The sides of the triangle are (x + 2), (x + 3), and (x + 4). Find the perimeter of the triangle.

Answer:

2 is the correct answer

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The required value of P(A ∩ B ∩ C) is 0.045, which is determined by conditional probability.

Given the provided probabilities:

P(A) = 0.3

P(B | A) = 0.75

P(C | A ∩ B) = 0.20

To find P(A ∩ B ∩ C), we can use the formula for conditional probability:

P(A ∩ B ∩ C) = P(C | A ∩ B) * P(B | A) * P(A)

Substituting these values into the formula, we get:

P(A ∩ B ∩ C) = 0.20 * 0.75 * 0.3

P(A ∩ B ∩ C) = 0.045

Therefore, P(A ∩ B ∩ C) is equal to 0.045.

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The complete question is as follows:

Pollution of the rivers in the United States has been a problem for many years. Consider the following events: A: the river is polluted, B: a sample of water tested detects pollution, C : fishing is permitted.

Assume P(A) = 0.3, P(B|A) = 0.75, P(B|A’) = 0.20, P(C|A∩B) = 0.20.

Find P(A ∩B ∩C).

Answer:

No solutions

Step-by-step explanation:

I graphed the equations and the lines overlap, so no solution.

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The height of the nearby lemon tree is 8 feet using the property of similar triangles.

Triangles that are similar to one another in shape but differ in size are called similar triangles. Their respective sides are proportional to one another, and their corresponding angles are equal. The ratio of the corresponding sides of two triangles that are comparable is constant across all pairs of corresponding sides. Problems involving unknown lengths or heights in comparable forms can be resolved using this attribute.

The given situation represent two proportional triangles.

We know that the ratio of lengths of similar triangles are equal thus,

height of plum tree / length of plum tree's shadow = height of lemon tree / length of lemon tree's shadow

Substituting the values we have:

12 / 9 = height of lemon tree / 6

Using cross multiplication:

height of lemon tree = 12 * 6 / 9 = 8 feet

Hence, the height of the nearby lemon tree is 8 feet using the property of similar triangles.

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Answer:

perseveration

Step-by-step explanation:

The term you are looking for is "perseveration."

Answer:1533

Step-by-step explanation:

7006-5,479=1533

The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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The total number of campers surveyed is 150.

The symbol for percentage is "%". Percentages are commonly used in a wide range of contexts, such as in finance, statistics, and everyday life.

We can use the information provided about the percentage of campers in each time interval to set up an equation to solve for the total number of campers surveyed.

Let n be the total number of campers surveyed. Then:

15% of n spend more than 3 hours reading daily.

10% of n spend between 2 and 3 hours reading daily.

35% of n spend less than 1 hour reading daily.

40% of n spend between 1 and 2 hours reading daily.

We know that 60 campers spend between 1 and 2 hours reading daily, which represents 40% of the total number of campers surveyed. So we can set up the following equation:

0.4n = 60

Solving for n, we get:

n = 60 / 0.4 = 150

Therefore, the total number of campers surveyed is 150.

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To determine the number of high fives that will be exchanged, we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person .

To calculate the number of unique pairs, we can use the formula for combinations, which is nC2, where n is the number of people .So, for Ronnie's class with 20 people, the number of high fives exchanged is:20C2 = (20 * 19) / (2 * 1) = 190.Therefore, a total of 190 high fives will be exchanged in Ronnie's class on National High Five Day. we need to find the total number of unique pairs of students in Ronnie's class Since there are 20 people in the class, each person needs to give a high five to every other person, excluding themselves.

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Answer: To solve this question, you would first measure yourself and your self and your shadow, and then the shadow of the tower while the sun is in spot in the sky, you will then use the ratio (your height/your shadow) = (towers height/ towers shadow)

You will then cross multiply and divide to find the towers height

Step-by-step explanation:

let convert to decimal

From the smallest ot the largest

In the special case of two degrees of freedom, the chi-squared distribution does not coincide with the exponential distribution. The chi-squared distribution is a continuous probability distribution that arises in statistics and is used in hypothesis testing and confidence interval construction. It is defined by its degrees of freedom parameter, which determines its shape.

On the other hand, the exponential distribution is also a continuous probability distribution commonly used to model the time between events in a Poisson process. It is characterized by a single parameter, the rate parameter, which determines the distribution's shape.

While both distributions are continuous and frequently used in statistical analysis, they have distinct properties and do not coincide, even in the case of two degrees of freedom. The chi-squared distribution is skewed to the right and can take on non-negative values, while the exponential distribution is skewed to the right and only takes on positive values.

The chi-squared distribution is typically used in contexts such as goodness-of-fit tests, while the exponential distribution is used to model waiting times or durations until an event occurs. It is important to understand the specific characteristics and applications of each distribution to appropriately utilize them in statistical analyses.

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Answer:

\(x=\sqrt{23}\)

Step-by-step explanation:

So the eqaution for the hypotonuse is \(a^{2}+b^{2} =c^{2}\)

Therefore...

\(\sqrt{16} +\sqrt{x^{2} }=\sqrt{27}\\ 4+x =\sqrt{27} \\x=\sqrt{23}\)

39 is separated into two parts 9 and 30

Step-by-step explanation:

The given is:

Separate 39 into two parts

4 times the smaller part exceeds the larger part by 6

Assume that the smaller part is x and the larger part is y

∵ 39 is separate into two parts x and y

∴ x + y = 39 ⇒ (1)

∵ x is the smaller part

∵ y is the larger part

∵ 4 times the smaller part exceeds the larger part by 6

- Multiply x by 4 and subtract y from it to get 6

∴ 4x - y = 6 ⇒ (2)

Now we have a system of equations to solve it

Add equations (1) and (2) to eliminate y

∵ (x + 4x) + (y - y) = (39 + 6)

∴ 5x = 45

- Divide both sides by 5

∴ x = 9

Substitute the value of x in equation (1) to find y

∴ 9 + y = 39

- Subtract 9 from both sides

∴ y = 30

∴ The smaller part is 9 and the larger part is 30

39 is separated into two parts 9 and 30

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

The answer is 4

Step-by-step explanation: I did the work and it works out like that I hope this helps

150 students scored between 42 and 56 on the district geometry test.

Box whisker plots are used to abstract a collection of data that has been approximated using an interval scale. Just a box plot is another name for it. They are mostly employed while interpreting data. It is one of the graphical approaches that shows how the dataset's data varies from one another. The histogram may be used to display the data as well. Yet a histogram offers a useful presentation. Box and whisker plots are preferable to histograms because they may exhibit numerous sets of data on a single graph, which adds more information.

From the box whisker plot we see that the lower quartile is 42 and the median is 56.

The median represents the 50th percentile whereas lower quartile is 75%.

The difference is:

75 - 50 = 25%.

Now, for 600 scores we have:

25% of 600

= 25/100 (600) = 150

Hence, 150 students scored between 42 and 56 on the district geometry test.

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A possible second point with a y-coordinate of 8 is equal to 5.

In Mathematics, the slope of a straight line can be calculated by using this this mathematical expression;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following slope and data points on the line:

Points on x-axis = (1, 2).

Points on y-axis = (_, 8).

Slope, m = 3/2

Substituting the given points into the slope formula, we have the following;

Slope, m = (y₂ - y₁)/(x₂ - x₁)

3/2 = (8 - 2)/(x₂ - 1)

3/2 = 6/(x₂ - 1)

Cross-multiplying, we have:

3(x₂ - 1) = 12

x₂ - 1 = 12/3

x₂ - 1 = 4

x₂ = 4 + 1

x₂ = 5

In conclusion, we can logically deduce that the second point (x₂) is 5.

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The equation represents a circle with the same radius as the circle shown but with a center at (-1, 1) is (x + 1)² + (y - 1)² = 16.

We know that, the center of a circle is (-1, 1).

We know that, the standard form for an equation of a circle is

(x - h)² + (y - k)² = r²

The (h, k) are co-ordinate of your Centre of circle, which in this case is (-1,1) and r is the radius of circle.

As we can see in the figure radius = 4units

From Centre (1,-2) to (1,-2)

Put these into the equation

(x + 1)² + (y - 1)² = 4²

(x + 1)² + (y - 1)² = 16

Therefore, option D is the correct answer.

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Answer:

Step-by-step explanation:

baskets times apples

47 times 35

=1645

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Hello,

Third degree and zeroes are -3, -1 and 2 so we can write the function as below, a being a real

\(a(x+3)(x+1)(x-2)\)

and we know that f(1)=7

so

a * 4 * 2 *(-1) = -8a=7

a = -7/8

Then

\(\dfrac{-7(x+3)(x+1)(x-2)}{8}\)

thanks

Using the Factor Theorem, the polynomial function is given by:

\(p(x) = -\frac{7}{8}(x^3 + 2x^2 - 5x - 6)\)

The Factor Theorem states that a polynomial function with roots \(x_1, x_2, ..., x_n\) is given by:

\(p(x) = a(x - x_1)(x - x_2)...(x - x_n)\)

In which a is the leading coefficient.

In this problem, the zeros are -3, -1 and 2, hence \(x_1 = -3, x_2 = -1, x_3 = 2\).

The function is given by:

\(p(x) = a(x - x_1)(x - x_2)...(x - x_n)\)

\(p(x) = a(x + 3)(x + 1)(x - 2)\)

\(p(x) = a(x^2 + 4x + 3)(x - 2)\)

\(p(x) = a(x^3 + 2x^2 - 5x - 6)\)

It passes through the point (1,7), which means that when \(x = 1, p = 7\), and this us used to find a.

\(7 = a(1 + 2 - 5 - 6)\)

\(-8a = 7\)

\(a = -\frac{7}{8}\)

Hence, the polynomial is:

\(p(x) = -\frac{7}{8}(x^3 + 2x^2 - 5x - 6)\)

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If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not reliable. So the option 4 is correct.

A set of standardized tests or subtests created to measure human intellect result in a total score known as an intelligence quotient (IQ). When an intelligence test was given, a person's mental age score was calculated. This score was then divided by their chronological age, which was also expressed in years and months. The resulting fraction (quotient), which yielded the IQ score, was multiplied by 100.

Test results that measure intelligence are estimates of intelligence.

A vast range of item material can be found on the many distinct IQ test types. There are both verbal and visual test items. Test questions can range from being grounded on abstract reasoning issues to focusing on math, language, or general knowledge.

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If you take an intelligence test three times within a week and get scores of 100, 75, and 125, the IQ test is probably not:

1. powerful.

2. accurate.

3. valid.

4. reliable.

The approximate volume of ice cream in the cone, rounded to two decimal places, is 16.36 cubic inches.

To calculate the approximate volume of ice cream in the cone, we can use the formula for the volume of a cone, which is given by V = (1/3) * π * r^2 * h, where V is the volume, π is a constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.

In this case, we are given that the diameter of the cone is 2.5 inches, so the radius can be calculated as half of the diameter, which is 1.25 inches. The height of the cone is given as 5 inches.

Substituting these values into the formula, we have V = (1/3) * 3.14159 * (1.25)^2 * 5.

Evaluating this expression, we find V ≈ 16.36 cubic inches.

Therefore, the approximate volume of ice cream in the cone, rounded to two decimal places, is 16.36 cubic inches

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A confidence interval is constructed to estimate the value of a parameter.

In statistics, a parameter refers to a numerical characteristic of a population, such as the population mean or population proportion. When we want to estimate the value of a parameter, we construct a confidence interval.

A confidence interval provides a range of values within which we believe the true parameter value is likely to fall, based on our sample data. It is constructed using sample statistics and takes into account the variability and uncertainty in the estimation process.

A confidence interval is constructed to estimate the value of a parameter, not a statistic.

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Answer:

I think the total number of combinations of 3 from 6 = 6C3 = 20

All possible combinations of 3 which have a product divisible by 3 must contain either a 3 or a 6.

So the number not divisible must be 3 combinations from the number 1, 2, 4, and 5.= which is 4

So the required probability is 20-4 ? 20 = 16/20 = 0.8 Answer

Hope this help you! :)

When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5.

The link between two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.

The definition an equation in algebra is a mathematical expression that indicates the equivalence of two mathematical terms. In equation 6x + 11 = 14, for instance, the two expressions 6x + 11 and 14 are separated by the symbol "equal."

When Merida divides her age by 3 and adds 5, the result is 9, now the equation becomes: 9 = (m + 3) ÷ 5, this represents the situation where m is Merida's age.

correct option: D

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Answer:

593775

Step-by-step explanation:

Answer:

6 1/2

Step-by-step explanation:

The difference between 13 9/20 and 6 7/8 can be found by converting both fractions to decimals and subtracting the two values.

13 9/20 can be expressed as a decimal as 13.45.

6 7/8 can be expressed as a decimal as 6.875.

So, the difference between 13 9/20 and 6 7/8 can be expressed as:

13.45 - 6.875 = 6.575

So the reasonable difference between 13 9/20 and 6 7/8 is 6.575.

Answer:

Volume of a cylinder=1/2πr^2h.

1/2×3.142×10^2×5.

1/2×3.142×100×5.

1/2×1571

=785.5

Answer:

About 1570.8

Step-by-step explanation:

Start by looking at the equation for solving a cylinder, which is V = π x r² x h. Since r = radius (5) and h = height (10), you add those numbers into the equation. Now you have to solve V = π x 5² x 10, which will get you your repeating decimal of 1570.79633...which then can be rounded your answer of 1570.8.

Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

Therefore the mass of the element is given by:

If the initial mass is 760 g and the final mass is 15 g, we have:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

Element X take 32.6 minutes to decay to 87 grams.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Element X decays radioactively with a half life of 15 minutes.

And, there are 400 grams of Element X.

Now, By the given information, we can formulate;

⇒ \(y = x (0.5)^{t/h}\)

Substitute all the values we get;

⇒ 400 = 87 × \((0.5)^{t/15}\)

⇒ 400 / 87 =  \((0.5)^{t/15}\)

⇒ 4.6 =  \((0.5)^{t/15}\)

Take log both side,

⇒ ln 4.6 = t/15 (ln 0.5)

⇒ 1.52 = t/15 x 0.7

⇒ t = 32.6 minutes

Thus, Element X take 32.6 minutes to decay to 87 grams.

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