Over which interval is the graph of f(x) = one-halfx2 5x 6 increasing? (–6. 5, [infinity]) (–5, [infinity]) (–[infinity], –5) (–[infinity], –6. 5).

Answer:

Hey there!

Area=1/2bh

Area=1/2(120)(90)

Area=60(90)

Area=5400

Let me know if this helps :)

Answer:

A: 6, 12, 18, 24, 30

10, 20, 30, 40

B: 30

C: 5/6= 25/30 and 7/10= 21/30

D: 25/30>21/30 so 5/6>7/10

The book that weighs 3/4 pounds is greater than 1/2 pounds.

To compare the weights of the two books with 1/2 pound, we need to convert 1/2 pound into a fraction with a common denominator as the given weights. The common denominator of 8 and 4 is 8. So, we can convert 1/2 pound to 4/8 pound.

Now we can compare the weights of the two books with 4/8 pounds. The weight of the first book is 3/8 pounds, which is less than 4/8 pounds. The weight of the second book is 3/4 pounds, which is greater than 4/8 pounds.

Therefore, the book that weighs 3/4 pounds is greater than 1/2 pound.

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The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Look at the coordinates, y=4 in that coodinate meaning it is the y=intercept.

The slope u already know,

The formula for equation --> Y=mx+b

Answer: Y=3/4+4

Answer:

To determine whether the given measurements produce one triangle, two triangles, or no triangle at all, we can apply the Law of Sines and consider the possible cases.

Step-by-step explanation:

Given:

a = 8

b = 7

A = 30°

First, we can use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.

Using the Law of Sines, we have:

sin(A)/a = sin(B)/b

Plugging in the given values:

sin(30°)/8 = sin(B)/7

sin(30°) = 1/2, so we have:

1/2/8 = sin(B)/7

Simplifying:

1/16 = sin(B)/7

Cross-multiplying:

7 = 16sin(B)

Dividing by 16:

sin(B) = 7/16

Now, let's consider the possible cases:

If sin(B) > 1, then there are no triangles possible.

If sin(B) = 1, then we have a right triangle.

If 0 < sin(B) < 1, then we have two possible triangles.

If sin(B) = 0, then we have a degenerate triangle.

In our case, sin(B) = 7/16, which falls into the range of 0 < sin(B) < 1. Therefore, we have two possible triangles.

To solve each triangle, we can use the Law of Sines and Law of Cosines. However, since we already have an angle and two sides, we can use the Law of Cosines to find the remaining angle and then find the third side using the Law of Sines.

Case 1:

Triangle 1:

Using the Law of Cosines:

c^2 = a^2 + b^2 - 2abcos(C)

c^2 = 8^2 + 7^2 - 287cos(30°)

c^2 = 64 + 49 - 112cos(30°)

c^2 = 113 - 112(√3/2)

c^2 = 113 - 56√3

c ≈ 3.53 (approx.)

Triangle 2:

Using the Law of Cosines:

c^2 = a^2 + b^2 - 2abcos(C)

c^2 = 8^2 + 7^2 - 287cos(30°)

c^2 = 64 + 49 - 112cos(30°)

c^2 = 113 - 112(√3/2)

c^2 = 113 + 56√3

c ≈ 16.22 (approx.)

Therefore, we have two possible triangles: Triangle 1 with sides approximately 8, 7, and 3.53, and Triangle 2 with sides approximately 8, 7, and 16.22.

In summary, the given measurements produce two triangles.

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Answer:

0.5 in.

Step-by-step explanation:

Answer:

We all make mistakes, I just make more of them!

Kevin needs the following ingredients for the recipe for 3 people 90g strawberry jelly, 6 sponge fingers, 315 ml custard, and 135g tinned fruit.

To find the amounts of each ingredient to make this recipe for three people we must carry out the following procedure:

1. We must make a rule of three to find the exact amounts of each ingredient as shown below:

According to the above, the following ingredients are needed for this recipe:

Note: This question is incomplete because there is some information missing. Here is the complete information:

120g strawberry jelly

8 sponge fingers

420ml custard

180 g tinned fruit

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If a 10-digit phone number has the following format: (XYZ)-ABC-DEFG. With these limitations, there are 25,200,000 phone numbers that can have seven digits.

Possible methods

XYZ=4 C'4 could be an area code.

A numbers 2 through 8 equal C'7

C'10 + B = C'9

D,E,F, and G are the same as C'10 C'10 C'10

Hence,

Alternatives: C'4 C'7 C'10 C'9 C'10 C'10 C'10

Possible methods: 4 7 10 9 10 10 10 10

Numbers of possible ways: 25,200,000

In light of this, if a ten-digit phone number has the format (XYZ)-ABC-DEFG. These limitations make the following seven-digit phone numbers possible: 25.2 million phone numbers

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The correct option regarding when Chicago first exceeded Phoenix in the percentage of calls answers within 10 seconds is given as follows:

C. Between September and October.

The output of the graph represents the percentage of calls answered within 10 seconds.

Chicago and Phoenix are represented as follows:

At the beginning of September, the red line was above the green line, but at the beginning of October, the green line was above the red line, hence the correct option is given by option C.

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(a) If A and B are disjoint, it implies that P(A and B) = 0, and (b) the General Addition Rule simplifies to the simpler Addition Rule for disjoint events, where the probability of either event occurring is the sum of their individual probabilities.

Disjoint events refer to events that cannot occur simultaneously, meaning they have no outcomes in common. If events A and B are disjoint, it implies that they cannot happen together, and therefore the probability of both events occurring, denoted as P(A and B), is equal to 0.

(a) If A and B are disjoint events, it means that they do not have any outcomes in common. In the given scenario, joint applications and having a mortgage are the two events being considered. The Venn diagram for this setup would have two circles representing these events, with no overlapping region since they are disjoint. The total number of loans in the data set is 10,000.

(b) To determine the probability of a randomly drawn loan from the data set being from a joint application where the couple had a mortgage, we need to find the intersection of the two events in the Venn diagram. The given data states that 1495 loans were from joint applications, 4789 applicants had a mortgage, and 950 had both of these characteristics. Therefore, the probability of a loan being from a joint application with a mortgage is 950/10,000 or 0.095.

(b) The probability that the loan had either of these attributes can be found by adding the probabilities of the two disjoint events, i.e., the probability of a loan being from a joint application (1495/10,000 or 0.1495) and the probability of a loan having a mortgage (4789/10,000 or 0.4789), since these events cannot occur simultaneously. Therefore, the probability of a loan having either of these attributes is 0.1495 + 0.4789 = 0.6284.

Therefore, (a) If A and B are disjoint, it implies that P(A and B) = 0, and (b) the General Addition Rule simplifies to the simpler Addition Rule for disjoint events, where the probability of either event occurring is the sum of their individual probabilities.

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Answer:

x=55

Step-by-step explanation:

Answer:

3A+6B≤72

7A+5B≤84

Step-by-step explanation:

Just took the exam and got it right

Answer:

t≤4

Step-by-step explanation:

t+6≤10

Subtract 6 from each side

t+6-6≤10-6

t≤4

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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To test the hypothesis H₁: μx = μy versus Hoxy, where μx and μy represent the means of X and Y respectively, we can perform a two-sample t-test. The test compares the means of two independent samples to determine if they are significantly different from each other.

The given information provides the sample means (X = 33.8, Y = 32.5) and the sample standard deviations (Sx = 3.9, Sy = 5.1). The sample sizes for both X and Y are n = m = 25.

Using this information, we can calculate the test statistic, which is given by:

t = (X - Y) / sqrt((Sx^2 / n) + (Sy^2 / m))

Plugging in the values, we get:

t = (33.8 - 32.5) / sqrt((3.9^2 / 25) + (5.1^2 / 25))

Next, we need to determine the degrees of freedom for the t-distribution. Since the sample sizes are equal (n = m = 25), the degrees of freedom for the test is given by (n + m - 2).

Using the t-distribution table or software, we can find the critical value corresponding to a significance level of α = 0.05 and the degrees of freedom.

Finally, we compare the calculated test statistic with the critical value. If the test statistic falls within the rejection region (i.e., the absolute value of the test statistic is greater than the critical value), we reject the null hypothesis. The p-value can also be calculated, which represents the probability of observing a test statistic as extreme or more extreme than the calculated value, assuming the null hypothesis is true.

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The first step in developing a competency-model is to gather background information and analyze the existing standards within the workplace.

The first-step involves conducting a thorough examination of the organization's goals, strategies, and the specific job roles or positions for which the competency-model will be developed.

By gathering background information, organizations can understand the context in which the competency-model will be applied.

Analyzing existing standards within the workplace involves assessing the current performance expectations, competencies, and criteria used for evaluating employees in their respective roles.

The purpose of this step is to identify any gaps or areas for improvement in the existing standards and to ensure that the development of the competency model aligns with the organization's overall objectives.

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The first step in developing a competency model is conducting a job analysis.

developing a competency model is a systematic process that helps organizations define the key competencies needed for their employees. The first step in this process is conducting a job analysis.

A job analysis involves gathering information about the job, such as its purpose, tasks, responsibilities, and required qualifications. This information can be collected through methods like interviews, observations, and surveys. By analyzing the job, organizations can identify the critical competencies that are necessary for effective job performance.

These competencies can then be used to guide various HR processes, including recruitment, selection, training, and performance management. By aligning the competencies with job requirements, organizations can ensure that they have the right people with the right skills in the right positions.

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Answer:

option d is the correct answer

Answer:

the answer 50

Step-by-step explanation:

this is because of the triangle therom thing which is all triangles are equal to 180 degrees which means you gotta add 35+95 which gives 130 then subtract 180-130 which equals 50 and thats the missing angle.

Answer:

50

Step-by-step explanation:

'Cause I love my mama UnU

The net annual percentage growth rate of the city population is 0.4%

To calculate the net annual percentage growth rate of a population, we can use the following formula:

Net Annual Percentage Growth Rate = ((Births + Immigrants) - (Deaths + Emigrants)) / Initial Population x 100%

Plugging in the given values, we get:

Net Annual Percentage Growth Rate =\(((100 + 10) - (40 + 30)) / 10,000 x 100%\)

Net Annual Percentage Growth Rate = \((40 / 10,000) x 100%\)

Net Annual Percentage Growth Rate =\(0.4%\)

The net annual percentage growth rate of the city population is 0.4%

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In this step, we are dividing both sides by -8.

The division property of equality says that if a = b, then a/c = b/c where c is any nonzero real number.

We can conclude that log10(7) is irrational using a proof by contradiction with the steps given below.

To prove that log10(7) is irrational using a proof by contradiction, we start by assuming that log10(7) is rational, which means that it can be expressed as a ratio of two integers p and q:

log10(7) = p / q

where p and q have no common factors.

We can then use the definition of logarithms to rewrite this equation in exponential form:

10^(p/q) = 7

Next, we raise both sides of the equation to the power of q to eliminate the denominator:

10^p = 7^q

Now, we can assume the opposite, which is that log10(7) is rational and then find a contradiction. If log10(7) is rational, then 10^p and 7^q are also integers. However, 7 and 10 are relatively prime, which means that they do not share any common factors.

This implies that the prime factorization of 7^q cannot include any factors of 2 or 5, which are the prime factors of 10. But since 10^p is an integer, it must have a prime factorization that includes at least one factor of 2 or 5.

Therefore, we have arrived at a contradiction, which shows that our assumption that log10(7) is rational is false. Hence, we can conclude that log10(7) is irrational.

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Therefore, the formula for P(A | B^c) is given by the probability of the intersection of events A and B divided by the probability of the complement of event B.

To derive a formula for P(A | B^c), we can use the definition of conditional probability:

P(A | B) = P(A ∩ B) / P(B)

Since B and B^c are complementary events (i.e., B and B^c together cover the entire sample space S), we can write:

P(B^c) = 1 - P(B)

Multiplying both sides of the equation by P(B), we have:

P(B^c) * P(B) = P(B) - P(B ∩ B)

Since B and B^c are disjoint events (i.e., they have no elements in common), we have:

P(B^c ∩ B) = 0

Therefore, the equation simplifies to:

P(B^c) * P(B) = P(B)

Dividing both sides by P(B), we get:

P(B^c) = 1

Now, we can rewrite the formula for conditional probability as:

P(A | B) = P(A ∩ B) / P(B)

Multiplying both sides of the equation by P(B^c), we have:

P(A | B) * P(B^c) = P(A ∩ B) / P(B) * P(B^c)

Since P(B^c) = 1, the equation simplifies to:

P(A | B) = P(A ∩ B)

Finally, rearranging the equation, we obtain the formula for P(A | B^c):

P(A | B^c) = P(A ∩ B) / P(B^c)

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The distance further that Miguel ran on Monday than the distance ran on Tuesday was 2 / 3 miles.

To find how much farther Miguel ran on Monday than on Tuesday, we need to find the difference between the two distances. We can do this by subtracting the distance he ran on Tuesday from the distance he ran on Monday.

= 2 ¹ / ₃ - 1 ² / ₃

= 7 / 3 - 5 / 3

= 2 / 3 miles

In conclusion, Miguel ran 2/ 3 mile farther on Monday than on Tuesday.

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The terminal side of the angle -240 lies in the third quadrant when drawn in the standard position.

In the standard position, an angle is drawn with its initial side along the positive x-axis and its vertex at the origin. The terminal side of the angle is the side that rotates from the initial side.

The angle -240 starts from the positive x-axis (initial side), rotates clockwise for 240 degrees, and ends up in the third quadrant. Since one full revolution or circle is 360 degrees, a rotation of 240 degrees in the clockwise direction goes beyond the negative x-axis and into the third quadrant.

The third quadrant is characterized by negative x-coordinates and negative y-coordinates. In this quadrant, both the x and y values are negative. Therefore, when the angle -240 is drawn in the standard position, its terminal side lies in the third quadrant.

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