-1
-2
1
Determine the period.

8
10 12 14/
2

Answer:

Step-by-step explanation:

a) 4/10 = 40%

b) 3/10 = 30%

c) 1/10 = 10%

d) 2/10 = 20%

e) 8/12 = 67%

f) 10/12 = 83%

g) 9/12 = 75%

h) 12/12 = 100%

i) 4/12 = 33%

j) 5/12 = 42%

k) 2/12 = 16%

l) 3/12 = 25%

Answer:

See below

Step-by-step explanation:

Starting with 42, there would be two branches of 2 and 21 connected to 42. Since 2 is prime, there are no more branches. Since 21 is composite, then two more branches are drawn of 3 and 7 connected to 21. Since 3 and 7 are prime, there are no more branches.

Therefore, the prime factorization of 42 is 2*3*7, and its factors would be 1,2,3,6,7,14,21,42.

Check the picture below.

Answer:

C = 18.2 in.

Step-by-step explanation:

Step 1:  Find the diameter of the circle:

The normal formula for the circumference of a formula is given by:

C = πd, where

We're given the radius, r, and since the diameter is simply twice the radius, we can find the diameter by multiplying 2.9 by 2:

d = 2r

d = 2(2.9)

d = 5.8

Thus, the diameter is 5.8 in.

Step 2:  Find the circumference, C (rounded to the nearest tenth), by plugging in 5.8 for d and 3.14 for π in the circumference formula:

C = 3.14(5.8)

C = 18.212

C = 18.2

Thus, the circumference of the circle is about 18.2 in.

The sum of the infinite geometric series representing the population of the local species of flies is given by the sigma notation ∑ (from n = 1 to ∞) 940 * (1/5)^(n-1). The series converges, and the sum, which represents the upper limit of the population, is 1175.

To write the sum in sigma notation, let's break down the given information step by step:

The first term of the infinite geometric series is a1 = 940.

The common ratio (r) is one fifth (1/5), which means each term is obtained by multiplying the previous term by 1/5.

In sigma notation, the sum of an infinite geometric series can be expressed as follows:

∑ (from n = 1 to ∞) a1 * r^(n-1)

In this case, the first term a1 is 940, and the common ratio r is 1/5. Therefore, the sigma notation for the sum of this series is:

∑ (from n = 1 to ∞) 940 * (1/5)^(n-1)

To calculate the upper limit of this population, we need to find the sum of the series. However, to determine if the sum is possible, we can check if the series converges or diverges.

For a geometric series to converge, the absolute value of the common ratio (|r|) must be less than 1. In this case, |1/5| = 1/5, which is less than 1. Therefore, the series converges.

The sum of an infinite convergent geometric series can be calculated using the formula:

S = a1 / (1 - r)

In our case, a1 = 940 and r = 1/5. Substituting these values into the formula, we can calculate the sum:

S = 940 / (1 - 1/5)

S = 940 / (4/5)

S = 940 * (5/4)

S = 1175

So, the upper limit of the population is 1175.

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The equation that best represents the relationship between x and y is:

y = -1/2x + 11

To determine the equation that best represents the relationship between the quantities x and y, we can examine the pattern in the table.

Looking at the x-values and their corresponding y-values, we can observe that as x increases by 2 units, y decreases by 1 unit.

Using this pattern, we can find the equation that represents the relationship.

When x = 2, y = 10

When x = 4, y = 9

When x = 6, y = 8

When x = 8, y = 7

Based on the pattern, we can see that y decreases by 1 unit for every 2 units increase in x.

Therefore, the equation that best represents the relationship is:

y = -1/2x + b

To find the value of b (the y-intercept), we can substitute the values of x and y from any point in the table. Let's use the first point (x = 2, y = 10):

10 = -1/2(2) + b

10 = -1 + b

b = 11

So the equation that best represents the relationship between x and y is:

y = -1/2x + 11

Therefore, the correct answer is: y = -1/2x + 11.

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Based on the calculations, option D, which is $5,000 at 2 percent interest compounded for four years, will result in the least amount of interest paid.

To determine which loan will result in the least amount of interest paid, we need to calculate the total interest for each option and compare them. Let's calculate the interest for each loan:

A. $10,000 at 2 percent interest compounded for four years:

To calculate the compound interest, we use the formula A = P(1 + r/n)^(nt), where A is the future value, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For option A, the future value (A) can be calculated as:

A = 10,000(1 + 0.02/1)^(1*4) ≈ 10,816.65

The interest paid would be the difference between the future value and the principal:

Interest = 10,816.65 - 10,000 = 816.65

B. $10,000 at 2 percent simple interest for four years:

For simple interest, we use the formula I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the number of years.

For option B:

Interest = 10,000 * 0.02 * 4 = 800

C. $5,000 at 4 percent interest compounded for four years:

Using the compound interest formula:

A = 5,000(1 + 0.04/1)^(1*4) ≈ 5,897.77

Interest = 5,897.77 - 5,000 = 897.77

D. $5,000 at 2 percent interest compounded for four years:

Using the compound interest formula:

A = 5,000(1 + 0.02/1)^(1*4) ≈ 5,407.10

Interest = 5,407.10 - 5,000 = 407.10

Comparing the total interest paid for each option:

A: $816.65

B: $800

C: $897.77

D: $407.10

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Based on the given information, we can determine the number of pupils who like only Science and only Mathematics.

1. The number of learners who like both Mathematics and Science is 4.

2. The number of learners who like Science is 21, including those who like both Science and Mathematics.

3. The number of learners who like neither Science nor Mathematics is 8.

4. To find the number of pupils who like only Science, we subtract the number of learners who like both from the total number of Science likers: 21 - 4 = 17. Therefore, there are 17 pupils who like only Science.

Similarly, to find the number of pupils who like only Mathematics, we subtract the number of learners who like both from the total number of Mathematics likers. Since the number of learners who like only Mathematics is not given explicitly, we cannot determine it based on the given information.

To illustrate this information on a Venn diagram, we would draw two overlapping circles representing Mathematics and Science. The area where the circles overlap would represent the learners who like both subjects (4).

The remaining portion of the Science circle outside the overlap would represent the learners who like only Science (17). The portion of the Mathematics circle outside the overlap would represent the learners who like only Mathematics (unknown). The learners who like neither subject would be represented outside both circles.

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The correct statement about the distribution in this problem is given as follows:

The distribution is unimodal.

The mode of a data-set is the observation that appears the most times in the data-set.

Considering the stem-and-leaf plot, we have that the observations have the following format:

7|6 = 76.

As 6 is the only observation that appears twice, it is the only mode of the distribution, meaning that the distribution is unimodal.

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Answer:

To list the sides of triangle ∆ from shortest to longest, we need the lengths of the sides. However, the given information only provides the measures of the angles (∠). Without the side lengths, we cannot determine the order of the sides from shortest to longest.

The table that represents g(x) when f(x) = 3x - 4 and g(x) = f(2x) include the following: D. table D.

Based on the information provided above, we can logically deduce the following functions;

f(x) = 3x - 4

g(x) = f(2x)

g(x) = f(2x)

g(x) = 3 × (2x) - 4

g(x) = 6x - 4

By evaluating g(x) based on the given x-values in the tables (x = 1, 2, 3), we have the following:

g(1) = 6 × 1 - 4

g(1) = 6 - 4

g(1) = 2

g(2) = 6 × 2 - 4 '

g(2) = 12 - 4

g(2) = 8

g(3) = 6 × 3 - 4

g(3) = 18 - 4

g(3) = 14

Therefore, the correct table is given by:

x      g(x)

1         2

2         8

3         14

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The payback period for Project A is 3 years, and the payback period for Project B is also 3 years.

To calculate the payback period for Project A and Project B, we need to determine the time it takes for the cumulative cash flows to equal or exceed the initial investment of $40,000.

For Project A:

Year 1 cash flow: $42,000

Year 2 cash flow: $22,000

Year 3 cash flow: $10,000

To find the payback period, we start by subtracting the cash flows from the initial investment until we reach a cumulative cash flow equal to or greater than $40,000:

Year 1: $40,000 - $42,000 = -$2,000

Year 2: -$2,000 + $22,000 = $20,000

Year 3: $20,000 + $10,000 = $30,000

The cumulative cash flow reaches $30,000 in Year 3. However, it does not exceed the initial investment of $40,000. Therefore, we can estimate the payback period as follows:

Payback period for Project A = 2 years + ($40,000 - $30,000) / $10,000

= 2 years + 1 year

= 3 years

For Project B:

Year 1 cash flow: $40,000

Year 2 cash flow: $21,000

Year 3 cash flow: $15,000

Using the same process as above, we calculate the cumulative cash flows:

Year 1: $40,000 - $40,000 = $0

Year 2: $0 + $21,000 = $21,000

Year 3: $21,000 + $15,000 = $36,000

The cumulative cash flow reaches $36,000 in Year 3, which is greater than the initial investment. Therefore, the payback period for Project B is:

Payback period for Project B = 3 years

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Answer:

The domain of a function is the set of all values for which the function is defined. When determining the domain of a function, we need to identify any values that would make the function undefined or result in an error. For instance, in the function f(x) = 1/x, the denominator cannot be zero since division by zero is undefined. Thus, the domain of f(x) would be all real numbers except 0, since substituting 0 for x would result in an undefined expression. The following are some guidelines that can help determine the domain of a function:

1. Check for values that would make the function undefined or result in an error. This includes dividing by zero, taking the square root of a negative number, and taking the logarithm of a non-positive number.

2. Identify any restrictions on the variable or inputs. For instance, if the function represents a physical problem, there may be restrictions on the input values based on the conditions of the problem.

3. Check for any implicit assumptions or requirements in the problem. This could include assumptions about the sign of variables or the existence of certain values.

4. Determine the set of all real numbers that satisfy the above conditions as the domain of the function.

I hope this helps you understand how to determine the domain of a function defined by an equation.

Hello!

distance = speed * time

distance

= 40km/h * 1.5h

= 60km

She travel 60km.

Answer:

60 km

Step-by-step explanation:

In order to find the distance that Anna has travelled, we can derive the formula from the speed formula which is:

[tex]\displaystyle{v=\dfrac{s}{t}}[/tex]

where v is speed, s is distance and t is time. So by solving for distance (s), we have:

[tex]\displaystyle{s=vt}[/tex]

Apply the distance travelled formula, we know that speed (v) = 40 km/h and time (t) = 1.5 hours. Thus,

[tex]\displaystyle{s=40 \ \text{km/h} \cdot 1.5 \text{h}}\\\\\displaystyle{s=60\ \text{km}}[/tex]

Therefore, Anna travels 60 kilometers.

Answer:

Step-by-step explanation:

You want the values of x and z in the figure where one pair of parallel lines crosses another.

Where a transversal crosses parallel lines, corresponding angles are congruent. This gives rise to several other relationships, each with its own name. The net result is that all acute angles are congruent, and all obtuse angles are congruent. The acute and obtuse angles are supplementary. (If the crossing is at right angles, then all angles are congruent.)

Here, the angle marked x° is supplementary to the one marked 77°:

  x = 180 -77 = 103

The angle marked (3z -19)° is congruent to the one marked 77°:

  3z -19 = 77

  3z = 96 . . . . . . add 19

  z = 32 . . . . . . . divide by 3

The value of x is 103; the value of z is 32.

__

Additional comment

The various pairs of angles at a transversal can be described as "consecutive", "alternate", "interior", "exterior", "same-side". Of course, where lines cross, the angles can also be "vertical" or "opposite" or "adjacent" or a "linear pair."

Depending on the relationship, the angles will be congruent or supplementary. For example, "alternate exterior angles" are congruent; "consecutive interior angles" are supplementary.

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Answer:

ST ≈ 15.3

Step-by-step explanation:

given a tangent and a secant from an external point to the circle , then

the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant , that is

ST² = TU × TV = 9 × (9 + 17) = 9 × 26 = 234

take the square root of both sides

ST = [tex]\sqrt{234}[/tex] ≈ 15.3 ( to the nearest tenth )

Given the mathematical expression, it must be solved with the result [tex](\text{a} + \text{b})[/tex]

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

We are given the expression:

[tex]\dfrac{(\text{x} + 100)}{(\text{x} - 100)} = \dfrac{(\text{a} + \text{b} + 100)}{(\text{a} + \text{b} - 100)}[/tex]

The Denominators go to the other side of the equality by multiplying, so that we now have:

[tex](\text{x} + 100)(\text{a} + \text{b} - 100) = (\text{a} + \text{b} + 100)(\text{x} - 100)[/tex]

The products of the binomials are developed by the trinomials.

[tex]\text{ax} + \text{bx} - 100\text{x} + 100\text{a} + 100\text{b} - 10000 = \text{ax} + \text{bx} + 100\text{x} - 100\text{a} - 100\text{b} - 10000[/tex]

Like terms are removed.

[tex]100\text{a} + 100\text{b} - 100\text{x} = 100\text{x} - 100\text{a} - 100\text{b}[/tex]

[tex]100\text{a} + 100\text{b} - 100\text{x} - 100\text{x} + 100\text{a} + 100\text{b}[/tex]

[tex]200\text{a} + 200\text{b} - 200\text{x} =[/tex]

Grouping.

[tex]200(\text{a} + \text{b})[/tex]

Result.

[tex](\text{a} + \text{b})[/tex]

Hence, the solution to the mathematical expression is [tex](\text{a} + \text{b})[/tex]

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The equation of the perpendicular line is y = 1/5x + 2

From the question, we have the following parameters that can be used in our computation:

Line; y = -5x + 1

The slope of the above line is

m = -5

The slopes of perpendicular lines are opposite reciporcals

So, the new slope is 1/5

New = 1/5

The line passes through (10, 4)

So, we have

y = mx + c

Where

m = 1/5

This gives

1/5 * 10 + c = 4

Evaluate

c = 4 - 1/5 * 10

c = 2

So, we have

y = 1/5x + 2

Hence, the equation of the perpendicular line is y = 1/5x + 2

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The property that allows you to write the expression (3+7^) + (8-6^) + (3+7^) is the Commutative Property of Addition and the Commutative Property of Exponents.

The Commutative Property of Addition states that when two or more numbers are added, the sum remains the same even if the order of the numbers is changed. For example, a + b = b + a. Therefore, in the given expression, we can add the terms in any order we want, without changing the result. So, we can add (3 + 8 + 3) and (7^ + 6^ + 7^) in any order we want.

Applying the Commutative Property of Addition, we can write the expression as (3+8+3) + (7^+6^+7^).
Then, applying the Commutative Property of Exponents, we can write the expression as (3+8+3) + (7^+7^+6^).
Simplifying further, we get (14) + (2 * 7^) + (6^).

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Sean to guarantee a B in the course, he needs to score at least 97 on the fourth and last 100-point test.

To determine the range of scores on the fourth test that will guarantee a B in the course, we can set up an equation using the average score formula.

The average score across the four exams should be at least 84.

Since Sean has already taken three exams with scores of 89, 71, and 79, respectively, we can set up the equation as follows:

[tex]\frac{(89 + 71 + 79 + x) }{4} \geq 84[/tex]

Here, x represents the score on the fourth test.

We need to solve this inequality to find the range of scores that will guarantee a B.

Let's simplify the equation and solve for x:

[tex]\frac{(239 + x) }{4} \geq 84[/tex]

Multiply both sides of the inequality by 4 to eliminate the fraction:

[tex]239 + x \geq 336[/tex]

Subtract 239 from both sides:

[tex]x \geq 336 - 239[/tex]

[tex]x \geq 97[/tex]

Therefore, for Sean to guarantee a B in the course, he needs to score at least 97 on the fourth and last 100-point test.

Any score equal to or greater than 97 will ensure an average of at least 84 across all four exams.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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The correct pairs of the given rational numbers with the points on the number line are:A - 7/4B - 5/4C - 1/2D - 1E - 13/8

To form the correct pairs of the given rational numbers with the points on the number line, the given points on the number line and their corresponding rational numbers are:A at 1.75, which is the same as 7/4B at 1.25, which is the same as 5/4C at 0.5, which is the same as 1/2D at 1, which is the same as 1E at 1.625, which is the same as 13/8Let's take a look at the number line:|-2---|---|---|---|---2...-1   0   1   2

We can see that point C is exactly at the center of the number line, at 0.5. This is the same as the rational number 1/2.Point D is located at 1 on the number line, which is the same as the rational number 1.Point A is located between 1 and 2 on the number line, closer to 2. The exact location is 1.75, which is the same as the rational number 7/4.Point B is located between 1 and 1.5 on the number line, closer to 1.5. The exact location is 1.25, which is the same as the rational number 5/4.Point E is located between 1.5 and 2 on the number line, closer to 1.5. The exact location is 1.625, which is the same as the rational number 13/8.

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The measure of the arc AWJ between the tangent AT and chord AJ is equal to 226°

The angle m∠JAT between the intersection of the chord and a tangent is equal to the arc measure of arc AWJ divided by 2

Given the measure of the angle m∠JAT to be equal to 113°, then the measure of arc AWJ is calculated as:

angle JAT = 108°/2

m∠JAT = arc AWJ/2

113° = arc AWJ/2

arc AWJ = 2 × 113°

arc AWJ = 226°

Therefore, the measure of the arc AWJ between the tangent AT and chord AJ is equal to 226°

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To write a division expression with a quotient greater than 10 using only two of the numbers -10, 5, and 2, we can choose 5 and 2.

The expression can be:

5 / 2

When we divide 5 by 2, the quotient is 2.5. Since 2.5 is greater than 10, this division expression satisfies the given condition of having a quotient greater than 10.

In mathematical terms, the division expression 5 / 2 = 2.5 meets the criterion requested. Dividing 5 by 2 yields a quotient greater than 10, specifically 2.5.

It is important to note that when working with numbers, careful attention must be paid to the problem statement and the conditions provided. In this case, selecting 5 and 2 and dividing them correctly results in a quotient greater than 10.

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The sample space of a spinner refers to the set of all possible outcomes that can occur when the spinner is spun. In order to determine the sample space, we need to consider the different sections or options on the spinner.

For example, if the spinner has 4 equal sections, each labeled with a different color (red, blue, green, and yellow), then the sample space would consist of these 4 possible outcomes: {red, blue, green, yellow}.
Alternatively, if the spinner has 6 sections with numbers 1 to 6, then the sample space would be {1, 2, 3, 4, 5, 6}.
In general, the sample space of a spinner depends on the number and nature of its sections. It can include colors, numbers, or any other distinct options available on the spinner.

In summary, the sample space of a spinner is the set of all possible outcomes, which can vary depending on the specific design and labeling of the spinner.

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when the tablet runs for x hours, the battery remaining percentage can be calculated as y = -5x + 50.

The given graph represents the percent of battery remaining, y, on a tablet's battery after x hours. The tablet starts with 50 percent of battery remaining. The tablet loses 5 percent of battery every hour.From the graph, it is observed that the line passes through the point (0,50) and (10,0) as the maximum battery life is for 10 hours. The slope of the line can be calculated as: Slope = Rise/Run Slope = (Change in y)/(Change in x) Slope = (0 - 50)/(10 - 0) Slope = -5The slope of the line represents the rate of change of battery percentage per hour. Thus, the given information can be concluded as: The tablet loses 5% of battery every hour. Therefore, the equation of the line can be written in the form of y = mx + b where m is the slope of the line and b is the y-intercept. Hence, y = -5x + 50This equation represents the battery remaining percentage, y, as a function of time, x in hours.

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(f/g)(-5) is equal to 1/4, and the value -1 is not in the domain of f/g.

To find (f/g)(-5), we need to substitute -5 into the functions f(x) and g(x) and then divide f(-5) by g(-5).

Given:

f(x) = (4+x)(6+x)

g(x) = 1+x

Substituting -5 into the functions:

f(-5) = (4+(-5))(6+(-5)) = (-1)(1) = -1

g(-5) = 1+(-5) = -4

Now, we can calculate (f/g)(-5):

(f/g)(-5) = f(-5) / g(-5) = -1 / -4 = 1/4

Therefore, (f/g)(-5) equals 1/4.

Now let's determine the values that are not in the domain of f/g. The values that are not in the domain of f/g are the values that make the denominator g(x) equal to zero. In this case, the denominator is g(x) = 1+x.

To find the values that make the denominator zero, we solve the equation:

1 + x = 0

Subtracting 1 from both sides, we get:

x = -1

So, the value x = -1 is not in the domain of f/g because it would make the denominator equal to zero.

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The values of the compound probabilities are

From the question, we have the following parameters that can be used in our computation:

The cubes

Where we have

Blue = 2

Green = 3

Red = 4

Yellow = 6

Givn the the cubes are not replaced after they are chosen, we have

P(Blue then Red) = 2/15 * 4/14

P(Blue then Red) = 4/105 = 3.81%

Next, we have

P(Red then Green) = 4/15 * 3/14

P(Red then Green) = 2/35 = 5.71%

P(Green then Green) = 3/15 * 2/14

P(Green then Green) = 1/35 = 2.85%

P(Yellow then Yellow) = 6/15 * 5/14

P(Yellow then Yellow) = 1/7 = 14.29%

P(Red then Red then Red) = 4/15 * 3/14 * 2/13

P(Red then Red then Red) = 4/455 = 0.88%

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