construct independent equilateral triangle PQR
​

To calculate the discharge through the circular channel, we can use Manning's equation, which relates the flow rate (Q) to the channel properties and flow conditions. Manning's equation is given by:

Q = (1/n) * A * R^(2/3) * S^(1/2)

where:

Q is the discharge (flow rate)

n is Manning's coefficient (0.014 in this case)

A is the cross-sectional area of the channel

R is the hydraulic radius of the channel

S is the slope of the channel bed

First, let's calculate the cross-sectional area (A) of the circular channel. The diameter of the channel is given as 6m, so the radius (r) is half of that, which is 3m. Therefore, the area can be calculated as:

A = π * r^2 = π * (3m)^2 = 9π m^2

Next, let's calculate the hydraulic radius (R) of the channel. For a circular channel, the hydraulic radius is equal to half of the diameter, which is:

R = r = 3m

Now, we can calculate the slope (S) of the channel bed. The given slope is 1 in 600, which means for every 600 units of horizontal distance, there is a 1-unit change in vertical distance. Therefore, the slope can be expressed as:

S = 1/600

Finally, we can substitute these values into Manning's equation to calculate the discharge (Q):

Q = (1/0.014) * (9π m^2) * (3m)^(2/3) * (1/600)^(1/2)

Using a calculator, the discharge can be evaluated to get the final result.

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Answer:

Can you post a picture of the figure?

x=224/8

x=25+3=28

So: 28

Answer:

The resulting expression is;

Explanation:

Given the expression;

collecting the like terms (bringing all the like terms together);

Therefore, the resulting expression is;

Answer: (-1, 0)

Step-by-step explanation: It is the only point that crosses the x-axis and is an answer choice.

Please mark BrainliesT!

Answer:

-23.33 °C

Step-by-step explanation:

C = 5/9 (-10 - 32)

C = 5/9 (-42)

C = -23.3333 ≈ -23.33 °C

hope it helps :)

mark brainliest!

Therefore, the probability that exactly 4 out of 20 randomly chosen college students are near-sighted is closest to 0.7988 or approximately 0.80.

To find the probability that exactly 4 out of 20 randomly chosen college students are near-sighted, we can use the binomial probability formula.

The formula for the probability of k successes in n trials, with a probability of success p in each trial, is given by:

\(P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)\)

In this case, n = 20, k = 4, and p = 0.28 (probability of a student being near-sighted).

Plugging in these values into the formula, we get:

\(P(X = 4) = (20 choose 4) * (0.28)^4 * (1 - 0.28)^{(20 - 4)\)

Calculating the values:

(20 choose 4) = 4845

\((0.28)^4\) ≈ 0.006859

\((1 - 0.28)^{(20 - 4)\) ≈ 0.19224

P(X = 4) ≈ 4845 * 0.006859 * 0.19224

≈ 0.7988

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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:

it would be about 3 ft I would say from where he hits the brake to the last place he is at

Step-by-step explanation:

it really depends wether it's raining or not caus if it's raining it would be close to 5 or 6 but if not than 2 to 3 feet

Step-by-step explanation:

no, we have no way to prove that they are equal. is DEF equaled JKL then ABC would be equal to it, but it's not

The probability of the patient having each of the three diseases after a positive test result is 4/9 for D1, 1/3 for D2, and 2/9 for D3. The doctor should now assign these updated probabilities to each disease.

Let D1, D2, and D3 be the events that the patient has disease 1, disease 2, and disease 3, respectively.

The doctor initially assumed that each disease is equally probable, so P(D1) = P(D2) = P(D3) = 1/3.

Let T be the event that the test is positive. Then, by the Law of Total Probability

P(T) = P(T|D1)P(D1) + P(T|D2)P(D2) + P(T|D3)P(D3)

where P(T|D1) = 0.8, P(T|D2) = 0.6, and P(T|D3) = 0.4.

P(T) = (0.8)(1/3) + (0.6)(1/3) + (0.4)(1/3) = 0.6.

Now, by Bayes' Theorem, the probability of having disease Di given that the test is positive is:

P(Di|T) = P(T|Di)P(Di)/P(T)

where i = 1, 2, or 3.

P(D1|T) = (0.8)(1/3)/0.6 = 4/9

P(D2|T) = (0.6)(1/3)/0.6 = 1/3

P(D3|T) = (0.4)(1/3)/0.6 = 2/9

Therefore, the probabilities that the patient has diseases D1, D2, and D3 given that the test is positive are 4/9, 1/3, and 2/9, respectively.

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Answer:

AB=DE

Step-by-step explanation:

they're literally the only pair on the same sides lol

The side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.

Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.

We have two triangles shown in the picture.

As we know from the definition of the congruent triangle, the same size, and shape.

The three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle

Thus, the side AB is equal to DE or AB ≅ DE option (A) AB ≅ DE is correct.

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Answer:

D

Step-by-step explanation:

The area of a rectangle is given by the formula:

\(A=\ell w\)

So, we are given that the area is:

\(x^3-5x^2+3x-15\)

And the width is:

\(x^2+3\)

And we want to find the length. To do so, first substitute the expressions into the equation:

\(x^3-5x^2+3x-15=(x^2+3)\ell\)

Thus, to find the length, divide by (x²+3):

\(\displaystyle \ell = \frac{x^3-5x^2+3x-15}{x^2+3}\)

We can factor the numerator:

\(x^3-5x^2+3x-15\)

From the first two terms, factor out a x².

From the third and fourth terms, factor out a 3:

\(=x^2(x-5)+3(x-5)\)

Combine:

\(=(x^2+3)(x-5)\)

Putting this back:

\(\displaystyle \ell = \frac{(x^2+3)(x-5)}{x^2+3}\)

Cancel:

\(\ell =x-5\)

Hence, our answer is D.

Answer:

D on Edge 2021 ;))

Step-by-step explanation:

The number of ways to form a string of length 5 from the set {u,v,w,x,y,z} that must contain the letter x is 1,296.

Permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.

To form a string of length 5 from the set {u,v,w,x,y,z} that must contain the letter x, we have 1 choice for the third character, which is x. For the remaining 4 characters, we can choose from any of the 6 letters in the set, including x. Therefore, we have:

1 choice for the third character (x)

6 choices for the first character (including x)

6 choices for the second character (including x)

6 choices for the fourth character (including x)

6 choices for the fifth character (including x)

Using the multiplication principle, we can multiply these choices together to get the total number of ways to form a string of length 5 that must contain the letter x:

1 x 6 x 6 x 6 x 6 = 1,296

Therefore, the number of ways to form a string of length 5 from the set {u,v,w,x,y,z} that must contain the letter x is 1,296.

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He missed 2.

90% of 10 is 9. So he makes 9 shots and misses 1 for every 10 free throws.

So just double that number (1 shot missed) and so you get 2 missed shots

Hope this helps, and please consider marking branliest if this did

Answer:

Drag and drop expressions to the boxes to correctly complete the statements.

After applying the distributive property, Gustavo's expression was 9w + 45.

After he used the commutative property, his expression was 45 + 9w.

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

I think this is correct hope this helps

Answer:

She can never travel a distance of 1 foot for the given condition.

Step-by-step explanation:

In every jump, she goes 1/2 as far as her prior jump.

In the 1st jump, she covered a distance, d_1= \frac 1 2 foot.

The distance covered in the 2nd jump

\(d_2= \frac 12 \times d_1 = = \frac 12 \times \frac 12= \frac 1 4\) (given)

So, the distanve covered in the 3rd jump

\(=\frac 12 \times d_2= \left(\frac 1 2\right )^2\times \frac 1 2= \left(\frac 1 2\right)^{3-1}\times \frac 1 2.\)

Similarly, the distance covered in the \(r^{th}\) jump

\(=\left(\frac 12 \right)^{r-1}\times \frac 1 2.\)

Assuming she requires \(n\) jumps to travel 1 foot of distance.

So, the sum of all the distances covered in n jumps = 1 foot

\(\Rightarrow \frac 1 2 + \frac 1 4 + \cdots + \left(\frac 12 \right)^{r-1}\times \frac 1 2+\cdots+ \left(\frac 12 \right)^{n-1}\times \frac 1 2=1\)

\(\Rightarrow \frac 1 2 + \left(\frac 12 \right)^2 + \cdots + \left(\frac 12 \right)^{r}+\cdots+ \left(\frac 12 \right)^{n}=1\)

This a geometric progression, G.P., of \(n\) terms having common ration, r= 1/2 and the first term \(a_1= 1/2\).

As sum of all the n terms of  G.P \(=\frac {a_1(r^n-1)}{r-1}\),

\(\Rightarrow \frac {1/2((1/2)^n-1)}{1/2-1}=1\)

\(\Rightarrow - \left(\left(\frac 1 2\right)^n-1\right)=1\)

\(\Rightarrow \left(\frac 1 2\right)^n-1=-1\)

\(\Rightarrow \left(\frac 1 2\right)^n=-1+1=0\)

\(\Rightarrow \frac {1}{2^n}=0\)

This is only possible, mathematically, when \(n\rightarrow \infty\), But in real life situation reaching infinity is not possible.

Hence, she can never travel a distance of 1 foot for the given condition.

Answer:

all but 15 over three

Step-by-step explanation:

because 1/6 x2 =2/12, 1.5=9 since 1=6 and half would be 3, and 4x1/6=4/24

Answer: -7/5=-9

Step-by-step explanation:

I hope it helps

Answer: - 7/5 = -9

Step-by-step explanation: Combine like terms into single fraction, multiple by 1, subtract 3, simply.

Answer:  The probability that 2 freshmen and 1 sophomore are selected is 42/91.

Step-by-step explanation:

To obtain the probability that 2 freshmen and 1 sophomore are selected from a group of 8 freshmen and 6 sophomores, we can use the combinations formula:

The total number of ways to select 3 people from a group of 8 + 6 = 14 people is:  

C(14, 3) = 14! / (3! * 11!) = 364

The number of ways to select 2 freshmen from a group of 8 freshmen is: C(8, 2) = 8! / (2! * 6!) = 28

The number of ways to select 1 sophomore from a group of 6 sophomores is: C(6, 1) = 6! / (1! * 5!) = 6

Therefore, the number of ways to select 2 freshmen and 1 sophomore from the group of 14 people is: 28 * 6 = 168

The probability of selecting 2 freshmen and 1 sophomore is:P(2F, 1S) = 168 / 364 = 42 / 91

Therefore, the probability that 2 freshmen and 1 sophomore are selected is 42/91.

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Answer:

1/6x or just 1/6

Step-by-step explanation:

the equation is y = mx + b and 1/6x is in place m which is the slope

stream blueberry eyes by MAX AND SUGA periodTt

The slope is also known as the gradient and the rate of change of the line. The slope of the line for the equation y= 1/6x + 1/4 is 1/6

The slope is also known as the gradient and the rate of change of the line, The equation of aline in slope intercept form is expressed as:

y = mx + b

where

m is the slope

b is the y-intercept

Given the equation y = 1/6x + 1/4

Compare

mx = 1/6x

m = 1/6

Hence the slope of the line for the equation y= 1/6x + 1/4 is 1/6

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The row of the table that reveals the x-intercept of the function f is given as follows:

Second row.

A function has two intercepts, which are listed as follows:

The definition of each type of intercept is given as follows:

From the second row of the table, we have that when x = -4, f(x) = 0, hence the x-intercept of the function is of x = -4.

The y-intercept is of y = -16, as from the fourth row, when x = 0, y assumes a value of 16.

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a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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The inflection points of the curve \(y=x + log3(x^2+5)\)are at x = -√(5) and x = √(5).

To find the inflection point(s) of a function, we need to find the second derivative of the function and set it equal to zero. If there are multiple solutions to this equation, then those values of x are the inflection points.

Let's start by finding the first derivative of the function:

\(y = x + log3(x^2+5)\)

\(y' = 1 + (2x)/(ln(3)(x^2+5))\)

Next, let's find the second derivative:

\(y'' = (2ln(3)(x^2+5) - 4x^2ln(3))/(x^2+5)^2\)

Now, let's set y'' equal to zero and solve for x:

\((2ln(3)(x^2+5) - 4x^2ln(3))/(x^2+5)^2 = 0\)

\(2ln(3)(x^2+5) - 4x^2ln(3) = 0\)

\(2ln(3)x^2 + 10ln(3) - 4ln(3)x^2 = 0\)

\(2ln(3)x^2 - 4ln(3)x^2 + 10ln(3) = 0\)

\(-2ln(3)x^2 + 10ln(3) = 0\)

\(2x^2 = 10\)

\(x^2 = 5\)

x = ±√(5)

Therefore, the inflection points of the curve \(y=x + log3(x^2+5)\) are at x = -√(5) and x = √(5).

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Answer:

1/6

Step-by-step explanation:

We know that 1/2 are apples and 1/3 are bananas

we also know that

apples+bananas+oranges=1

Which means that

1/2+1/3+oranges=1

Add 1/2 + 1/3 by getting the denominators equal

3/6+2/6=5/6

Which means that 5/6+oranges=1

1-5/6=1/6

1/6

write everything below this

1/2+1/3+oranges=1

1/2+1/3=5/6

5/6+oranges=1

oranges=1-5/6

oranges=1/6

Answer:

20%

Step-by-step explanation:

Step 1.) Construct a proportion. Let x = the percent of Rachel's money that went into her savings.

375 - x

1875 - 100

Step 2.) Cross multiply.

375*100 = 1875*x

37500 = 1875x

Step 3.) Divide to isolate x.

37500/1875 = 1875x/1875

20 = x or x = 20.

Step 4.) Answer: 20% of Rachel's money went into her savings.

Answer:

Leah has 80 less paychecks than the weekly person.

Step-by-step explanation:

Leah is getting 24 paychecks in 2 years, Weekly person gets 104 paychecks in 2 years, 104 - 24 = 80 paychecks.

Given

Number squared subtracted fom 3 times the number is equal to negative 70.

Find

Set up quadratic equation and solve by factoring

Explanation

Let the number be x.

according to the question,

then,

by solving , we get

Final Answer

quadratic equation =

and factors are -7 and 10

for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

For a two-tailed test at a 12.66% significance level, we need to find the critical value of z.

Step 1: Determine the significance level for each tail.
Since this is a two-tailed test, we need to divide the overall significance level (12.66%) by 2. This gives us 6.33% (or 0.0633 in decimal form) in each tail.

Step 2: Find the z-score associated with the given significance level.
To find the critical value of z, you can use a z-table or an online calculator. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

Using a z-table or calculator, you'll find that the z-score is approximately ±1.53.

So, for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53.

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Answer:

below

Step-by-step explanation:

In short, we will add both coefficients together to combine like terms.

3x + 5x → x(3 + 5) → 8x

If you have a value like 2x and 2, you cannot combine them because they do not have the same variable.

Best of Luck!