Which expression represents a negative value?
2 - |-7 + 31
5- |-12 + 91
15| + |-111
9 - 18 - 141

Answer:

Hello,

Here is your answer:

2/6

To determine the value of q for which the lines qx - 7y + 10 = 20 and 4y + 3x + 9 = 0 are parallel to each other, we need to compare their slopes.

First, we'll rewrite the equations in the standard form y = mx + b, where m represents the slope of the line:

For the line qx - 7y + 10 = 20, rearranging the equation gives us:

qx - 7y = 10

-7y = -qx + 10

y = (q/7)x - 10/7

For the line 4y + 3x + 9 = 0, rearranging the equation gives us:

4y = -3x - 9

y = (-3/4)x - 9/4

From the equations, we can see that the slopes are q/7 for the first line and -3/4 for the second line.

For two lines to be parallel, their slopes must be equal. Therefore, we can equate the slopes and solve for q:

q/7 = -3/4

Cross-multiplying, we have:

4q = -21

Dividing both sides by 4, we find:

q = -21/4

Therefore, the value of q for which the lines are parallel to each other is -21/4.

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Answer:

in a monthly shy much $3500

in a weekly she much $807.69

Step-by-step explanation:

Answer:

Below! : )

Step-by-step explanation:

$3,500 monthly

$807.69 per week

$1,615.38 biweekly

Hope this helps! : )

The age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the age of the grandsons is x years and

age of the grandfather's age is y years

Here some data are misprinted, so we are assuming the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

Then according to the problem:

12x = y  (as in 1 year, there are 12 months)

y -x = 77 (as difference in age is 77)

After solving both equations, we get:

x = 7 years and y = 84 years

Thus, the age of the grandson is 7 years and the grandfather is 84 years if the grandson's age in months is equal to the age of grandpa in years and the difference in age is 77.

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Answer:

1,700 milliliters

Step-by-step explanation:

Convert the liters that Javier and his brother got into milliliters.

In 1 liter, there are 1000 milliliters.

So, Javier's brother bought 1000 milliliters of soda.

And, in 1/2 liter of soda, there are 500 milliliters. So, Javier bought 500 milliliters of soda.

Add these two amounts to how much Javier's mom bought:

500 + 1000 + 200

= 1700

So, for his party, Javier has 1,700 total milliliters of soda.

Answer:

324

Step-by-step explanation:

(6*3)*2

(6*16)*2

(16*3)*2

36+192+96=324

hope this helps :D

Chimerism, the presence of two or more distinct sets of DNA within an individual, can cause problems in cases other than parentage, such as forensic investigations and identification in criminal investigations.

In forensic investigations, chimerism can complicate DNA profiling and identification processes, as it may result in mixed DNA profiles that make it challenging to determine an individual's true genetic identity. This can create difficulties in accurately linking suspects to crime scenes or identifying victims.

In transplant compatibility assessments, chimerism can lead to inconclusive results when determining whether a potential donor's DNA matches the recipient's DNA. The presence of two or more sets of DNA may affect the reliability of compatibility tests, potentially impacting the success of organ or tissue transplants.

In criminal investigations, chimerism can raise issues when DNA evidence is used to establish a suspect's presence at a crime scene. The presence of multiple DNA profiles within an individual may create doubt or confusion when attempting to match DNA evidence to a specific person, potentially affecting the outcome of criminal cases.

In summary, chimerism can cause problems in forensic investigations, transplant compatibility assessments, and criminal investigations by introducing complexities and uncertainties into DNA profiling and identification processes.

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Stan's average speed for the total trip is 55 miles per hour.

Given,

Stan drove 300 miles in 5 hours 20 minutes

Again, Stan drove 360 miles in 6 hours 40 minutes

To find,

Stan's average speed in miles per hour for the total trip

Solution

We can start the problem by calculating the total distance and the total time for the trip. Then we can use the formula for average speed which is;

Average speed = Total distance / Total time

First, let's calculate the total distance covered by Stan in the entire trip;

Total distance covered = 300 + 360= 660 miles

Now, let's calculate the total time taken by Stan in the entire trip;

Total time taken = 5 hours 20 minutes + 6 hours 40 minutes= 12 hours

Now, let's use the formula for average speed and calculate the average speed for the entire trip;

Average speed = Total distance / Total time= 660 / 12= 55 miles per hour

Therefore, Stan's average speed for the total trip is 55 miles per hour.

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Using the values provided in the ordered pair, The linear inequality is satisfied by putting the ordered pair values and checking if the statement is true or false.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence.

When two mathematical statements or two numbers are compared in an unequal way, it is known as an inequality in mathematics. Inequalities can generally be classified as either algebraic or numerical, or as a combination of the two.

ordered pair=(1,2)

linear inequality equation,

\(4x_{1}-x_{2} > 0\)

using value from ordered pair,

\(4*1 - 2 > 0\)

\(2 > 0\)

which is true. That is it satisfies the given linear inequality.

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Answer:

144

Step-by-step explanation:

The simplified equation would be 4x2x3x3x2 and that put into a calculator is 144

Answer: to the right

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

480 total

1/2 = 240 are cows

1/8 = 60 are goats

remaining = 480-240-60 = 180 are chickens & ducks

33.3333% of 180 = chickens  =180/3 = 60 chickens

so ducks = 180-60 =120

Answer:

120

Step-by-step explanation:

given that out of 480 animals 0.5 of the animals are cows . So ,

no. of cows = 0.5*480 = 240

Again, we are given that 1/8 of the animals are goats , so the number of goats would be ,

no. of goats = 1/8*480 = 60

Total no. of goats and cows ,

= 240 + 60 = 300

No. of remaining animals= 480 -300 = 180

Now out of these 180 animals 33⅓ % animals are chickens and remaining are ducks.

Percentage of ducks = (100 - 33⅓ )% = 66.67%

So the number of ducks would be ,

180 * 66.67/100 = 120

And we are done!

Answer:

A. 1/220   B. 1/22   C. 3/11

Step-by-step explanation:

This question uses combinations -- counting the number of ways a selection can be made from a set of objects (without arranging them after the selection is done).

Notations for combinations:

The number of ways to select  r  things from a set of  n  things is

\(C(n,r)=\frac{n!}{r!(n-r)!}\)  where the exclamation points mean factorial.

\(n!=1\cdot2\cdot3\ldots\cdot n\)  and 0! is defined to be 1.

There are two other commonly used symbols for this:

\(_nC_r\)  and  \(n \choose x\).

In all three parts, the number of ways to choose 3 balls from a set of 12 is

\(C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10 \cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot4\cdot3\cdot2\cdot1}{(3\cdot2\cdot1)(9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1)}\)

Notice that 9 factors in the denominator cancel 9 factors in the numerator, leaving

\(C(12,3) = \frac{12!}{3!(12-3)!}=\frac{12\cdot 11 \cdot 10}{3\cdot2\cdot1}=220\)

A. The number of ways to choose 3 red balls from the 3 red balls is C(3, 3) = 1, so the probability is 1 / 220.

B)  The number of ways to choose 3 green balls from the set of 5 green balls is \(C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}=\frac{5\cdot 4}{2}=10\)  out of 220, so the probability is 10/220 = 1/22.

C)  The number of ways to choose 1 red is C(3, 1) = 3.  Choose 1 green in C(5, 1) = 5 ways.  Choose 1 white in C(4, 1) = 4 ways.

The probability is  \(\frac{3\cdot 5 \cdot 4}{220}=\frac{60}{220}=\frac{3}{11}\)

Answer:

a) 1/220

b) 1/22

c) 3/11

Step-by-step explanation:

Check the attachment.

Of the boys surveyed, more preferred apples. Of the girls surveyed, more preferred apples. There does not appear to be association between gender and fruit preference.

More than half of both boys and girls prefer apples relative to oranges.

As the preference is the same between the two genders, there does not appear to be association between gender and fruit preference.

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Answer:

ur really weird we are not dating you weirdo

Step-by-step explanation:

Answer:

WR = 14.5

QR = 6.8

Step-by-step explanation:

Use SOH CAH TOA and sin cos tan to find missing side lengths

Answer:

Step-by-step explanation:trisha is running a marathon race  she runs th erace at a steady pace she makes a graph to show how far from the finsh line she will be as she runs the race

=2

Answer:

slope: -0.0625

Explanation:

To find slope of a function, we have to find the derivative of the function.

\(\rightarrow \sf \dfrac{dy}{dx} = \dfrac{d}{dx} ( \sqrt{12-x} )\)

\(\rightarrow \sf \dfrac{dy}{dx} = \dfrac{d}{dx} ( (12-x)^{\frac{1}{2} }} )\)

\(\rightarrow \sf \dfrac{dy}{dx} = \dfrac{1}{2} ( (12-x)^{\frac{1}{2}-1 }} )(-1)\)

\(\rightarrow \sf \dfrac{1}{2\sqrt{12-x}}\left(-1\right)\)

\(\rightarrow \sf -\dfrac{1}{2\sqrt{12-x}}\)

\(\bold{\star}\) Tangent/Parallel Line Has Same Slope

To find slope at x = -52, simplify insert x = -52 in derivative we found

\(\rightarrow \sf -\dfrac{1}{2\sqrt{12-(-52)}} \ = \ -\dfrac{1}{16} \ \ = \ -0.0625\)

Answer:

\(-\dfrac{1}{16}\)  or -0.0625

Step-by-step explanation:

To find the slope of the tangent line at a point, differentiate the function (using the chain rule for this particular function), then input the x-coordinate of the point into the first derivative.

\(\begin{aligned}f(x) & = \sqrt{12-x}\\& = (12-x)^{\frac{1}{2}}\\\\\implies f'(x) & =\dfrac{1}{2}(12-x)^{-\frac{1}{2}} \cdot -1\\& = -\dfrac{1}{2\sqrt{12-x}}\end{aligned}\)

Therefore, the slope of the tangent line to f(x) at x = -52 is:

\(\begin{aligned}f'(-52) &=-\dfrac{1}{2\sqrt{12-(-52)}}\\\\&=-\dfrac{1}{2\sqrt{64}}\\\\&=-\dfrac{1}{2 \cdot 8}\\\\&=-\dfrac{1}{16}\\\\&=-0.0625\end{aligned}\)

The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.0091 ounces.

Given that: Mean weight of 49 turtles = 68 ounces, Population standard deviation = 4.3 ounces, Confidence level = 90% Formula to calculate the maximal margin of error is:

Maximal margin of error = z * (σ/√n), where z is the z-score of the confidence level σ is the population standard deviation and n is the sample size. Here, the z-score corresponding to the 90% confidence level is 1.645. Using the formula mentioned above, we can find the maximal margin of error. Substituting the given values, we get:

Maximal margin of error = 1.645 * (4.3/√49)

Maximal margin of error = 1.645 * (4.3/7)

Maximal margin of error = 1.645 * 0.61429

Maximal margin of error = 1.0091

Thus, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 1.0091 ounces.

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The maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 0.1346.

The formula for the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is shown below:

Maximum margin of error = (z-score) * (standard deviation / square root of sample size)

whereas for the 90% confidence level, the z-score is 1.645, given that 0.05 is divided into two tails. We must first convert ounces to decimal form, so 4.3 ounces will become 0.2709 after being converted to a decimal standard deviation. In addition, since there are 49 turtle weights in the sample, the sample size (n) is equal to 49. By plugging these values into the above formula, we can find the maximal margin of error as follows:

Maximal margin of error = 1.645 * (0.2709 / √49) = 0.1346.

Therefore, the maximal margin of error associated with a 90% confidence interval for the true population mean turtle weight is 0.1346.

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Therefore, in either partial derivatives, we have u = 0 or v = 0.

The given information implies that two vectors u and v satisfy:

u * v = 0, where * denotes the dot product between vectors.

u X v = 0, where X denotes the cross product between vectors.

From the first equation, we know that the angle between u and v is either 90 degrees or 270 degrees. That is, u and v are orthogonal (perpendicular) to each other.

From the second equation, we know that the magnitude of the cross product u X v is equal to the product of the magnitudes of u and v multiplied by the sine of the angle between them. Since u and v are orthogonal, the angle between them is either 90 degrees or 270 degrees, which means that the sine of the angle is either 1 or -1. Therefore, we have:

|u X v| = |u| * |v| * sin(θ)

= 0

Since the magnitudes of u and v are non-negative, it follows that sin(θ) must be zero. This can only happen if the angle between u and v is either 0 degrees (i.e., u and v are parallel) or 180 degrees (i.e., u and v are anti-parallel).

In the case where u and v are parallel, we have:

u * v = |u| * |v| * cos(θ)

= |u|²

= 0

This implies that |u| = 0, which means that u = 0.

In the case where u and v are anti-parallel, we have:

u * v = |u| * |v| * cos(θ)

= -|u|²

= 0

This again implies that |u| = 0, which means that u = 0.

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The price elasticity of demand (PED) for the logo T-shirts is 1.67, indicating that the demand for T-shirts is elastic. Lowering the price from $15 to $10 increased the total revenue, suggesting that the T-shirt made a good decision in lowering the price. This is because the price change led to a significant increase in quantity demanded and overall revenue.

To calculate the price elasticity of demand (PED), we can use the following formula:

PED = ((Q2 - Q1) / ((Q2 + Q1) / 2)) / ((P2 - P1) / ((P2 + P1) / 2))

Given that Q1 = 25, Q2 = 50, P1 = $15, and P2 = $10, we can substitute these values into the formula:

PED = ((50 - 25) / ((50 + 25) / 2)) / (($10 - $15) / (($10 + $15) / 2))

Simplifying this expression:

PED = (25 / 37.5) / (-5 / 12.5)

PED = (-2/3) * (-2.5) = 1.67

The price elasticity of demand (PED) for the logo T-shirts is 1.67.

Since PED is greater than 1, it indicates that the demand for T-shirts is elastic. This means that a decrease in price by 1% will result in a greater than 1% increase in quantity demanded. To determine if lowering the price was a good decision, we can analyze the effect on total revenue. The price-total revenue test states that:

If PED is elastic (greater than 1), a decrease in price will lead to an increase in total revenue.

If PED is inelastic (less than 1), a decrease in price will lead to a decrease in total revenue.

If PED is unit elastic (equal to 1), a change in price will have no effect on total revenue.

Let's calculate the total revenue at both prices:

Total Revenue at $15 = $15 * 25 = $375

Total Revenue at $10 = $10 * 50 = $500

Comparing the total revenue at each price, we can see that lowering the price from $15 to $10 increased the total revenue from $375 to $500. Therefore, the T-shirt made a good decision in lowering the price because it led to an increase in total revenue.

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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If you use a level of significance in a (two-tail) hypothesis test, your decision rule for rejecting a null hypothesis that the population mean is if you use the z test is based on the critical values of the test statistic. Specifically, you would reject the null hypothesis if the test statistic falls in the rejection region, which is determined by the level of significance and the critical values of the z distribution.

In a two-tail hypothesis test, the rejection region is the area in the tails of the distribution that falls outside of the critical values. For example, if you use a level of significance of 0.05, the critical values for the z test would be -1.96 and 1.96. This means that you would reject the null hypothesis if the test statistic is less than -1.96 or greater than 1.96.

In summary, the decision rule for rejecting a null hypothesis in a two-tail hypothesis test using the z test is based on the level of significance and the critical values of the z distribution. If the test statistic falls in the rejection region, you would reject the null hypothesis.

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The person's actual score is 135 , To find the actual score of a person who is 1.5 standard deviations below the mean, we can use the following formula:

Actual Score = Mean - (Number of Standard Deviations * Standard Deviation)

Given that the mean is 150 and the standard deviation is 10, and the person's score is 1.5 standard deviations below the mean, we can substitute these values into the formula:

Actual Score = 150 - (1.5 * 10)

Actual Score = 150 - 15

Actual Score = 135

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Answer:

r ≈ 3.82

Step-by-step explanation:

Using the formula:

C = \(2\pi r\)

We rearrange to get r as the subject:

r = \(\frac{C}{2\pi }\)

r = 24÷(2×\(\pi\))

r ≈ 3.82

The graph of the equation or inequality 2y – 4x < 8 is given the in the attachment.

The term inequality refers to a mathematical expression with unequal sides. An inequality compares two values and determines whether one is less, greater, or equal to the value on the other side of the equation. In general, inequality equations are represented by five inequality symbols.

The inequality symbols are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠).

Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.

Given that:

2y – 4x < 8

2y < 4x +8

y < 2x + 4

Plot this on graph.

Thus, y < 2x + 4 is inequality to be plotted on the graph.

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Answer: 3

Step-by-step explanation: 345

For the sample given if the confidence level for both surveys is 95% (z*-value 1.96), then the statement that is true is -

Option A: The margin of error for the Camp Verde survey is larger than the margin of error for the Gilbert survey.

What is a sample?

A sample is characterised as a more manageable and compact version of a bigger group. A smaller population that possesses the traits of a bigger group. When the population size is too big to include all participants or observations in the test, a sample is utilised in statistical analysis.

Since we know the sample size, the sample proportion, and the desired confidence level, we can calculate the margin of error for each survey.

For the Gilbert survey -

Margin of error = z*(√(p*(1-p)/n))

where -

z* is the z-value corresponding to the desired confidence level (1.96 for 95% confidence)

p is the sample proportion (0.15)

n is the sample size (300)

Plugging in the values, we get -

Margin of error = 1.96 × √(0.15 * 0.85 / 300) ≈ 0.034

So we can say with 95% confidence that the true proportion of Gilbert residents who want Arizona to start using daylight savings is between 0.15 - 0.034 = 0.116 and 0.15 + 0.034 = 0.184.

For the Camp Verde survey -

Margin of error = z*(√(p*(1-p)/n))

where -

z* is the z-value corresponding to the desired confidence level (1.96 for 95% confidence)

p is the sample proportion (0.15)

n is the sample size (100)

Plugging in the values, we get -

Margin of error = 1.96 × √(0.15 * 0.85 / 100) ≈ 0.07

So we can say with 95% confidence that the true proportion of Camp Verde residents who want Arizona to start using daylight savings is between 0.15 - 0.07 = 0.08 and 0.15 + 0.07 = 0.22.

Therefore, the correct statement is -

Option A: The margin of error for the Camp Verde survey is larger than the margin of error for the Gilbert survey.

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For the given Rayleigh distribution with \(f(x)= 2axe^{-ax^{2} }\) , the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

the Rayleigh distribution is characterized by a probability density function (PDF) of the form \(f(x)= 2axe^{-ax^{2} }\), where a > 0. This distribution is used to model the magnitude of a two-dimensional vector whose components are independently and identically distributed Gaussian random variables.

For the Rayleigh distribution with the PDF \(f(x)= 2axe^{-ax^{2} }\) , the expected value (mean) is E[X] = sqrt(pi/(4a)), and the variance is :

Var[X] = (2 - pi/2a²).

Now, let's explain the answer in detail. To find the expected value, we integrate the product of the random variable X and its PDF over the range of possible values:

\(E[x] = \int\limits {(0 to a)x* 2axe^{-ax^{2} }} \, dx\)

By substituting u = -ax², du = -2ax dx, the integral becomes:

E[X] = ∫(0 to ∞) -ueⁿ du

Using integration by parts, we have:

E[X] = [-ueⁿ] - ∫(-eⁿ du)

= \([-xe^{-ax^{2}](0 to a) - \int\limits {0 to a}e^{-ax^{2} }\, dx }\)

The first term evaluates to 0 at both limits. The second term can be rewritten as:

E[X] = ∫(0 to ∞) e⁻ᵃˣ² dx

= √(π/4a) (by evaluating the Gaussian integral)

Thus, the expected value of X is E[X] = sqrt(pi/(4a)).

Next, to find the variance, we use the formula Var[X] = E[X²] - (E[X])². First, we calculate E[X²]:

E[X²] = ∫(0 to ∞) x² * 2axe⁻ᵃˣ²) dx

= ∫(0 to ∞) -x * d(e^(-ax²))

= [-x * e^(-ax²)](0 to ∞) + ∫(0 to ∞) e⁽⁻ᵃˣ²⁾ dx

The first term evaluates to 0 at both limits. The second term is the same as the integral calculated for E[X]. Hence:

= √(π/4a)

Substituting the values into the variance formula:

Var[X] = E[X^2] - (E[X])^2

= (√(π/4a)) - (sqrt(pi/(4a)))²

= (2 - π/(2a²))

Thus, the variance of X is Var[X] = (2 - π/(2a^2)).

Therefore, for the given Rayleigh distribution with f(x) = 2axe⁽⁻ᵃˣ²⁾,

the expected value is E[X] = sqrt(pi/(4a)), and the variance is Var[X] = (2 - π/(2a²)).

Complete Question:

A random variable X has a Rayleigh distribution if its probability density is given by f(x) = 2oxe or for x > 0, where a > 0. Show that for this distribution 1. Al l vandle has a Rayleigh distribution if its probability density i f(x) = 2axe-ar' for I > 0, where a > 0. Show that for this distribution a) The expected value is b) The variance is o? = (1-5)

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