Evaluate q2 + (r5 -10) if q = 5 and R = 2

To find the least common multiple (LCM) of 12 and 9, we can list their multiples and find the smallest multiple they have in common:

Multiples of 12: 12, 24, 36, 48, 60, ...

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...

We can see that the smallest multiple they have in common is 36. Therefore, the LCM of 12 and 9 is 36.

Alternatively, we can use the prime factorization method to find the LCM:

Prime factorization of 12: 2^2 x 3

Prime factorization of 9: 3^2

To find the LCM, we need to take the highest power of each prime factor that appears in either number. In this case, the highest power of 2 is 2^2, and the highest power of 3 is 3^2. Therefore, the LCM of 12 and 9 is 2^2 x 3^2 = 36.

Answer:

The least common multiple of 12 and 9 is 36.

Step-by-step explanation:

The multiples of 12 are: 12, 24, 36, 48, 60, ...

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, ...

The least common multiple is the smallest number that both lists share, which is 36.

The area of the walkaway is 216.66 feet squared.

The circular swimming pool has a diameter of 20 feet. A 3 foot tile walkaway is being installed around the pool.

Therefore, the area of the walkaway can be calculated as follows:

Hence,

area of the walkaway = area of the bigger circle - area of the smaller circle

area of the bigger circle = πr²

area of the bigger circle = 3.14 × 13²

area of the bigger circle  = 530.66

area of the smaller circle = πr²

area of the smaller circle  = 3.14 × 10²

area of the smaller circle = 314

area of the walkaway = 530.66 - 314  = 216.66 ft²

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Answer:

yes

Step-by-step explanation:

The answer to 3 divided by 8 can also be written as a mixed fraction as follows: 0 3/8 Note that the numerator in the fraction above is the remainder and the denominator is the divisor.

For the given following frequency table of values 351, 362, 373, 381, 391, The mode is likely to be the best measure of the center for the data set.

The given frequency table is as follows:

        Value frequency 351, 362, 373, 381, 391.

        To find the most appropriate measure of central tendency for a dataset, we need to analyze the spread of data.

The mean, median, and mode are measures of central tendency in statistics.

We can find the following measures from the given data set:

       Mean: It is calculated by summing up all the values and then dividing the result by the total number of values. This measure of central tendency is appropriate when the data are symmetrical.

      Median: It is the middle value of the data set when arranged in order. It is suitable for skewed data.

      Mode: It is the most common value in the data set. It is appropriate when data is discrete. The data in the frequency table appear to be discrete.

      Because the data are discrete, the most appropriate measure of central tendency is the mode. So, the mode is likely to be the best measure of the center for the given value frequency data set.

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Probability is a branch of mathematics that deals with the measurement of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event.

The events A and B are not independent.

To see this, note that the probability of A is given by:

[tex]P(A) = 1/2[/tex] , since there are 6 ways to get an odd sum[tex](1+2, 2+1, 3+4[/tex] ,   [tex]4+3, 5+6, 6+5)[/tex] out of a total of 12 possible outcomes when rolling two dice.

The probability of B is also 1/2, since there are 3 odd numbers on a standard die and 6 possible outcomes for the second die.

Now, to calculate P(A ∩ B), we need to find the probability that both events A and B occur simultaneously.

This happens when we roll an odd sum (which has a 1/2 probability) and then get an odd number on the second die (which has a 1/2 probability). Multiplying these probabilities together, we get:

[tex]P(A ∩ B) = (1/2) * (1/2) = 1/4[/tex]

Finally, we can check whether the events A and B are independent by comparing P(A ∩ B) to P(A)P(B):

[tex]P(A)P(B) = (1/2) * (1/2) = 1/4[/tex]

Therefore, Since [tex]P(A ∩ B) ≠ P(A)P(B)[/tex]  , we can conclude that the events A and B are not independent.

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Events A and B are not independent. Let A = {the sum of the dice is odd}, and let B = {the second die shows an odd number}.

what is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

The probability of two events A and B being independent is determined by whether the occurrence of one event affects the occurrence of the other. In the given problem, event A is the sum of two dice being odd, and event B is the second die showing an odd number.

The probability of A and B occurring separately can be calculated, as can the probability of A and B occurring together. While P(A ∩ B) = P(A) * P(B), the events are not independent since knowing that one event has occurred affects the probability of the other event.

If A occurs, the probability of B changes, and if B occurs, the probability of A changes.

No, because P(A∩B) = P({1,3,5})∩P({1,3,5}) = P({1,3,5}) = 1/2, and P(A)P(B) = (1/2) * (1/2) = 1/4, which are not equal.

Therefore, events A and B are not independent.

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Answer:

First, you distribute 2(2x-1/2)

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

Now, you have 3x-2=4x-1

Then, you move 2 to the right side by adding so you can cancel it out.

Then, you move 4x to the left side by doing the same thing with 2

Now, divide both sides by -1

The answer is C, z= -1.

3x-2=2(2x-1/2)

3x-2=4x-1

3x=4x+1

-x=1

-x/-1 = 1/-1

= x=-1

The dimensions of a rectangular prism are 6 cm long, 3 cm wide, and 4 ½ cm tall. 648 cubes are required to completely fill the rectangular prism.

The formula for calculating the rectangular prism's volume is:

Volume = Length x Width x Height

Substituting the given values, we get:

Volume = 6 cm x 3 cm x 4 ½ cm

Volume = 81 cm³

Since the cubes have an edge length of ½ cm, their volume is:

Volume of one cube = (1/2 cm)³ = 1/8 cm³

To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of one cube:

Number of cubes = Volume of prism / Volume of one cube

Substituting the values, we get:

Number of cubes = 81 cm³ / (1/8 cm³)

Number of cubes = 81 cm³ x 8

Number of cubes = 648

Therefore, 648 cubes are needed to fill the rectangular prism.

The complete Question is:-

A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 1/2cm. the prism is filled with cubes that have edge lengths of ½ cm. how many cubes are needed to fill the rectangular prism?

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The cost of the tabletop is $251.10. Option C

The formula for calculating the area of a rectangle is expressed as;

Area = lw

Such that the parameters are;

From the diagram shown, we have;

The width = 6 3/4 feet = 27/4 feet

The length = 3 feet

Substitute the values

Area = 27/4 × 3

Multiply

Area = 20. 25 square feet

But;

1 square foot = $12.40

Then  20. 25 square feet = x

x = $251. 10

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The weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.

Since the weight of miniature Tootsie Rolls is normally distributed with a mean of 3.30 grams and a standard deviation of 0.13 grams, we can use the standard normal distribution to find the weight range within which the middle 95% of all miniature Tootsie Rolls will fall.

We need to find the z-scores that correspond to the middle 95% of the normal distribution. The area between the two z-scores will be 0.95. Using a standard normal distribution table or calculator, we can find that the z-scores that correspond to the middle 95% of the distribution are -1.96 and 1.96.

We can use the formula z = (x - μ) / σ to find the corresponding weight values for these z-scores. Substituting -1.96 for z and solving for x, we get:

-1.96 = (x - 3.30) / 0.13

x = 3.04

Similarly, substituting 1.96 for z and solving for x, we get:

1.96 = (x - 3.30) / 0.13

x = 3.56

Therefore, the weight range within which the middle 95% of all miniature Tootsie Rolls will fall is approximately between 3.04 grams and 3.56 grams.

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The value of x is the measure of the angle between the tangent lines with arc 46° and is equal to 134°

Given the tangents to the circle intersecting at a point forming the angle x, the measure of the angle x between the tangents is 180 degrees minus the measure of the arc between the two points of tangency.

hence;

x = 180° - arc length

x = 180° - 46°

x = 134°

Therefore, the value of x is the measure of the angle between the tangent lines with arc 46° and is equal to 134°.

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The solution of the given inequality is x ∈ (-1,5). The graph has been plotted and attached below.

What is an inequality?

In mathematics, an inequality is a relationship that unfairly compares two numbers or other mathematical expressions. Size comparisons between two numbers on the number line are most usually made.

We are given an inequality as -4 < 4x < 20.

Now, on splitting the inequality, we get two inequalities which are:

-4 < 4x and 4x < 20.

On solving -4 < 4x, we get

⇒ -4 < 4x

⇒ -1 < x

Similarly, on solving 4x < 20, we get

⇒  4x < 20

⇒  x < 5

So, we get -1 < x < 5 which means x ∈ (-1,5).

The graph of the inequality has been plotted and attached below.

The red part represents -1 < x and the blue part represents x < 5.

Hence, the solution of the given inequality is x ∈ (-1,5).

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When comparing two group means, the degree of freedom refers to the number of scores free to vary once the means are known. Correct option is D.

The degree of freedom (df) is the number of independent pieces of information available in a study that may be used to estimate the value of the population parameter in question.

In layman's terms, the degree of freedom is the number of independent pieces of information that can be used to calculate a population parameter estimate in a statistical study. The degree of freedom (df) refers to the number of scores free to vary once the means are known.

This implies that there are a certain number of scores (or values) in the study that can be changed freely without affecting the mean of the study's scores. For instance, if the study's mean score is 75, the degree of freedom is the number of scores that may be adjusted without altering the mean score of 75.

As a result, the degree of freedom represents the number of values that can be varied to get a given statistic, such as the mean.

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Jasmin, who is 5 feet tall, is standing in the 15-foot lamppost's light. Her shadow is 4 feet long. If she walks 1 feet farther away from the lamppost, her shadow will lengthen by 3/2 feet.

Let ‘x’ be the distance between Jasmin and the base of the lamppost when she is casting a 4-foot shadow. We can use similar triangles to set up a proportion:

15/x = 5/4

Solving for 'x', we get:

X = 15/3

X = 5 feet

This means that Jasmin is standing 5 feet away from the base of the lamppost when she is casting a 4-foot shadow.

Now, let’s find the distance between Jasmin and the base of the lamppost when she walks 1 foot farther away. This will be ‘5+1=6’ feet.

Again, we can use similar triangles to set up a proportion:

15/6 = y/4+z

Where 'y' is the length of Jasmin’s shadow when she is 6 feet away from the lamppost, and 'z' is the additional length of her shadow.

Simplifying this proportion, we get:

Y = 5/2 + 5z/6

We want to find ‘z’, the additional length of Jasmin’s shadow. We can do this by using the fact that when Jasmin is 6 feet away from the lamppost, her shadow is 4+z feet long. Setting up an equation using this information, we get:

4+z=y

Substituting the expression for ‘y’ from the proportion we set up earlier, we get:

4+z = 5/2 + 5z/6

Solving for 'z', we get:

Z = 3/2

Therefore, Jasmin’s shadow will lengthen by 3/2 feet when she walks 1 foot farther away from the lamppost.

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Answer:No

Step-by-step explanation:

Since it is difficult to evaluate this integral exactly, use technology to approximate it. After calculation, the length is approximately 3.9205 (rounded to four decimal places).

To find the length of the function y =[tex]2x^(3/2)/3 - x^(1/2)/2[/tex] over the interval [1, 4], you need to evaluate the integral of the square root of [1 + (y')^2] with respect to x, where y' is the derivative of y with respect to x.

First, find the derivative y':
y'(x) = d(2x^(3/2)/3 - x^(1/2)/2)/dx = x^(1/2) - 1/(4x^(1/2))

Now, find (y')^2:
[tex](y')^2 = (x^(1/2) - 1/(4x^(1/2)))^2[/tex]
Next, find the square root of [1 + (y')^2]:
[tex]√[1 + (y')^2] = √[1 + (x^(1/2) - 1/(4x^(1/2)))^2][/tex]

Finally, evaluate the integral:
Length = [tex]∫(√[1 + (y')^2]) dx[/tex] from x = 1 to x = 4

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As per central angle theorem, James in incorrect because he calculated the number of slices of pizza that were eaten instead of the number of slices of pizza that were left. James needed to divide 360 by the appropriate number of slices of pizza, 8. He then would have needed to multiply the result by 5 in order to find how many degrees of pizza was left over. After that, James would have needed to divide by 180 and multiply by π to get 1.257 radians as the amount of pizza that was left.

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors.

In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

Here,

out of 8 slices 5 are left.

So 360/8

= 45

5 × 45 = 225°

Now 225° = 225× π/180

= 3.927 Rad

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James ordered a large pizza cut into eight equal pieces. Of the 8 slices, only 3 were edible. James thought the rest of the pizza was 0.75 pi radians. Option A) correctly describes James' claim.

The central angle is the angle an arc of a circle makes at its center. The central angle arm is formed by the radius vector. That is, the angle at which the arms with the apex at the center of the circle and the arms at his two radii of the circle intersect at two different positions. Combining these two points forms an arc. The angle that this arc makes at the center of the circle is called the central angle.  

Here,

out of 8 slices 5 are left.

So 360/8

= 45

5 × 45 = 225°

Now 225° = 225× π/180

= 3.927 Rad

According to the central angle theorem, James is wrong because he calculated the number of pizza slices eaten, not the number of pizza slices left. James had to divide his 360 by 8, the number of pizza slices. Then he had to multiply the result by 5 to see how many pizzas were left. Then James had to divide him by 180 and multiply by π, so he got 1.257 radians as the remaining amount of pizza.

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Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.

We know that the cost per mile is $0.20, so we can set up an equation:

Cost = $20 + $0.20 x Distance

We can substitute $50 for Cost and solve for Distance:

$50 = $20 + $0.20 x Distance

$30 = $0.20 x Distance

Distance = $30 / $0.20

Distance = 150 miles

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Area of the solid composite shape with triangle and rectangle is =832cm².

The area of a composite shape can be determined by adding or subtracting its component pieces.

Hence, we can use two formulas:

Area of Composite Shape + Area of Composite Shape + Area of Basic Shape A (additive)

Basic Shape Area A, Basic Shape Area B, and Composite Shape Area (subtractive)

In the figure,

Dimensions of the triangle are height, h = 16cm and base, b = 12cm.

Area = 1/2 ×b ×h

= 1/2 × 16× 12

=96cm²

There are two triangles, so the total area = 96+ 96 = 192cm².

Now area of the rectangle = length × width

= 20 × 32

= 640cm².

Total area of the solid= 192 + 640 = 832cm².

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The algebraic expressions for each statement is given below:

Here are the algebraic expressions for the given statements:

One-third a decreased by 2: (1/3)a - 2

Six times a number divided by 3: (6b)/3 = 2b

Eight more than a number n squared: n^2 + 8

Twice the difference of 8 and a number: 2(8 - c) = 16 - 2c

9 more than the quotient of 14 and a number n: (14/n) + 9

The sum of 15 and twice m: 15 + 2m

Four more than twice a number y is 72: 2y + 4 = 72

One-half a number x is 6 less than the number: (1/2)x = x - 6

4 times the sum of a number n and 7 is 16: 4(n + 7) = 16

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A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and  [tex]B = -2x^2 - 6x + 7[/tex] .

A mathematical expression is a grouping of digits, variables, operators, and symbols that denotes a mathematical amount or relationship. It can be analyzed or condensed using mathematical operations and rules, and it can be a single word or a group of terms. Numerous mathematical ideas, including equations, variables, functions, and formulas, can be represented by expressions. Standard form, factored form, extended form, and polynomial form are just a few of the different ways they can be expressed in writing.

given

We must deduct the expression B from the expression A in order to obtain A-B. To accomplish this, we subtract the appropriate coefficients from terms of the same degree. Here are the facts:

[tex]A = 3x^2 + 5x - 6\\B = -2x^2 - 6x + 7[/tex]

A - B =[tex](3x^2 + 5x - 6) (-2x^2 - 6x + 7)[/tex]

= 3x2 + (5x - 6) + (2x2 - 6) + (7x - 5x2 + 11x - 13 (distributing the negative sign)

A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and  [tex]B = -2x^2 - 6x + 7[/tex] .

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Answer:

the answer is the last one

Projective personality tests are most widely used by the Psychodynamic perspective.

According to Sigmund Freud's theory of personality, people's personalities are shaped by their unconscious motivations and past experiences. The theory also emphasizes the role of the unconscious mind in human behavior.Projective personality tests are based on this psychodynamic theory, which posits that people's unconscious emotions, thoughts, and desires can reveal much about their personalities. The tests seek to uncover this unconscious content by asking people to interpret ambiguous stimuli.

Projective tests are more effective than self-report measures in discovering unconscious thoughts, desires, and motivations because they bypass a person's defenses. Self-report measures, on the other hand, are more susceptible to response bias or social desirability bias.There are many types of projective personality tests, including the Rorschach Inkblot Test, the Thematic Apperception Test, and the Draw-A-Person Test. Although the reliability and validity of projective tests have been debated in the psychological community, they remain popular in clinical and forensic settings today.

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The sum of all eight factors is 96

Let's express the integer as a product of its prime factors, in the form

n = p1^a1 × p2^a2 × ... × pn^an

where p1, p2, ..., pn are prime numbers and a1, a2, ..., an are positive integers.

We know that the integer has 8 factors, which means that its prime factorization must have the form:

n = p1^2 × p2^2 × p3^4

since (2+1) × (2+1) × (4+1) = 3 × 3 × 5 = 45, which is the total number of factors for this product.

We also know that 15 and 21 are factors of the integer, so they must be expressible in terms of the prime factors of n. We can write

15 = 3 × 5 = p1 × p2

21 = 3 × 7 = p1 × p3

From these expressions, we can see that p1 = 3, p2 = 5, and p3 = 7.

Therefore, the prime factorization of n is

n = 3^2 × 5^2 × 7^4

The eight factors of n are

1, 3, 5, 7, 9, 15, 21, and 35

Their sum is

1 + 3 + 5 + 7 + 9 + 15 + 21 + 35 = 96

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Based on this linear equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F.

What is linear equation ?

A linear equation is an algebraic equation that describes a straight line relationship between two variables, typically denoted as x and y. The general form of a linear equation is:

y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

The slope, m, represents the rate of change of y with respect to x.

According to the question:
Assuming that the relationship between the high temperature and the number of hot cocoas sold is roughly linear, we can use the equation of the line of best fit to estimate the number of hot cocoas sold at a high temperature of 30 F.

If we know the equation of the line of best fit in the form y = mx + b, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 and solve for y.

For example, if the equation of the line of best fit is y = 2x - 10, where y is the number of hot cocoas sold and x is the high temperature, then we can substitute x = 30 to get:

y = 2(30) - 10 = 50

Therefore, based on this equation, we would predict that John would sell 50 hot cocoas if the day's high temperature were 30 F. However, it's important to note that this is just an estimate and the actual number of hot cocoas sold could be different.

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Answer:

We can use trigonometry to solve this problem. In a right triangle, the sine, cosine, and tangent ratios relate the side lengths of the triangle to the angles.

Since we know that angle X is 60 degrees, we can use the sine ratio to find the length of side XY:

sin(60°) = XY / YZ

Simplifying this expression, we get:

sqrt(3) / 2 = XY / 4

Multiplying both sides by 4, we get:

XY = 2sqrt(3)

Therefore, XY is equal to 2 times the square root of 3.

After answering the presented question, we can conclude that With an IQR of  [tex]2.5[/tex] , Player B is the most consistent. Thus, option D is correct.

The IQR is a more robust measure of variability that is less vulnerable to outliers or extreme results. It is the difference between the dataset's 75th percentile (Q3) and 25th percentile (Q1). Player A has an IQR of [tex]5-2.5 = 2.5[/tex] , while Player B has an IQR of [tex]3-1.5 = 1.5[/tex]  .

Based on these calculations, we can see that Player A has a wider range, suggesting more variability in the data, but Player B has a narrower range and IQR, indicating less variability and higher consistency in the data. As a result, the right answer is:

Therefore, With an IQR of [tex]2.5[/tex]  , Player B is the most consistent.

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The surface area of the box is (D) 184 square inches.

What is surface area?

Surface area is the measurement of the total area that the surface of an object occupies. It is the sum of the areas of all the faces or surfaces that make up the object. For example, the surface area of a cube can be found by adding up the area of all six of its square faces.

To find the surface area of the box, we need to add up the areas of each face.

The front face has an area of 5 x 4 = 20 square inches.

The back face has the same dimensions, so it also has an area of 20 square inches.

The left face has an area of 4 x 8 = 32 square inches.

The right face also has an area of 4 x 8 = 32 square inches.

The top face has an area of 5 x 8 = 40 square inches.

The bottom face also has an area of 5 x 8 = 40 square inches.

Adding up all of these areas, we get:

20 + 20 + 32 + 32 + 40 + 40 = 184 square inches

Therefore, the answer is (D) 184 square inches.

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