(4/25) = 1/2 x 24 = (15/2) - 2​

The inequality that represents the situation is given by:

\(g \geq 14\)

---------------------

---------------------

From the bullet points, it is found that the minimum amount of goals that Bo may have scored is:

\(M = 7\times2 = 14\)

That is, in each game, he scored exactly 2 goals, leading to a minimum total of 14 goals.

---------------------

Thus, the inequality that models the situation is:

\(g \geq 14\)

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The resulting p-value would decrease in both scenarios if we sampled twice as many students but found the same sample proportion as before.

The p-value is the probability of observing a sample proportion as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true. When we increase the sample size, the standard error of the sample proportion decreases, which means that the sample proportion becomes more representative of the population proportion.

In other words, the larger the sample size, the more accurate the estimate of the population parameter (in this case, the proportion of students who support the change). As a result, the difference between the sample proportion and the hypothesized population proportion (under the null hypothesis) is likely to be smaller, leading to a smaller p-value.

To compute the p-value, we use the test statistic, which is a measure of how many standard errors the sample proportion is from the hypothesized population proportion under the null hypothesis. When we increase the sample size, the test statistic becomes larger, which means that the p-value becomes smaller. Therefore, the p-value would decrease if we sample twice as many students but find the same sample proportion as in exercise 6.

In summary, increasing the sample size while keeping the sample proportion constant would result in a smaller p-value, indicating stronger evidence against the null hypothesis.

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No, it is not necessarily true that both ABT and ATB are defined for matrices A and B of size m × n.

In order for the matrix product ABT to be defined, the number of columns in A (which is n) must be equal to the number of columns in BT (which is also n). This means that the number of rows in B (which is m) must be equal to the number of rows in A (which is also m). So, if A and B are both square matrices of size n × n, then ABT is defined

On the other hand, in order for the matrix product ATB to be defined, the number of columns in AT (which is m) must be equal to the number of columns in B (which is also n). This means that the number of rows in A (which is m) must be equal to the number of rows in B (which is also m). So, if A and B are both square matrices of size m × m, then ATB is defined.

However, if A and B are not square matrices, then it is possible that only one of ABT or ATB is defined, or neither of them are defined. In general, the product of two matrices is only defined if the number of columns in the first matrix is equal to the number of rows in the second matrix.

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Answer:

Midpoint is (0.5,6.5)

the distance is 7.1

Step-by-step explanation:

hope this helps u have a nice day :)

Answer:

\( x = 4 \sqrt{3} \)

Step-by-step explanation:

By geometric mean theorem and Pythagoras theorem:

\( {x}^{2} = { (\sqrt{8 \times 4} )}^{2} + {4}^{2} \\ \\ {x}^{2} = { (\sqrt{32} )}^{2} + {4}^{2} \\ \\ {x}^{2} = 32 + 16 \\ \\ {x}^{2} = 48 \\ \\ x = \sqrt{48} \\ \\ x = 4 \sqrt{3} \)

Answer:

28

Step-by-step explanation:

5(6) + (-2) = 30 + (-2) = 30-2 = 28

Answer:

28

Step-by-step explanation:

x=5  y=2

5x + y

5(6) + (-2)

30 + (-2)

30 - 2

28

The midpoint has coordinates (19,19) as per the midpoint formula.

The statement is false.

The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).

To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:

(x1 + x2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.

To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:

(y1 + y2) / 2

= (0 + 38) / 2

= 38 / 2

= 19

The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.

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We reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

The null and alternative hypotheses are:

H_0: mu <= 42

H_a: mu > 42

Using the sample mean, sample size, and population standard deviation given, we can calculate the test statistic:

z = (x - mu) / (sigma / sqrt(n))

z = (42.85 - 42) / (2.65 / sqrt(68))

z = 2.56

Using a standard normal distribution table or calculator, we can find the critical values for each significance level:

a = 0.10: z_crit = 1.28

a = 0.05: z_crit = 1.645

a = 0.01: z_crit = 2.33

a = 0.001: z_crit = 3.09

Since our test statistic is greater than the critical value at a = 0.10 and a = 0.05, we reject the null hypothesis at these levels. However, we fail to reject the null hypothesis at a = 0.01 and a = 0.001.

To calculate the p-value, we can use a standard normal distribution table or calculator to find the probability that a z-score is greater than or equal to our test statistic:

p-value = P(Z >= 2.56)

p-value = 0.0052

Since the p-value is less than all of the given significance levels, we reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

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Answer:

c(12 + 9 + 6)

12(2.25c)

Step-by-step explanation:

12c + 12 (3/4c) + 12 (1/2c)

12(1c) + 12(3/4c) + 12 (1/2c)

12(c + 3/4c + 1/2c)

12(2 1/4c)

12(2.25c)

Or

12c + 12 (3/4c) + 12 (1/2c)

12c + 9c + 6c

c(12 + 9 + 6)

Answer:

49.3 ft

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan48° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{30}\) ( multiply both sides by 30 )

30 × tan48° = x , then

x ≈ 33.3

Height of tower = 33.3 + 16 = 49.3 ft ( to the nearest tenth )

The height of the tower is 36.8 feet.

The height of the tower is the hypotenuse of a right triangle with legs of length 16 feet and 30 feet.

The angle opposite the leg of length 16 feet is 48 degrees.

We can use the sine function to find the length of the hypotenuse.

The sine function is opposite over hypotenuse, so sin(48°) = 16/h.

We can solve for h by rearranging the equation sin(48°) = 16/h to get h = 16/sin(48°).

The value of sin(48°) is approximately 0.7431, so h = 16/0.7431 ≈ 36.8 feet.

Therefore, the height of the tower is 36.8 feet.

To round to the nearest tenth, we would round 36.8 to 36.9.

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Answer:

I need more info to answer the question.

Step-by-step explanation:

Answer:

72:56

Explanation:

is the answer because 9 can be divided by 18 and 36. 7 can also be divided by 14 and 21. So, that leaves you with the answer 72:56

a) The maximum normal stress is -50 psi and displacement is  -0.090 inch. b)  The maximum normal stress is -50 psi and displacement is -0.023 inch.

To solve this problem, we'll use the slender beam theory. The slender beam theory assumes that the beam is long and slender, meaning its length is much greater than its thickness. Let's solve the problem step by step.

(a) Slender Beam (L = 40 inch, h = 4 inch)

Step 1: Calculate the maximum normal stress on the support (σx).

The formula for the maximum normal stress on the support of a cantilevered beam under uniform pressure is given by:

σx = -0.5 * P * h / t

where P is the pressure, h is the height of the beam, and t is the thickness of the beam.

Substituting the given values:

P = 25 psi

h = 4 inch

t = 1 inch

σx = -0.5 * 25 * 4 / 1

= -50 psi

The negative sign indicates that the stress is compressive.

Therefore, the maximum normal stress on the support is -50 psi.

Step 2: Calculate the displacement at the center of the free end.

The formula for the displacement at the center of the free end of a cantilevered beam under uniform pressure is given by:

δ = -P * \(L^{3}\) / (3 * E * t * \(h^{2}\))

where δ is the displacement, P is the pressure, L is the length of the beam, E is the elastic modulus of the material, t is the thickness of the beam, and h is the height of the beam.

Substituting the given values:

P = 25 psi

L = 40 inch

E = 29.5×\(10^{6}\) psi

t = 1 inch

h = 4 inch

δ = -25 * \(40^{3}\) / (3 * 29.5×\(10^{6}\) * 1 * \(4^{2}\))

≈ -0.090 inch

Therefore, the displacement at the center of the free end is approximately -0.090 inch.

(b) Deep Beam (L = 10 inch, h = 4 inch)

Step 1: Calculate the maximum normal stress on the support (σx).

Using the same formula as in the previous step:

σx = -0.5 * P * h / t

Substituting the given values:

P = 25 psi

h = 4 inch

t = 1 inch

σx = -0.5 * 25 * 4 / 1

= -50 psi

The negative sign indicates that the stress is compressive.

Therefore, the maximum normal stress on the support is -50 psi.

Step 2: Calculate the displacement at the center of the free end.

Using the same formula as in the previous step:

δ = -P * \(L^{3}\) / (3 * E * t * \(h^{2}\))

Substituting the given values:

P = 25 psi

L = 10 inch

E = 29.5×\(10^{6}\) psi

t = 1 inch

h = 4 inch

δ = -25 * \(10^{3}\) / (3 * 29.5×\(10^{6}\) * 1 * \(4^{2}\))

≈ -0.023 inch

Therefore, the displacement at the center of the free end is approximately -0.023 inch.

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Answer:

Step-by-step explanation:

As per the diagram we got:

As FH = 7x + 4 and EH = 9x - 2, we solve the following equation for x:

So each segment is:

Therefore:

So the variables are:

Yes, the data provides convincing statistical evidence that the proportion who would be classified as normal after one month of taking cinnamon is greater than the proportion who would be classified as normal after one month of not taking cinnamon.

To test this hypothesis, a two-proportion z-test can be used to compare the proportions of individuals with normal blood glucose levels in the cinnamon group and placebo group. Using the given data, the test statistic is calculated to be 1.78 with a p-value of 0.038.

Since the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference between the proportions of individuals with normal blood glucose levels in the cinnamon and placebo groups. Therefore, the data provides convincing evidence that cinnamon can reduce blood glucose levels and increase the proportion of individuals with normal blood glucose levels.

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Answer:

Step-by-step explanation:

\(\sqrt{g}\) = 7-w

(\(\sqrt{g}\) )^2 = (7-w)^2

g = (7-w)^2

After solving the given equations we know that the value of x and y are -4 and -7 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

This form is also highly useful when solving systems involving two linear equations.

So, we have the equations:

y=2x+1 ...(1)

-4x+y=9 ...(2)

Now, substitute y=2x+1 in equation (2):

-4x+y=9

-4x+2x+1=9

-2x=8

x=-4

Now, insert x=-4 in equation (1):

y=2x+1

y=2(-4)+1

y=-8+1

y=-7

Therefore, after solving the given equations we know that the value of x and y are -4 and -7 respectively.

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Answer:

\(2\sqrt{14}\)

D.

Step-by-step explanation:

10 in half is 5

\(b = \sqrt{c^{2} - a^{2} }\)

b = \(\sqrt{81 - 25}\) = \(\sqrt{56}\) = \(2\sqrt{14}\)

The Discussion section of a report is an essential part where you can delve into the theories related to your research topic, irrespective of the results.

In this section, you have the opportunity to analyze and interpret your findings and draw conclusions from them.

You can also discuss the implications of your research and suggest future directions for further investigation.

Additionally, it is crucial to discuss relevant literature in this section to provide context for your findings and demonstrate your knowledge of the subject area.

However, it is essential to avoid merely restating points already made in previous sections but instead reformulate them and provide additional insights.

In summary, the Discussion section is a crucial part of the report, providing a space for reflection and critical thinking about your research findings.

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Answer:

  D, E

Step-by-step explanation:

The applicable formula is ...

  s = rθ

so, for θ = 1.5, the arc length is 1.5 times the radius. The true statements are ...

  D) The length of the arc defined by the angle is 1.5 times longer than the radius.

  E) The ratio of arc length to radius is 1.5.

Answer:

\((x^{2}-3)(x+1)=0\\\\x^{3}+x^{2} -3x-3=0\)

Answer:

1345.01694448 days

Step-by-step explanation:

24 weeks = 24 x 7 = 168 days

24 months = 24 x 30 x 7 =  168 x 7 = 1176 days

24 seconds = 0.000277778 days

24 minutes = 0.0166667 days

24 hours = 1 day

Total = 1345.01694448 days

Answer:

≈100∘

Step-by-step explanation: I checked delta math

To define a default field value in a form or a database, you can use the attribute "default". When you add the "default" attribute to a field, it will automatically assign the specified value to that field if no other value is provided by the user or system.

This can be particularly useful when designing forms or databases that require certain fields to have a value even when the user does not provide one.
For example, in a web form, you might have a "Country" field that requires users to select their country from a dropdown list. By setting a default value for this field, such as "United States," the system ensures that there is always a value associated with that field even if the user does not make a selection.
Similarly, in a database schema, you might have a "DateCreated" field that automatically assigns the current date and time as the default value. This ensures that the date and time are always recorded for each new entry, even if the user does not manually input a value.
In both cases, the "default" attribute allows you to streamline the data collection process and ensure that your forms and databases maintain consistent and complete data. Using default values can also improve the user experience by reducing the amount of input required, making it easier for users to complete forms and submit their data.

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For the given matrix A, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. The determinant det(A) is 68.

To find the minors of a matrix, we need to find the determinants of the submatrices obtained by removing the row and column corresponding to the element of interest. In this case, the minors M13, M23, and M33 correspond to the determinants of the 2x2 submatrices obtained by removing the first row and the third column, second row and third column, and third row and third column, respectively.

To find the cofactors, we multiply each minor by a positive or negative sign based on its position in the matrix. The signs alternate starting with a positive sign for the top left element. In this case, the cofactors C13, C23, and C33 correspond to the minors M13, M23, and M33 respectively.

Finally, the determinant of a 3x3 matrix can be found by using the formula det(A) = a11C11 + a12C12 + a13C13, where a11, a12, and a13 are the elements of the first row of the matrix and C11, C12, and C13 are their corresponding cofactors. In this case, the determinant det(A) is 68.

Therefore, the minors M13, M23, M33 are 8, -4, and 10 respectively. The cofactors C13, C23, C33 are 8, 4, and 10 respectively. And the determinant det(A) is 68.

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Answer:

Firstly we will divide all 8 marbles into 2 sections. Each section contains 4 marbles.

Then we balance each section and find that one section is lighter than other.

Then we take lighter section and further divide it into 2 sections and each section contains 2 marbles.

Then we balance them again and we find the lighter section further divide it into 2 sections and each section contains 1 marble, balance them and we get the lightest marble.

Answer:

Step-by-step explanation:

Given the height in feet represented by the equation H = -16t²+32t+48, at maximum height, the velocity of the water balloon is zero.

Velocity = dH/dt = 0

dH/dt = -32t+32 = 0

-32t+32 = 0

-32t = -32

t = -32/-32

t = 1sec

Substituting t = 1sec into the modeled equation of the height

H = -16t²+32t+48

H = -16(1)²+32(1)+48

H = -16+80

H = 64 feet

The maximum height of the water balloon is 64 feet

b) In order to know how long it takes to reach its maximum height, we will substitute H = 64 feet into the equation of the height.

64 = -16t²+32t+48

-16t²+32t = 16

16t²-32t+16 = 0

t²-2t+1 = 0

t²-t-t+1 = 0

t(t-1)-1(t-1) = 0

(t-1)² = 0

t-1 = 0

t = 1sec

It took the water balloon 1 sec to reach its maximum height.

To find the average value of the function f(x, y) = 8x + 5y over the given triangle, we need to calculate the double integral of f(x, y) over the region and then divide it by the area of the triangle.

The vertices of the triangle are (0, 0), (2, 0), and (0, 7). We can set up the integral as follows:

∬R f(x, y) dA = ∫₀² ∫₀ᵧ (8x + 5y) dy dx

Integrating with respect to y first, the inner integral becomes:

∫₀ᵧ (8x + 5y) dy = 8xy + (5y²/2) |₀ᵧ = 8xᵧ + (5ᵧ²/2)

Now integrating with respect to x, the outer integral becomes:

∫₀² (8xᵧ + (5ᵧ²/2)) dx = (4x²ᵧ + (5ᵧ²x)/2) |₀² = (8ᵧ + 10ᵧ² + 20ᵧ)

To find the area of the triangle, we can use the formula for the area of a triangle: A = (1/2) * base * height.

The base of the triangle is 2 and the height is 7.

A = (1/2) * 2 * 7 = 7

Finally, to find the average value, we divide the double integral by the area of the triangle:

Average value = (8ᵧ + 10ᵧ² + 20ᵧ) / 7

Simplifying this expression gives:

Average value = (8 + 10ᵧ + 20ᵧ) / 7 = (8 + 10(7) + 20(7)) / 7 = 142/7 = 20 2/7

Therefore, the correct answer is not listed among the options provided.

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