How can you use your knowledge of evaluating expressions involving square roots to
identify and correct an error in calculating the period of a pendulum?
the period of a pendulum is the time in seconds) it takes the pendulum to swing back
and forth. the period t is represented by t = 1.1vi, where l is the length of the
pendulum (in feet).

Answer:

Step-by-step explanation:

\(\sqrt[3]{\frac{0.008}{0.125} }\\ =\sqrt[3]{\frac{8}{125} }\\ = \frac{2}{5}\)

The combine ratios will be a1:a2:a3 = 1:2:3  as the a1 is equal to a2 and the 2:4 shows the mixing 2 red with 4 blue paint.

It is defined as the comparison between two quantities that how many times the one number acquires the other number. The ratio can be presented in the fraction form or the sign : between the numbers.

We have:

Purple 1 is made by mixing red(a1) and blue(a2) in a ratio of 1 : 2.

Purple 2 is made by mixing red(a3) and blue(a4) in a ratio of 1 : 3.

Here the options are not given, but we can combine the above ratios like:

a1:a2:a3 = 1:2:3  (a1 = a3)

If we multiply with any number (let's say 2) in the ratio 1 : 2 and 1 : 3

We get:

2:4  (mixing 2 red with 4 blue paint) and

2:6  (mixing 2 red with 6 blue paint)

Thus, the combine ratios will be a1:a2:a3 = 1:2:3  as the a1 is equal to a2 and the 2:4 shows the mixing 2 red with 4 blue paint.

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In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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$384.72

The square feet for a rectangle is length times width. You get your square footage from that then multiply it by $2.29

Answer:

$384.72

Step-by-step explanation:

area of room = 12 X 14 = 168 ft²

2.29 X 168 = 384.72.

Answer:

2

Step-by-step explanation:

Do 15 minus 9

Then do 6 divided by 3

Trust me

If u don’t believe me substitute the 2 and you can find that it is greater than or equal to 15

Answer:

Sin A = 5/13; tan C = 12/5

Step-by-step explanation:

Sin = opposite / hypotenuse. The opposite of A is 5, and the hypotenuse is 13, therefore Sin A = 5/13.

Tan = opposite / adjacent. The opposite of C is 12, and the adjacent is 5, so tan C = 12 / 5

Answer:

56 + 24y

Step-by-step explanation:

8(7 + 3y) = 56 + 24y

Because

8 * 7 = 56

8 * 3y = 24y

Answer:

Step-by-step explanation:

Let n represent the unknown number-

\(\frac{3}{4}n-3=-9\\ \\ \frac{3}{4} n-3+3=-9+3\\ \\ \frac{3}{4} n=-6\\\\ \frac{4}{3}(\frac{3}{4}n)=\frac{4}{3}(-6)\\ \\ n=-8\)

Unknown number = -8

Saying it in digits = \(\frac{3}{4}n-3=9\)

Answer: Its very simple to solve slopes

Step-by-step explanation:

All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.

Answer:

True

Step-by-step explanation:

One is the opposite of the other

Answer:

true

Step-by-step explanation:

These vectors are not linearly independent

To determine whether the vectors (1, 3, 2), (1, -7, -8), and (2, 1, -1) are linearly dependent or independent, we can create a matrix using these vectors as columns and perform row operations to check for linear dependence.

We construct the matrix A as follows:

\(A = \left[\begin{array}{ccc}1&1&2\\3&-7&1\\2&-8&-1\end{array}\right]\)

We can row-reduce matrix A to determine its row-echelon form or reduced row-echelon form. If any row of the reduced matrix is all zeros, it indicates that the vectors are linearly dependent. Otherwise, if all rows are non-zero, the vectors are linearly independent.

Performing row operations on matrix A:

\(R_2 = R_2 - 3R_1\\R_3 = R_3 - 2R_1\)

\(A = \left[\begin{array}{ccc}1&1&2\\0&-10&-5\\0&-10&-5\end{array}\right]\)

Now, further simplifying:

\(\\R_3 = R_3 - R_2\)

\(A = \left[\begin{array}{ccc}1&1&2\\0&-10&-5\\0&0&0\end{array}\right]\)

The reduced row-echelon form of matrix A has a row of all zeros, indicating that the vectors (1, 3, 2), (1, -7, -8), and (2, 1, -1) are linearly dependent.

Therefore, these vectors are not linearly independent.

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The general solution of the given differential equation be \(y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}\)

For given question,

We have been given a differential equation y'' − y' − 12y = e^(4x)

We need to solve the given differential equation by undetermined coefficients.

We can write given differential equation as \((D^2-D-12)y=e^{4x}\) where \(D=\frac{d}{dx}\)

First solve the corresponding homogeneous differential equation:

y'' - y' - 12y = 0

The characteristic equation is:

m² - m - 12 =0

Let's find the roots of above quadratic equation by factorization.

⇒ m² - m - 12 = 0

⇒ (m - 4)(m + 3) = 0

⇒ m - 4 = 0   OR  m + 3 = 0

⇒ m = 4   OR   m = -3

Hence the complementary solution is,

\(y_c=C_1e^{4x}+C_2e^{-3x}\)

Let the general solution of a second order homogeneous differential equation be \(y(x)=C_1(x)e^{4x}+C_2(x)e^{-3x}\)

The unknown functions C1(x) and C2(x) can be determined from the system of two equations:

\(C'_1e^{4x}+C'_2e^{-3x}=0~~~~~~~............(1)\\\\C'_1(4e^{4x})+C'_2(-3e^{-3x})=e^{4x}~~~~~~~...................(2)\)

from (1),

\(C'_2e^{-3x}=-C'_1e^{4x}\)

Substitute this value in equation (2)

\(4C'_1e^{4x}+3C'_1e^{4x}=e^{4x}\)

\(\Rightarrow C'_1=\frac{1}{7}\)  and  \(C'_2=-\frac{1}{7}e^{7x}\)

\(\Rightarrow C_1=\frac{1}{7} x+c_3\)     and     \(C_2=\frac{1}{49}e^{7x}+c_2\)

Therefore, the general solution of the given differential equation be \(y(x)=c_1e^{4x}+c_2e^{-3x}+\frac{1}{7} xe^{4x}\)

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Answer:

\(\sqrt{122}\)

Step-by-step explanation:

Given that,

Vector n = 4i-j

Vector m = 3i+3j

We need to find the value of m+2n.

Put all the values,

m+2n = (3i+3j)+2(4i-j)

= (3i+3j)+8i-2j

=11i+j

Magnitude of vector,

\(|m+2n|=\sqrt{11^2+1^2} \\\\=\sqrt{121+1}\\\\=\sqrt{122}\)

So the correct option is (c).

Answer: 3054 in^3

Step-by-step explanation: The formula for the volume of a sphere is V = 4/3 pi r^3, where r is radius.

Since the diameter is 18in, the radius would be 1/2 or 9in, and plugged in V is

V = 4/3(3.1415)(9)^3

Answer:

1/6*π*18^3≈3053.62806

Step-by-step explanation:

If an observed statistic from a study turns out to be a likely value under the chance model, then it is possible that the observed result occurred by chance.

In statistics, a chance model is a model that describes the distribution of outcomes that would be expected if there were no underlying effect of the variable being studied.

In other words, it represents the distribution of outcomes that would be expected purely by chance.

When conducting a hypothesis test, researchers compare the observed statistic (such as a mean, proportion) from their study to the distribution of values that would be expected under the chance model.

If the observed statistic is a likely value under the chance model, then this suggests that the observed result could plausibly have occurred by chance, and not due to the effect of the variable being studied.

For example, imagine a study that investigates whether a new drug is effective at reducing cholesterol levels in patients.

The researchers compare the mean cholesterol levels of patients who received the drug to those who received a placebo.

If the observed difference in means is a likely value under the chance model then this suggests that the observed difference could have occurred by chance, and not necessarily due to the drug's effect.

However, it's important to note that just because an observed statistic is a likely value under the chance model does not necessarily mean that the result was due to chance.

There may be other factors at play that are not accounted for in the chance model. That's why statistical inference is always probabilistic and subject to some degree of uncertainty.

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Answer:

m = \(\frac{k + 7}{3}\)

Step-by-step explanation:

k = 3m - 7

k + 7 = 3m - 7 + 7

k + 7 = 3m

\(\frac{k + 7}{3}\) = m

(I'm not 100% sure fyi)

Answer:ndjsoalwjjdlq bc hxlansbdlmdnwb

Step-by-step explanation:

The graph meets the vertical line test requirement, it must represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

According to the function, every value in the domain is associated to exactly one value in the range, and they have a predefined domain and range. It is characterized as a certain kind of relationship.

Please refer to the image instead of the graph, which is related to it.

The graphic displays a graph.

A parabola is seen on the graph.

The vertical line test determines if a graph can be a function, as is common knowledge.

The graph passes the vertical line test option, indicating that it does in fact represent a function (C) The vertical line test shows that the graph is correct, hence the answer is yes.

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The coordinates of the center is (32, 40.5).

length of the radius of the circle is 73 units.

The coordinates of the center is solved using the formula for midpoints expressed as

Midpoint x-coordinate = (x₁ + x₂) / 2

Midpoint y-coordinate = (y₁ + y₂) / 2

Plugging in the values:

x₁ = 8 and y₁ = 13

x₂ = 56 and y₂ =68

Midpoint x-coordinate

= (8 + 56) /2

= 64/2

= 32

Midpoint y-coordinate

= (13 + 68) /2

= 81/ 2

= 40.5

distance formula will be used to find the length of the radius of the circle

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Plugging in the values:

= √[(56 - 8)² + (68 - 13)²]

= √(48² + 55²)

= √(2304 + 3025)

= √5329

= 73

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Answer: b

Step-by-step explanation:

B

Answer:

The American Revolutionary War (1775–1783), also known as the American War of ... Britain remained under siege in Gibraltar but scored a major victory over the French navy. ... in America, and the colonial legislatures argued that they had exclusive right .... Howe then seized control of New York City on September 15

Step-by-step explanation:

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Answer:

\(x=6+8i\)

\(x=6-8i\)

Step-by-step explanation:

\(x^2-12x+100=0\)

solve by quadratic formula.

\(\frac{-b+-\sqrt{b^2-4(a*c)} }{2*a}\)

\(\frac{12+\sqrt{(-12)^2-4*(1*100)} }{2*1}\)

\(\frac{12-\sqrt{(-12)^2-4*(1*100)} }{2*1}\)

which is

\(x=\frac{12+16i}{2}\)

\(x=\frac{12-16i}{2}\)

Simplify.

\(x=6+8i\)

\(x=6-8i\)

Solved.

Hope this helps.

Given:

A figure of a circle with radius 8. The central angle of the blue sector is 60 degrees.

To find:

The area of the blue sector.

Solution:

Area of a sector is:

\(A=\pi r^2\dfrac{\theta}{360^\circ}\)

Where, r is the radius and \(\theta \) is the central angle of the sector in degrees.

Putting \(r=8, \theta=60^\circ, \pi=3.14\), we get

\(A=(3.14)\cdot (8)^2\cdot \dfrac{60^\circ}{360^\circ}\)

\(A=(3.14) \cdot (64)\cdot \dfrac{1}{6}\)

\(A=33.49333....\)

Approximate the value to the nearest tenth.

\(A\approx 33.5\)

Therefore, the area of the blue sector is about 33.5 sq. units.

By 2228 ways i can select the team to have more girls than boys

We have, total number of boys = 6, while the total number of girls = 8

Total size of team = 6

Condition given: In every case the total number of girls should be more than the total number of boys.

As for that we can choose the team like

(6G, 0B) + (5G, 1B) + (4G, 2B)

Making the combination as per above arrangements:

We will get it as:

=8C6*6C0+8C5*6C1+8C4*6C2

As we know,

The formula of combination is:

\($${ }_n C_r=\frac{n !}{r !(n-r) !}$$\)

\(${ }_n C_r=$\) number of combinations

n= total number of objects in the set

r= number of choosing objects from the set

So, applying the concept of combination in the above,

So, from above we can write it as:

8C6*6C0+8C5*6C1+8C4*6C2

=\([\frac{8!}{6! \times 2!}\times \frac{6!}{6!\times 0!}]+[\frac{8!}{5!\times 3!}\times \frac{6!}{5!\times 1}]+[\frac{8!}{4!\times 4!}\times \frac{6!}{2!\times 4!}]\\\\\)

\([\frac{8 \times7\times6! }{6!\times2} \times \frac{1}{1}]+[\frac{8\times7\times6\times5!}{5!} \times \frac{6\times5!}{5!}]+[\frac{8\times7\times6\times5\times4!}{4!\times24} \times \frac{6\times5\times4!}{4!\times2}]\)

[28*1]+[336*6]+[70*2]

=28+2016+140

=2228

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Answer : The integral value is: ∫∫sin(r^2) dr dθ = -π(cos(49) - cos(9))

Given:  we have 3 ≤ r ≤ 7.

The integral becomes: ∫∫sin(r^2) dr dθ

with r ranging from 3 to 7 and θ ranging from 0 to 2π.

Now we can evaluate the integral:

∫(0 to 2π) dθ ∫(3 to 7) r sin(r^2) dr

To solve the inner integral, we use substitution. Let u = r^2, so du = 2r dr.

Then: (1/2)∫(9 to 49) sin(u) du = [-(1/2)cos(u)](9 to 49) = -(1/2)[cos(49) - cos(9)]

Now, evaluate the outer integral:

∫(0 to 2π) [-(1/2)(cos(49) - cos(9))] dθ = -[(1/2)(cos(49) - cos(9))][θ](0 to 2π)

= -(1/2)(cos(49) - cos(9))(2π - 0) = -π(cos(49) - cos(9))

So the integral value is:

∫∫sin(r^2) dr dθ = -π(cos(49) - cos(9))

The angle B of a triangle ABC is 26.87°.

Given that, ∠A=92°, b=6.93 cm and a=15.31 cm.

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The sine rule formula=sin A/a = sin B/b =sin C/c.

Now, sin 92°/15.31 = sin B/6.93

⇒sin B/6.93=0.0652

⇒sin B=0.452

⇒B=26.87°

Therefore, angle B of a triangle ABC is 26.87°.

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Answer:

50.33962264

Step-by-step explanation:

brainlest pls

Answer:

the answer is 50.33

Step-by-step explanation:

someone check out my recent question

Answer:

No solution.

Step-by-step explanation:

1-2k+5k<-4+3k  Combine like terms on each side wherever you can.

1+3k<-4+3k        Subtract -3k on both sides (it's less confusing when you get

  -3k      -3k        rid of the variable first).

1<-4                     1 is not less than or equal to -4, so there is no solution.

I hope this helped you out!! Have a great day (*^3^)╭