Convert 3x - 5y = 30 into Slope-Intercept Form

1) y = -3x - 6

2) y = -3x + 5y + 30

3) y = 3/5x - 6

4) y = 5/3x - 6

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

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Answer:

Step-by-step explanation:

49

The measure of arc BC is 720 times the measure of angle BAC.

Given that AC is the diameter of the circle and AB is a chord with a length of 16 units, we need to find BC (the length of the other chord) and mBC (the measure of angle BAC).

To find BC, we can use the property of chords in a circle. If two chords intersect within a circle, the products of their segments are equal. In this case, since AB = BC = 16 units, the product of their segments will be:

AB * BC = AC * CE

16 * BC = 2 * r * CE (AC is the diameter, so its length is twice the radius)

Since the area of the circle is given as 289 square units, we can find the radius (r) using the formula for the area of a circle:

Area = π * r^2

289 = π * r^2

r^2 = 289 / π

r = √(289 / π)

Now, we can substitute the known values into the equation for the product of the segments:

16 * BC = 2 * √(289 / π) * CEBC = (√(289 / π) * CE) / 8

To find mBC, we can use the properties of angles in a circle. The angle subtended by an arc at the center of a circle is double the angle subtended by the same arc at any point on the circumference. Since AC is a diameter, angle BAC is a right angle. Therefore, mBC will be half the measure of the arc BC.

mBC = 0.5 * m(arc BC)

To find the measure of the arc BC, we need to find its length. The length of an arc is determined by the ratio of the arc angle to the total angle of the circle (360 degrees). Since mBC is half the arc angle, we can write:

arc BC = (mBC / 0.5) * 360

arc BC = 720 * mBC

Therefore, the length of the arc BC equals 720 times the length of the angle BAC.

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The example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

Statistical significance is a measure of whether your research findings are meaningful. It is concerned with whether a research result is due to chance or sampling variability. Where, practical significance is concerened with wheteher the result is useful in the real world.

Therefore, the example that illustrates the difference between statistical significance and practial significance is

In a survey arranged by school-authority of a district on participation in sports by school-going boys and girls, it is found that 60% of boys and 57% of girls participate in outdoor sports. Thus the survey shows a 3% difference between school-going boy-participants and girl-participants in outdoor sports. Now the point is how much significance this 3% difference has statistically as well as practically. Statistical significance of this 3% depends upon the size of data used in determining the percentage of boys and girls participate in sports. If a sufficiently big sample size is used then the difference is statistically significant, and if a very small sample size is used then the difference is statistically insignificant. Thus bigger the sample size more is the statistical significance of a computed figure.

On the other hand practical significance of this 3% difference arises if decision is made or action is taken or needs to be taken on the basis of this 3% difference. If cost permits, the authority may consider promoting girl students participation in sports in order to bring about more gender parity in outdoor sports. In this case the 3% difference though small, may be practically significant.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Answer:

3 goes with 8 and 5 goes with 2

Step-by-step explanation:

I hope this helps!

a) The expected number of people to die before their 71st birthday is given as follows: 128.

b) The probability that a 67 year old woman will live to her 68th birthday is given as follows: 0.8876 = 88.76%.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

0.025679 of the 70 year old men die, hence the expected number out of 5000 is given as follows:

0.025679 x 5000 = 128.

The probability for item b is given as follows:

0.016798/0.018925 = 0.8876 = 88.76%.

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Answer:

c

Step-by-step explanation:

Answer:

Line A

Step-by-step explanation:

Answer:

7.7 km

Explanation:

Use cosine rule as here given two sides and one angle.

Cosine rule states:

a² = b² + c² - 2bc cos(A)

While solving, treat a = 7.5 km as to that opposite angle is given of 68°

then b = missing side, c = 5.2 km, A = 68°

Applying rule:

7.5² = b² + 5.2² - 2(b)(5.2) cos(68)

56.25 = b² + 27.04 - 3.8959b

56.25 - 27.04 = b² - 3.8959b

b² - 3.8959b = 29.21

b² - 3.8959b - 29.21 = 0

apply quadratic equation, Here [a = 1, b = - 3.8959, c = -29.21]

\(\sf b = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{2a} \quad\:when \:\ ax^2 + bx + c = 0\)

\(\sf b = \dfrac{ -(-3.8959) \pm \sqrt{(-3.8959)^2 - 4(1)(-29.21)}}{2(1)}\)

\(\sf b = 7.69 291 \quad or \quad b = -3.797\)

\(\sf b = 7.7 \quad (rounded \ to \ nearest \ tenth)\)

As length cannot be negative. Hence the value of b is only 7.7 km

The answer is 7.7 km.

Let's apply the Cosine Law in this situation.

a² = b² + c² - 2bc cos(A)

Now, substitute the values based on the given diagram.

Here, using the Quadratic Equation, we can solve :

Answer:

2(3(8))+2(8)=64

Step-by-step explanation:

Here, w represents the width of the rectangle,

∵ length of the rectangle is 3 times the width of the rectangle,

So, length = 3w,

Since, the perimeter of a rectangle, P = 2(length + width)

= 2(w + 3w)

= 2w + 2(3w)

If P = 64 feet,

⇒ 2w +2(3w) = 64

⇒ 2w + 6w = 64

⇒ 8w = 64

⇒ w = 8

Verification :

P = 2(8) + 2((3(8)) = 16 + 48 = 64 feet

Hence, the first step that should be taken to verify that the width of the rectangle is 8 is 2(3(8))+2(8)=64

Note : a solution obtain from an equation is verified by substituting the value in the equation.

Answer:

im sorry this doesn't help but its not d

Step-by-step explanatio

Given:

Gretchen's gross annual salary = $97,300

The maximum amount of rent she can afford to pay per month can be found using the formula:

\(\text{Max amount of rent she can pay}=\frac{\text{\it{Gross annual salary}}}{\text{\it{Number of months in a year}}}\)

Applying the formula:

\(\text{Max amount of rent she can pay}=\dfrac{97300}{12}\)

                        \(= \ \$811\)

Hence, the maximum amount of rent she can afford to pay per month is $811

Answer: $811

A full circle is 360 degrees.

The arc length would be 48/360 of the full circumference.

12 x 48/360 = 576/360 = 1.6

Answer:

Step-by-step explanation:

Interior Angle to a Circle Theorem.

X° = 1/2 (130° + 142°)

x° = 1/2 (272°)

x° = 136°

Answer:

C

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The arrow is pointing to the right which means its greater than, and the circle is open so it doesn't include 4

It was likely that the person bought a tiny cup of coffee, which could have been regular or decaf, in section (a).

If two events "A" and "B" are such that the occurrence of either one of the two events before the occurrence of another event affects the event occurring later, the probability that event "A" will happen given that the event "B" has occurred is:

\($P(A \mid B)=\frac{P(A \cap B)}{P(B)}$$\)

a) The likelihood that the person bought a small cup, P(S) = 0.34

The likelihood that the person bought a cup of decaf coffee, P(D) = 0.40

b) If the selected individual purchased a small cup then the probability that he/she chose decaf coffee:

\($P(D \mid S) & =\frac{P(S \cap D)}{P(S)} \\\)

\($& =\frac{0.20}{0.34} \\\)

= 0.5882

If it is a tiny cup, the likelihood that someone bought a decaf coffee is 0.5882.

c) If we learn that the selected individual purchased decaf, the probability that small size was selected

\($P(S \mid D) & =\frac{P(S \cap D)}{P(D)} \\\)

= 0.20/0.40

= 0.5000

When compared to the equivalent unconditional probability of part(a),

It was likely that the person bought a tiny cup of coffee, which could have been regular or decaf, in section (a). If the coffee is decaf, there is a chance that the buyer only bought a little cup.

The complete question is:

The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport kiosk.

Consider randomly selecting such a coffee purchaser.

a. What is the probability that the individual purchased a small cup? A cup of decaf coffee?

b. We learn that the selected individual purchased a small cup. What now is the probability that he/she chose decaf coffee, and how would you interpret this probability?

c. If we learn that the selected individual purchased decaf, what now is the probability that a small size was selected, and how does this compare to the corresponding unconditional probability of (a)?

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Answer: C

Step-by-step explanation:

See attached image.

Answer:

{1,1,2,2,4,4,8,8}

Step-by-step explanation:

In Finding The Factor Of A Number You Need To Find A multiplication of Two Numbers That Gives The Product 8.

•So keeping this in mind you can make multiples of numbers which has an outcome of 8. So;

1×8=8 {So 1 is a factor of 8 and note that any number multiplied by 1 is the number itself}

2×4=8{Two multiplied by four is going to give you 8 that's why it's a factor of 8}

3×?=8{There is no number which can be multiplied by 3 which has it's outcome as 8 so 3 isn't a factor}

4×2=8{4 multiplied by 2 is the same as 2 multiplied by 4 so you can see that when you multiply two numbers and it has it's product as 8 those two numbers that you multiplied to get the 8 is a factor of 8}

5×?=8{With the number 5 you can see that there is no number which can be multiplied by 5 which has its outcome as 8 so 5 is not a factor of 8}

6×?=8{With the number 6 you will not get any number which can be multiplied by 6 to give you 8 so 6 isn't a factor of 8}

7×?=8{With the number 7 too you won't get any number to be multiplied by 7 which is going to give you 8 that's why it isn't a factor of 8}

8×1=8{With the number 8 you can clearly see that when 8 is multiplied by 1 the product is 8 so that makes it its factor}

After finding the multiplication of Two Numbers that are going to give you 8, you can conclude that you have found the factors of 8 and note that any number above 8 can't be a factor of 8.

So we can conclude that the Factors of 8 are;

{1,2,4,8}

The 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B is (0.027, 0.173). Treatment A appears to be more effective than Treatment B.

To find the 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B, we can use the formula:

CI = (p₁ - p₂) ± z * SE

where:

p₁ is the proportion of patients who survived in Treatment A

p₂ is the proportion of patients who survived in Treatment B

z is the z-score associated with the desired level of confidence (in this case, 95%)

SE is the standard error of the difference between two proportions, calculated as:

\(SE = \sqrt{p_1 \times \dfrac{(1-p_1)}{n_1} + p_2 \times \dfrac{(1-p_2)}{n_2}}\)

where n₁ and n₂ are the sample sizes for Treatment A and Treatment B, respectively.

Using the given proportions, we have:

p₁ = (0.8 + 0.6 + 0.4)/3 = 0.6

p₂ = (0.7 + 0.5 + 0.3)/3 = 0.5

n₁ = n₂ = 3

Plugging these values into the formula, we get:

SE = √((0.6 * 0.4)/3 + (0.5 * 0.5)/3) = 0.1768

z = 1.96 (for a 95% confidence level)

CI = (0.6 - 0.5) ± 1.96 * 0.1768 = (0.027, 0.173)

A possible conclusion based on this interval is that the true difference in proportions of patients who survived between Treatment A and Treatment B lies somewhere between 0.027 and 0.173, with 95% confidence. Since the interval does not include 0, we can conclude that there is a statistically significant difference in the proportions of patients who survived between the two treatments. Specifically, Treatment A appears to be more effective than Treatment B.

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--The complete question is, A medical study looked at the effectiveness of two different treatments for a certain disease. The study summarized the data by banding patients by age group and reporting the proportion of patients in each band who survived over a ten-year period. The proportions for the two treatments are as follows:

Treatment A:

Proportion survived in band 1: 0.8

Proportion survived in band 2: 0.6

Proportion survived in band 3: 0.4

Treatment B:

Proportion survived in band 1: 0.7

Proportion survived in band 2: 0.5

Proportion survived in band 3: 0.3

Assuming normal-based inference is appropriate, what is the 95% confidence interval for the difference in proportions of patients who survived between Treatment A and Treatment B, based on the given data? Based on this interval, what is a possible conclusion about the true difference in proportions?--

Step-by-step explanation:

3 is missinh to make this question true

3×(4+9)

Answer:

27.83

The 3 is repeating

Step-by-step explanation:

Answer:

13.08

Step-by-step explanation:

Step 1: find the sum of all numbers

= 104.65

Step 2: divide by how many values there are

=8

Step 3: solve

104.65 ÷ 8 = 13.08125....

Step 4: round to the hundredths place

= about 13.08

Answer:

15

Step-by-step explanation:

Answer:

Step-by-step explanation:

f ( x ) = 3 x ^ { 3 } - 5 x ^ { 2 } + x - 2 g ( x ) = x + 2

Subtract 3x³ from each sides.

-5x^{2}+x-2gx=x+2-3x^{3}

Add 5x² to both sides.

x-2gx=x+2-3x^{3}+5x^{2}

Subtract x from both sides.

-2gx=x+2-3x^{3}+5x^{2}-x

Combine x and -x to get 0.

-2gx=2-3x^{3}+5x^{2}

The equation is in standard form.

\left(-2x\right)g=2+5x^{2}-3x^{3}

Divide both sides by -2x.

\frac{\left(-2x\right)g}{-2x}=\frac{2+5x^{2}-3x^{3}}{-2x}

Dividing bu -2x undoes the multiplication by -2x.

g=\frac{2+5x^{2}-3x^{3}}{-2x}

Divide 2-3x³ +5x² by -2x.

g=\frac{3x^{2}}{2}-\frac{5x}{2}-\frac{1}{x}

3 / 0.8 = z / 5.6

To find z, we need to isolate z. How can we do this? Right now, we know z / 5.6 is equal to 3 / 0.8.

This will cancel the divide by 5.6 or the 1/5.6 on the right side to isolate z!

(3 × 5.6) / 0.8 = z

16.8 / 0.8 = z

All we have to is simplify!

z = 21

Answer:

Step-by-step explanation:

There are sixty minutes in an hour, so Ahmed can type 1920/60 words in a minute, or 32 words in a minute.

The location of point B'' on the graph after the transformations is (8, 9)

The coordinates of the triangle are given as:

A = (1, 1)

B = (3, 2)

C = (3, 1)

First, the triangle is dilated by a factor of 3 across the origin.

This is represented as:

B' (x, y) = B(x, y) * 3

So, we have:

B' (x, y) = B(3, 2) * 3

Evaluate the product

B' (x, y) = B(9, 6)

The vector is given as:

<-1, 3>

This represents a translation, and the translation rule is

B'' (x, y) = B(x - 1, y + 3)

So, we have:

B'' (x, y) = (9 - 1, 6 + 3)

Evaluate the sum and the difference

B'' (x, y) = (8, 9)

Hence, the location of point B'' on the graph after the transformations is (8, 9)

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