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Ryan checked out 3 books from the library: one mystery (M), one history book (H), and one biography (B). Which tree diagram shows all the possible orders in which Ryan can read the 3 books?





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The value of the investment at the end of 10 years would be $3,905.76 if the interest rate is 5% per year and compounds annually.

The value of an investment after a certain number of years depends on several factors, including the initial amount invested, the interest rate, and the compounding frequency.

Assuming a fixed interest rate and compounding frequency, we can use the formula for compound interest to calculate the value of the investment after 10 years.

For example, if the interest rate is 5% per year and the investment compounds annually, the formula would be:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times interest is compounded per year

t = the number of years

Plugging in the given values, we get:

A = 2400(1 + 0.05/1)^(1*10)

A = 2400(1.05)^10

A = 2400(1.6289)

A = $3,905.76

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Step-by-step explanation:

If you take the sides you already have, 2, 7, 4, and 3, and add them together, you get 16. Lets take the portion of the perimeter you already have, and lets say this figure is a rectangle.

Divide 16 by 2 to give two sides of the rectangle a portion of the perimeter.
Since the area of a rectangle is width times height, lets create a formula:

8x = 44, 44 being the area, and 8x being the width times the variable of the height.

You get 5.5. for the height of the rectangle.

Add 8+8 to 5.5+5.5
you get 27

The standard form of a quadratic function is:

`f(x) = ax^2 + bx + c`

If the zeros of the function are 3 and 1/2, then the factors of the function are:

`(x - 3)` and `(x - 1/2)`

To find the quadratic function using these factors, you can first multiply them together:

`(x - 3)(x - 1/2) = x^2 - 7/2x + 3/2`

Now we have:

`f(x) = x^2 - 7/2x + 3/2`

This is the quadratic function in standard form that has zeros of 3 and 1/2.

Answer: 27.50

Step-by-step explanation: 2.50 X 7 =17.50 + 10 = 27.50

We may conclude after answering the presented question that rectangle Therefore, the expression for the width of the porch is x + 2 feet.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

area of a rectangle

Area = length x width

To do this, we can factor the expression for the area, which gives us:

x² + 9x + 14 = (x + 2)(x + 7)

Area = length x width

(x + 2)(x + 7) = (x + 7) x width

x + 2 = width

Therefore, the expression for the width of the porch is x + 2 feet.

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Answer:

275

Step-by-step explanation:

You have a 1 in 2 chance

550/2

275 times

Answer:

Step-by-step explanation:

minor, semi, minor, major   (in that order)

minor is smaller than a semi-circle while major is larger than a semi-circle.

The smallest font size that Doug should use in the text on his slides is 24 points.

The reason for this is that smaller font sizes can make the text difficult to read, especially from a distance.

According to industry standards, the recommended minimum font size for slide presentations is 24 points.

This is because smaller font sizes can be challenging to read, especially if the audience is sitting at the back of the room or if the slides are being viewed on a small screen.

While 20 points may seem like a reasonable font size, it's still small enough to make it difficult for some people to read the text.

Therefore, to ensure that all members of the audience can read the text on the slides, it's best to use a font size of at least 24 points.

In addition to using a larger font size, it's also essential to use a clear and legible font.

Sans-serif fonts such as Arial, Helvetica, or Calibri are recommended for presentations as they are easy to read, even from a distance.

It's also important to keep the contrast between the text and the background high to make it easier to read the text.

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Answer:

the whole is always 180 so take away the x and y and add up the remaining problems and whatever is left after that is your answer.

Step-by-step explanation:

Answer:

i don't know i haven't done integers in a long time

Step-by-step explanation:

When they are 111 miles apart, the current time is 4:10 p.m.

If the time taken for two trains to be apart by 111 miles by "t" time.

Then at that time, t, the train which is at 82 mph, should have traveled a distance of 82T miles.

d1 = 82t

At the same time, t, the train which is at 66 mph, should have traveled a distance of 66T miles.

d2= 66t

The total distance traveled by both trains is d1 + d2 = D

D = 82t + 66t

D = 148t

From the given data, D = 111

Hence, 148t = 111

Solving the equation, the time t

t = 111÷148

t = 0.75

Converting it into minutes,

t = 0.75*60

t = 45 mins.

The current time ( T ) = the time at which both the trains left ( t1 ) + 45 mins.

T = t1+t

T = 3:25 + 45 min.

T =4:10 pm

Therefore, the current time is 4:10 p.m

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The complete question is-

At 3:25 p.m., two trains left Kalamazoo, Michigan. one train traveled westward at a constant rate of 82 miles per hour, while the other traveled eastward at a constant rate of 66 miles per hour. if they are now 111 miles apart, what time is it now? show your work on how you solved this situation.

Marissa will need 4 cups of olive oil for a recipe. If olive oil costs two dollars per cup, she will need 4 x 2 = 8 dollars to buy the olive oil.

To make a recipe, Marissa needs 4 cups of olive oil. At a cost of $2 per cup, she would need to spend a total of 4 x $2 = $8 to buy the necessary amount of olive oil. This is a straightforward multiplication problem where the quantity of olive oil required is multiplied by the cost per cup. By using the multiplication operator, we can find the total cost needed to purchase the olive oil. Therefore, the total cost of the olive oil is directly proportional to the quantity of olive oil needed, with the cost per unit remaining constant at $2 per cup.

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To calculate the number of different special pizzas possible with any 6 toppings out of 16, we can use the combination formula:C(16,6) = 16! / (6! * (16-6)!) = (161514131211) / (654321) = 8008

there are 8,008 different special pizzas possible with any 6 toppings out of 16.

To calculate the number of different special pizzas possible with any 6 toppings out of 16, we need to use the combination formula, which is given by:

C(n, k) = n! / (k! * (n - k)!)

where n is the total number of items to choose from, and k is the number of items we want to choose.

In this case, n = 16 (the total number of toppings available), and k = 6 (the number of toppings we want to choose).

Plugging these values into the formula, we get:

C(16, 6) = 16! / (6! * (16 - 6)!)

= (16 * 15 * 14 * 13 * 12 * 11) / (6 * 5 * 4 * 3 * 2 * 1)

= 8008

Therefore, there are 8,008 different special pizzas possible with any 6 toppings out of 16.

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Step-by-step explanation:

[tex]volume = {x}^{3 \\} \\ so \: 1000000 = {x}^{3 \\} \\ x = \sqrt[3]{1000000} \\ x = 100[/tex]

Answer:

Step-by-step explanation:

4x - 5y = -17

-4x - 24y = -244

-29y = -261

y = 9

x + 54 = 61

x = 7

(9,7) Option B

Larger the value of r² (R²) imply that the observations are more closely grouped about the least squares line (regression line) option C.

The dependent variables on the y-axis and the independent variables on the x-axis are shown as a linear connection by a regression line. By examining the data pattern the variables' effects have created, the correlation is established.

As the (R2) is large therefore, the model is a good fit or bounded close to  regression line least squares line (regression line).

In a regression graph, the regression line that is closest to the data points is shown. By changing the value of x in the regression equation, this statistical tool helps study how a dependant variable y behaves when the independent variable x changes.

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Complete question:

Larger values of r2 (R2) imply that the observations are more closely grouped about the

Group of answer choices:

The longest side of a triangle with angles of 50°, 60°, and 70° and a length of 9 furlongs on the shortest side is approximately 12.2 furlongs.

             The Law of Cosines is used to find the remaining parts of an oblique (non-right) triangle when either the lengths of two sides and the measure of the included angle are known (SAS) or the lengths of the three sides (SSS) are known.

         To calculate this, using the Law of Cosines formula,

  which is:

                [tex]c^2 = a^2 + b^2 - 2abcosC[/tex]

where c is the longest side, a is the shortest side, b is the other side of the triangle, and C is the angle

between a and b.

In this case, c = 12.2 furlongs,

                    a = 9 furlongs,

                    b is the side opposite the angle 70°, and C = 70°.

So the formula becomes:

        [tex]c^2 = 92 + b^2 - 2(9)(b)cos70^{o}[/tex]

Solving for b gives us b = 12.2 furlongs, which is the length of the longest side.

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Answer:

KN bisects <K calculate MN

Using area of the rectangle, we can find that the new flower garden will be 13m in length (greater dimension).

The formula for calculating a rectangle's area can be used to determine how much space the rectangle takes up within its perimeter. Multiplying the length by the width yields the area of a rectangle (breadth).

As a result, the following formula can be used to determine the area of a rectangle whose length and breadth are "l" and "w," respectively. The rectangle's area is L × W. A rectangle's area is therefore equal to length * width.

Now here the dimensions of the rectangle are, l = 13m and b, = 9m.

Area of the rectangle is 13 × 9 = 117m².

Now the area of the rectangle is increased to 221m².

So, when we increase the length from 13 m to 17m and the breadth from 9m to 13m, we get area = 17 × 13 = 221m².

Therefore, length of the new garden will be 17m long.

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There are 720 ways the first three positions of the order of finish can occur assuming no ties in a race with 10 horses.

To calculate the number of ways the first three positions can occur, we use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we are choosing.

In this case, we have 10 horses and we want to choose the first three positions, so we get:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 x 9 x 8) / (3 x 2 x 1) = 720

Therefore, there are 720 ways the first three positions of the order of finish can occur assuming no ties.

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The z-score for a raw score of 12 in a distribution with a mean of 6 and a standard deviation of 3 is 2.

The z-score is a measure of how many standard deviations a raw score is above or below the mean of a distribution. It is calculated by subtracting the mean from the raw score and then dividing the result by the standard deviation.

In this case, we have a mean of 6 and a standard deviation of 3. To find the z-score for a raw score of 12, we can use the formula:

z = (x - μ) / σ

where x is the raw score, μ is the mean, and σ is the standard deviation.

Substituting the values we have, we get:

z = (12 - 6) / 3 = 2

Therefore, the z-score for a raw score of 12 in this distribution is 2. This means that the raw score of 12 is 2 standard deviations above the mean of 6. The z-score can be used to compare scores from different distributions, and to calculate probabilities and percentiles.

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Therefore, based on this collection of data during a significance level of 0.05, there is insufficient proof to draw the conclusion that the average annual precipitation in the Amazonian rain forest is less than 200 cm.

Hypothesis The amount of pleasure increases with daily solar exposure. The presumed reason in this case and the factor that is independent is sun exposure. The expected impact, or dependent variable, is the degree of happiness.

To determine if the data provide sufficient that the annual rainfall in the Amazon rainforest is different than 200 cm, we can perform a hypothesis test with the following hypotheses:

Null hypothesis: The true mean annual rainfall in the Amazon rainforest is equal to 200 cm.

Alternative hypothesis: The true mean annual rainfall in the Amazon rainforest is different than 200 cm.

We can use a two-sided t-test with a significance level of 0.05 to test this hypothesis.

We must first determine the population mean and standard variation.

x = (188 + 232 + 210 + 198 + 202 + 193 + 219 + 202 + 252 + 156 + 184 + 222)/12 = 202.17 cm

Sample standard deviation, s = 26.770 cm

Next, we can calculate the t-statistic:

t = (x - μ) / (s / sqrt(n)) = (202.17 - 200) / (26.770 / sqrt(12)) = 0.491

Using a t-distribution table with 11 degrees of freedom (n-1), at a significance level of 0.05, we find the critical values to be ±2.201. Since the calculated t-statistic of 0.491 is within the range of -2.201 to 2.201, we fail to reject the null hypothesis.

Therefore, there is not sufficient evidence to conclude that the annual rainfall in the Amazon rainforest is different than 200 cm based on this sample data at a significance level of 0.05.

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The expression "p(8 or less than 7)" suggests that we are looking for the probability of an event that satisfies one of two conditions: either the outcome is 8 or the outcome is less than 7. However, we need to know the specific probability distribution or situation in which this function p is being used to calculate a meaningful answer.

For example, if p represents the probability of rolling a certain number on a fair six-sided die, then p(8 or less than 7) would be 0, because 8 is not a possible outcome and all outcomes less than 7 are equally likely. However, if p represents the probability of a certain event occurring in a particular situation, then we would need more information about the nature of the event to calculate the probability.

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The height of the office building is 187.5 feet.

It is typically measured horizontally along the X-axis. Height is defined as the distance between the bottom and top of an object. In Geometry, it is sometimes referred to as altitude.

Let's call the office building's height h. We can use a proportion to find h:

height of office building / length of shadow cast by office building = height of tree / length of shadow cast by tree

h / 15 = 5 / (2/5)

The right side of the equation can be simplified as follows:

5/(2/5) = 5 * 5/2 = 12.5

When we plug this into the proportion and solve for h, we get:

h / 15 = 5 / (2/5)

h / 15 = 12.5 \sh = 15 * 12.5 \sh = 187.5

As a result, the office building's height is 187.5 feet.

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The enthalpy change of each step in the cycle must be added together to obtain the enthalpy of formation of the desired compound.

The enthalpy of formation of a compound that cannot be synthesized directly from the constituent elements can be calculated using the Hess's Law. Hess's Law states that the enthalpy change of a reaction is independent of the route taken from reactants to products. This law allows for the enthalpy of formation of a compound to be determined by summing the enthalpy changes of a series of known reactions, referred to as a ‘thermochemical cycle’, which lead to the compound of interest. To use this law, the enthalpy of formation of the intermediate species formed during the reaction must be known.

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The surface area of this rectangular prism is equal to 68 mm².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

SA = 2(WH + LW + LH)

Where:

By substituting the given parameters into the formula for the surface area of a rectangular prism, we have the following;

SA = 2(1 × 4 + 6 × 1 + 6 × 4)

SA = 2(4 + 6 + 24)

SA = 2(34)

SA = 68 mm².

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Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

Using Pythagorean theorem, the perimeter of the plot of land is 1783/16 feet.

What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental mathematical concept that outlines the relationship between a right triangle's three sides. It states that the square of the hypotenuse's (triangle's longest side) length equals the sum of the squares of the other two sides (the legs).

The Pythagorean theorem can be expressed numerically as follows:

a² + b² = c²

Let x= length of the shorter leg. Then, using the given ratio, the length of the hypotenuse can be expressed as 16x/65.

By the Pythagorean theorem, we have:

x² + 189² = (16x/65)²

Simplifying this equation, we get:

4225x² + 189² * 65² = 16² * x²

Solving for x, we get:

x = 315/4

Therefore, the perimeter is

189 + 315/4 + √(189² + (16/65)² * 315²/16)

Simplifying this expression, we get:

189 + 315/4 + 243/4 = 207/4 + √(2134441/256)

207/4 + 1463/16 = 1783/16

Therefore, the perimeter of the plot of land will be  1783/16 feet.

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