If PQR is congruent TSR what are the congruent corresponding parts?

Twice a number decreased by four is less than 8 is x< 6.

2x - 4 < 8

2x < 8 + 4

2x < 12

x < 12 / 2

x < 6

Inequality refers to the unequal distribution of resources, opportunities, and outcomes among individuals or groups in a society. It can manifest in various forms, including economic inequality, social inequality, gender inequality, and racial inequality. Economic inequality refers to the unequal distribution of wealth and income, where some individuals or groups have access to more resources and opportunities than others.

Social inequality refers to the unequal distribution of social status and power, which can lead to marginalized groups being excluded from certain societal benefits. Gender and racial inequality refer to the unequal treatment and opportunities that certain genders or races face in society. Inequality can have negative consequences on individuals and society, including lower levels of social trust, reduced economic growth, and increased social tensions.

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Complete Question: -

Twice a number decreased by four is less than 8 is equation or inequality

There is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

Given that,

Over 62% of a newsletter publisher's subscribers, in their estimation, own a Rolls-Royce. A potential advertiser wants to verify this claim for marketing purposes. The advertiser decides to reject the null hypothesis following a test with a significance threshold of 0.02 after executing the analysis.

We have to find what is the verdict in relation to the publisher's assertion.

We know that,

First we have to write the null hypothesis and alternative hypothesis for the hypothesis test.

H₀:P=0.62

H₁:P>0.62

At 0.02 level of significance, rejecting H₀ then accepting H₁.

That is sufficient evidence that percentage over 62%.

Therefore, there is sufficient evidence at the 0.02 level of significance that the percentage is over 62% for hypothesis.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

I don't see the main question but this is the binomial expansion of the expression (4x-2y)^5

Answer:

below

Step-by-step explanation:

The answer of the first expert is correct, this is from Pascal triangle 5th level.

shown in the attached picture, when we extend the brackets the whole function will become...

f(x) = 1*(4x)⁵(-2y)⁰ + 5*(4x)⁴(-2y)¹ + 10*(4x)³(-2y)² + 10* (4x)²(-2y)³ + 5*(4x)¹(-2y)⁴ +   1*(4x)⁰(-2y)⁵

     = (4x - 2y)⁵

The proportion of scores below 12.5 in a normally distributed population with a mean of 10 and a standard deviation of 2 can be calculated using the Z-score and the standard normal distribution table. In this case, we need to find the area under the curve to the left of the value 12.5.

The Z-score is calculated as (X - μ) / σ, where X is the value we want to find the proportion for, μ is the mean, and σ is the standard deviation. Substituting the given values, we have (12.5 - 10) / 2 = 1.25.

Using the standard normal distribution table or a statistical calculator, we can find that the area to the left of a Z-score of 1.25 is approximately 0.8944. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

In a normal distribution, the Z-score measures the number of standard deviations a value is from the mean. By calculating the Z-score for the value 12.5, we can use the standard normal distribution table to find the proportion of scores below that value.

The table provides the cumulative probability up to a certain Z-score. In this case, the Z-score of 1.25 corresponds to a cumulative probability of approximately 0.8944.

Since the normal distribution is symmetric, the proportion of scores above 12.5 is equal to the proportion below the mean minus the proportion below 12.5.

Hence, subtracting 0.8944 from 1 (or 100%) gives us approximately 0.1056 or 10.56%. Therefore, the proportion of scores below 12.5 is approximately 89.44%.

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A theorem which is used to find the rational solutions of a polynomial equation is known as the rational root theorem.

A polynomial expression is given and after solving them we get the two values known as the roots of the function.

These are also known as the zeros of polynomial as after putting these values in the equation we get the result as 0 .

We should use the rational root theorem only when the value of coefficients are small.

The theorem states that each rational solution x = p ⁄ q, when on simplified satisfies the below mentioned points,

p is an integer factor of the constant term a0, and

q is an integer factor of the leading coefficient an.

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The position of -1 and > -1 it would be located on the right side of -1 on the number line

In the above question,

We need to indicate > -1 about the positions of and −1 on the number line

The horizontal straight lines in mathematics known as number line are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

So, if we look at the position of -1 and > -1 it would be located on the right side of -1 on the number line

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Answer:

see the attachment!

=============================================================

Explanation:

The best case scenario is that you get 3 of the same color in a row on the first three attempts. The lower bound is 3.

However, we have to consider the worst case scenario when we want to guarantee something like this, without looking at the candies we selected.

Consider the case of something like this sequence:

As you can see above, I've listed the colors in the order presented by your teacher. I pick one candy at a time. Once I reach yellow, I restart the cycle. In slots 1, 7 and 13, we have a black candy selected. This example shows that we must make 13 selections to guarantee that we get at least 3 candies of the same color (that color being black). The order of the candies selected doesn't matter. We could easily use any other color except yellow to do this example. The black candy just happened to be the first listed, so I went with that.

Note how we have 6 unique colors in the set {black, white, green, red, blue, yellow}. If we pick 2 candies of each color, then we've selected 6*2 = 12 candies so far. That 13th candy (some color other than yellow) is guaranteed to be a color we already selected; therefore, we'll be guaranteed to have 3 of the same color. We won't know what color it is but we will know we have a match like this.

For more information, check out the Pigeonhole Principle.

Answer:

There is no slope because the slope is zero. The line has no slope because it's a vertical line.

Step-by-step explanation:

Slope = \(\frac{2-2}{3.6-0} = \frac{0}{3.6} =0\)

Slope =  0

The line has no slope.

Answer: 6 candies

Step-by-step explanation:

So if the teacher buys 12 packs of 8 candies she will have 96 candies in total giving each of the 30 students 3 candies. That leaves her with 6 candies to enjoy by herself.

Answer:

12 + 8k² + k³ - 9k⁴

Step-by-step explanation:

(8 + k³ - 6k⁴) + (4 - 3k⁴ + 8k²)

8 + k³ - 6k⁴ + 4 - 3k⁴ + 8k²

(8 + 4) + (8k²) + (k³) + (-6k⁴ -3k⁴)

(12) + (8k²) + (k³) + (-9k⁴)

12 + 8k² + k³ - 9k⁴

Answer:

B: 375 ft^2

Step-by-step explanation:

20 x 15 + 10 x 15/2 = 375

The liters of milk  litres you can buy with $20 is mathematically given as

v=22.8571L

Question Parameter(s):

Suppose milk is selling for 87.5¢ per litre

Generally, the equation for the Volume of milk  is mathematically given as

1=87.5c

v=20,00c

Therefore

v=2,000/87.5

v=22.8571

In conclusion, volume of milk

v=22.8571L

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Answer:

25.40

Step-by-step explanation:

Answer:

25.40

Step-by-step explanation:

5 rounds up but 9 rounds up to ten so you add one to the tenths

He rented the pressure washer for 4 hours, given that the total bill was $86.

An algebraic expression is the combination of numbers and variables in expressing and solving a particular mathematical question. An equation is the equality of expressions.

Let x = total number of hours he rented the pressure washer

The total bill, which was $86, includes the flat fee of $50 plus $9 per hour of use.

Hence, the equation will be 50 + 9x = 86.

Solve for x.

50 + 9x = 86

9x = 86 - 50

9x = 36

x = 4

total number of hours he rented the pressure washer = 4

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For this problem, we are given the mean and standard deviation for the height of men. We need to calculate the minimum height to be considered in the top 10% of tallest men, and the maximum height to be considered in the shortest 15% of men.

The first step we need to solve this problem is to calculate the z-score. The z-score can be found by using the following expression:

For the first situation, we want a z-score for the top 10% of tallest men. This means that we need to go on the z-table and find the z-score that represents 90% of probability to the left because this will give us the minimum height to be at the 10% tallest. From the z-table we have:

Now we can use the z-score expression to find the value of x. We have:

The man should be at least 71.85 inches tall to be considered among the 10% of tallest men.

For the second situation, we have something similar. We need to find the maximum height for a man to be considered between the 15% of men. We need to go into the z-table and find the z-score that produces a result close to 0.15. We have:

Now we need to use the z-score expression to determine the height:

In order to be considered among the smallest men, someone needs to be 64.88 inches tall.

Without specific information about the data set, it is not possible to determine which equation is the best fit.

To determine the linear function equation that best fits the data set, we need more information about the data set itself. Without the data points or any other details, we cannot accurately determine which linear function equation is the best fit.

However, I can provide a general explanation of the four options:

y = -2x + 5: This is a linear equation with a negative slope of -2. It represents a line that decreases as x increases. The y-intercept is 5.

y = 2x + 5: This is a linear equation with a positive slope of 2. It represents a line that increases as x increases. The y-intercept is 5.

y = -1/2x + 5: This is a linear equation with a negative slope of -1/2. It represents a line that decreases at a slower rate as x increases. The y-intercept is 5.

y = 1/2x - 5: This is a linear equation with a positive slope of 1/2. It represents a line that increases at a slower rate as x increases. The y-intercept is -5.

Without specific information about the data set, it is not possible to determine which equation is the best fit. The best fit would depend on how well the equation aligns with the actual data points.

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Answer:

y = 50

Step-by-step explanation:

Firstly, let's make an equation. We know that when y is 15, x is 3. Or, in other words, y is 5 times what x is. Therefore we can use the equation, y = 5x.

Now, just plug x into the equation.

y = 5(10)

y = 50

Answer:

59/130

Step-by-step explanation:

The mood of the categorical syllogism in example 2 is AIO.

In your example, we have the following premises and conclusion:

1. Major Premise: No dogmatists are scholars who encourage free thinking.
2. Minor Premise: Some theologians are scholars who encourage free thinking.
3. Conclusion: Some theologians are not dogmatists.

The major premise in example 2 is an A proposition (All S are not P). The minor premise in example 2 is an I proposition (Some S are P). The conclusion in example 2 is an O proposition (Some S are not P).

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Answer:

4

Step-by-step explanation:

\(3b+12+5b=44 \\ \\ 8b+12=44 \\ \\ 8b=32 \\ \\ b=4\)

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

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The equation of the line would be y = (-3/4)x + 5.

What is the slope-point form of the line?

For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be

                      y - y1 = m(x - x1)

The given equation is \(y=-\frac{3}{4}x-17\)

The required line is parallel to the given line.

and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4

And the required line passes through (8, -1)

so by using slope - point form of the line,

      y - (-1) = (-3/4)(x - 8)

      y + 1 = (-3/4)x - (-3/4)8

       y + 1 = (-3/4)x + 24/4

       y = (-3/4)x + (12/2 - 1)

       y = (-3/4)x + 5

Hence, the equation of the line would be y = (-3/4)x + 5.

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The required solutions are:

a) The expression for the amount of water in the tank after t minutes is W(t) = 110 + 6t

b) At the instant the tank begins to overflow, there will still be 24 grams of salt in the tank.

(a) Let's denote the amount of water in the tank after t minutes as W(t). Initially, the tank contains 110 litres of water, and water is pumped into the tank at a rate of 9 litres per minute while being pumped out at a rate of 3 litres per minute.

Therefore, the expression for the amount of water in the tank after t minutes can be calculated as follows:

W(t) = Initial amount of water + (Rate of inflow - Rate of outflow) * t

W(t) = 110 + (9 - 3) * t

Simplifying further:

W(t) = 110 + 6t

(b) Let's denote the amount of salt in the tank after t minutes as x(t). Initially, there are 24 grams of salt in the tank. Brine containing 15 grams of salt per litre is pumped into the tank at a rate of 9 litres per minute. The well-mixed solution is pumped out at a rate of 3 litres per minute.

The rate of change of the amount of salt in the tank is given by the difference between the rate of inflow and the rate of outflow of salt.

Therefore, the differential equation for x(t) is:

dx/dt = (Rate of inflow of salt) - (Rate of outflow of salt)

dx/dt = (15 grams/litre * 9 litres/minute) - (x(t)/W(t) * 3 litres/minute)

Simplifying further:

dx/dt = 135 - (3/110) * x(t)

This is the differential equation for x(t).

Now, considering the scenario where the tank has a total capacity of 278 litres and it begins to overflow, we need to determine the amount of salt in the tank at that instant.

Since the tank is open and overflows, the amount of salt in the tank will remain constant at its maximum value, which is 24 grams. Therefore, the instant the tank begins to overflow, there will still be 24 grams of salt in the tank.

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Answer:

∠WXY = 107°

Step-by-step explanation:

In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°. ∠W and ∠WXY are adjacent, so they are supplementary. 180° - 73° = 107°.

Another way to do this is to know that there are 360° in a trapezoid. This is a right trapezoid, so two of the angles are 90°. One angle is 73°. 90° + 90° + 73° = 253°. 360° - 253° = 107°.

I hope this helps :))

The measure of angle WXY is,

= 107°

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Sides XY and WZ are parallel.

And, Angle W is 73 degrees and angles Y and Z are right angles.

Now, In a trapezoid, adjacent angles are supplementary, meaning they add up to 180°.

Here, ∠W and ∠WXY are adjacent, so they are supplementary.

Hence, We get;

The measure of angle WXY is,

= 180° - 73°

= 107°.

Thus, The measure of angle WXY is,

= 107°

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Answer:

The picture I attached will have the line already drawn for you.

Step-by-step explanation:

Answer:

Hope you have understood the sum

Answer: 5

Step-by-step explanation:

tan(32) = x/8

8 x tan(32) = x

x = 4.998 ≈ 5