Question 1 (2 points)
The image below represents a dilation. Find the value of x
6
24
9
Х
36
24
c
6
d
33

Answer:

25%

Step-by-step explanation:

We can find this by dividing 1/6 by 2/3 to and then converting to percent. 1/6 divided by 2/3 is equal to 1/6 * 3/2, which is equal to 1/4. 1/4 in percent is 25%.

You can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

To calculate the probability P(1 < z < 2) for a standard normal random variable, we can use the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives us the probability that a standard normal random variable is less than or equal to a given value. We can use this information to calculate the probability between two values.

Let's denote the CDF of the standard normal distribution as Φ(z). The probability P(1 < z < 2) can be calculated as follows:

P(1 < z < 2) = Φ(2) - Φ(1)

To calculate this, we need to look up the values of Φ(2) and Φ(1) from a standard normal distribution table or use a calculator/computer software. However, since I don't have access to real-time computations in this environment, I am unable to provide the exact numerical value.

But you can use statistical software or online calculators to find the precise value. Alternatively, you can approximate the probability using the standard normal distribution table by looking up the closest values for Φ(2) and Φ(1).

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Answer:

guys i have no idea

Step-by-step explanation:

The volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that, a hemisphere fits snugly inside a cylinder with a radius of 8 cm. A cone fits snugly inside the same hemisphere.

Since, all of them are tightly packed in one another therefore, radius of all them will be equal,

And, and the radius of the cylinder is 6 cm, the radius of the hemisphere equals the radius of the cylinder. Also, the height of the cylinder equals the radius of the hemisphere.

r = radius of cylinder = 8 cm and

h = height of cylinder = radius of hemisphere = 8 cm

We know that,

Volume of a cylinder = π × radius² × height

Volume of a cone = 1/3 × π × radius² × height

Therefore,

a) The volume of cylinder =

π × 8² × 8 = 512π cm³  

b) The volume of cone =

1/3 × π × 8² × 8 = 170.6π cm³  

c) Volume of the hemisphere = (512π + 170.6π) / 2

= 341.3π cm³  

Hence, the volumes of the cylinder, the cone and the hemisphere are 512π cm³, 170.6π cm³ and 341.3π cm³ respectively.

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The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number

The code provided indicates that each number corresponds to a letter in the alphabet. Since 1 is A, 2 is B, and so on, the code 1814151418 would decode as RADE. This is an example of a simple substitution cipher, a type of encryption where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which in this case is the code that maps each letter to a number. Knowing this, it is a simple task to decode any message that has been encrypted with this code.

The code 1814151418 decodes to RADE using a simple substitution cipher, where each letter is replaced with a different letter or number. To decipher the message, one must know the key, which is the code that maps each letter to a number

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x equals 3/10 or .33

Answer:

Step-by-step explanation:

2 or 6 i think im probaly wrong

Answer:

The container can hold 6 cups.

Step-by-step explanation:

Since the container is 1/3 full, and it currently has 2 cups, we know that it can only hold 6 cups as 3 × 2 is equal to 6.

Answer:

\(7:4:2\)

Step-by-step explanation:

Assign variables for the 3 numbers. Let the first number be x, the second number be y, and the third number be z.

"The sum of the 3 numbers is 145", therefore:

"Seven times the second number is twice the first number":

"Twice the second number is six times the third number":

We can solve for x, y and z using this system of equations. Let's solve for y in the first equation by putting the other variables in terms of y in Equations II and III.

Solve for x in \(\text{Equation II}\):

Solve for z in \(\text{Equation III}\):

Substitute these values into \(\text{Equation I}\) to solve for y.

Combine like terms using common denominators. The least common denominator is 6. Multiply \(\frac{7}{2} y\) by \(\frac{3}{3}\), multiply \(y\) by \(\frac{6}{6}\), and multiply \(\frac{1}{3} y\) by \(\frac{2}{2}\) to make all of the denominators = 6.

Add the fractions together.

Solve for y by multiplying both sides by \(\frac{6}{29}\).

We have found that y = 30. Now we can use this known value in order to solve for both x and z in Equations II and III.

\(\text{Equation II}:\)

\(\text{Equation III}:\)

We have found that x = 105, y = 30, and z = 10. Now we can write the new ratio of these 3 numbers:

"Write the new ratio of the three numbers if the second number doubles and the third number is increased by one less than one fifth of the first number":

The question asks for the new ratio once we evaluate these expressions. The variable x is the only one that stays the same at the end: 105.

Our final numbers are x = 105, y = 60, and z = 30. We can create the ratio between these numbers by fully simplifying them. Right now we have \(x:y:z=105:60:30\). Start by dividing all of the numbers by 5.

We get \(21:12:6\). This ratio can be simplified further by dividing all of the numbers by 3. We then get the ratio of: \(7:4:2\).

This ratio cannot be simplified any further, therefore, it is the new ratio of the three numbers.

Answer:

3/5

Step-by-step explanation:

The rise is 3 while the run is 5, so the slope = rise over run = 3/5.

Answer:

5/6

Step-by-step explanation:

slope = change in y over change in x 

A differential equation with some initial conditions is used to solve an initial value problem.

The required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

An initial value problem in multivariable calculus is an ordinary differential equation with an initial condition that specifies the value of the unknown function at a given point in the domain. In physics or other sciences, modeling a system frequently entails solving an initial value problem.

Let the given equation be \($y^{1/2} dy\ dx y^{3/2} = 1\), y(0) = 9

\($(\sqrt{y } ) y^{\prime}+\sqrt{(y^3\right\left) }=1\) …..(1)

Divide the given equation (1)  by \($\sqrt{ y} $\)  giving

\($y^{\prime}+y=y^{(-1 / 2)} \ldots(2)$\), which is in Bernoulli's form.

Put \($u=y^{(1+1 / 2)}=y^{(3 / 2)}$\)

Then \($(3 / 2) y^{(1 / 2)} \cdot y^{\prime}=u^{\prime}$\).

Multiply (2) by \($\sqrt{ } y$\) and we get

\(y^{(1 / 2)} y^{\prime}+y^{(3 / 2)}=1\)

(2/3) \(u^{\prime}+u=1$\) or \($u^{\prime}+(3 / 2) y=3 / 2$\),

which is a first order linear equation with an integrating factor

exp[Int{(2/3)dx}] = exp(2x/3) and a general solution is

\(u. $e^{(2 x / 3)}=(3 / 2) \ln \[\left[e^{(2 x / 3)} d x\right]+c\right.$\)  or

\(\mathrm{y}^{(3 / 2)} \cdot \mathrm{e}^{(2x / 3)}=(9 / 4) \mathrm{e}^{(2x / 3)}+{c}\)

To obtain the particular solution satisfying y(0) = 4,

put x = 0, y = 4, then

8 = (9/4) + c

c = (23/4)

Hence, the required particular solution is given by the relation:

\($4y^{(3/2)} = 9e^{(-2x/3)} + 23\)

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

To express the area under the graph of f(x) as a limit, we divide the interval [2, 4] into n subintervals of equal width Δx = (4 - 2)/n = 2/n.

Let xi be the right endpoint of each subinterval, with i ranging from 1 to n. The area of each rectangle is given by f(xi)Δx.

By summing the areas of all the rectangles, we obtain the Riemann sum: A = Σ[f(xi)Δx], where the summation is taken from i = 1 to n.

To find the expression for the area under the graph of f(x) as a limit, we let n approach infinity, making the width of the rectangles infinitely small.

This leads to the definite integral: A = ∫[2, 4] f(x) dx.

In this case, the expression for the area under the graph of f(x) over the interval [2, 4] is given by the limit as n approaches infinity of the Riemann sum: A = lim(n→∞) Σ[f(xi)Δx].

Evaluating this limit would yield the actual value of the area under the curve.

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The length of the segment BC equal to the distance between the two points C and D, and that is 6.32 units.

Remember that the length of a segment whose endpoints are (x₁, y₁) and (x₂, y₂) is given by:

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\)

Here we can see that the endpoints of the segment whose length we want to find, which is CD, are the two points:

C = (-1, -3)

B = (1, 3)

Replacing the correspondent values in the formula for the distance we will get the expression you can see below, and then we can solve it.

\(d = \sqrt{(1 + 1)^2 + (3 + 3)^2}\\d = \sqrt{40} = 6.32\)

The correct option is the third one.

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Answer:

A.

Step-by-step explanation:

   Factor out x^2-3x-40.  Know that the zeroes of a function multiply to be equal to the constant (-40) and add up to the coefficient of the x term (-3).  The two numbers that do that are -5 and 8.  Recall that to be zeroes, at least one of the x-values must make the equation equal 0.  So if x=-5, (x+5) is the term that would be 0.

You could also multiply the factored forms that are given to find the correct one.

The correct option (a) 2000, is the miles are driven on each tire.

For the stated question-

Miles are driven on each tire = Total distance/number of tires.

Miles are driven on each tire = 10000/5

Miles are driven on each tire = 2000

Thus, the number of miles are driven on each tire is 2000 miles.

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Answer:

2:7

Step-by-step explanation:

4 sea turtles:14 seals = 2 sea turtles:7seals

Answer:

y = (2 x)/3 + 1/4

Step-by-step explanation:

Solve for y:

8 x - 12 y = -3

Subtract 8 x from both sides:

-12 y = -8 x - 3

Divide both sides by -12:

Answer: y = (2 x)/3 + 1/4

Answer:

  (-1, 3)

Step-by-step explanation:

Only the first question is complete.

You want to solve ...

  2x +y = 1

  3x -y = -6

You can add these two equations to get ...

  5x = -5

  x = -1 . . . . . divide by 5

This matches the first choice: (-1, 3).

Answer:

A: (-1,3) is the correct answer to the problem.

Step-by-step explanation:

I just did the a quiz with that question and A is the answer.

Answer:

2^27

Step-by-step explanation:

Given the following expression:

[(2^10)^3 x (2^-10)] ÷ 2^-7

This can be easily simplified. Let us simplify the numerator first. To do that, we have

(2^10)^3 making use of the power rule of indices that says:

(A^a)^b = A^ab where a and b are powers, we have:

2^(10x3) = 2^30

Therefore the numerator becomes:

2^30 x 2^-10. Also making use of the multiplication rule that says:

A^a x A^b = A^(a + b), we have

2^30 x 2^-10 = 2^(30 – 10) = 2^20.

Now we have:

(2^20) ÷ (2^-7)

To simplify this, we need the division rule of indices which says:

A^a ÷ A^b = A^(a – b)

Therefore we have:

(2^20) ÷ (2^-7) = 2^[20 – (–7)] = 2^(20+7) = 2^27

Following are the solution to the given expression:

Given:

\(\to \frac{[(2^{10})^3 \times (2^{-10})]}{2^{-7}}\)

To find:

value=?

Solution:

\(\to \frac{[(2^{10})^3 \times (2^{-10})]}{2^{-7}}\)

Using formula:

\(\to (A^a)^b = A^{ab}\\\\\to A^a \div A^b = A^{(a - b)}\)

Solve the equation:

\(\to \frac{[(2^{30}) \times (2^{-10})]}{2^{-7}} \\\\\to \frac{(2^{30})}{2^{-7}} \times \frac{(2^{-10})}{2^{-7}} \\\\ \to \frac{(2^{30})}{2^{-7}} \times \frac{(2^{-10})}{2^{-7}} \\\\\to (2^{30 - (-7)}) \times (2^{-10- (-7)}) \\\\\to 2^{37} \times 2^{-3} \\\\\to 2^{37 -3} \\\\\to 2^{34} \\\\\)

Therefore, the final answer is "\(\bold{2^{34}}\)".

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Answer:

see explanation

Step-by-step explanation:

AD = BC = 8 ( opposite sides of a parallelogram are congruent )

DC = AB = 15 ( opposite sides of a parallelogram are congruent )

Consecutive angles in a parallelogram are supplementary , sum to 180° , so

∠ A + ∠ D  = 180° , that is

∠ A + 68° = 180° ( subtract 68° from both sides )

∠ A = 112°

the opposite angles of a parallelogram are congruent , then

∠ B = ∠ D = 68° , and

∠ C = ∠ A = 112°

The first four nonzero terms of the Maclaurin series for the function g(x) are:

1 - x + 1/2 x^2 - 1/6 x^3

So the correct answer is option (c).

To find the Maclaurin series for the given function g(x) = (1 + x)e^(-x), we can use the formula for the Maclaurin series:

f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...

First, we find the first few derivatives of g(x):

g(x) = (1 + x)e^(-x)

g'(x) = -xe^(-x) + e^(-x)

g''(x) = xe^(-x) - 2e^(-x)

g'''(x) = -xe^(-x) + 3e^(-x)

Evaluating these derivatives at x = 0, we get:

g(0) = 1

g'(0) = 0

g''(0) = -2

g'''(0) = 3

Using the Maclaurin series formula and substituting in these values, we get:

g(x) = 1 + 0x - 2/2! x^2 + 3/3! x^3 + ...

Simplifying this expression, we get:

g(x) = 1 - x + 1/2 x^2 - 1/6 x^3 + ...

Therefore, the first four nonzero terms of the Maclaurin series for the function g(x) are:

1 - x + 1/2 x^2 - 1/6 x^3

So the correct answer is option (c).

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The expression will give two different values can be obtained by inserting a single set of parentheses 13.3, and 23.3.

The total number of values that can be obtained by inserting a single set of parentheses, we need to consider the different possible placements of the parentheses within the expression 23-4.7-5.

The given expression is: 23 - 4.7 - 5

We can place the parentheses around any two adjacent terms in the expression. Let's consider the possibilities

A) (23 - 4.7) - 5

Resulting value

18.3 - 5 = 13.3

B) 223 - (4.7 - 5)

Resulting value

23 - (-0.3) = 23 + 0.3

= 23.3

So, with the given expression, two different values can be obtained by inserting a single set of parentheses: -10, 13.3, and 23.3.

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Answer:

You will make 75 dollars.

Step-by-step explanation:

5% of 100 is 5. Multiply 5 by 15 to get 75.

The appropriate simulation applet to calculate an approximate p-value is 0.0077.

The strong evidence that a short delay hinders the memorization process is strong data suggests that a brief delay impairs memorization.

Delay or no delay, answer: the number of words remembered

The mean distance between words remembered with and without delay over time is null, or zero.

Alt: The mean distance in words remembered over the long term (with no delay minus with delay) is higher than 0.

Yes, the majority of the lines do skew to the right. The mean for no delay is 10.55 whereas that for with delay is 8.7.

The mean distance in words remembered is 1.85.

1)0.0077 as the p-value

2)Strong data suggests that a brief delay impairs memorization.

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The probability distribution of the number of hours per day people are able to relax is constructed, and probabilities of relaxing more than 4 hours, between 2 to 6 hours, and not relaxing at all are 0.283, 0.767 and 0.068 respectively. The mean and standard deviation are 3.326 hours and 1.950 hours (approx.) respectively.

The probability distribution of X is:

X Frequency Probability

0 114                    0.068

1 156                    0.093

2 336                    0.201

3 251                     0.150

4 316                      0.189

5 231                     0.138

6 149                    0.089

7 33                    0.020

8 60                    0.036

      1676                     1.000

The probability that a person relaxes more than 4 hours per day is:

P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)

= 0.138 + 0.089 + 0.020 + 0.036

= 0.283

The probability that a person relaxes from 2 to 6 hours per day is:

P(2 ≤ X ≤ 6) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= 0.201 + 0.150 + 0.189 + 0.138 + 0.089

= 0.767

The probability that a person does not relax at all is:

P(X = 0) = 0.068

The mean Mx is:

Mx = Σ(X * P(X))

= 00.068 + 10.093 + 20.201 + 30.150 + 40.189 + 50.138 + 60.089 + 70.020 + 8*0.036

= 3.326 hours

The standard deviation Ox is:

Ox = sqrt[Σ(X^2 * P(X)) - Mx^2]

= sqrt[(0^20.068)+(1^20.093)+(2^20.201)+(3^20.150)+(4^20.189)+(5^20.138)+(6^20.089)+(7^20.020)+(8^2*0.036) - 3.326^2]

= 1.950 hours (approx.)

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f(x) is increasing on the intervals (−∞, π/4) and (5π/4, ∞), and decreasing on the interval (π/4, 5π/4).

To determine the intervals on which f(x) = 3sin(x) + 3cos(x) is increasing and decreasing, we need to find the derivative of f(x) and examine its sign.

f'(x) = 3cos(x) - 3sin(x)

To find where f'(x) = 0, we set the derivative equal to zero and solve:

3cos(x) - 3sin(x) = 0

cos(x) - sin(x) = 0

From this equation, we can see that it is satisfied when x = π/4 and x = 5π/4.

Now, we analyze the sign of f'(x) in different intervals:

For x < π/4: f'(x) > 0, so f(x) is increasing.

For π/4 < x < 5π/4: f'(x) < 0, so f(x) is decreasing.

For x > 5π/4: f'(x) > 0, so f(x) is increasing.

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Answer:

We have the angles as;

8.9 and 72.2

Step-by-step explanation:

When two angles are complementary, they add up to 90

Let the first angle be x , the second angle is 72.2 degrees less and it is x-72.2

Thus, mathematically;

x + x - 72.2 = 90

2x = 90+ 72.2

2x = 162.2

x = 81.1

x = 81.1

The other will be

81.1 - 72.2 = 8.9

Therefore, the solution set for the inequality |7x-3| + 1 >= 9 is x ≤ -5/7 or x ≥ 11/7, which can be expressed in interval notation as (-∞, -5/7] ∪ [11/7, +∞).

To solve the inequality |7x-3| + 1 >= 9, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.

Case 1: (7x - 3) ≥ 0

In this case, the absolute value becomes |7x - 3| = 7x - 3. Substituting this into the inequality, we have:

7x - 3 + 1 ≥ 9

7x - 2 ≥ 9

7x ≥ 11

x ≥ 11/7

Case 2: (7x - 3) < 0

In this case, the absolute value becomes |7x - 3| = -(7x - 3) = -7x + 3. Substituting this into the inequality, we have:

-7x + 3 + 1 ≥ 9

-7x + 4 ≥ 9

-7x ≥ 5

x ≤ -5/7

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To find the sum of the vertex angles in various polygons, we need to sketch the polygons and then calculate the sum. For a hexagon, octagon, and dodecagon, the sums of the vertex angles are 720°, 1,080°, and 1,800°, respectively.

a. Hexagon: A hexagon is a polygon with six sides. To find the sum of the vertex angles, we can divide the hexagon into triangles. Since each triangle has an interior angle sum of 180°, the hexagon can be divided into four triangles. Therefore, the sum of the vertex angles in a hexagon is 4 * 180° = 720°.

b. Octagon: An octagon is a polygon with eight sides. Similar to the hexagon, we can divide the octagon into triangles. Dividing it into six triangles, each with an interior angle sum of 180°, the sum of the vertex angles in an octagon is 6 * 180° = 1,080°.

c. Dodecagon: A dodecagon is a polygon with twelve sides. Dividing it into ten triangles, each with an interior angle sum of 180°, the sum of the vertex angles in a dodecagon is 10 * 180° = 1,800°.

Therefore, the sum of the vertex angles in a hexagon is 720°, in an octagon is 1,080°, and in a dodecagon is 1,800°.

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Find the sum of the vertex angles of the following polygons---

a. A hexagon

b. An octagon

c. A dodecagon.

Answer: 1/6

Step-by-step explanation:

5/6 - 4/6 = 1/6

Answer:

1

-

6

Step-by-step explanation: