a cylindrical tank of radius r , filled to the top with a liquid, has a small hole in the side, of radius r , at distance d below the surface. find an expression for the volume flow rate through the hole. express your answer in terms of the variables d , r , r , and appropriate constants

Polynomial expressions of \(2^{nd}\) degree with one unknown (only \(x\)) have \(2\) roots. We use the formula below to determine these roots;

This formula is valid for equations of the form \(ax^2+bx+c\). We can convert the equation given in the question into this format to get the result;

Hence, the value of \(a\): \(8\),

the value of \(b\): \(16\),

the value of \(c\): \(3\).

Now, we can find the roots of this equation by using this formula;

Answer:

1

Step-by-step explanation:

4+1=5

5-4=1

Answer:

you have 1 friend

Step-by-step explanation:

you have 4 then you add another

that's 5

then you lose 4

5-4 is 1

The given statement "In performing a lower-tailed z-test for one mean, the value of the test statistic was z=0.51, which would yield a p-value of 0.695." is true because we perform null hypothesis.

In a lower-tailed z-test for one mean, we test a null hypothesis that the population mean (μ) is greater than or equal to a certain value, against an alternative hypothesis that the population mean is less than that value.

To perform the test, we calculate the z-test statistic using the sample mean, sample standard deviation, sample size, and the hypothesized population mean. If the calculated z-test statistic falls in the rejection region (below the critical value), we reject the null hypothesis and conclude that the population mean is less than the hypothesized value.

In this case, the calculated z-test statistic is 0.51, which falls in the non-rejection region (above the critical value) for a lower-tailed test with a significance level of 0.05. Therefore, the p-value is greater than 0.05, and we do not reject the null hypothesis. The statement that the p-value is 0.695 is consistent with this conclusion.

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Answer:

49 sqrt

Step-by-step explanation:

Answer:

The third option.

Step-by-step explanation:

sqrt 49

=7.

A)an = 2*2^(n-1)`. B) `The sum of the first n fractions is `2*(2^n - 1)`.

a. The sequence is a geometric sequence with the first term `a1 = 2` and common ratio `r = 2`.Therefore, the nth term `an` is given by:`an = a1*r^(n-1)`

Substituting `a1 = 2` and `r = 2`, we have:`an = 2*2^(n-1)`

b. To find the sum of the first n terms, we use the formula for the sum of a geometric series:`S_n = a1*(1 - r^n)/(1 - r)

`Substituting `a1 = 2` and `r = 2`, we have:`S_n = 2*(1 - 2^n)/(1 - 2)

`Simplifying:`S_n = 2*(2^n - 1)

`The sum of the first n fractions is `2*(2^n - 1)`.As `n` gets larger and larger, the sum approaches `infinity`.

Thus, the sum is getting closer and closer to infinity.

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The amount of minute to reach a distance of 9 inches from the rock is 3 minutes

The complete question is added at the end of this solution

From the question, we have the equation to be

d = 3t

A distance of 9 inches from the rock means that

d = 9

So, we have

3t = 9

Divide both sides by 3

t = 3

Hence, the amount of time is 3 minutes

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Complete question

The equation d=3t represents the relationship between the distance (d) in inches that a snail is from a certain rock and the time (t) in minutes.

How many minutes does it take for the snail to reach a distance of 9 inches from the rock?

The total surface area painted is 644.16 square inches.

Let the radius of the cylindrical rod be r. The circumference of the base is given as 12π, which can be converted to the diameter as:

diameter = circumference / π = 12π / π = 12 inches.

So, the radius of the cylindrical rod is half of that. That is 6 inches.

The area of one base of the cylindrical rod can be calculated as π \(r^2\), which is:

π * \(6^2\) = 3.14 * 36 = 113.04 square inches.

The surface area of one-half of the cylindrical rod can be calculated by:

2 * π * r * l + 2 * π * \(r^2\), where l is the length of the rod.

Since the length of the rod is 4 inches, the surface area of one-half of the cylindrical rod can be calculated by:

2 * π * 6 * 4 + 2 * 113.04 = 96 + 226.08 = 322.08 square inches.

Given that two equally sized pieces are cut, the total surface area painted would be 2 * 322.08 = 644.16 square inches.

Therefore, the total surface area painted is 644.16 square inches.

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Answer:

Gradient: m = 3

Step-by-step explanation:

m = change in y/change in x

m = \(\frac{Y2-Y1}{X2-X1}\)

m = \(\frac{9-(-3)}{6-(2)}\)

m = 12/4

m = 3

Answer:

The value of k is 1

Step-by-step explanation:

If x-1 is a factor, if we equate x - 1 to 0 and substitute the value of x

Then, we should have 0 as the f(x) value

so;

x-1= 0

x = 1

Substitute this

0 = 1^3 + k(1) - 2

0 = 1 + k-2

0 = k-1

k = 1

Answer: The value for X is 16!~

x = 16

I had this question before!

Answer:

5x-3= x=5-3= 2=2x

then, 6×2x =12x

Answer:

is it 5y/8_5y/16 or 5y/8-5y/16 ?

Step-by-step explanation:

Answer:

\(\frac{5y}{16}\)

Step-by-step explanation:

Given

\(\frac{5y}{8}\) - \(\frac{5y}{16}\)

To subtract the fractions we require them to have a common denominator.

Multiply numerator/ denominator of \(\frac{5y}{8}\) by 2

= \(\frac{5y(2)}{8(2)}\) - \(\frac{5y}{16}\)

= \(\frac{10y}{16}\) - \(\frac{5y}{16}\)

Now subtract the numerators, leaving the denominator

= \(\frac{10y-5y}{16}\)

= \(\frac{5y}{16}\)

The ordered pair that is a solution to the system y ≥ -1/2x - 8 and y < 8x + 2 is option D, (4, 7).

To find which ordered pair is a solution to the system y ≥ -1/2x - 8 and y < 8x + 2, we need to check each option.

A (-7, -4):

y ≥ -1/2x - 8 becomes -4 ≥ -1/2(-7) - 8, which simplifies to -4 ≥ -4.5.

This is true.

y < 8x + 2 becomes -4 < 8(-7) + 2, which simplifies to -4 < -54.

This is false.

Since one of the inequalities is false, option A is not a solution to the system.

B (0, 2):

y ≥ -1/2x - 8 becomes 2 ≥ -1/2(0) - 8, which simplifies to 2 ≥ -8.

This is true.

y < 8x + 2 becomes 2 < 8(0) + 2, which simplifies to 2 < 2.

This is false.

Since one of the inequalities is false, option B is not a solution to the system.

C (2, -12):

y ≥ -1/2x - 8 becomes -12 ≥ -1/2(2) - 8, which simplifies to -12 ≥ -9.

This is false.

y < 8x + 2 becomes -12 < 8(2) + 2, which simplifies to -12 < 18.

This is true.

Since one of the inequalities is false, option C is not a solution to the system.

D (4, 7):

y ≥ -1/2x - 8 becomes 7 ≥ -1/2(4) - 8, which simplifies to 7 ≥ -10.

This is true.

y < 8x + 2 becomes 7 < 8(4) + 2, which simplifies to 7 < 58.

This is true.

Since both inequalities are true, option D is a solution to the system.

Therefore, the ordered pair that is a solution to the system y ≥ -1/2x - 8 and y < 8x + 2 is option D, (4, 7).

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Rounding 0.4571 to the nearest hundredth will be 0.46.

To round the nearest hundredth, look at the number that is three places to the right of the decimal point.  If the number is greater than or equal to 5, then round up.  If the number is less than 5, then round down.

0.4571

7 ≥ 5

Therefore, we round up.

0.4571 --> 0.46

Therefore, 0.4571 rounded to the nearest hundredth is 0.46.

For example, if the number is 123.456, the digit in the thousandths place is 6. Since 6 is greater than 5, 123.456 rounded to the nearest hundredth would be 123.46.

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Round 0.4571 to the nearest hundredth.

Answer:

1) 678.24

2)366.333.... repeating

3) 254.34

Step-by-step explanation:

1) 3.14 x 6² = 113.04 ---> 113.04 x 6 = 678.24

2) 3.14 x 5² = 78.5 ---> 78.5 x 14 = 1099 ---> 1099/3 = 366.333.... repeating

3) 3.14 x 9² = 254.34

½×½ which will be ¼

Step-by-step explanation:

because

Probability that the starting player wins:

\(P_{n} =\)  m /n + m + n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

Let us say that the probability that the first player wins is \(P_{n}\). Then this can be happen in two ways:

If the first player wins in the first move which has a probability: m /n + m

If the first player wins after the second move which has a probability :

n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

Therefore by the law of probability,

\(P_{n} =\)  m /n + m + n(n-1) /(n + m)(n+m -1) × \(P_{n-2}\)

This will allow us to find out the probability of first player winning the game recursively.

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Answer:

64

Step-by-step explanation:

put branileist

Answer:

Step-by-step explanation:

72 cuz u multiply 6x3x4=72

Answer:

  r ≈ 44.25 cm

Step-by-step explanation:

You want the hypotenuse of a right triangle in which the side adjacent to the angle of 57° is 24.1 cm.

The cosine relation is ...

  Cos = Adjacent/Hypotenuse

  cos(57°) = (24.1 cm)/r

Solving for r gives ...

  r = (24.1 cm)/cos(57°) ≈ 44.25 cm

The length r is about 44.25 cm.

__

Additional comment

The calculator shown in the attachment has its angle mode set to degrees.

<95141404393>

Answer:

1

Step-by-step explanation:

The answer is 1 because anything taken to the power of 0 will be 1. Hope this helps :)

Answer:

-3

Step-by-step explanation:

Answer:

-4.5, -3, 22/7 , 16/5, sqrt(17)

Step-by-step explanation:

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

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Answer:

\(Y = -1x + 4\)

Step-by-step explanation:

Hope this helps

Answer:

79.875, or 79.88

Step-by-step explanation:

first ya do 75*0.065=4.875

then you add that to 75

Part A

\(4x^2 -7x-15=0\\\\(4x+5)(x-3)=0\\\\x=-\frac{5}{4}, 3\)

So, the x-intercepts are \(\boxed{\left(-\frac{5}{4}, 0 \right), (3,0)}\)

Part B

The vertex will be a minimum because the coefficient of \(x^2\) is positive.

The x-coordinate of the vertex is \(x=-\frac{-7}{2(4)}=\frac{7}{8}\)

Substituting this back into the function, we get \(f\left(\frac{7}{8} \right)=4\left(\frac{7}{8} \right)^2 -7\left(\frac{7}{8} \right)^2 -15=-\frac{289}{16}\)

So, the coordinates of the vertex are \(\boxed{\left(\frac{7}{8}, -\frac{289}{16} \right)}\)

Part C

Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.

The graph is shown in the attached image.

Answer:

oh dang.. imma head out, no big brain time for me..

Step-by-step explanation:

Answer:

2.88 ...........................

Answer:

Step-by-step explanation:

Given polynomials:

(6x+7+x²)+(2x²-3)

Solution:

Removing brackets,

Collecting like terms,

Simplifying ,

Done!

Hence option 3 is correct.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the following generic form:  ax² + bx + c = 0.

The given expression is;

(6x+7+x²)+(2x²-3)

Now add the like term in the given expression,

⇒   x² + 2x² + 6x + 7 - 3

⇒ 3x² + 6x + 4

Hence,

The sum of polynomial is 3x² + 6x + 4.

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Based on the given information, we can expect the p-value for a two-sided test using this data to be smaller than 0.05. This is because the 95% confidence interval for the mean does not contain 0, which indicates that there is a statistically significant difference between the yield of silver queen and country gentlemen.

A p-value is a measure of the evidence against the null hypothesis (which in this case would be that there is no difference between the two corn varieties). The smaller the p-value, the stronger the evidence against the null hypothesis and the more likely we are to reject it. In general, if the p-value is smaller than the chosen significance level (usually 0.05 or 0.01), we reject the null hypothesis and conclude that there is a significant difference between the two groups being compared.

Therefore, in this case, we can expect the p-value to be smaller than 0.05 and conclude that there is a significant difference in the yield of silver queen and country gentlemen.

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Answer:

D

Step-by-step explanation: