Simplify: –3|–2| + 4|–5| Please show work for full credit for full credit.

The completed tiles are placed in the appropriate slots to prove that line j is parallel to k, as follows;

Statements         \({}\) Reasons

1. ∠6 ≅∠3 \({}\)          1. Given

2. ∠3 ≅∠2 \({}\)         2. Vertical ∠s ≅

3. ∠6 ≅ ∠2 \({}\)        3. Transitive Property

4. j ║ k       \({}\)         4. Corresponding ∠s ≅, lines ║

Parallel lines are are two lines that continue indefinitely and do not meet, such that they make the same or congruent corresponding angles with a common transversal.

The details of the reasons used to prove that line j is parallel to line k are as follows;

Vertical ∠s ≅

The vertical angles theorem states that vertical angles, which are angles formed by the intersection of two lines and which are located, opposite to each other are congruent.

Transitive property

The transitive property of congruency states that if a is congruent to b and b is congruent to c, them a is congruent to c

Corresponding ∠s ≅

The corresponding angles formed between parallel lines are congruent.

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Hello!

We have the point (-5,3). We will plug this into each equation and see which ones are true.

3=-10+13

True

3=5-2

True

3=-15-5

False

3=2.5+6

False

3=10-2

False  

Therefore, the correct answers are A and B.

I hope this helps!

The answer  is that the standard error is the standard deviation of the sampling distribution. This means that it measures the amount of variability or spread in the means of multiple samples drawn from the same population.

To understand the concept of standard error, it is important to distinguish it from the standard deviation, which measures the amount of variability or spread in a single sample. The standard error, on the other hand, reflects the precision of the sample mean as an estimate of the population mean. It takes into account the fact that different samples will produce different means due to chance variation.

More specifically, the standard error is calculated by dividing the standard deviation of the population by the square root of the sample size. This formula reflects the fact that larger sample sizes tend to produce more precise estimates of the population mean, while smaller sample sizes are more likely to have greater sampling error or deviation from the true mean.

The standard error is used in many statistical analyses, particularly in hypothesis testing and constructing confidence intervals. For example, if we want to determine whether a sample mean is significantly different from a hypothesized population mean, we would calculate the standard error and use it to compute a t-value or z-value. This value would then be compared to a critical value to determine the statistical significance of the difference. Similarly, in constructing a confidence interval, we use the standard error to estimate the range of values that are likely to contain the true population mean with a certain level of confidence.

The standard error is the standard deviation of the sampling distribution, and it reflects the precision of the sample mean as an estimate of the population mean. It is calculated by dividing the standard deviation of the population by the square root of the sample size, and it is used in many statistical analyses to test hypotheses and construct confidence intervals.

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Answer:

y=16

Step-by-step explanation:

Notice that the first equation was multiplied by 4, so you have to multiply the result by 4 to keep it as a true equation

Statistics computed for larger random samples tend to be less variable compared to statistics computed for smaller random samples.

This statement is based on the concept of the Central Limit Theorem (CLT) in statistics. According to the CLT, as the sample size increases, the distribution of the sample mean approaches a normal distribution regardless of the shape of the population distribution. This means that the variability of the sample mean decreases as the sample size increases.

The variability of a statistic is commonly measured by its standard deviation or variance. When working with larger random samples, the individual observations have less impact on the overall variability of the statistic. As more data points are included in the sample, the effects of outliers or extreme values tend to diminish, resulting in a more stable and less variable estimate.

In practical terms, this implies that estimates or conclusions based on larger random samples are generally considered more reliable and accurate. Researchers and statisticians often strive to obtain larger sample sizes to reduce the variability of their results and increase the precision of their statistical inferences.

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As x increases from x=1 to x=5, the value of h remains constant at 4 and the output of the function v(x) changes from v(1) = 5 to v(5) = 29, with a difference of 24.

A function is a mathematical rule that assigns a unique output for every input.

Given the function h = 4, we can see that the output is always 4, regardless of the input value.

Now, if we consider the function

=> v(x) = x² + h,

we can see that the output is dependent on the input x and the constant value of h. As x increases from x=1 to x=5, the output of v(x) will also change.

We can calculate the value of v(1) as

=> v(1) = 1² + 4 = 5.

And similarly, we can calculate the value of v(5) as

=> v(5) = 5² + 4 = 29.

The difference between v(5) and v(1) can be calculated as

=> v(5) - v(1) = 29 - 5 = 24.

This represents the change in the output of the function v(x) as x increases from x=1 to x=5.

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Answer:

a) 6(6x-5)

=(6×6x) - (6×5)

=36x-30

b)11y+4y+10y

=y(11+4+10)

=y(25)

=25y

Answer:

Dividing negative exponents is almost the same as multiplying them, except you're doing the opposite: subtracting where you would have added and dividing where you would have multiplied. If the bases are the same, subtract the exponents. Remember to flip the exponent and make it positive, if needed.

Step-by-step explanation:

The multiplier for the given economy is 4.

The multiplier represents the magnification effect of an initial change in autonomous spending on the overall output of an economy. It is calculated using the formula 1 / (1 - MPC), where MPC is the marginal propensity to consume.

In this case, the MPC is given as 0.75, which means that for every additional dollar of income, individuals spend 75 cents. The multiplier is calculated as 1 / (1 - 0.75) = 4.

The multiplier of 4 indicates that a change in autonomous spending, such as investment or consumption, will have a four times larger impact on the overall output of the economy. In other words, for every dollar increase in autonomous spending, the total output of the economy will increase by four dollars.

In this scenario, since the intended investment is $130, the total increase in output would be 4 * $130 = $520. Therefore, the multiplier effect amplifies the initial change in autonomous spending and leads to a larger increase in output in the economy.

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a. The null hypothesis (H0) is that the proportion of those who are adequately prepared financially for retirement is the same for people in the 66-69 age group who did not complete high school as it is for the population of the 66-69-year-old (71%).

The alternative hypothesis (Ha) is that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.

b. To calculate the p-value for this hypothesis test, we can use a one-sample proportion test. The sample proportion (p-hat) is 165/300 = 0.55. Using a z-test, with a z-score of -2.35 and a standard deviation of 0.058, the p-value is 0.011.

c. At a significance level of 0.01, the p-value of 0.011 is less than the significance level, so we reject the null hypothesis. We can conclude that there is evidence that the proportion of those who are adequately prepared financially for retirement is smaller for people in the 66-69 age group who did not complete high school than it is for the population of the 66-69-year-old.

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Step-by-step explanation:

To simplify the given radical expression, we can first break down 2401 into its prime factors, which gives us:

2401 = 7^4

We can then simplify the given expression as follows:

^4 sqrt (2401x^12y^16) = ^4 sqrt (7^4 * x^12 * y^16)

= ^4 sqrt (7^4) * ^4 sqrt (x^12) * ^4 sqrt (y^16)

= 7 * x^3 * y^4

Therefore, the simplified form of the given expression is 7x^3y^4.

Answer:

(X+2) (X-2) . This is the final answer

Step-by-step explanation:

Solving f(x) = x^2 - 4

A^2 - B^2 is a special case where the original equation before it was foiled is

(A + B) (A - B) because the middle terms will cancel out when foiled.

This means that the equation can be written as

(X + 2)(X - 2) = 0

Each of these you will then set equal to 0 and then solve

X + 2 = 0, X - 2 = 0

X = -2, 2

I hope this helps you! let me now if its right ok <3 :)

Answer:

x=152.5

Step-by-step explanation:

subtract from both sides 25 so it will be

10x=1525

then divide both by 10 so it will be

x=152.5

Answer:

add the diagram

Step-by-step explanation:

Answer:

line of symmetry , x = 3

Step-by-step explanation:

Standard form of quadratic equation  is y = ax^2 + bx + c, where a, b, and c equal all real numbers. You can use the formula x = -b / 2a to find the line of symmetry.

\(y = (x+ 2)(x-8)\\\\y = (x^2 -8x + 2x -16)\\\\y = x^2 -6x -16\)

a = 1, b = -6, c = -16

Line of symmetry is ,

                           \(x = -\frac{b}{2a} = -\frac{-6}{2} = 3\)

Answer:

Perpendicular: \(y=-\frac{1}{3}x+\frac{19}{3}\)

Parallel: \(y=3x-7\)

Step-by-step explanation:

So when two lines are perpendicular, that means the the slope is the reciprocal with the opposite sign so: \(\frac{a}{b} \text{ has a slope perpendicular to } -\frac{b}{a}\). In this case we have the equation in slope-intercept form, so it's easy to determine the slope, it's 3. So that means the perpendicular line will have a slope of: \(-\frac{1}{3}\). Since you have a slope of 3/1 which becomes 1/3 and also an opposite sign. This gives you the equation: \(y=-\frac{1}{3}x+b\). We can solve for b, by plugging in a coordinate it passes through. This is given in the problem, with it being (4, 5) = (x, y). So plugging these values in as (x, y) gives you the equation: \(5=-\frac{1}{3}(4)+b\implies\frac{15}{3}=-\frac{4}{3}+b\implies\frac{19}{3}=b\). This gives you the complete equation: \(y=-\frac{1}{3}x+\frac{19}{3}\)

So when two lines are parallel, that means they have the slope, and a different y-intercept. This is because if they had the same y-intercept, then the two lines would be the same exact line. We already know the slope, it's 3. So we have the general equation: \(y=3x+b\text{ where b}\ne-3\). The restriction on b, was explained on the previous sentence, if b=-3, then we have the same equation, which is not parallel, they would be the same line, meaning they would intersect at infinite points, which is completely different than two lines that never intersect. So now we can plug in the given point (4, 5) to solve for b. Plugging these coordinates in gives you: \(5=3(4)+b\implies5=12+b\implies-7=b\). This gives you the complete equation: \(y=3x-7\)

Answer:

Step-by-step explanation:15.6

Answer:

slope is -1/2 and y- intercept is 1/3

Step-by-step explanation:

use y=mx+b

m=slope

b= y-intercept

rearrange your equation

y=1/3-1/2x

y=-1/2x+1/3

The Taylor series expansion around x=1 of the function \(\(f(x) = \frac{1}{2x-x^2}\) is \(f(x) = -\frac{1}{x-1} + \frac{1}{2(x-1)^2} - \frac{1}{3(x-1)^3} + \ldots\).\)

To find the Taylor series expansion of f(x) around x=1, we need to calculate its derivatives at x=1 and evaluate the coefficients in the series.

First, we find the derivatives of f(x) with respect to x. Taking the derivative term by term, we have \(\(f'(x) = -\frac{1}{(2x-x^2)^2}\) and \(f''(x) = \frac{4x-2}{(2x-x^2)^3}\).\)

Next, we evaluate these derivatives at x=1. We have f'(1) = -1 and f''(1) = 2.

Using these values, we can construct the Taylor series expansion of f(x) around x=1 using the general formula \(\(f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \ldots\). Plugging in \(a=1\)\) and the respective coefficients, we obtain \(\(f(x) = -\frac{1}{x-1} + \frac{1}{2(x-1)^2} - \frac{1}{3(x-1)^3} + \ldots\).\)

In summary, the Taylor series expansion around x=1 of the function\(\(f(x) = \frac{1}{2x-x^2}\) is \(f(x) = -\frac{1}{x-1} + \frac{1}{2(x-1)^2} - \frac{1}{3(x-1)^3} + \ldots\).\) This series allows us to approximate the function \(f(x)\) near \(x=1\) using a polynomial with an increasing number of terms.

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Answer: 16m²

Step-by-step explanation:

A large rectangle has side lengths of 8 meters and 6 meters. This means that the area of the large rectangle will be:

= 8m × 6m

= 48m²

A smaller rectangle with side lengths of 4 meters and 2 meters is cut out of the large rectangle. Then, the area of the smaller rectangle will be:

= 4m × 2m

= 8m²

Since the smaller rectangle with side lengths of 4 meters and 2 meters is cut out of the large rectangle whose length is 8, meters and 6 meters, the remaining part of the rectangle will have length of (8m - 4m) = 4m and (6m - 2m) = 4m.

Area of the remaining part of the large rectangle will be:

= 4m × 4m

= 16m²

Answer:

rational

Step-by-step explanation:

Answer:

a. $14.99k + $24+ $25 = x

b. $14.99(3) + $24+ $25 = x

   $44.97 + $24 + $25 = $93.97

Step-by-step explanation:

Answer:

i) C= $14.99 k + $24

ii) $93.97

Step-by-step explanation:

Let the number of models be represented by -----------k

Let the amount spent on books to be--------$24

The equation that represent amount spent in the mall is given as;

C= $14.99 k + $24   ---------------where ;

C= the equation for the total amount spent in the mall

k = the number of plane models

ii)

Using the equation : C= $14.99 k + $24    and if k = 3 and the amount spent on the store is $25  then ;

C= $14.99 * 3 + $24 = $44.97 + $24 = $68.97

C+ 25 = $68.97 + 25 =$93.97

Answer:

26r^2 + 36r.

Step-by-step explanation:

Answer:

a=5 b=8 c=4

Step-by-step explanation:i hope this is right

The 98% confidence interval for the proportion of all adults in the United States who exercise on a regular basis is (0.393, 0.507).

We can use the formula for the confidence interval of a proportion:

p ± zα/2 * √(p(1-p)/n)

where p is the sample proportion, zα/2 is the z-score corresponding to the desired level of confidence (98% in this case), and n is the sample size.

Using the given information, we have p = 81/184 ≈ 0.44 and n = 184.

To find the z-score, we can use a standard normal distribution table or calculator, or we can use the formula:

zα/2 = invNorm(1 - α/2)

where invNorm is the inverse cumulative distribution function of the standard normal distribution.

For a 98% confidence level, α/2 = 0.01, so zα/2 ≈ 2.33.

Substituting these values into the formula, we get:

0.44 ± 2.33 * √((0.44 * 0.56)/184) ≈ (0.393, 0.507)

Therefore, we can be 98% confident that the true proportion of all adults in the United States who exercise on a regular basis lies between 0.393 and 0.507.

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Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.

Here are the details for the given frequency distribution:

Lower class limits are the least number among the pair

Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.

Upper class limits are the greater number among the pair

Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.

Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).

Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.

Class boundaries are the extreme points of the classes which are  [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.

Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1

                                     = 76

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First, we want to note two things:

We can describe this with an inequality:  x ≥ -10
Be sure you use ≥ and not >, since -10 is included.

We can describe this with interval notation: [ -10, infty )
Be sure you use [ and not ( on -10, since -10 is included.

You can also use set-builder notation: { x | x ≥ -10 }

a) the population cannot be negative, the limiting population is 4300.

b)the population is increasing when 0 < p < 4300 and decreases when p > 4300.

c)the equilibrium solutions are p = 0 and p = 4300.

(a) To determine when the population is increasing or decreasing, we need to look at the sign of dp/dt.

\(\frac{dp}{dt} = 1.2p(1 - \frac{p}{4300})\)

For dp/dt to be positive (i.e. population is increasing),

we need\(1 - \frac{p}{4300} > 0, or \ p < 4300.\)

For dp/dt to be negative (i.e. population is decreasing),

we need\(1 - \frac{p}{4300} < 0, or p > 4300.\)

Therefore, the population is increasing when 0 < p < 4300 and decreases when p > 4300.

(b) To find the limiting population, we need to find the value of p as t approaches infinity.

As t approaches infinity,\(\frac{dp}{dt}\)approaches 0. Therefore, we can set \(\frac{dp}{dt}\) = 0 and solve for p.

0 = 1.2p(1 - p/4300)

Simplifying, we get:

0 = p(1 - p/4300)

So, either p = 0 or 1 - p/4300 = 0.

Solving for p, we get:

p = 0 or p = 4300.

Since the population cannot be negative, the limiting population is 4300.

(c) Equilibrium solutions occur when\(dp/dt = 0.\)We already found the equilibrium solutions in part (b): p = 0 and p = 4300.

Therefore, the equilibrium solutions are p = 0 and p = 4300.

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a)  The population is increasing when 0 < p < 4300, and  decreasing when p > 4300.

b)  The population cannot be negative, the limiting population is 4300.

c)  these are the equilibrium solutions.  At p = 0, the population is not

increasing or decreasing, and at p = 4300,  the population is decreasing

but not changing in size.

(a) To determine when the population is increasing or decreasing, we

need to find the sign of dp/dt. We have:

dp/dt = 1.2p(1 - p/4300)

This expression is positive when 1 - p/4300 > 0, i.e., when p < 4300, and

negative when 1 - p/4300 < 0, i.e., when p > 4300.

Therefore, the population is increasing when 0 < p < 4300, and

decreasing when p > 4300.

(b) To find the limiting population, we need to solve for p as t approaches infinity. To do this, we set dp/dt = 0 and solve for p:

1.2p(1 - p/4300) = 0

This equation has two solutions: p = 0 and p = 4300. Since the population cannot be negative, the limiting population is 4300.

(c) To find the equilibrium solutions, we need to solve for p when dp/dt = 0. We already found that the only solutions to dp/dt = 0 are p = 0 and

p = 4300.

Therefore, these are the equilibrium solutions.

At p = 0, the population is not increasing or decreasing, and at p = 4300,

the population is decreasing but not changing in size.

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