if y varies directly as the square root of x and y=3, x=3. calculate y when x=64​

Given the expression:

3x² + x - 10

We can rewrite it as:

3x² + 6x - 5x - 10

Which can be factoriced as:

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

(x + 2)(3x - 5)

The probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

The power of a hypothesis test is the probability of rejecting the null hypothesis when the alternative hypothesis is true. In this case, the power of the test is given as 0.8, and the null hypothesis is that the true value of the parameter is 10, while the alternative hypothesis is that the true value is 8.

We are given the sample size, n = 25, and the standard deviation, σ = 4. To calculate the probability of a Type I error, we need to determine the significance level of the test, denoted by α.

The significance level is the probability of rejecting the null hypothesis when it is actually true. It is usually set before conducting the test, and commonly set at 0.05 or 0.01.

To calculate α, we can use the following formula:

α = 1 - power = 1 - 0.8 = 0.2

So, the probability of a Type I error is 0.2 or 20%. This means that there is a 20% chance of rejecting the null hypothesis when it is actually true.

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The formula for the area of a circle is A = πr^2, where r is the radius.
When the radius is 5 centimetres, the area of the circle is A = π(5)^2 = 25π square centimetres.

To find the rate of change of the area of a circle, we need to take the derivative of the area formula with respect to time:
dA/dt = 2πr(dr/dt)

We know that dr/dt = 10 centimeters per minute, and when r = 5 centimeters,
dA/dt = 2π(5)(10) = 100π square centimeters per minute.

Rounding to one decimal place, the rate of change of the area is approximately 314.2 square centimetres per minute.
Therefore, the rate of change in the area of a circle is 314.2 square centimetres per minute.

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If the data shows that overweight children do not suffer from diabetes as predicted by your model, indicating a lower than 80% probability, it suggests that there may be a discrepancy between the model's predictions and the actual observations. In this case, your next step would be to reevaluate and potentially revise your model.

Here are some possible steps to consider:

1. Review the data: Double-check the accuracy and reliability of the data used to validate your model. Ensure that the data is representative, comprehensive, and properly collected.

2. Analyze potential errors: Look for potential errors or biases in the data collection, analysis, or interpretation process. Consider factors such as sample size, sampling method, data collection methods, or any confounding variables that may have affected the results.

3. Assess model assumptions: Review the assumptions made in developing the model and determine if any of them may have been invalid or inappropriate for the specific context or population under study. Adjust the model if necessary to better align with the observed data.

4. Consider additional variables: Examine if there are any other relevant variables that were not initially included in the model but may influence the relationship between child obesity and diabetes. Incorporating additional variables or adjusting the existing ones might lead to a more accurate model.

5. Seek expert opinions: Consult with experts or researchers in the field of child obesity and diabetes to gain insights and validate your findings. They may provide guidance on potential factors or mechanisms that could explain the discrepancy between the model and the observed data.

6. Further data collection: If necessary, consider collecting additional data to refine and improve the model. This could involve expanding the sample size, targeting specific subgroups, or collecting more detailed information on relevant variables.

7. Model refinement or reconstruction: Based on the findings from the above steps, refine or reconstruct the model to better capture the relationship between child obesity and diabetes. This may involve modifying the assumptions, incorporating new variables, or applying alternative modeling techniques.

8. Test and validate the revised model: After making revisions, test the updated model using independent data sets or conducting further studies to validate its accuracy and reliability.

Remember, the scientific process often involves iteration and continuous improvement. If the initial model does not align with the observed data, it is essential to critically evaluate the model and make necessary adjustments to improve its accuracy and usefulness.

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7.702 is the proper decision.

What exactly is a p-value?

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

Answer below.

Step-by-step explanation:

CDEF = MSKX

FCD =  XMS

ED = XS

CFE = MXK

XK = FE

Answer:

27

Step-by-step explanation:

Length * width * height to find the volume so it is 3*3*3=27

Step-by-step explanation:

I love how everyone is just waiting and not saying anything

Answer: C) His creative imagination

Step-by-step explanation:

J.R.R. Tolkien's creative imagination most helped him to become a successful writer

The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

To solve the given initial-value problem, we start by rearranging the equation:
3 11 16 × -(: * *:)* X' = 1 1 3
-(: * *:)* X' = (1/16)  (1/11)  (1/3)
Integrating both sides with respect to t:
-(: * *:)* X = (1/16) t + C1, where C1 is the constant of integration.
Multiplying both sides by the inverse of the matrix -(: * *:) gives:
X = (-1/8) t + C1/8 + C2, where C2 is another constant of integration.
To find the values of C1 and C2, we use the initial condition X(0) = (0) - (5):
X(0) = (-1/8) (0) + C1/8 + C2 = -5
C1/8 + C2 = -5
Since X'(t) = (-3/8), we have X'(0) = (-3/8). Using the equation X'(t) = (-3/8) and the initial condition X(0) = (0) - (5), we can solve for C1:
X'(t) = (-1/8) => (-3/8) = (-1/8) + C1/8 => C1 = -2
Substituting C1 = -2 into C1/8 + C2 = -5 gives:
(-2)/8 + C2 = -5 => C2 = -39/8
Therefore, the solution to the initial-value problem is:
X = (-1/8) t - 1/4 - (39/8)

The solution to the given initial-value problem is X = (-1/8) t - 1/4 - (39/8). The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

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Answer:

C, Almost fifty percent

Step-by-step explanation: I just got it right.

The values of a, b, c, and the critical and inflection points, we can plot the graph by considering the shape and behavior of the polynomial function.

To sketch a graph with specific characteristics, such as 4 roots, 6 critical points, and 6 inflection points, we need to consider a higher degree polynomial function. Let's construct a polynomial function that satisfies these requirements.

To have a single root, we can use a linear factor, (x - a). To have double roots, we can use a quadratic factor, (x - b)^2. And for a triple root, we can use a cubic factor, (x - c)^3.

Considering these factors, let's construct a polynomial function:

f(x) = (x - a)(x - b)^2(x - c)^3

To have 4 roots, we need to choose appropriate values for a, b, and c.

To have 6 critical points, we can set the derivative of f(x) equal to zero and solve for x. The number of critical points corresponds to the number of distinct solutions.

f'(x) = 0

Expanding and solving for x, we'll obtain 6 values for x that correspond to the critical points.

To have 6 inflection points, we can set the second derivative of f(x) equal to zero and solve for x. The number of inflection points corresponds to the number of distinct solutions.

f''(x) = 0

Expanding and solving for x, we'll obtain 6 values for x that correspond to the inflection points.

After determining the values of a, b, c, and the critical and inflection points, we can plot the graph by considering the shape and behavior of the polynomial function.

Please note that without specific values for a, b, and c, it's not possible to provide an exact graph. The process described above is a general approach to construct a graph with the given characteristics.

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Answer:

explanation:

given data

15% amount = 30

to find out

Calculate the whole amount

solution

a pictorial model is attach find that

where we can see easily whole amount is 200 for 15 % is 30

and

15% is 30

here 15% = \frac{15}{100}

100

15

and \frac{15}{100}

100

15

= \frac{30}{200}

200

30

so whole amount is 200 for 15 % is 30

Answer:

henxe required equation of circle is solved

Given the functions:

Solve the equations means finding the values of x provided that f(x) = g(x)

so,

Make the square root alone on the right-side

Square both sides to eliminate the square root:

Simplifying the equation:

Solve the last equation to find the values of x

We can use the calculator to find the values of x

So,

Rounding to the nearest tenth

So, the answer will be x = {-1.7, 4.1 }

The function f is increasing on the interval (6, ∞).

The function f will be increasing in the intervals where f'(x) > 0.

To find these intervals, we can examine the sign of each factor of f'(x), which is (x + 1)²(x - 3)⁵(x - 6)⁴.

We can analyze the sign of f(x) by considering the factors individually:

(x+1)²: This factor is always positive since it is the square of a real number.

(x - 3)⁵: This factor is positive when x>3 and negative when x< 3.

(x - 6)⁴: This factor is positive when x>6 and  negative when x< 6.

We need to consider the overlapping regions of positivity for each factor.

When x>6, all three factors are positive, so  f ′ (x) is positive.

When 3<x<6: In this interval, the factor  (x+1)² is positive, but both (x−3)⁵ and (x−6)⁴ are negative.

Thus, f ′ (x) is negative.

When x<−1: In this interval,  (x+1)² is negative, while (x−3)⁵ and (x−6)⁴ are positive.

Hence, f ′ (x) is negative.

Therefore,  the function f(x) is increasing on the interval x>6.

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Question has errors in typing that 572 should be √57/2

Because if it's 572 then 2a=1 so

Also

c also comes different

If it's like what I said

then

and

By putting values

Option B can be correct

Answer:

B: a = 1, b= 7, c = -2

Step-by-step explanation:

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0\)

Given:

\(x=\dfrac{-7\pm\sqrt{57}}{2}\)

Comparing the terms of the given x-value with those of the quadratic formula:

\(\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}=\dfrac{-7\pm\sqrt{57}}{2}\)

Therefore:

Using the found values of a and b to solve for c:

\(\implies b^2-4ac=57\)

\(\implies (7)^2-4(1)c=57\)

\(\implies 49-4c=57\)

\(\implies -4c=57-49\)

\(\implies -4c=8\)

\(\implies c=-2\)

In summary:   a = 1,  b = 7,  c = -2

\(\implies x^2+7x-2=0\)

Therefore, option B is the correct solution.

The matrix A must have the following form:
A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

In order for a matrix A to define a mapping from R4 into R5 by the rule T(x) = Ax, the matrix A must have 5 rows and 4 columns.

This is because the number of rows in the matrix determines the dimension of the output space, while the number of columns determines the dimension of the input space. In this case, the output space is R5 and the input space is R4, so the matrix must have 5 rows and 4 columns.

In general, if a matrix A is used to define a mapping from Rn into Rm by the rule T(x) = Ax, then the matrix A must have m rows and n columns.

So, the matrix A must have the following form:

A = [ a11 a12 a13 a14 ]
   [ a21 a22 a23 a24 ]
   [ a31 a32 a33 a34 ]
   [ a41 a42 a43 a44 ]
   [ a51 a52 a53 a54 ]

where each aij is a scalar.

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104/-120

=-13/15

Devishri1977 gave a better example of how she got to the answer

Answer:

-13/15

Step-by-step explanation:

104/-120 should be reduced to lowest term and - should be in the numerator

\(\dfrac{104}{-120}= -\dfrac{2*2*2*13}{2*2*2*3*5}=\dfrac{-13}{15}\)

This means that the larger triangle is 2.25 times larger than the smaller triangle.

To find the actual distance between the two cities, we can use proportions. Let x be the actual distance between the two cities.

Using the scale of the map, we can write:

2 inches on the map represents 30 miles in reality

And using the length of the line representing the distance between the two cities on the map, we can write:

4.5 inches on the map represents x miles in reality

To find x, we can set up a proportion:

2/30 = 4.5/x

Cross-multiplying, we get:

2x = 30 * 4.5

Simplifying:

2x = 135

x = 67.5

Therefore, the actual distance between the two cities is 67.5 miles.

To find the scale factor, we can use the ratio of the length of the larger triangle to the length of the smaller triangle. Since the length of the larger triangle is 4.5 inches and the length of the smaller triangle is 2 inches, the scale factor is:

4.5/2 = 2.25

This means that the larger triangle is 2.25 times larger than the smaller triangle.

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Answer: larger triangle is 2.25 times larger than the smaller triangle.

Answer:

5x4 x 3 /10

20x 3 /10

60/10

6

Answer:

Step-by-step explanation:

\(5* 4 \frac{3}{10}=5* \frac{(4*10)+3}{10}\\\\= 5*\frac{43}{10}\\\\= \frac{43}{2}\\\\= 21 \frac{1}{2}\)

Answer:

0.09(x)=70

Step-by-step explanation:

The limit is less than 1, by the Ratio Test, the series converges. We can use the Ratio Test to determine whether the series converges or diverges:

lim n→∞ \(|(4n+1/5n)/(4(n+1)+1/5(n+1))|\)

= lim n→∞ \(|(4n+1/5n) * (5n+6/4n+2)|\)

= lim n→∞ \(|(20n^2 + 34n + 6) / (20n^2 + 46n + 24)|\)

= 1/2

Since the limit is less than 1, by the Ratio Test, the series converges.

To find the sum, we can use the formula for a geometric series:

S = a/(1-r)

where S is the sum of the series, a is the first term, and r is the common ratio.

In this case, a = 5/4 and r = 4/5, so

S = (5/4)/(1-4/5) = 25

Therefore, the sum of the series is 25.

(b) We can use the Ratio Test again:

lim n→∞ \(|((n+1)!)^2/(2(n+1))! * 2n!/(n!)^2|\)

= lim n→∞\((n+1)^2/4(n+1)\)

= lim n→∞ \((n+1)/4\)

= ∞

Since the limit is greater than 1, by the Ratio Test, the series diverges.

(c) We can use the Limit Comparison Test with the series 1/n:

lim n→∞ \((3n+2/5n+3) / (1/n)\)

= lim n→∞ \(3n^2+n / 5n^2+3n\)

= 3/5

Since the limit is positive and finite, by the Limit Comparison Test, the series converges.

(d) We can use the Root Test:

lim n→∞ \(|3n+2/5n+3|^n\)

= lim n→∞ \(3n+2/5n+3\)

= 0

Since the limit is less than 1, by the Root Test, the series converges.

(e) We can use the Ratio Test again:

lim n→∞ \(|(10^2n+5 n!)/(2(n+1))! * (2n)!/(10^2n+7 (n+1))!|\)

= lim n→∞ \((10^2n+5 * 10^2 * (n+1)) / (4(n+1)^2 * (10^2n+7))\)

= ∞

Since the limit is greater than 1, by the Ratio Test, the series diverges.

(f) We can use the Ratio Test:

lim n→∞ \(|(n+1)!/(n+1)^(n+1) * n^n/n!|\)

= lim n→∞\((n+1)/e * n^n/(n+1)^n\)

= lim n→∞ \((n+1)/e * (n/(n+1))^n\)

= 1/e

Since the limit is less than 1, by the Ratio Test, the series converges.

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Answer:

b.d-6 that's the correct answer

Answer:

it is a

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{g(x) = 3x + 5}\\\mathsf{g(x) = 3(-6) + 5}\\\mathsf{g(x) = -18 + 5}\\\mathsf{g(x) = -13}\)

\(\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathsf{g(x) = -13}}\huge\checkmark\\\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\)

\(1. \frac{13}{15} \times \frac{2}{3} \\ = \frac{26}{45} \\ 2. \frac{4}{5} \times \frac{8}{16} \\ = \frac{4}{5} \times \frac{1}{2} \\ = \frac{2}{5} \)

\(3. \frac{4}{24} \times \frac{2}{6} \\ = \frac{1}{6} \times \frac{1}{3} \\ = \frac{1}{18} \)

\(4. \frac{1}{2} \times \frac{1}{5} = \frac{1}{10} \\ 5.1 \frac{1}{3} \times 4 \frac{4}{5} \\ = \frac{4}{3} \times \frac{24}{5} \\ = 4 \times \frac{8}{5} \\ = \frac{32}{5} \\ = 6 \frac{2}{5} \)

Answer:

Step-by-step explanation:

To solve an algebraic expression in simplest form, you can follow these steps:

1. Use the order of operations (PEMDAS) to simplify any arithmetic in the expression (parentheses, exponents, multiplication and division, addition and subtraction).

2. Combine like terms by adding or subtracting any coefficients in front of similar variables.

3. Divide or multiply both sides of the equation by the same non-zero number to solve for the variable.

4. If possible, factor the expression to make it simpler.

5. If the expression is a fraction, check for a common denominator and then simplify by canceling any common factors in the numerator and denominator.

6. If the expression is a radical, check for a perfect square and simplify by taking the square root of the number inside the radical.

7. Use the properties of exponents and logarithms to simplify the expression.

8. Evaluate the expression by plugging in the values of any known variables.

It's important to keep in mind that there may be multiple ways to simplify an algebraic expression and the solution that is in simplest form may not always be obvious.

Answer:

The answer is -285

Step-by-step explanation: