile score of the worker is the proportion of the standard normal distribution below this z-score. Using the standard normal distribution table, we can find the proportion that corresponds to the z-score of 0.4. We look for the value in the table that is closest to 0.4 and locate the proportion in the z-score column. For the value of 0.4, we get 0.6554.The percentile score of the worker is 0.6554 or 65.54 percent. We used the standard normal distribution table to calculate a worker's percentile score. The first step was to convert the observed value of a variable to a z-score using the formula: X - μ / σ = Z  .The worker's completion time was 0.4 standard deviations above the mean. This means that the worker's completion time is greater than the mean by 0.4 times the standard deviation. Using the formula above, we can calculate the z-score. The standard deviation for the worker's completion time was not given, so we used the standard deviation of the distribution. We were not given the mean, so we could not calculate the z-score directly. Instead, we calculated the z-score as follows: Z = (X - μ) / σ = 0.4.  We can use this equation to find the worker's completion time if we know the mean and standard deviation. The standard normal distribution table was used to calculate the worker's percentile score. We looked up the value that was closest to 0.4 in the z-score column. The proportion in the table that corresponds to a z-score of 0.4 is 0.6554 or 65.54%.The percentile score of the worker is 65.54%.The worker's percentile score was 65.54%. A percentile score is the proportion of a distribution that is below a certain point. We used the standard normal distribution table to calculate the proportion that corresponds to the worker's z-score of 0.4.

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Answer: can i have the brains? ;)

Step-by-step explanation:

1/2 an hour =30 minutes

1/6 of an hour=10 minutes

30÷10=3

3×1= 3 miles

Answer:

AAS.....................

Answer:

6 minutes

Step-by-step explanation:

48/8=6

The equation of the directrix to the right of the center is equal to 2.8.

Given the following data:

(x - 1)²/9 - (y - 2)²/16 = 1.

Mathematically, the standard equation of the directrix lines for a hyperbola of the form (x - h)²/a² - (y - k)²/b² = 1 is given by:

x = h ± a²/√(a² + b²)

Where:

Substituting the given parameters into the standard equation, we have;

x = 1 ± a²/√(a² + b²)

x = 1 ± 9/√(9 + 16)

x = 1 ± 9/√25

x = 1 ± 9/5

x = 1 + 9/5

x = 1 + 1.8

x = 2.8.

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Answer: The answer is 2.8

Step-by-step explanation:

Answer:

It’s 4

Step-by-step explanation:

Answer:B

Step-by-step explanation:

It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

In mathematics, an algorithm is a process, a description of a series of steps that may be used to solve a problem; however, they are now far more prevalent than that.

Although many areas of research (and daily life) employ algorithms, long division's step-by-step process is probably the most prevalent example.

Thus, It is true that when you design an algorithm, it should be general enough to provide a solution to many problem instances, not just one or a few of them.

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