In two or more complete sentences describe the process in writing the equation of a line given two points?

9514 1404 393

Answer:

  an increase of 26.44%

Step-by-step explanation:

The 9% increase multiplies the value by 1 +9% = 1.09.

The 16% increase multiplies the value by 1 +16% = 1.16.

Either followed by the other will multiply the value by ...

  1.09 · 1.16 = 1.2644 = 1 + 26.44%

The effect of both increases is an increase in the original value of 26.44%.

Here's the solution,

figure 1.

by using trigonometry,

=》

\( \sin(60) = \dfrac{5 \sqrt{3} }{y} \)

=》

\( \dfrac{ \sqrt{3} }{2} = \dfrac{5 \sqrt{3} }{y} \)

=》

\( \dfrac{1}{y} = \dfrac{ \sqrt{3} }{2 \times 5 \sqrt{3} } \)

=》

\( \dfrac{1}{y} = \dfrac{1}{10} \)

=》

\(y = 10\)

And,

=》

\( \cos(60) = \dfrac{w}{y} \)

=》

\( \dfrac{1}{2} = \dfrac{w}{10} \)

=》

\(w = 5\)

So, values are :

figure 2.

Since, it's an isosceles triangle, w = y,

So, by pythagoras theorem :

=》

\( {w}^{2} + {y}^{2} = (7 \sqrt{2} ) {}^{2} \)

=》

\( {w}^{2} + {w}^{2} = 98\)

=》

\(2 {w}^{2} = 98\)

=》

\( {w}^{2} = 49\)

=》

\(w = \sqrt{49} \)

=》

\(w = 7\)

and we know, w = y, so their values will be equal to 7 units.

Answer:

Step-by-step explanation:

3x + 4x + x = 16

7x + x = 16

8x = 16

x = 16 : 8

x = 2

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

3 × 2 + 4 × 2 + 2 = 16  (remember PEMDAS)

6 + 8 + 2 = 16

16 = 16

same value the answer is good

All parts are define in the below points.

A random sample is a subset of a population in which each individual or element in the population has an equal chance of being selected. It is a sampling method used in statistics and research to minimize bias and increase the generalizability of the findings to the larger population.

a. Hypotheses: Null Hypothesis: The mean DNA concentration of the ocean floor specimens is not significantly different from the healthy concentration (µ = 0.31g/m2). Alternative Hypothesis: The mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration (µ ≠ 0.31g/m2). Using a two-tailed t-test with alpha = 0.05, we find a p-value of 0.0003, which is less than the significance level. Therefore, we reject the null hypothesis and conclude that the mean DNA concentration of the ocean floor specimens is significantly different from the healthy concentration.

b. We would perform a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than 0.31g/m2 if the goal was to determine whether the mean DNA concentration of the floor specimens was lower than what is regarded as a healthy concentration. It would have a p-value of 0.00015.

c. Using the 95% confidence interval approach, we construct a one-sided confidence interval for the mean DNA concentration. If the lower bound of the confidence interval is less than 0.31g/m2, we can conclude that the mean DNA concentration is less than the healthy concentration. The 95% confidence interval for the mean is (0.2457g/m2, 0.3105g/m2), which does not include the healthy concentration of 0.31g/m2. Therefore, we can conclude that the mean DNA concentration of the ocean floor specimens is less than the healthy concentration.

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a). We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level.

b). Its p-value would be 0.00015.

c). The safe concentration of \(0.31g/m^2\) is not included in the 95% confidence interval for the mean, which is \((0.2457g/m^2,\ 0.3105g/m^2)\).

A random sample is a portion of a community in which every person or component has an equal chance of being chosen. In statistics and research, it is a sampling technique used to reduce bias and improve the generalizability of the results to a broader population.

A). An hypothesis is a The null hypothesis states that there is no discernible difference between the mean DNA concentration of the ocean bottom samples and the healthy concentration \((\mu=0.31g/m^2)\). Alternative Hypothesis: The mean DNA concentration of the ocean floor samples differs considerably from the healthy concentration \((\mu\neq 0.31g/m^2)\) in a statistically significant way. We discover a p-value of 0.0003 using a two-tailed t-test with alpha = 0.05, which is below the significance level. We therefore reject the null hypothesis and come to the conclusion that the mean DNA concentration of the samples from the ocean bottom differs significantly from that of healthy individuals.

B). If the objective was to determine whether the mean DNA concentration of the floor specimens was lower than what is considered as a healthy concentration, we would conduct a one-tailed t-test with the alternative hypothesis that the mean DNA concentration is less than \(0.31g/m^2\). Its p-value would be 0.00015.

C). We create a one-sided confidence interval for the mean DNA concentration using the 95% confidence interval method. The mean DNA concentrationis less than the healthy concentration if the lower limit of the confidence interval is less than \(0.31g/m^2\). The safe concentration of \(0.31g/m^2\) is not included in the 95% confidence interval for the mean, which is \((0.2457g/m^2,\ 0.3105g/m^2)\). As a result, we can say that the average DNA concentration of the samples from the ocean bottom is lower than the healthy concentration.

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After 15 years, the scholarship fund will have approximately $1,076,123.79. The total interest earned over this period will be approximately $826,123.79.

To calculate the value of the annuity after 15 years, we need to use the formula for the future value of an annuity:

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future Value

P = Periodic Payment (amount invested every three months)

r = Interest rate per compounding period

n = Number of compounding periods

In this case, the periodic payment (P) is $25,000, the interest rate (r) is 11.5% per year compounded quarterly (or 2.875% per quarter), and the number of compounding periods (n) is 15 years multiplied by 4 (since compounding is done quarterly). Therefore:

FV = $25,000 * [(1 + 0.02875)^(15*4) - 1] / 0.02875

≈ $1,076,123.79

The interest earned can be calculated by subtracting the total amount invested ($25,000 per quarter multiplied by the number of quarters in 15 years) from the future value:

Interest = FV - Total amount invested

= $1,076,123.79 - ($25,000 * 4 * 15)

≈ $826,123.79

Therefore, after 15 years, the scholarship fund will have approximately $1,076,123.79, and the total interest earned will be approximately $826,123.79.

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Answer:

90 Degrees

Step-by-step explanation:

The square at the bottom left corner of the triangle is ALWAYS equal to 90 degrees. I hope this helps :)

Answer:

y=-8x+48

Step-by-step explanation:

Slope is -8 because perpendicular slopes are negative reciprocals

Plug it in:

-8=7(-8)+b

48=b

The Factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

The quadratic expression 3x^2 - 11x + 6, we can use the method of factoring by grouping. Here's the step-by-step process:

Step 1: Multiply the coefficient of x^2 (3) by the constant term (6) in the expression.

  3 * 6 = 18.

Step 2: Find two numbers that multiply to give 18 and add up to the coefficient of x (-11).

  The numbers -2 and -9 fit this criteria because -2 * -9 = 18 and -2 + (-9) = -11.

Step 3: Split the middle term (-11x) into two terms using the numbers found in step 2.

  3x^2 - 2x - 9x + 6.

Step 4: Group the terms and factor out the greatest common factor (GCF) from each group.

  (3x^2 - 2x) - (9x - 6).

  x(3x - 2) - 3(3x - 2).

Step 5: Notice that the terms (3x - 2) are common in both groups. Factor it out.

  (x - 3)(3x - 2).

So, the factored form of 3x^2 - 11x + 6 is (x - 3)(3x - 2).

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(a) Here is a sketch of the normal distribution for the weights of male Persian cats:

```

                   |

                   |

                   |

                   |

                   |

                   |

                   |     . . . . . . . . . . . . . . . . . . . . . .

                   |   .                                               .

                   | .                                                 .

                   |.                                                   .

--------------------|----------------------------------------------------

                μ-3σ           μ             μ+3σ

```

The x-axis represents the weights of the cats, and the y-axis represents the probability density. The curve is symmetric around the mean (μ) and has a standard deviation (σ) of 0.5 kg.

(b) To find the proportion of male Persian cats weighing between 5.5 kg and 6.5 kg, we need to calculate the area under the normal distribution curve between these two weights.

Using statistical software or tables for the normal distribution, we can find the corresponding z-scores for the weights 5.5 kg and 6.5 kg. Let's assume these z-scores are z1 and z2, respectively.

Then, we can find the proportion by subtracting the cumulative probability for z2 from the cumulative probability for z1. This represents the proportion of cats within the weight range.

(c) To determine the expected number of cats in the group that have a weight of less than 5.3 kg, we first need to find the z-score corresponding to this weight. Let's assume this z-score is z3.

Next, we calculate the cumulative probability for z3. This represents the proportion of cats in the population with a weight less than 5.3 kg.

To find the expected number of cats in the group, we multiply this proportion by the total number of cats in the group (80).

(d) To estimate the value of x for the statement "12 of the cats weigh more than x kg," we need to find the z-score corresponding to the cumulative probability of 12 cats in a group of 80.

Using statistical software or tables for the normal distribution, we can find the z-score that corresponds to this cumulative probability.

Then, we can convert the z-score back to the weight scale to estimate the value of x.

(e) To find the probability that exactly one cat out of ten weighs over 6.25 kg, we can use the binomial probability formula:

\(P(X = 1) = (nCk) * p^k * (1-p)^{(n-k)}\)

In this case, n = 10 (number of cats chosen), k = 1 (number of cats weighing over 6.25 kg), and p represents the probability of a cat weighing over 6.25 kg, which can be calculated using the normal distribution and the corresponding z-score.

By substituting these values into the formula, we can calculate the probability.

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Given:

To find the angle between v and w:

Using the formula,

Rationalising the denomiantor, we get

Hence, the angle is,

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent and the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

The maximum possible error that will be associated with the estimate when the analyst uses a sample size of 400 observations is 3.78 percent.

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^

              = 0.3n

              = 400

Substitute the given values into the formula:

Maximum possible error = 1.65 * √(0.3 * (1-0.3)/400)

Maximum possible error = 1.65 * √(0.3 * 0.7/400)

Maximum possible error = 1.65 * √0.0021

Maximum possible error = 1.65 * 0.0458

Maximum possible error = 0.0756 or 7.56% (rounded to two decimal places)

b. The sample size that the analyst would need in order to have the maximum error be no more than ±5 percent can be calculated as follows:

Error formula for proportion:

Maximum possible error = z * √(p^ * (1-p^)/n)

Where z = 1.65 for 90 percent confidencep^ = 0.3n = ?

Maximum possible error = 0.05

Substitute the given values into the formula:

0.05 = 1.65 * √(0.3 * (1-0.3)/n)0.05/1.65

        = √(0.3 * (1-0.3)/n)0.0303

        = 0.3 * (1-0.3)/nn

        = 0.3 * (1-0.3)/(0.0303)n

        = 296.95 or 297 (rounded up to the nearest whole number)

Therefore, the sample size that the analyst would need in order to have the maximum error be no more than ±5 percent is 297 observations.

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In the equation y = $7.20x + $790, "y" represents the total cost. An equation is a mathematical statement that shows the relationship between two or more variables. In this equation, there are two variables - "x" and "y". The variable "x" represents the number of units produced or sold, while "y" represents the total cost.

The coefficient of "x" in the equation, which is 7.20, represents the variable cost per unit. This means that for each unit produced or sold, there is an additional cost of $7.20. The constant term, which is $790, represents the total fixed costs. Fixed costs are those costs that do not vary with the number of units produced or sold.To find the total cost of producing or selling a certain number of units, we can plug in the value of "x" into the equation and solve for "y". For example, if we want to find the total cost of producing 100 units, we can substitute x=100 into the equation:
y = $7.20(100) + $790
y = $720 + $790
y = $1510
Therefore, the total cost of producing 100 units is $1510. In summary, "y" represents the total cost in the given equation, which is determined by both fixed and variable costs.
In the equation y = $7.20x + $790, "y" represents option C: total costs. This equation has two components: "$7.20x" represents the variable costs per unit, where x is the number of units, and "$790" represents the total fixed costs. By adding these two components together, you get the total costs (y) for producing x units.

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Answer:

Step-by-step explanation:

Possible number of pairs of given cards:

Number of sums with odd score, two odd numbers added to an even number from each box:

Required probability:

Answer:

g(5)=-2(5)+1

g(5)=-10+1

g(5)=-9

The number of periods is approximately 26.98.

To calculate the number of periods it takes to double your money at 5.25 percent interest, you can use the formula for compound interest:

Future value = Present value * (1 + interest rate) ^ number of periods

In this case, the future value is twice the present value, so the equation becomes:

2 = 1 * (1 + 0.0525) ^ number of periods

To solve for the number of periods, you can take the logarithm of both sides:

log(2) = log((1 + 0.0525) ^ number of periods)

Using the logarithmic properties, you can bring the exponent down:

log(2) = number of periods * log(1 + 0.0525)

Finally, you can solve for the number of periods:

number of periods = log(2) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 13.27.

To calculate the number of periods it takes to quadruple your money at 5.25 percent interest, you can follow the same steps as above, but change the future value to four times the present value:

4 = 1 * (1 + 0.0525) ^ number of periods

Solving for the number of periods using logarithms:

number of periods = log(4) / log(1 + 0.0525)

Using a calculator, the number of periods is approximately 26.98.

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a. X can be an instrument for itself if relevant.
b. Exogenous variables don't affect instrument relevance.

a. The reasoning or statement is correct. X can serve as an instrumental variable for itself in certain cases. This occurs when X is endogenous (correlated with the error term in the regression equation) and there is a valid reason to believe that X affects the outcome variable but is not directly affected by other factors.

b. In the presence of exogenous variables (W's) in the model, the F-statistic described above, which tests whether all first-stage parameters are zero, is not used to determine the relevance of instruments. The concept of relevance of instruments is concerned with whether the instruments are correlated with the endogenous variable (X) in the first stage. Exogenous variables (W's) are not part of the relevance assessment because they are assumed to be unrelated to the endogenous variable. Therefore, the F-statistic used to test relevance would only consider the instruments (Z1, Z2, Z3, Z4) and their correlation with X, disregarding the presence of exogenous variables.

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To examine the given function z = 2x^2 + y^2 + 8x - 6y + 20 for relative maximum and minimum points, we need to analyze its critical points and determine their nature using the second derivative test. The critical points correspond to the points where the gradient of the function is zero.

To find the critical points, we need to compute the partial derivatives of the function with respect to x and y and set them equal to zero. Taking the partial derivatives, we get ∂z/∂x = 4x + 8 and ∂z/∂y = 2y - 6.

Setting both partial derivatives equal to zero, we solve the system of equations 4x + 8 = 0 and 2y - 6 = 0. This yields the critical point (-2, 3).

Next, we need to examine the nature of this critical point to determine if it is a relative maximum, minimum, or neither. To do this, we calculate the second partial derivatives ∂^2z/∂x^2 and ∂^2z/∂y^2, as well as the mixed partial derivative ∂^2z/∂x∂y.

Evaluating these second partial derivatives at the critical point (-2, 3), we find ∂^2z/∂x^2 = 4, ∂^2z/∂y^2 = 2, and ∂^2z/∂x∂y = 0.

Since ∂^2z/∂x^2 > 0 and (∂^2z/∂x^2)(∂^2z/∂y^2) - (∂^2z/∂x∂y)^2 > 0, the second derivative test confirms that the critical point (-2, 3) corresponds to a relative minimum point.

Therefore, the function z = 2x^2 + y^2 + 8x - 6y + 20 has a relative minimum at the point (-2, 3).

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Answer:

x = .464

Step-by-step explanation:

Assumptions: Equation is \(-2x^3+20\). Thus having an asymptote at the value x=0.

True. If the derivative (dy/dx) of a function f(x) is zero at a particular value of x, then the slope of the tangent line at that point is also zero, which means it is a horizontal line.

A tangent line is a straight line with the same slope as the curve it touches at a single point on a curve. A local approximation of the curve close to the point of contact is provided. Finding the slope of the curve at a given location, which is determined by the derivative of the curve at that position, is necessary to determine the equation of a tangent line to a curve at that point. The equation of the tangent line is then written using the point-slope form of a line. Calculus relies on tangent lines to help students comprehend how functions and their derivatives behave.

This is because the derivative represents the rate of change (slope) of the function at any given point, and if it is zero, then the function is not changing (not curving) at that point.

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Answer:

either 32/3 or if that was supposed to be 4(-1) then the answer would be -8

Step-by-step explanation:

Answer: in explanation

Step-by-step explanation:

Rate is simplest form, so 3 napkins for 5 cents.

Unit rate is for 1 x value, so 1 napkin for 0,6 cents.

The probability of selecting a defective battery followed by another defective battery is 0.031.

There are 20 AAA batteries in a box and 4 are defective. If two batteries are selected without replacement, the probability of selecting a defective battery will be 4/20.

The probability of selecting another defective battery will be 3/19 as there will be 19 batteries left and 3 defective.

Then, the probability of selecting a defective battery followed by another defective battery will be:

= 4/20 × 3/19

= 12/380

= 0.031

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The probabilistic approach characterized by PERT does not use the median activity times.

The probabilistic approach characterized by PERT stands for Program Evaluation and Review Technique. It is a statistical tool used to evaluate and estimate the time required to complete a project. The PERT method is based on a three-point estimation technique, which takes into account the best case, worst case, and most likely case scenarios for each activity involved in the project management process.

The PERT formula is used to calculate the expected time required to complete a project. The formula is based on the three-point estimation technique used by the PERT method. The formula for calculating the expected time for an activity is as follows:

Expected time = (optimistic time + (4 x most likely time) + pessimistic time) / 6Where,Optimistic time is the shortest possible time required to complete an activityMost likely time is the most probable time required to complete an activityPessimistic time is the longest possible time required to complete an activity

The PERT method is a valuable tool for project managers as it provides a statistical estimation of the time required to complete a project. By using the three-point estimation technique, project managers can evaluate the best case, worst case, and most likely case scenarios for each activity involved in the project management process.

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Answer:

x = 10, x = 0

I dont know if you wanted an answer but yeah-

The median number of cans consumed by students is 2.

To find the median number of cans consumed by students according to the pictograph, we need to arrange the numbers in order from smallest to largest:

1 1 1 1 2 2 2 2 2 3 3 4 4

There are 13 numbers in total, so the median is the middle value. In this case, the middle value is the 7th number, which is 2. Therefore, the median number of cans consumed by students is 2.

To find the mean number of cans consumed by the 13 students, we need to sum up all the values and divide by the total number of values:

Mean = (1 x 4 + 2 x 5 + 3 x 2 + 4 x 2) / 13 = 1.95

Therefore, the mean number of cans consumed by the 13 students is 1.95 cans.

To find the mode, we need to look for the value that appears most frequently. In this case, the value that appears most frequently is 2, which appears 5 times. Therefore, the mode is 2 cans consumed.

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Answer: C

Step-by-step explanation: (x+2) 2+(y-1) 2=3

The probability of being dealt 4​, ​5, 6​, 7​, and 8​, not necessarily in the same​ suit is  0.00039.

The cards 4,5,6,7, and 8 are given to us. We must figure out the probability of obtaining these cards in a deal. As we already know, probability equals the number of possible card selection methods divided by the total number of possible card selection methods. The amount of card selection options will therefore be determined initially.

We know that there are four cards of each number, 4, 5, 6, 7 and 8, in a deck of 52 cards. This means that there will be an equal number of possibilities to choose one card from the decks of 4, 5, 6, 7 and 8 when raised to the power of five.

Possible ways= 4^5= 1024

Total selection= C(52,5)= 2598960

Probability of being dealt with  4​, ​5, 6​, 7​, and 8​ is 1024/2598960 which is equal to 0.00039.

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Answer:

33

Step-by-step explanation:

x-15=18

X=18+15

X=18+15

X=33

inferential statistics allows for someone to draw conclusions about a population from the information collected in a population sample.

the qestion is incomplete .please read below to find the missing content

Which of the following allows for someone to draw conclusions about a population from the information collected in a population sample?

a. magnitude statistics

b. central tendency

c. inferential statistics

d. effect size

The population is the number of people living together in a place. The population of a city is the number of people living in that city. These people are called residents or residents. The population includes all individuals living in that particular area.

Population refers to the total number of organisms living in a particular area. Population helps us estimate the number of beings and know how to act accordingly. For example, knowing the exact population of a city allows us to estimate the number of resources required. Similarly, animals can do the same.

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The limit of lim (x − 9)/ (x² − 81)  using the l'Hospital's Rule is 1/18.

                  x→9

We can directly substitute the value 9 in the given limit expression.

We get,

lim (x − 9)/ (x² − 81) = (9 - 9)/(9^2 - 81)

= 0/0

The given limit is in indeterminate form. We can apply L'Hospital's rule here.

Differentiating both the numerator and the denominator with respect to x, we get,

lim (x − 9)/ (x² − 81) = lim (1)/(2x)

Now we can directly substitute the value of x in the above expression.

lim (x − 9)/ (x² − 81) = lim (1)/(2x) = 1/18

Therefore, the limit of the given expression is 1/18.

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