the sum of three numbers is 131. the third number is 4 times the first. the second number is 5 more than the first. what are the numbers

Given the inequality

Re-arranging

If we make x the subject of the formula

Answer:

(x -3)² + (y - 2)² = 4

Step-by-step explanation:

Equation of circle:

     (x - h)² + (y - k)² = r²

Here, (h,k) is the center of the circle and r is the radius of the circle.

(h, k) = (3 , 2) and r = 2

From the graph, the perpendicular distance from the point (3,0) at x-axis to the center gives the radius.

   (x - 3)² + (y -2)² = 2²

   (x - 3)² + (y -2)² = 4

Answer:

Step-by-step explanation:

Answer:

p=10

Step-by-step explanation:

subtract 5 on both sides and you'll get p=10 :]

The triangle area of ABC is 26 square units.

To find the area of triangle ABC using the coordinates of points A(1, 4), B(8, 0), and C(7, 8), we can use the formula:

Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

In this formula, the coordinates of each point are represented by x and y values. For example, A(1, 4) can be denoted as x1 = 1 and y1 = 4, B(8, 0) as x2 = 8 and y2 = 0, and C(7, 8) as x3 = 7 and y3 = 8.

Substituting these values into the formula, we have:

Area = 0.5 * |1(0 - 8) + 8(8 - 4) + 7(4 - 0)|

Simplifying the expression within the absolute value, we get:

Area = 0.5 * |-8 + 32 + 28|

Calculating the sum within the absolute value, we have:

Area = 0.5 * |52|

Taking the absolute value, we find:

Area = 0.5 * 52

Evaluating the expression, we obtain:

Area = 26 square units.

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The statistical method that would be best to use in this situation is b) Regression analysis.

Regression analysis is a statistical technique used to examine the relationship between a dependent variable (in this case, the number of students registering each semester) and one or more independent variables (such as time, semester, or any other relevant factors). By analyzing past data on the number of students registering each semester, regression analysis can help identify trends, patterns, and the average number of students registering.

Using regression analysis, the university can estimate the average number of students registering each semester based on historical data and use this information to plan how many classes to run in the upcoming semester. It allows for a quantitative analysis and prediction based on the relationship between variables, making it a suitable choice for estimating the average number of students in this scenario.

Hence the answer is Regression analysis.

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Answer:

11) -x to the power of 9/y to the power of 8

ᴍᴀᴛʜᴡᴀʏ can help you with the other problems.

Hope I could help!

The assumptions and conditions that must be met to find a 95% confidence interval for a population proportion are: Independence Assumption, Random Sampling, and Sample size condition: np and nq > 10.

Independence Assumption: This assumption states that the sampled individuals or observations should be independent of each other. This means that the selection of one individual should not influence the selection of another. It is essential to ensure that each individual has an equal chance of being selected.

Random Sampling: Random sampling involves selecting individuals from the population randomly. This helps in reducing bias and ensures that the sample is representative of the population. Random sampling allows for generalization of the sample results to the entire population.

Sample size condition: np and nq > 10: This condition is based on the properties of the sampling distribution of the proportion. It ensures that there are a sufficient number of successes (np) and failures (nq) in the sample, which allows for the use of the normal distribution approximation in constructing the confidence interval.

The condition n > 30 is not specifically required to find a 95% confidence interval for a population proportion. It is a rule of thumb that is often used to approximate the normal distribution when the exact population distribution is unknown.

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Strategies such as fast-tracking, crashing, prioritization, and resource optimization can be employed to reduce the project completion time by 5 weeks.


To reduce the completion time of the project by 5 weeks, we need to analyze the provided information and make appropriate adjustments. The initial completion time of the project is 25 weeks.

To achieve a reduction of 5 weeks, we can consider several strategies:

1. Fast-tracking: This involves overlapping or parallelizing certain project activities that were initially planned to be executed sequentially. By identifying tasks that can be performed concurrently, we can potentially save time. However, it's important to evaluate the impact on resource allocation and potential risks associated with fast-tracking.

2. Crashing: This strategy focuses on expediting critical activities by adding more resources or adopting alternative approaches to complete them faster. By compressing the schedule of critical tasks, we can reduce the overall project duration. However, this may come at an additional cost.

3. Prioritization: By reevaluating the project tasks and their priorities, we can allocate resources more efficiently. This ensures that critical activities receive higher attention and are completed earlier, resulting in an accelerated project timeline.

4. Resource optimization: Analyzing the resource allocation and identifying potential areas for optimization can lead to time savings. By ensuring that resources are utilized effectively and efficiently, we can streamline the project execution process.

It's important to note that implementing any of these strategies requires careful evaluation, considering factors such as project constraints, risks, cost implications, and stakeholder agreements. A comprehensive analysis of the project plan, resource availability, and critical path can guide the decision-making process for reducing the project completion time.

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Answer:

rate of change is 1/2

Step-by-step explanation:

formula for rate of change is f(b)-f(a)/b-a

Answer:

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Step-by-step explanation:

Answer:

(7-3i)

Step-by-step explanation:

You add them together so 3+4 and 2i + - 5i but since the 5 is negative it would be negaitive

The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. So the correct option is D.

Correlational method is a research technique used to explore the relationship between two or more variables. In this method, researchers collect data on the variables of interest and analyze their patterns of association. The fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way. This means that researchers are interested in exploring whether changes in one variable are associated with changes in another variable.

For instance, a researcher may be interested in exploring the relationship between stress and job performance. The researcher may collect data on the levels of stress and job performance in a sample of employees and then use statistical analysis to determine if there is a systematic relationship between the two variables. If the results show that higher levels of stress are associated with lower levels of job performance, then the researcher can conclude that there is a negative correlation between the two variables.

It is important to note that correlation does not imply causation. While a correlation between two variables indicates that they are related, it does not necessarily mean that changes in one variable are causing changes in the other variable. Therefore, researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

Therefore, the fundamental question addressed by the correlational method is whether two or more variables are related in some systematic way, and researchers must be cautious when interpreting correlational data and should consider other factors that may be influencing the relationship between variables.

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The table in this problem is completed as follows:

The equation is given as follows:

y = 20 + 2x.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The parameters for this problem are given as follows:

Hence the function is given as follows:

y = 2x + 20.

One example of a numeric value is given at x = 7, hence:

y = 2(7) + 20 = 14 + 20 = 34.

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Answer:

it will be a straight line side to side, on the -5 y

Answer:

x=-1

Step-by-step explanation:

f(x) = 2x - 3

f(x)=-5

-5=2x-3

-2=2x

x=-1

Answer:

2 i think

Step-by-step explanation:

Answer:

[B] 1/25

Step-by-step explanation:

From the given:

There are letter tiles in a bag. Four A’s, five B’s, six C’s and five D’s. You select one tile, replace it, and then draw another.

To Find:

P( A and A)=______

Solution:

Since it given that:

Four A’s, five B’s, six C’s and five D’s.

Thus we have:

A,A,A,A,B,B,B,B,B,C,C,C,C,C,C,D,D,D,D,D

Total number of letters tiles = 20

Probability of selecting A = 4/20  = 1/5

Probability of selecting A  = 4/20 = 1/5

P( A and A)= 1/5 × 1/5 = 1/25

Thus, the answer is [B] 1/25

Kavinsky

Answer:

This is a right triangle.

Step-by-step explanation:

\( \sqrt{ {9}^{2} + {12}^{2} } = \sqrt{81 + 144} = \sqrt{225} = 15\)

Answer:

square root of 7

Step-by-step explanation:

2 times 2 is 4

3 times 3 is 9

7 is the only option between 4 and 9

(this was more the easy method lol but hope this helps)

The z-score of x = 4.2 for a normal distribution with a mean of 5 and a variance of 4 is approximately -0.7. Given that P(A) = 0.3, P(AUB) = 0.4, and P(A ∩ B) = 0.2, the value of P(B) can be determined by using the formula for the probability of the union of two events.

To calculate the z-score of x = 4.2, we need to use the formula: z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. In this case, the mean is 5 and the variance is 4, so the standard deviation is √4 = 2. Plugging in the values, we get z = (4.2 - 5) / 2 = -0.8 / 2 = -0.4. Therefore, the z-score for x = 4.2 is approximately -0.4.

Moving on to the probability question, we have P(A) = 0.3, P(AUB) = 0.4, and P(A ∩ B) = 0.2. The probability of the union of two events can be calculated using the formula: P(AUB) = P(A) + P(B) - P(A ∩ B). Plugging in the known values, we have 0.4 = 0.3 + P(B) - 0.2. Solving this equation, we find P(B) = 0.3 + 0.2 - 0.4 = 0.1. Therefore, the value of P(B) is 0.1 or 10%.

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Answer:

22 bagssss i am right because i did 4 time 4 times 1 and got 16 and then i divided that by 0.75 and got 21.33333 and since you can't get a 0.3333333 of a bag you have to get one extra so it would be 22

Step-by-step explanation:

Answer:

125235

Step-by-step explanation:

There are n=495 integers from a₁=6 to aₙ=500:

\(\displaystyle S_n=\frac{n}{2}(a_1+a_n)\\\\S_{495}=\frac{495}{2}(6+500)\\\\S_{495}=(247.5)(506)\\\\S_{495}=125235\)

Therefore, the sum of the integers will be 125235

We know that SR is parallel to MN and MP is parallel to NP. This means that quadrilateral SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

A quadrilateral has four enclosed sides. Quadrilaterals include the following shapes: It was produced by Raphael. It has four sides. The shape has only one set of parallel sides and no straight angles.

In order to prove that quadrilateral SRNP is a trapezoid, we need to show that it has one pair of parallel sides.

We know that SR and MP are both medians of triangle MNP, which means they each pass through the midpoint of the opposite side. Let's call the midpoint of MN point Q.

Since SR passes through the midpoint of MN at point Q, we know that SR is parallel to side MN (by the converse of the midpoint theorem). Similarly, we can show that MP is parallel to side NP (by using the midpoint of MP and the midpoint of NP).

Therefore, we have shown that SR is parallel to MN and MP is parallel to NP. This means that quadrilateral SRNP has one pair of parallel sides (SR and MN), which is the definition of a trapezoid. Hence, quadrilateral SRNP must be a trapezoid.

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Let the time for jogging be on y axis and number of weeks be on x axis.

Express the general equation of the line,

y=mx+c.

Here, m is slope and c is y intersept.

Given that, you start by jogging for 14 minutes each day. So, c is 14.

Also, given that you increase your jogging time by 7 minutes implies,

m=7.

Therefore, the equation is,

\(\sf f(x) = 3 \ * \ 2^x\)

insert x = -2

\(\sf f(-2) = 3 \ * \ 2^{-2}\)

\(\sf f(-2) = 3 \ * \ \dfrac{1}{4}\)

\(\sf f(-2) = \dfrac{3}{4}\)

option D. 3/4 will be the correct answer.

\(\\ \rm\Rrightarrow f(x)=3.2^x\)

\(\\ \rm\Rrightarrow f(-2)\)

\(\\ \rm\Rrightarrow 3.2^{-2}\)

\(\\ \rm\Rrightarrow 3(1/4)\)

\(\\ \rm\Rrightarrow 3/4\)

There is only one solution to this system of equations, which we found using the substitution method. The correct option is A.

To solve this system of equations using the substitution method, we need to solve one of the equations for one of the variables and then substitute that expression into the other equation.

Let's solve the first equation, x-y=1, for x. We can add y to both sides to get x=y+1. Now we can substitute this expression for x in the second equation, 6x+3y-12, to get 6(y+1)+3y-12.

Simplifying this expression, we get 9y-6=0. Solving for y, we get y=2/3. Now we can substitute this value for y into either equation to find x. Let's use x=y+1, so x=2/3+1=5/3.

Therefore, the solution of the system is (5/3, 2/3), so the correct choice is A. There is only one solution to this system of equations, which we found using the substitution method.

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a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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There are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

The number of ways to man the two sides of the boat can be calculated using the combination formula, C(n,r). In this case, n = 8 (the total number of crew members) and r = 5 (the number of crew members needed to man the two sides of the boat). The equation to calculate the number of ways to man the two sides of the boat can be written as C(8,5).

C(8,5) = 8!/(5!*3!) = 56.

This means that there are 56 possible ways to man the two sides of the boat with two crew members rowing on the stroke side and three crew members rowing on the bow side.

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The minimum is 29 cm and it represents the sensor's minimum height above the ground.

In Mathematics and Geometry, the standard form of a cosine function can be represented or modeled by the following mathematical equation (formula):

y = Acos(Bx - C) + D

Where:

By critically observing the graph which models the sensor's height above the ground (in centimeters) shown in the image attached below, we can reasonably infer and logically deduce that it has a minimum height of 29 centimeters.

In conclusion, the sensor's minimum height above the ground cannot exceed 29 centimeters.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The definition of sequence is an ordered list of objects.

The term ordered list is known as the way to uses numbers or some sort of notation that indicates a series of items.

in math the term sequence is defined as an arrangement of numbers in a particular order.

Where as which is also known as a series is defined as the sum of the elements of a sequence.

in the sequence the listed of objects are an arrangement of two or more things in a successive order and the successive order of two or more things which means that they are in chronological sequence.

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