please help me: A parabola with equation y= -2(x+p)²+q has axis of symmetry x=1 and range (-infinity;5]. Find x-intercepts of the parabola. correct to two decimals​

(a) Sketching a graph of the sinusoid: Connect the points (2.9, 200) and (5.1, 800) with a smooth curve.

(b) Writing the equation using the sine function: f(t) = 300 * sin((2π / 2.2) * (t - C)) + 200.

(c) Population when t = 7 cannot be determined without the value of C.

(d) The range of values for t when foxes are first endangered cannot be determined without the value of C.

(a) To sketch a graph of the sinusoidal variation of the fox population, we can plot the given points: (2.9, 200) and (5.1, 800). Connect these points with a smooth curve to represent the sinusoidal pattern.

(b) Using the sine function, we can write an equation to express the number of foxes as a function of time, t:

f(t) = A × sin(B × (t - C)) + D

Given that the minimum number of foxes is 200 (D = 200) and the maximum is 800, we can calculate the amplitude as half the difference between the maximum and minimum values (A = (800 - 200) / 2 = 300). The period, T, can be determined by the time difference between the maximum and minimum points (T = 5.1 - 2.9 = 2.2).

The coefficient B is calculated as B = 2π / T.

The equation becomes:

f(t) = 300 × sin((2π / 2.2) × (t - C)) + 200

(c) To predict the population when t = 7, substitute t = 7 into the equation from part (b):

f(7) = 300 × sin((2π / 2.2) * (7 - C)) + 200

However, without the value of C (the phase shift), we cannot provide an exact prediction.

(d) To determine the range of values for t when the fox population first becomes endangered (drops below 300), we need to solve the equation:

300 = 300 × sin((2π / 2.2) × (t - C)) + 200

Once again, without the value of C, we cannot determine the exact range of values for t.

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Answer:

42

Step-by-step explanation:

256/6

To find the point of intersection (P) of the lines r1 and r2. First, let's express the parametric equations of the lines as follows:r1(t) = (2, 1 - 2t, 8 + t)
           r2(t) = (6.5 - 3t, 0.5 + 3t, 10.5 - 3t)

For these lines to intersect, the corresponding coordinates must be equal. Let's denote the parameter for r1 as t1 and for r2 as t2. This gives us the following system of equations:

1. 2 = 6.5 - 3t2
2. 1 - 2t1 = 0.5 + 3t2
3. 8 + t1 = 10.5 - 3t2

Solving equation 1 for t2, we get t2 = (6.5 - 2) / 3 = 1.5. Now, we can plug this value into equations 2 and 3:

1 - 2t1 = 0.5 + 3(1.5) => t1 = -2
8 + (-2) = 10.5 - 3(1.5) => t1 = -2

Since both equations result in t1 = -2, we have a consistent solution. Now, we can find the point of intersection P by plugging t1 and t2 into the parametric equations of r1 and r2:

P = r1(-2) = (2, 1 - 2(-2), 8 - 2) = (2, 5, 6)

Therefore, the point of intersection P is (2, 5, 6).

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Answer:

v=8

Step-by-step explanation:

–9v + 1 = –8v − 7

Add 9v to each side

–9v+9v + 1 = –8v+9v − 7

1 = v-7

Add 7 to each side

1+7 = v-7+7

8 =v

Answer:

V=6

Step-by-step explanation:

Answer:

a₂₀ = 69

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 15 - 12 = 3 , then

a₂₀ = 12 + (3 × 19) = 12 + 57 = 69

Answer:

answer is 7.5 miles

Step-by-step explanation:

30/8=3.75 mi in one hour

3.75*2=7.5 miles in 2 hours

hope it helps

The best description for the lines on the graph is OPTION d. Not enough information to tell

To determine the best description for the lines on the graph, it's important to understand the characteristics of each option: skew, perpendicular, parallel, not enough information to tell, or neither.

Skew lines are lines in three-dimensional space that are not parallel and do not intersect. They have different slopes and are not in the same plane. However, since the graph is not described in detail, it is difficult to determine if the lines on the graph are skew.

Perpendicular lines are two lines that intersect at a right angle (90 degrees). If the lines on the graph intersect at a right angle, they can be described as perpendicular. However, without the specific details of the graph, it is impossible to ascertain if the lines meet this criterion.

Parallel lines are lines that do not intersect and are always equidistant. If the lines on the graph appear to run side by side without intersecting, they can be described as parallel. Nonetheless, this can only be confirmed if there is sufficient information about the graph's axes, scales, and line equations.

Without additional information about the graph, it is not possible to determine if the lines are skew, perpendicular, or parallel. Hence, the correct answer is d. Not enough information to tell.

It is important to note that the description of the lines on the graph may be subject to change or refinement based on the specific characteristics and context provided.

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Answer:

10 eheyyahwhwhahwhwhwhwhwhhe

Answer:

52.948 m²

Step-by-step explanation:

→ State the formula for the area

length × width

→ Substitute in the numbers

8.68 × 6.1 = 52.948 m²

The series Σ tan(13k), k=1 diverges. By comparing it to the harmonic series Σ 1/k, we can show that 0 ≤ tan(13k) ≤ 1/k, and since Σ 1/k diverges, the given series also diverges.

To determine the convergence of the series Σ tan(13k), k=1, we can use the Comparison Test.

The Comparison Test states that if 0 ≤ aₙ ≤ bₙ for all n and the series Σ bₙ converges, then the series Σ aₙ also converges. Conversely, if 0 ≤ aₙ ≥ bₙ for all n and the series Σ bₙ diverges, then the series Σ aₙ also diverges.

In our case, we have the series Σ tan(13k), k=1. The term tan(13k) involves trigonometric functions, which can be difficult to analyze directly. However, we can compare it to a known series that has a clear convergence or divergence behavior.

Let's consider the series Σ 1/k, which is the harmonic series. This series is known to diverge. Now, we can compare the given series Σ tan(13k) to Σ 1/k.

Since tan(13k) is positive for k ≥ 1, we can write tan(13k) ≤ 1/k for all k ≥ 1. This inequality implies that 0 ≤ tan(13k) ≤ 1/k.

We know that the harmonic series Σ 1/k diverges. Therefore, by the Comparison Test, if 0 ≤ tan(13k) ≤ 1/k, then the series Σ tan(13k) also diverges.

Hence, the series Σ tan(13k), k=1, diverges.

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A concave hexagon with 2 pairs of congruent sides is a shape that has six sides and two pairs of sides that are of equal length, but the shape curves inward at one or more angles, creating a concave indentation.

A hexagon is a six-sided polygon, and when two pairs of its sides are congruent,

it means that four of its sides have the same length, if the shape curves inward at one or more angles,

it creates a concave hexagon, which means that the indentation on the shape is facing inward, rather than outward, a concave hexagon with 2 pairs of congruent sides is a six-sided polygon with four sides of equal length, but with a curvature that creates an inward indentation.

Hence, a concave hexagon with 2 pairs of congruent sides is a six-sided figure with an indentation and two sets of sides with equal lengths.

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All the values that are possible here are (1, 36) (4,9) (9,4), and (36,1).

The possible values of and b are (1, 36) (4,9) (9,4), and (36,1).

Given: The LCM of a and b is 36 and HCF is 1

To find: The values of a and b?

Here is the solution:

The two numbers are a and b.

LCM of a and b is 36.

HCF of a and b is 1

We know that,

product of two numbers = LCM * HCF

                                       =       A*B=36*1

i.e                                  =        a, b=36,1

in a similar way:

The all-possible values of and b are (1, 36) (4,9) (9,4), and (36,1).

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Answer:

volume = ⅓×π×4²×9 = 48π sq. meters

We accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

What is standard deviation?

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

We have given: μ = 14, x bar = 16, n = 40, s = 6,  α = 5%, = 0.05

To test μ0 : μ = 14   Vs  H1: μ > 14

Test statistics = (X bar - μx)√n / sx = (2 x 6.3245) / 6 = 2.1081

So, P value = 0.021

Conclusion: There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

P value for the hypothesis test

n = 50, x bar = 420, sx = 81, μ = 400,

To test:  H0: μ 400    Vs   H1:  μ > 400

It is right tail test

Test statistics =  (X bar - μx)√n / sx = (420 - 400) √50 / 81 =

z = 1.7459

P value = 0.04093

Declsion: We reject H0 is p value < α

Here α = 0.05

Hence P value < α

Conclusion: We accert H1 alternative that is result is population mean greater than 400.

Hence, we accert H1 alternative that is result is population mean greater than 400.

There is a 2.1% chance than mean second Trimester weight gain for all expectant mothers is 14 pounds in 2015.

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We can see that the statement is not always true for any vectors u and v in V3.

The statement is not always true.

The cross product of vectors u and v in V3 is a vector that is orthogonal to both u and v. That is,

u x v ⊥ u and u x v ⊥ v

However, this does not necessarily mean that (u x v) * u = 0 for all u and v in V3.

For example, let u = <1, 0, 0> and v = <0, 1, 0>. Then,

u x v = <0, 0, 1>

(u x v) * u = <0, 0, 1> * <1, 0, 0> = 0

So in this case, the statement is true. However, consider the vectors u = <1, 1, 0> and v = <0, 1, 1>. Then,

u x v = <1, -1, 1>

(u x v) * u = <1, -1, 1> * <1, 1, 0> = 0

So in this case, the statement is also true. However, if we take the vector u = <1, 0, 0> and v = <0, 0, 1>, then

u x v = <0, 1, 0>

(u x v) * u = <0, 1, 0> * <1, 0, 0> = 0

So in this case, the statement is true as well.

However, if we take the vector u = <1, 1, 1> and v = <0, 1, 0>, then

u x v = <1, 0, 1>

(u x v) * u = <1, 0, 1> * <1, 1, 1> = 2

So in this case, the statement is not true.

Therefore, we can see that the statement is not always true for any vectors u and v in V3.

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Answer: D

Step-by-step explanation:

Domain is x and Range is y

The integrals that represent the area between the positive x-axis, positive y-axis, and the curve x^2 + y^2 = 16 are: ∫[0, 4] √(16 - x^2) dx and ∫[0, 4] √(16 - y^2) dy.

The equation x^2 + y^2 = 16 represents a circle centered at the origin with a radius of 4. To find the area between the positive x-axis, positive y-axis, and the curve, we need to evaluate integrals that represent the area enclosed by the curve. One way to approach this is by using horizontal slices. We can integrate with respect to x and consider a small horizontal slice at height y between x = 0 and x = 4. The width of the slice is given by √(16 - x^2) (the positive square root to stay within the desired region). Therefore, the integral representing the area is ∫[0, 4] √(16 - x^2) dx. Alternatively, we can use vertical slices. We integrate with respect to y and consider a small vertical slice at x between y = 0 and y = 4. The width of the slice is given by √(16 - y^2) (the positive square root to stay within the desired region). Thus, the integral representing the area is ∫[0, 4] √(16 - y^2) dy. In summary, the area between the positive x-axis, positive y-axis, and the curve x^2 + y^2 = 16 can be represented by the integrals ∫[0, 4] √(16 - x^2) dx and ∫[0, 4] √(16 - y^2) dy, which correspond to horizontal and vertical slices, respectively.

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Answer:

Step-by-step explanation:

Answer:

Mean: 12.9

Standard deviation: 14.8

Step-by-step explanation:

The mean is calculated adding all of the values and dividing by the number of elements:

\(m=\frac{2+3+7+12+1+4+27+49+11}{9}=\frac{116}{9}=12.9\)

to find the standard deviation, we first find the variance (which is defined as the sum of all the elements subtracting the mean and squared and then dividing by the total amount of elements):

\(v=\frac{(2-12.9)^2+(3-12.9)^2+(7-12.9)^2+(12-12.9)^2+(1-12.9)^2+(4-12.9)^2+(27-12.9)^2+(49-12.9)^2+(11-12.9)^2}{9}\\\)

\(v=\frac{1978.89}{9}\\\)

\(v=219.88\)

Noe that we have the variance, we can calculate the standard deviation.

The stardard deviation is defined as the squared root of the variance:

\(standardDeviation=\sqrt{v}\)

we substitute the variance:

\(standardDeviation=\sqrt{219.88} \\standardDeviation=14.8\)

Thus, the answer is:

Mean: 12.9

Standard deviation: 14.8

Answer:

Raju can read one chapter 16 minutes so in if you divide 64 by 16 you get 4 meaning he can read 4 chapters in 64 minutes.

The solution to the system of equations is x = 2 and y = 0.

To solve the system of equations:

3x - 5y = 6 ...(1)

-3x - 8y = -6 ...(2)

We can use the method of elimination or substitution. Let's use the elimination method.

Step 1: Multiply equation (1) by 3 and equation (2) by 1 to create coefficients for x that will cancel each other out when added.

Multiply equation (1) by 3:

9x - 15y = 18 ...(3)

Multiply equation (2) by 3:

-9x - 24y = -18 ...(4)

Step 2: Add equations (3) and (4) together to eliminate the x variable.

(9x - 15y) + (-9x - 24y) = 18 + (-18)

-15y - 15y = 0

-39y = 0

Simplifying, we find that -39y equals 0.

Step 3: Solve for y.

Divide both sides of the equation by -39 to isolate y:

-39y / -39 = 0 / -39

y = 0

Step 4: Substitute the value of y back into either equation (1) or (2) to solve for x.

Let's substitute y = 0 into equation (1):

3x - 5(0) = 6

3x = 6

x = 6 / 3

x = 2

Therefore, the solution to the system of equations is x = 2 and y = 0.

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Answer:C

Step-by-step explanation:

I am not that sure.. but I think the answer is C.

Answer:

x = √3

Step-by-step explanation:

Find the diagram attached

Given

Opposite = √3

Adjacent = x

Acute angle theta = 45degrees

According to SOH CAH TOA;

tan theta = opp/adj

tan 45 = √3/x

x = √3/tan45

x = 1

x = √3

Hence the value of x in its simplest radical form is √3

This is a classic river crossing puzzle. To safely get all three across take the goat across, leave the goat, take the lion across, take the cabbage across,  return with the empty boat, Take the goat across to reunite with the cabbage and lion

Here's one possible solution:

By following these steps, you will have successfully transported all three items across the river without violating the rules.

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Answer:

C. x=42

Step-by-step explanation:

16 + 3x + y = 180

126 + 16 + y = 180

y = 38

16 + 3x + 38 = 180

54 + 3x = 180

3x = 126

x=42

The probability of the P(F or G) is 0.667.

A probability experiment is conducted in which the sample space of the experiment is S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, event F={5, 6, 7, 8, 9}​, and event G={9, 10, 11, 12}. Assume that each outcome is equally likely.

To list the outcomes in F or G, we need to combine both events F and G and eliminate any duplicates.

So, the outcomes in F or G are:

F or G = {5, 6, 7, 8, 9, 10, 11, 12}

Hence, A. F or G = { 5, 6, 7, 8, 9, 10, 11, 12}

Next, to find P(F or G) by counting the number of outcomes in F or G, we can use the formula:

P(F or G) = n(F or G) / n(S)

where, n(F or G) is the number of outcomes in F or G and n(S) is the number of outcomes in the sample space.

So, n(F or G) = 8 and n(S) = 12

Hence, P(F or G) = n(F or G) / n(S) = 8/12 = 0.667 (rounded to three decimal places)

Therefore, B. P(F or G) = 0.667

Finally, to determine P(F or G) using the general addition rule, we can use the formula:

P(F or G) = P(F) + P(G) - P(F and G)

where, P(F) and P(G) are the probabilities of events F and G, and P(F and G) is the probability of the intersection of events F and G.

To find P(F and G), we can use the formula:

P(F and G) = n(F and G) / n(S)

where, n(F and G) is the number of outcomes in both F and G.

So, n(F and G) = 1

Hence, P(F and G) = n(F and G) / n(S) = 1/12

Therefore, A. P(F or G) = (5/12) + (4/12) - (1/12) = 8/12 = 0.667 (rounded to three decimal places)

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The expected profit for the car wash is $97.50.

Probability is the possibility of the happening of an event. its is the ration of a particular event upon total number of events.

Formula used is given below;

profit = (loss*probability of loss) + (profit*probability of profit)

μx = (−30)(.15) + (120)(.85)

= −4.50 + 102

= 97.50

Therefore we can conclude that the expected profit for the car wash is $97.50.

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Area of a triangle is half the area of a rectangle. The area of the triangle whose base length is 10 ft and the height is 30 ft is 1500 ft².

The area of a triangle is half the area of a rectangle, therefore, it's half the product of the base and height of the triangle.

We know about the formula of the area of a triangle, also, the length of the base(10 ft) and the height(30 ft) of the triangle is given to us, therefore, substitute the values in the formula of the area of the triangle,

\(Area\triangle = \dfrac{1}{2} \times base \times height\)

           \(= \dfrac{1}{2} \times 10\times 30\\\\=1500\rm\ ft^2\)

Hence, the area of the triangle whose base length is 10 ft and the height is 30 ft is 1500 ft².

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