The value of x is ___
°, and the value of y is

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

In hypothesis testing, if the null hypothesis is rejected, it means that there is sufficient evidence to support the alternative hypothesis. A null hypothesis is a statement that there is no significant difference or relationship between variables, while the alternative hypothesis states that there is a significant difference or relationship. To determine if the null hypothesis is true or not, we conduct a statistical test and calculate the p-value. If the p-value is less than the level of significance, usually set at 0.05, we reject the null hypothesis and accept the alternative hypothesis. Therefore, the correct answer is that the evidence supports the alternative hypothesis. This means that we have found significant results that support our research hypothesis.
Keep in mind that rejecting the null hypothesis does not prove the alternative hypothesis, but it does suggest that it's more plausible based on the data collected.

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

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To find the sum of the digits of all possible values of 'a', we need to add the sum of the digits of each value of abc. The sum of the digits for all possible values of a would be 8 + 7 + 15 + ... + 27, which can be calculated further.

The divisibility rule for 125 states that a number is divisible by 125 if the last three digits are divisible by 125. In the case of 24687abc, we know that the last three digits (abc) must be divisible by 125. This means that abc must be a multiple of 125. The smallest multiple of 125 is 125, and the largest is 999, so the possible values of abc are 125, 250, 375, 500, ..., 999.

The sum of the digits of each possible value of a can be calculated by adding the individual digits of each value of abc. For example, for the value 125, the sum of the digits is 1 + 2 + 5 = 8. For the value 250, the sum of the digits is 2 + 5 + 0 = 7. For the value 375, the sum of the digits is 3 + 7 + 5 = 15.

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Answer: B

Step-by-step explanation:

 In the systems of equation it already gives you the solution for x  which is -2 so all you have to do is substitute -2 into the first equation and solve for y.

y= 2/3x + 3    

x= -2

Substitute x for -2

y = \(\frac{2}{3}* \frac{-2}1} + 3\)  

y= \(\frac{-4}{3}\) + \(\frac{3}{1}\)    

y = \(\frac{5}{3}\)  

so now you have the solution like this \((-2,\frac{5}{3})\)

Answer:

C

Step-by-step explanation:

Marginal relative frequency for the people who do not like cantaloupe is 0.455

or

91/100

Answer:

C is correct

Step-by-step explanation:

The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85

Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).

Given the complex number is -

6 + 7i / 6-7i

⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i

⇒ (6+7i)² / 6² - 7²(i²)

Using (a+b)² = a² + b² + 2ab    

⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)

⇒ 36 - 49 + 84i / 36 + 49

⇒ -13 + 84i / 85

⇒ -13 / 85 + 84i/85

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Answer:

The blue dot is at 3.

Given:

A couple has 10 movies in their Netflix queue. They decide to randomly choose 2 movies from the queue.

So, the order is not important for the given situation

So, we will use the combinations

So, the number of possible 2-movie selections will be as follows:

So, the answer will be there are 45 possible ways

Answer:

\((x+2)(3x^3-5x-10)\)

Step-by-step explanation:

If you don't know how to divide polynomials then I can help with that too or you can just search it up

To find the slant asymptote of the function y = x^2 + 4x + 4, we need to perform polynomial long division. In this case, we will divide the function by y = x.


1. Divide the function y = x^2 + 4x + 4 by y = x using polynomial long division.
2. x goes into x^2 x times. Write x on top.
3. Multiply x by x, which is x^2. Write x^2 under x^2 in the dividend and subtract it.
4. Bring down 4x from the dividend.
5. x goes into 4x, 4 times. Write 4 next to x on top.
6. Multiply 4 by x, which is 4x. Write 4x under 4x in the dividend and subtract it.
7. Bring down the constant term 4 from the dividend.
8. Since the degree of the remaining dividend (constant term) is lower than the divisor's degree (x), we stop dividing.


After performing polynomial long division, we get the quotient y = x + 4, which is the equation of the slant asymptote for the given function.

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The measure of side b is 10.78 feet.

The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides of the opposing angles.

Given:

A right-angled triangle ABC with angle B equals 90 degrees.

m∠A = 22°.

c = 10 units.

Applying the law of sines,

SinB/b = SinC/10

1/b = Sin(68)°/10

b = 10/sin68°

The value of sin 68° is 0.9272 (approx).

b = 10/0.9272

b = 10.78 feet.

Therefore, b = 10.78 feet.

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AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.

We have,

The given triangle is an isosceles triangle.

So,

The angles opposite to the equal sides are equal.

The other angle = 90

Now,

The sum of the triangle = 180

So,

90 + 2x = 180

2x = 180 - 90

2x = 90

x = 45

Now,

In a right triangle with ∠A = 90 degrees, ∠B = 45 degrees, and ∠C = 45 degrees, we have a special case known as a 45-45-90 triangle.

In a 45-45-90 triangle, the sides are in a specific ratio: 1 : 1 : √2.

Let's use this ratio to find the lengths of the sides:

Since AB = AC, let's denote both lengths as x.

AB = AC = x

BC is the hypotenuse, which is √2 times the length of either leg:

BC = √2x

So, the lengths of the sides are:

AB = AC = x

BC = √2 * x

Therefore,

AB and AC are equal in length and are represented by x, while BC (the hypotenuse) is √2 times the length of either leg.

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Answer: 68.9

Step-by-step explanation:

65 x 0.06 = 3.9

3.9 + 65 = 68.9

Answer:

Neither

Step-by-step explanation:

Need same slope and diff y-intercept for parallel

Need the products of the slopes to equal -1 for perpendicular

\( {n}^{2} - 11n + 10 = \)

\((n - 1)(n - 10)\)

.................................................

15 liters of the 10% acid solution must be used

55 liters of the 80% acid solution must be used

Let the volume of the 10% acid solution be x

Let the volume of the 80% acid solution be y

The combination of the two solutions gives 70 liters

x + y = 70..............................(1)

The 70 liters solution is equivalent to 65%

10x + 80y = 70(65)

10x + 80y = 4550..........................(2)

Make x the subject of the formula in equation (1)

x = 70 - y...............................(3)

Substitute equation (3) into equation (2)

10(70 - y) + 80y = 4550

700 - 10y + 80y = 4550

70y = 4550 - 700

70y = 3850

y = 3850/70

y = 55 liters

Substitute y = 55 into equation (3)

x = 70 - 55

x = 15 liters

The correct expression that will form with one multiplication operation is 8 × (5.95 + 84 + 3.60 + 2.25).

Firstly rewriting the correct expression according to the amount spent by each person on different entities. The expression will be -

Total amount spent by 8 people = number of people × (amount spent on dinner + laser tag + bowling shoes + video games)

Now keeping the values in formula to find the total amount spent by eight people in desired format.

Total amount spent by eight people = 8 × (5.95 + 84 + 3.60 + 2.25)

Performing addition to simplify the expression is -

Total amount spent by eight people = 8 × 95.8

Thus, the correct simplified expression will be 8×95.8.

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Answer:

x < -4

Step-by-step explanation:

2(-3x - 4) > 16

-6x - 8 > 16

-6x > 16 + 8

-6x > 24

-x > 4

x < -4

Answer:

x < -4

Step-by-step explanation:

2(-3x - 4) > 16

Distribute.

-6x - 8 > 16

Add 8 to both sides.

-6x > 24

Divide by -6. When dividing by a negative, flip the sign.

x < -4.

Simplifying, the final result is:

∫(\(x^8 + 8x) dx = (1/9) * x^9 + 4x^2\) + C, where C = C1 + C2 is the constant of integration.

To evaluate the indefinite integral ∫\((x^8 + 8x\)) dx, we can use the power rule for integration. The power rule states that ∫\(x^n dx = (1/(n+1)) * x^{(n+1)} +\)C, where C is the constant of integration.

Using the power rule, we can integrate each term separately:

∫(\(x^8 + 8x) dx = ∫x^8\)dx + ∫8x dx

Integrating \(x^8\) using the power rule:

∫\(x^8 dx = (1/(8+1)) * x^{(8+1)} + C\)

        = (1/9) * \(x^9\) + C1

Integrating 8x:

∫8x dx = 8 * (1/2) * \(x^2\) + C

       = 4\(x^2\) + C2

Now, combining the two integrals:

∫\((x^8 + 8x) dx = (1/9) * x^9 + C1 + 4x^\)2 + C2

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Answer:

See explanation

Step-by-step explanation:

Every time x increases by 1, y decreases by 3.

To find matrices A and B such that rank(A) = rank(B), but rank(A^2) ≠ rank(B^2), we need to construct matrices that satisfy these conditions.

Let's calculate the ranks:

rank(A) = 1

rank(B) = 1

We can see that rank(A) = rank(B), which satisfies the first condition.

Now, let's calculate A^2 and B^2:

A^2 = A * A = [1 0] * [1 0] = [1 0]

[0 0]

B^2 = B * B = [1 1] * [1 1] = [2 2]

[0 0]

Next, let's calculate the ranks of A^2 and B^2:

rank(A^2) = rank([1 0])

[0 0]

= 1

rank(B^2) = rank([2 2])

[0 0]

= 1

We can see that rank(A^2) = rank(B^2) = 1, which satisfies the condition rank(A) = rank(B).

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When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Decidable languages are those for which there exists an algorithm that can determine whether any given input string belongs to the language or not. Turing-recognizable languages, on the other hand, are those for which there exists a Turing machine that can recognize any string belonging to the language, but may not halt on inputs that do not belong to the language.

The set of decidable languages is closed under subtraction, meaning that if L1 and L2 are decidable languages, then L1 - L2 (the set of strings that belong to L1 but not L2) is also decidable. This is because we can construct a Turing machine that first checks if an input string belongs to L2, and if it does not, then checks if it belongs to L1. If it does, then the machine accepts, otherwise it rejects.The set of Turing-recognizable languages is not closed under subtraction, meaning that there may exist some Turing-recognizable languages L1 and L2 for which L1 - L2 is not Turing-recognizable. This is because there may not exist a Turing machine that can recognize when an input string belongs to L1 - L2 without also being able to recognize some strings that do not belong to L1 - L2.

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Decidable languages are those for which there exists an algorithm that can determine whether any given input string belongs to the language or not. Turing-recognizable languages, on the other hand, are those for which there exists a Turing machine that can recognize any string belonging to the language, but may not halt on inputs that do not belong to the language.

The set of decidable languages is closed under subtraction, meaning that if L1 and L2 are decidable languages, then L1 - L2 (the set of strings that belong to L1 but not L2) is also decidable. This is because we can construct a Turing machine that first checks if an input string belongs to L2, and if it does not, then checks if it belongs to L1. If it does, then the machine accepts, otherwise it rejects.The set of Turing-recognizable languages is not closed under subtraction, meaning that there may exist some Turing-recognizable languages L1 and L2 for which L1 - L2 is not Turing-recognizable. This is because there may not exist a Turing machine that can recognize when an input string belongs to L1 - L2 without also being able to recognize some strings that do not belong to L1 - L2.

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Full Question ;

Are the decidable and Turing-recognizable languages closed under subtraction?

Answer:

-5p+7p^3

Step-by-step explanation: A rectangle has a height of 3p^2+13p

2

+13, p, squared, plus, 1 and a width of p^3+4p

3

+4p, cubed, plus, 4. we onnat

If the number of pieces of dog food in the scoop is Normally Distributed with mean of 205 pieces and standard deviation of 9.2 pieces , then the probability that the mean number of pieces of food will be less than 200 pieces is (b) 0.0177  .

The number of pieces of dog food in a one-cup scoop is approximately Normally Distributed ,

the mean number of pieces (μ) = 205 ;

the standard deviation is (σ²) = 9.2  ;

the sample size of dog food (n) = 15 ;

let the number of pieces of dog food in the one scoop be denoted by X ;

that means X follows N(205 , 9.2)

\(\bar x\) follows N(205 , 9.2²/n)

≡ N(205 , 5.643)     ....because n = 15 ,

we need to find the probability that mean number of pieces of food will be less than 200 pieces ,

which is P( \(\bar x\) < 200 )

= P( (\(\bar x\) - 205)/√5.643  <  (200 - 205)/√5.643 )

= P (Z < -2.10488 )

From the z value table ,

we get ,

= 0.0177  .

Therefore , the probability that the mean number of pieces of food will be less than 200 pieces is 0.0177  .

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Answer: x=14.75

2(2x+2)=3(21)

   4x+4 = 63

       4x = 63-4

          x = 59÷4

          x = 14.75

Check:  2(2*14.75+2)=3(21)

                             63 = 63

Answer: 63

Step-by-step explanation: It's stated that it equals 3(21) and that's 63.

The \(1\frac{2}{3}\)   flour should Heena take out of the bowl.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

Heena is baking a cake that requires two and one-half cups of flour. Heena poured four and one-sixth cups of flour into a bowl.

According to given question we have

Flour should Heena take out of  the bowl

=

\(4\frac{1}{6} -2\frac{1}{2} \\\\=\frac{25}{6} -\frac{5}{2} \\\\=\frac{5}{3}\\ \\=1\frac{2}{3}\)

Therefore, the \(1\frac{2}{3}\)   flour should Heena take out of the bowl.

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Answer:

x² + 4x - 12

Step-by-step explanation:

Roots: -6 and 2

Leading coefficient: x²

(x + 6)(x - 2)

x(x - 2) + 6(x - 2)

x² - 2x + 6x - 12

x² + 4x - 12

I hope this helps!

For a standard normal distribution, a negative value of z indicates that the observed value is below the mean of the distribution.

In a standard normal distribution, which has a mean of 0 and a standard deviation of 1, a negative value of z indicates that the observed value is located below the mean. The z-score represents the number of standard deviations a data point is away from the mean.

A negative z-score means that the observed value is lower than the mean, indicating that it falls to the left of the center of the distribution. This means that the data point is relatively lower compared to the average and can provide information about its position within the distribution and its deviation from the mean.

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Simple linear regression is a statistical technique used to model the relationship between two variables by fitting a straight line to the data. It provides a way to predict or estimate the value of one variable (dependent variable) based on the value of another variable (independent variable).

In simple linear regression, the relationship between the independent variable (x) and the dependent variable (y) is represented by a straight line. The goal is to find the best-fitting line that minimizes the differences between the observed values of the dependent variable and the predicted values from the regression line.

A graph illustrating simple linear regression includes the scatterplot of the data points, the regression line, and the residuals. The scatterplot shows the individual data points with the independent variable on the x-axis and the dependent variable on the y-axis. The regression line is the line that best fits the data, minimizing the sum of the squared residuals.

Residuals are the vertical distances between the observed data points and the regression line. They represent the differences or errors between the actual values and the predicted values. By examining the residuals, we can assess how well the regression line fits the data. If the residuals are randomly scattered around zero, it suggests that the linear regression model is appropriate. If there is a pattern or systematic deviation in the residuals, it indicates that the model may not be capturing the underlying relationship accurately.

The regression line is constructed by minimizing the sum of the squared residuals, which is known as the least squares method. This ensures that the line represents the best linear approximation of the relationship between the variables.

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