Use graph paper, or the Distance Formula, to graph the points. Find the
distance between the given points. When necessary, round to the nearest
tenth.
(-6, -3) and (6, 2)

the answer

155

324

5/9 (87/3(1/12)= 155/324

Answer:

angle R = 140 degrees

Step-by-step explanation:

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Answer:

Step-by-step explanation:

1. 2x>-6

2.  x-4<7

3. -x-5<=-2

4. 6+x<=3

hope this helps!

Answer:

1 2x>-6

2 x-4<-7

4 6+x _<_

3-x-5 _<_-2

Step-by-step explanation:

Lydia earns $52.5 more than Gabrielle after 3 years.

percentage, a relative value indicating hundredth parts of any quantity.

we can use the formula for compound interest:

\(A = P(1 + r/n)^n^t\)

where A is the final amount,

P is the principal (initial investment),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year, and

t is the number of years.

For Lydia (n=365)

A=1000(1+0.0525/365)¹⁰⁹⁵

A=1115.7

For Gabrille, we use the same formula but with n = 2 (compounded semi-annually):

A = 1000(1 + 0.0525/2)⁶

A = 1000(1.0265625)⁶

A = 1168.2

To find the difference in the amounts earned, we subtract Gabrielle's amount from Lydia's:

1168.2- 1115.7 = 52.5

Hence, Lydia earns $52.5 more than Gabrielle after 3 years.

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Answer:

28

Step-by-step explanation:

Determine which integer in the solution set will make the equation true. t − 42 = −14 {−56, −28, 3, 28}

replace 28 for t:

t − 42 = −14

28 − 42 = −14

−14 = −14

Answer:

  28

Step-by-step explanation:

You want the value of t that satisfies t − 42 = −14.

The solution to this 1-step linear equation is to add the opposite of the unwanted constant (-42).

Adding 42 to both sides of the equation gives ...

  t -42 +42 = -14 +42

  t = 28

The integer that makes the equation true is 28.

Since y_1(0) = 1, it satisfies the initial condition. However, y_2(0) = 0 does not satisfy the initial condition, as it should be y(0) = 1. Therefore, only y_1(t) is a solution of the initial value problem.

To verify that both y_1(t) = 1 - t and y_2(t) = -t^2/4 are solutions of the initial value problem, we first need to understand what the problem is. An initial value problem is a differential equation that includes an initial condition. In this case, we can assume that the initial condition is y(0) = 1.
Now, let's substitute both y_1(t) and y_2(t) into the differential equation and see if they satisfy the initial condition. The differential equation is not provided, but assuming it is y'(t) = -t/2, we have:
y_1'(t) = -1
y_2'(t) = -t/2
Substituting y_1(t) and y_2(t) into the differential equation gives:
y_1'(t) = -1

= -t/2 (when t = 2)
y_2'(t) = -t/2

= -t/2 (for all t)
Thus, both y_1(t) and y_2(t) satisfy the differential equation. Now, let's check if they satisfy the initial condition.
y_1(0) = 1 - 0

= 1
y_2(0) = -0^2/4

= 0
In conclusion, y_1(t) = 1 - t is the only solution that satisfies the differential equation and initial condition, while y_2(t) = -t^2/4 is not a solution since it does not satisfy the initial condition.

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Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.

The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).

Given:

Carlos gives  353535 minutes to harvest a total of 151515 cassavas.

Find:

We have to find the total number of cassavas.

Solution:

Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas

= 151515/353535

= 0.429

A formula for the quantity of cassava (C) that Carlos harvests each time (T).

This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.

Hence, the required constant rate is 0.429T.

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Answer: Angle AEF is 90°

Step by step explanation:

Given: CDF is a straight line, so the three angles that meet at D must total 180°

Given: ABCD is a square. By definition, all angles are 90° so CDA is 90°

Given: Triangle DEF is equilateral. By definition, all the angles are equal to 60° so angle EDF is 60°

Add angles EDF and ADC and subtract from 180

180 -(90 + 60) = 30

Given: Triangle ADE is iscoceles, so the angles opposite the given equal sides AE and AD are equal.

Angles AED and ADE are equal.

AED = 30°

Angle DEF of the equilateral triangle is 60°

The measure of angle AEF is the sum of angles AED + DEF 30 + 60 = 90.

Therefore the measure of angle AEF is 90°

Answer:

8100

Step-by-step explanation:

Answer:

........12......... ...............

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

maximum voltage = 121.5 volts

voltage read = 127.36 volts

Step 02:

127.36 volts - 121.5 volts = 5.86 volts

The answer is:

5.86 volts

Answer:22/15

Step-by-step explanation:

Answer:

x = 1/8

Step-by-step explanation:

2/5(x - 2) = -3/4

x - 2 = -15/8

x = -15/8 + 2

x = 1/8

Answer:

1036. this is easy.

Step-by-step explanation:

700 * 0.08 = 56

56 * 6 = 336.

700 + 336 = 1036.

At x=0 only, the function f with first derivative f'(x) = x(x-5)²(x+1) has a relative minimum.

Hence the correct option is (A) 0 only.

The first derivative of the function is,

f'(x) = x(x-5)²(x+1)

Differentiating the function with respect to x we get, The second derivative of the function is,

f''(x) = x(x-5)².(1) + x(x+1).2(x-5) + (x-5)²(x+1).1 = (x-5)² (x+x+1) + 2x(x+1)(x-5) = (x-5)²(2x+1) + 2x(x+1)(x-5)

Now, f'(x) = 0 gives,

x(x-5)²(x+1) = 0

We know that if product of more than one terms is zero then either of them is zero.

Either, x=0

Or, (x-5)² = 0

x-5 = 0

x = 5

Or, x+1 = 0

x = -1

So the extremum points of the function are, x = -1, 0, 5.

At x=-1, f''(-1) = (-6)²(-2+1) + 2(-1)(-1+1)(-6) = -36

At x=0, f''(0) = (-5)²*1 + 0 = 25

At x=5, f''(5) = 0 + 0 = 0

Since the value of second derivative is positive at only x = 0.

Thus, at x = 0 only the function has a relative minimum.

Hence the correct option is (A).

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Answer:

x = 10

Step-by-step explanation:

The secant- secant angle 3x is half the difference of the intercepted arcs, that is

3x = \(\frac{1}{2}\) (4x + 50 - 30 )

3x = \(\frac{1}{2}\) (4x + 20) = 2x + 10 ( subtract 2x from both sides )

x = 10

The probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0 (Option A).

The number of turns needed to sharpen a brand H pencil is approximately normal distributed with a mean of 5.2 and a standard deviation of 0.33.30 pencils of each brand are randomly selected and sharpened.

Now, we have to find the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H.

To find this, we use the Central Limit Theorem (CLT).

According to the Central Limit Theorem (CLT), if the sample size is sufficiently large (n > 30), then the distribution of sample means becomes approximately normal with a mean equal to the population mean and standard deviation equal to the population standard deviation divided by the square root of the sample size.

This is applicable for both brand W and brand H pencils. Mathematically, this can be represented as follows:
[4.6-5.2]/sqrt{0.67^2/30+0.33^2/30}
=-3.94This means that the sample mean of brand W pencils is 3.94 standard errors less than the sample mean of brand H pencils.

This can be visualized using the following normal distribution curve: Normal Distribution Curve.

Therefore, the probability that the brand W pencils will have a higher mean number of turns needed to sharpen than brand H is approximately 0 (Option A).

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To solve this equation for z, we can proceed as follows:

1. Subtract 19 from both sides of the equation:

2. Multiply by 4 to both sides of the equation (Multiplication property of equality):

Therefore, the value for z is equal to 84.

Answer:(a) "95% confidence" means that if we were to repeat this study many times, we would expect the true proportion of members who would quit to be within the calculated interval for 95% of those studies. In other words, we can be 95% confident that the true proportion of members who would quit falls within the interval.

(b) The interval is [0.18, 0.075]. This means that we are 95% confident that the true proportion of members who would quit if the fee was raised to $50 falls between 0.18 and 0.075.

(c) No, the owner cannot be confident that the fee increase will be worthwhile because the interval from part (b) includes 20%. If the true proportion of members who would quit is 20%, then the fee increase would not be worthwhile. Since the interval includes 20%, we cannot be confident that the true proportion is less than 20%.

(d) One of the conditions for calculating the confidence interval is that the sample size is large enough and that the number of successes and failures in the sample are both at least 10. This is necessary because the interval calculation relies on the normal distribution, which is only valid when the sample size is large enough and the number of successes and failures are both at least 10. If this condition is not met, then the interval calculation may not be accurate or valid.

Step-by-step explanation:

A regression model allows us to examine how the probability distribution of a dependent variable, Y, might be related to one or more independent variables (collectively called X). Therefore, the correct answer is (a) regression model.

A regression model is a statistical tool used to model the relationship between a dependent variable (often denoted as Y) and one or more independent variables (often denoted as X). It can help us understand how changes in the independent variables affect the values of the dependent variable, and can be used to make predictions or estimate values of the dependent variable based on specific values of the independent variables.

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Answer:

no

Step-by-step explanation:

no

The formula for calculating the effective annual rate of interest with quarterly compounding is:

(1 + r/4)^4 - 1 = A/P

where r is the quarterly interest rate, A is the final amount, and P is the principal.

In this case, P = $2,000, A = $3,000, and the time period is 7 years or 28 quarters.

So we have:

(1 + r/4)^4 - 1 = 3000/2000

(1 + r/4)^4 = 1.5

1 + r/4 = (1.5)^(1/4)

r/4 = (1.5)^(1/4) - 1

r = 4[(1.5)^(1/4) - 1]

To get the effective annual rate, we need to convert the quarterly rate to an annual rate by multiplying by 4:

effective annual rate = 4[(1.5)^(1/4) - 1] ≈ 8.84%

Therefore, the effective annual rate of interest at which $2,000 will grow to $3,000 in seven years if compounded quarterly is approximately 8.84%, rounded to 2 decimal places.

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Based on the given information, we know that Mr. Habib bought 8 gifts and spent between $2 and $5 on each gift. To find a reasonable total amount that Mr. Habib spent on all of the gifts, we can start by finding the minimum and maximum amounts he could have spent.

If Mr. Habib spent $2 on each gift, then the total amount he spent would be 8 x $2 = $16.
If Mr. Habib spent $5 on each gift, then the total amount he spent would be 8 x $5 = $40.

Therefore, the reasonable total amount that Mr. Habib spent on all of the gifts would fall somewhere between $16 and $40. It could be closer to the lower end of the range if he mostly bought gifts for $2 each, or closer to the higher end of the range if he mostly bought gifts for $5 each. Without more information about how much he spent on each gift, it is difficult to give a more precise estimate.

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a) We performed a hypothesis test for a proportion. With a sample size of 600 and a sample proportion of 0.57, we calculated the standard error, which measures the variability in our sample proportion estimate.

b) We then computed the test statistic using the formula for a z-test and found it to be approximately 4.951.

c) The p-value was less than the significance level of 0.05, we rejected the null hypothesis and concluded that there is evidence to support the alternative hypothesis that the true proportion is not equal to 0.5.

(a) To begin, let's calculate the standard error of the proportion. The standard error measures the variability or uncertainty in our sample proportion estimate. It is given by the formula:

Standard Error = √((p* (1 - p)) / n),

where p is the sample proportion and n is the sample size.

In this case, we are given that the sample proportion (p) is 0.57, and the sample size (n) is 600. Plugging these values into the formula, we get:

Standard Error = √((0.57 * (1 - 0.57)) / 600) ≈ 0.01414 (rounded to five decimal places).

Therefore, the standard error of the proportion is approximately 0.01414.

(b) The formula for the z-test statistic is given by:

z = (p- p0) / SE,

where p is the sample proportion, p0 is the hypothesized proportion under the null hypothesis, and SE is the standard error.

In this case, our null hypothesis (H0) states that the true proportion (p) is 0.5, and our sample proportion (p) is 0.57. The standard error (SE) is approximately 0.01414, as calculated in part (a).

Plugging these values into the formula, we get:

z = (0.57 - 0.5) / 0.01414 ≈ 4.951 (rounded to two decimal places).

Therefore, the value of the test statistic is approximately 4.951.

(c) The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. To determine the p-value, we need to compare the test statistic to the standard normal distribution.

Since the p-value is the probability of observing a test statistic as extreme as or more extreme than the one calculated, we compare it to the significance level (α) to make a decision. In this case, the significance level is given as α = 0.05.

Since the p-value (close to 0) is less than the significance level (0.05), we reject the null hypothesis. This means we have evidence to support the alternative hypothesis that the true proportion is not equal to 0.5.

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Answer:

1/6 = 0.1667

Step-by-step explanation:

sample space = 6

the probability of rolling a number equal to 1 = 1/6

Answer: 11, 16, 26, 41

Step-by-step explanation:

The point estimate of the population standard deviation is 5.91 (Option A)

Standard deviation refers to the spread of a data distribution and measures the distance between each data point and the mean. The sample standard deviation (s) is a point estimate of the population standard deviation σ.

The mean of the population ẋ = sum of all values/ total number of values = 97/6 ≈ 16

The point estimate of the population standard deviation S =√(∑(xi - ẋ)^2/n-1)

∑(xi - µ)^2 = (9 – 16)^2 + (13– 16)^2 + (15– 16)^2 + (15– 16)^2 + (21– 16)^2 + (24– 16)^2 = 79 + 9 + 1 + 1 + 25 + 64 = 179

s = √(179/5) = 5.98

Note: The question is incomplete. The complete question probably is: The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 5.91. O b. 7.688. O C. 7.018. O d. 4.925.

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Answer:

Interest at the end of the first year is $105.93

Step-by-step explanation:

$800 at 12.5% APR compounded monthly.

Interest at the end of the year

= $800 *( (1+0.125/12)^12 - 1 )

= $800 * 0.132416

= $105.93