Write an equation for the plane that contains the points (0, -1,3), (2,2,1), and (-3, 2,5) in (a) Point- Normal Form (b) General form (C) Vector form (d) Parametric form

Answer:

1m²

Step-by-step explanation:

Answer:

A = 157.3 units²

Step-by-step explanation:

A = 1/2(6.9)(8 x 5.7) = 157.3 units²

Answer: B

Step-by-step explanation:

The value g(x) if f(x) = x2 is g(x) = x2-3, the correct option is C.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

The function f(x)=x2

Now,

In the graph of g(x)

Coordinate x=0

Coordinate y=-3

Plugging in the values

g(x) = x2-y

y=3

g(x)=x2-3

Therefore, by the given function the answer will be g(x)=x2-3.

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Answer:

y=3x+6

Step-by-step explanation:

Just test this on like a graph or something and you will see it works. Let me know if there is a fault in my answer. Thanks! Have a good day.

Answer:

A- lll

B- l

C- lV

D- V

E- ll

Step-by-step explanation:

I think that is the answer.

Answer: 14.6

Step-by-step explanation:

I made a square around the triangle which I then counted the squares, found the Pythagorean theorem, and then added the missing sides together

To estimate the distance traveled between t=0 and t=8 using the average of the left and right sums with 4 subdivisions, we can approximate the area under the velocity curve.

The average of the left and right sums is a numerical integration technique used to estimate the area under a curve. In this case, we want to estimate the distance traveled, which corresponds to the area under the velocity curve.

Given that the velocity function is v(t) = t^2 - 8, we can divide the interval [0, 8] into 4 equal subdivisions. Using the left and right sums, we evaluate the velocity at the left and right endpoints of each subdivision and multiply it by the width of each subdivision.

Calculating the estimates for each subdivision and summing them will give us an approximation of the total distance traveled between t=0 and t=8.

To perform the calculation, we evaluate the velocity at the left endpoints of each subdivision (0, 2, 4, 6) and the right endpoints (2, 4, 6, 8). Then, we multiply each velocity value by the width of the subdivision (2 units). Finally, we sum these estimated distances to obtain the approximation of the total distance traveled.

The detailed calculations would involve substituting the values into the velocity function, multiplying by the width, and summing the results.

Therefore, by using the average of the left and right sums with 4 subdivisions, we can estimate the distance traveled between t=0 and t=8 for the given velocity function.

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Answer:

The inequality that can be used to determine the number of guitar lessons Gale could take using her birthday money is:

[tex]25x + 50 \leqslant 200[/tex]

The solution to the inequality is:

[tex]x \leqslant 6[/tex]

She can take at most, 6 guitar lessons

Step-by-step explanation:

Total amount Gale received is $200

For rental equipment, she paid $50

Each guitar lesson will cost $25

Let x represent the number of lessons she could take, then the total amount she will spend must bot exceed $200

The guitar lesson will cost a total of 25x

So, her total spending will be:

[tex]25x + 50[/tex]

This must be at most $200

[tex]25x + 50 \leqslant 20[/tex]

Solving the above inequality:

[tex]25x \leqslant 200 - 50 = 150[/tex]

[tex]x \leqslant \frac{150}{25} = 6[/tex]

To solve the given initial value problem using the method of Laplace transforms, we'll take the Laplace transform of both sides of the differential equation. Let's denote the Laplace transform of the function y(t) as Y(s).

The Laplace transform of the second derivative y" is s²Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions given.

The Laplace transform of the first derivative y' is sY(s) - y(0).

The Laplace transform of the term 6y is 6Y(s).

The Laplace transform of the term -24e^t can be found using the table of Laplace transforms.

Applying the Laplace transform to the entire differential equation, we get:

s²Y(s) - sy(0) - y'(0) + 5(sY(s) - y(0)) + 6Y(s) - 24/(s-1) = 0

Substituting the initial conditions y(0) = -5 and y'(0) = -19, we have:

s²Y(s) + 5sY(s) + 6Y(s) - 5s + 19 - 24/(s-1) = 0

Now, we can solve this equation for Y(s). Once we find Y(s), we can take the inverse Laplace transform to obtain y(t), the solution to the initial value problem.

Since the given question doesn't specify a particular form for Y(s), I'm unable to provide the exact solution y(t) in terms of e.

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Answer:

201.1 square feet

Step-by-step explanation:

The radius (r) of the patio is 16/2 = 8

Area of a circle is π[tex]r^{2}[/tex] so [tex]8^{2}[/tex]π = 201.0619298 or 64π

Answer:

It will take 113.10 ft² of tiles to cover the patio.

Step-by-step explanation:

area of a circle formula: A = πr²

The diameter is twice the length of the radius. To find the radius, divide the diameter by 2:

16/2 = 8

To find the area of the circular patio, apply the radius to the formula A = πr²:

A = π6²

A = 113.10 ft²

The required answer is  [61.77, 69.23].

Given: Mean height of all 9th grade students at one high school is estimated as ≈65.5 Population standard deviation is σ = 3 inches. Number of samples n = 6Margin of error at 99% confidence level = 1.23Margin of error = E = z(σ/√n)Now, z = inv Norm(0.995) (as it is 99% confidence interval, α=0.01 and 1-α=0.99)⇒ inv Norm(0.995) = 2.58∴ E = 2.58(3/√6) = 3.73∴ The margin of error at the 99% confidence level is 3.73 inches .

Confidence interval = [sample mean - E, sample mean + E]=[65.5 - 3.73, 65.5 + 3.73] = [61.77, 69.23]

∴ The 99% confidence interval for the population mean height of all 9th-grade students at that high school is [61.77, 69.23].

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Answer:

True

Step-by-step explanation:

Solutions to quadratic equations are often called

roots / zeros / x- intercepts

Answer:

The true statements are -: A f(3)>0 , C g(-1)=0.8 and D g(-1)< f(-1)

Step-by-step explanation:

  Given f(x)= 5- 0.2x and g(x)= 0.2(x+5)

(A)  f(3) > 0

    Putting this value in the given equation -

     f(3) =5 -0.2(3)

      f(3)=5 - 0.6

  f(3) =4.4

Therefore , f(3) > 0  . This is a true statement .

(B)  f(3) > 5

     We got the value of f(3) from the above equation,

     Therefore , f(3) = 4.4 , hence f(3) > 5 option is False.

(C)  g(-1) = 0.8

  Taking the second given equation ,

  g(-1) = 0.2 ( -1+ 5)

  g(-1) = 0.2 (-4)

Therefore,  g(-1) = -0.8 . Hence , this statement is true.

(D) g(-1) < f(-1)

  g(-1) = -0.8

f(-1) =5 - 0.2(-1)

f(-1) = 5 +0.2

f(-1) = 5.2

Therefore , g(-1) < f(-1) , Hence this option is true.

(E) f(0) =g(0)

  f(0) = 5 + 0.2(0)

  f(0) = 5

g(0) = 0.2(0+5)

g(0) =  0.2 +5

g(0) = 1

Therefore , f(0)[tex]\neq[/tex] g(0) , Hence , the option is false .

Hence , true statements about the functions are - A , C , D .  

Answer:

There were a total of 72 Easter eggs.

Step-by-step explanation:

Since five students participated in an Easter egg hunt, where Ally snatched up one quarter of all of the eggs, Brett only managed to get half of what Ally found, Lee snagged six more than Brett, Jen ended up with half of Lee's take, While Lisa snagged three times that, to determine how many eggs were there in total, the following calculation must be performed:

Ally: 0.25X

Brett: 0.125X

Read: 0.125X + 6

Jen: 0.0625X + 3

Smooth: 0.1875X + 9

X - 0.25X - 0.125X - 0.125X - 0.0625X - 0.1875X = 0.25

0.25X = 6 + 3 + 9

0.25X = 18

Ally: 18

Brett: 9

Read: 15

Jen: 7.5

Smooth: 22.5

18 + 9 + 15 + 7.5 + 22.5 = X

72 = X

Thus, there were a total of 72 Easter eggs.

The inverse Laplace transform of [tex]X(s) = (s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the region of convergence (ROC) includes all values of s to the right of -2 on the real axis. This means that the Laplace transform is valid for all values of s greater than -2.

To find the inverse Laplace transform, we can use partial fraction decomposition. The denominator of X(s) factors as [tex](s + 2)^2[/tex], indicating a repeated pole at s = -2. The numerator is (s + 1), which is a first-order polynomial.

Applying partial fraction decomposition, we can express X(s) as [tex](A/(s + 2)) + (B/(s + 2)^2)[/tex]. Solving for A and B, we find A = 1 and B = -1.

Now, we can take the inverse Laplace transform of each term. The inverse Laplace transform of A/(s + 2) is [tex]e^-^2^t[/tex], and the inverse Laplace transform of [tex]B/(s + 2)^2[/tex] is [tex]t * e^-^2^t[/tex].

Thus, the inverse Laplace transform of X(s) is [tex]x(t) = e^-^t * (t + 1)[/tex].

The poles of X(s) are located at s = -2. The region of convergence (ROC) can be determined by examining the values of s for which X(s) converges. In this case, since the poles are at s = -2, the ROC includes all values of s to the right of -2 on the real axis.

In summary, the inverse Laplace transform of X(s) = [tex](s+1)/(s^2 + 4s + 4)[/tex] is [tex]x(t) = e^-^t * (t + 1)[/tex]. The poles are located at s = -2, and the ROC includes all values of s to the right of -2 on the real axis.

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If the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

If the sample size decreases but the significance level (alpha) remains the same, the length of the confidence interval will typically increase.

In general, the length of a confidence interval is influenced by two main factors: the variability of the data (measured by the standard deviation or standard error) and the sample size. A larger sample size provides more information and reduces the variability, resulting in a shorter confidence interval.

When the sample size decreases, the amount of information available to estimate the population parameter decreases as well. This can lead to increased variability and uncertainty in the estimation process. As a result, the confidence interval tends to widen to account for the increased uncertainty and potential sampling error.

Therefore, if the sample size decreases while the significance level remains the same, the length of the confidence interval is expected to increase. It is important to note that the exact change in length will depend on the specific data and sample characteristics.

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Answer:

A. 4x¹² + 9x⁷ + 3x³ -x

Step-by-step explanation:

Hi!

==================================================================

To write a polynomial in descending order, we write the terms with higher degrees, or exponents, first.

3x³ + 9x⁷ -x + 4x¹²

4x¹² has the highest degree, so it is written as the first term.

⇒4x¹²

9x⁷ has the next highest degree, so it is written next.

⇒4x¹² + 9x⁷

3x³ has the next highest degree, so it is written next.

⇒4x¹² + 9x⁷ + 3x³

-x has the lowest degree, so it is written last.

⇒4x¹² + 9x⁷ + 3x³ -x

4x¹² + 9x⁷ + 3x³ -x

==================================================================

Hope I Helped, Feel free to ask any questions to clarify :)

Have a great day!

       -Aadi x

Using binomial probability, the probability that at least 26 people experience flu symptoms is 0.8788 and It indicates a potential adverse reaction to the drug, and further investigation or monitoring may be required to assess the relationship between the drug and flu symptoms.

To estimate the probability that at least 26 people experience flu symptoms, we can use the binomial distribution. The probability of flu symptoms for a person not receiving any treatment is given as 0.021.

Let's denote the number of people treated who experience flu symptoms as X, which follows a binomial distribution with parameters n (number of trials) and p (probability of success).

In this case, n = 1133 (number of people treated) and p = 0.021 (probability of flu symptoms for a person not receiving treatment).

We want to find P(X ≥ 26), which is the probability that at least 26 people experience flu symptoms. To calculate this probability, we need to sum the probabilities of the complementary event (X < 26), which is the probability that fewer than 26 people experience flu symptoms.

Using statistical software or a binomial distribution table, we can calculate the probability as follows:

P(X ≥ 26) = 1 - P(X < 26)

Using the binomial distribution, we can calculate the probability of X < 26 as:

P(X < 26) = Σ[P(X = k)] for k = 0 to 25

Now, let's calculate the probability:

P(X < 26) = Σ[C(n, k) * p^k * (1 - p)^(n - k)] for k = 0 to 25

However, calculating this probability manually for each value of k can be cumbersome. Therefore, I'll use statistical software to estimate the probability.

Using the binomial distribution with parameters n = 1133 and p = 0.021, we find:

P(X < 26) ≈ 0.1212

Therefore, the estimated probability that at least 26 people experience flu symptoms is:

P(X ≥ 26) ≈ 1 - 0.1212 ≈ 0.8788

This suggests that the observed number of people experiencing flu symptoms (26) is higher than what would be expected if the drug had no effect on the likelihood of flu symptoms.

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Answer:

A

Step-by-step explanation:

Answer:

To understand their poems better

Step-by-step explanation:

First you have a general knowledge on why the author made the poem

Second you now have more info to use in order to understand the poems

Third is the same reason why there are people in history books.

The integral for the area becomes:

A = ∫₀ᵃʳᶜᶜᵒˢ(ᵃ/₂) ∫ₐ(₁+ᶜᵒˢ(θ))³ᵃᶜᵒˢ(θ) r dr dθ

To find the area inside the circle r = 3acos(θ) and outside the cardioid r = a(1 + cos(θ)), we can set up a double integral in polar coordinates.

First, let's find the points of intersection between the two curves. The circle r = 3acos(θ) and the cardioid r = a(1 + cos(θ)) intersect when:

3acos(θ) = a(1 + cos(θ))

Simplifying, we get:

3acos(θ) - a(1 + cos(θ)) = 0

2acos(θ) - a = 0

acos(θ) = a/2

θ = arccos(a/2)

Now, let's set up the integral. We want to find the area inside the circle and outside the cardioid, so the region of integration is defined by:

0 ≤ θ ≤ arccos(a/2)

a(1 + cos(θ)) ≤ r ≤ 3acos(θ)

Evaluating this double integral will give us the desired area inside the circle and outside the cardioid.

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Answer:

See solutions below

Step-by-step explanation:

From the given diagram;

AC = opposite

AB = 7 = hypotenuse

Angle of elevation = 70 degrees

Using SOH CAH TOA

Sin theta = opp/hyp

Sin theta = AC/AB

Sin 70 = AC/7

AC = 7sin70

AC = 7(0.9397)

AC = 6.58

Similarly

tan 70 = AC/BC

tan 70 = 6.58/BC

BC = 6.58/tan70

BC = 6.58/2.7475

BC = 2.39

tan m<A = BC/AC

tanm<A = 2.39/6.58

tan m<A = 0.3632

m<A = 19.96degrees

Answer:

Yes, it will fit snugly in a 90º corner

Step-by-step explanation:

To do this, we simply need to check if the given sides of the shelf is right-angled.

So, we have:

[tex]Hypotenuse = \sqrt{242[/tex]

[tex]Side\ 1 = Side\ 2 = 11[/tex]

To check for right-angle triangle, we make use of:

[tex]Side\ 1^2 + Side\ 2^2 = Hypotenuse^2[/tex]

This gives:

[tex]11^2 + 11^2 = \sqrt{242}^2[/tex]

[tex]121 + 121 = \sqrt{242}^2[/tex]

[tex]242 = \sqrt{242}^2[/tex]

[tex]242 = 242[/tex]

This shows that the given sides of the shelf is a right-angled triangle.

Hence, it will fit the wall

Answer:

A

Step-by-step explanation:

The given set of vectors in R with the defined addition and scalar multiplication operations does not satisfy the closure properties, violating the vector space axioms.

In the first part, the set of vectors with the given operations does not satisfy all of the vector space axioms.

In the second part, let's examine the vector space axioms to determine which ones are not satisfied.

Closure under addition: The axiom states that for any vectors u and v in the set, the sum u + v must also be in the set. If we consider the vectors (1, 0) and (0, 1), their sum is (1, 1), which is not in the given set. Therefore, closure under addition is not satisfied.

Closure under scalar multiplication: The axiom states that for any scalar c and vector u in the set, the scalar multiple c * u must be in the set. If we consider the vector (1, 1) from the previous example, multiplying it by a scalar c will result in the vector (c, c). However, for certain values of c, such as c = 2, the resulting vector (2, 2) is not in the given set. Hence, closure under scalar multiplication is not satisfied.

Since the set does not satisfy closure under addition and closure under scalar multiplication, it does not satisfy the vector space axioms.

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Answer:

The distribution with the larger median is test scores after football.

The distribution with larger mean is test scores after half day.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

.305

Step-by-step explanation:

Step-by-step explanation:

2/33=6/x

x=99

since there are 11 rest stops and you are trying to find the space in the middle of the two rest stops.

99/11 rest stops

9 miles in between rest stops

9/y=30/1

9/30=y

3/10=y

.3 inches=y

Hope that helps :)

The frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.

The formula for angular velocity is given by;`ω = (2π / T)`.Where;ω = angular velocity of the object. T = time period (in seconds).`I = 185.0 kg m2` represents the moment of inertia of the flywheel.`ω = 350.0 rev/min = (350.0 * 2π) / 60 = 36.61 rad/s` represents the initial angular velocity of the flywheel.

The flywheel is brought to rest by friction in `5.0 min = 5.0 * 60 = 300 seconds`.

The formula for the angular acceleration is given by;`α = (ωf - ωi) / t`. Where;`α` = angular acceleration of the object.`ωi` = initial angular velocity.`ωf` = final angular velocity of the object.`t` = time taken (in seconds).

At rest, the final angular velocity of the flywheel is zero.

Therefore;`α = (- ωi) / t`.The formula for torque is given by;`τ = I * α`.Where;τ = torque exerted on the object.I = moment of inertia of the object.α = angular acceleration of the object.

Substituting the values;`τ = I * α = 185.0 * (-36.61) / 300 = -22.58 N.m`.

Therefore, the frictional torque on the flywheel is `22.58 N.m` in the clockwise direction.

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