Segment AC is the angle bisector of The figure is not to scale.


Which of the following additional statements would allow us to prove that

It will take 10 years for the account to reach $200, as determined by solving the equation A = [tex]325(1 + 0.047/12)^(12t)[/tex] for t.

[tex]A = 325(1+0.047/12)^(12t)[/tex]

[tex]200 = 325(1+0.047/12)^(12t)[/tex]

[tex]200/325 = (1+0.047/12)^(12t)[/tex]

[tex]log_((1+0.047/12))(200/325) = 12t[/tex]

[tex]t = log_((1+0.047/12))(200/325) / 12[/tex]

t = 8.75 years

It will take 9 years for the account to reach $200.

Hassan deposited $325 into an account that pays 4.7% annual interest compounded monthly. We can use a system of equations to determine how many years it will take for the account to reach $200. To do this, we first write an equation to represent Hassan's account balance A after t years. This equation is[tex]A = 325(1+0.047/12)^(12t)[/tex]. We then solve for t by taking the logarithm of both sides, which gives us means that it will take 8.75 years for the account to reach $200, which we round up to 9 years.

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The number of different sandwich possibilities is 1081.

To calculate this, we must use the multiplication principle. We will begin by calculating the number of possibilities for the bread, meat, and cheese. There are 6 different breads, 4 different meats, and 4 different cheeses. So, there are 6 x 4 x 4 = 96 possible combinations for the bread, meat, and cheese. Next, we must calculate the number of possibilities for the condiments. Since we are allowing repetition for the condiments, we can calculate the possibilities by multiplying 12 (the number of condiments) by itself. So, there are 12 x 12 = 144 possibilities for the condiments. Lastly, we can multiply 96 (the number of bread, meat, and cheese combinations) by 144 (the number of condiment combinations). This yields 1081 different sandwich possibilities.

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Answer:

<A=45°,<B=65°,<C=70°

Step-by-step explanation:

<A=3(x+5)=3x+15

<B=5x+15

<C=7x

sum angles in a triangle is 180°

so,<A+<B+<C=180

(3x+15)+(5x+15)+(7x)=180

C.L.T

3x+5x+7x+15+15=180

15x+30=180

15x=180-30

15x=150

divide both sides by 15

x=10

<A=3(x+5)=3(10+5)=3(15)=45°

<B=5(10)+15=50+15=65°

<C=7(10)=70°

Answer:

Step-by-step explanation:

To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.

In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.

This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.

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The amount of money that is take home pay would be = $3,491.91

The amount of money that is your fix expenses would be = $1,257.09

The amount of money that you make each month = $3,764.82.

The percentage of deduction made for FICA = 7.25%

That is;

= 7.25/100 × 3,764.82/1

= 27294.945/100

= $272.91

Therefore, the take home pay ;

= $3,764.82-$272.91

= $3,491.91

The percentage of the fixed expenses = 36% of the realised income.

That is, 36/100 × 3,491.91/1

= 125708.76/100

= $1,257.09.

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The solution to the equation 6(72(x - 2)) = 4(15 - 3x) is x = 77/37.

Given the equation in the question

6(72(x - 2)) = 4(15 - 3x)

To solve the equation, remove the parenthesis by applying distributive property.

6( 72 × x - 72 × 2 ) = 4 × 15 - 4 × 3x

6( 72x - 144 ) = 60 - 12x

6( 72x - 144 ) = 60 - 12x

6 × 72x - 6 × 144 = 60 - 12x

432x - 864 = 60 - 12x

Collect like terms

Add -12x to both sides

432x + 12x - 864 = 60 - 12x + 12x

432x + 12x - 864 = 60

Add 864 to both sides

432x + 12x - 864 + 864 = 60 + 864

432x + 12x = 60 + 864

444x = 924

x = 924/444

x  = 77/37

Therefore, the value of x is 77/37.

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If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are 15000 * (1/20) = 750 tourists daily.

And if 1/15 of the tourists are travel bloggers, then there would be 750 * (1/15) = 50 travel bloggers daily.

If there are 15000 average passengers on domestic flights daily, then 1/20 of the passengers are tourists, which means there are

15000 * (1/20) = 750 tourists daily

So, there would be a total of 50 tourist passengers on domestic flights who are travel bloggers.

It is important to note that these are average numbers and the actual number of tourists and travel bloggers on domestic flights can vary from day to day. However, this calculation provides a general idea of the proportion of tourist passengers who are travel bloggers on domestic flights.

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The scale factor for the area of the pre-image to get the image is 2.

Suppose a figure (pre image) is dilated (dilated image) by scale factor of k. So, if a side of the figure is of length L units, and that of its similar figure is of M units, then:

L = k × M

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

The quantities which are squares or multiple of linear things twice grow by square of scale factor. Thus, we need to multiply or divide by k² to get each other corresponding quantity from their similar figures' quantities.

So area of first figure = k² × area of second figure

Given that Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. Also, the area of the parallelogram CALM is 121.41 square feet.
Therefore, we can write,

Final Area / Initial Area = (Scale Factor)²

485.64 square feet / 121.41 square feet =  (Scale Factor)²

4 = (Scale Factor)²

(Scale Factor) = √4

Scale Factor = 2

Hence,  Scale Factor = 2

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The complete question is:

The area of Parallelogram CALM is 121.41 square feet. Parallelogram CALM is multiplied by a scale factor to create Parallelogram C'A'LM'. Parallelogram C'A'L'M' has an area of 485.64 square feet. What is the scale factor for the area of the pre-image to get the image?

The measure of the length NO after dilation will be 15.

The scale factor is the ratio of the actual size of the image to the new size of the image. It is used to Map the objects like if you want to increase or decrease the size without changing the original shape of the image it is done by the scale factor.

Given that to make JNO, Megan enlarges JKL by a scale factor of 3/5 around point J.

The measure of side NO will be calculated as:-

NO = 3 / 5  x 25

NO = 3 x 5

NO = 15

Therefore, the length of the side NO is 15.

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Without help, it would take Donald 8 hours to make 4 baked zitis.

Amount is the term used to describe a quantity or size of something it will stop to use to refer to a numbers of object items are people with as well as the measure of money time and distance.

This is due to the fact that, as Reynold and Donald work together, they are able to cut the time it takes to make 4 baked zitis in half. Therefore, when working alone, Donald would take twice as long to complete the same task.

For Reynold,  in 8 hour he make 4 zitis

Meaning,  in 1 hour he make 1/2 zitis

But with the help of Donald he make  in 4 hours 4 zitis

both in 1 hour makes  1 zitis

So we have,

Reynold time to make zitis + Donald time to make zitis = both time to make zities

⇒ 1/2 + x = 1

⇒ x = 1 - 1/2

⇒ x = 1/2

So, It take 1/2 hours Donald to make 1 baked zitis without help.

Therefore, It take 8 hours Donald to make 4 baked zitis without help.

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The total number of numbers less than 2016 with a digit sum of 8 is 116 numbers.

The sum of the digits in the positive whole numbers is to be 8.

So the possibilities are obtained by means of permutation as follows:

Three 0's and an 8;  ⁴P₁ = 4

One 1 and one 7, ⁴P₂ = 12

One 2 and one 6; ⁴P₂ = 12

One 3 and one 5; ⁴P₂ = 12

Two 1's and a 6; (⁴P₃/2!) = 12

One 1, one 2, and one 5; ⁴P₃ = 24

Two 2's and a 4; (⁴P₃/2!) = 12

Two 3's and a 2; (⁴P₃/2!) = 12

Two 4's and a 0; (⁴P₃/2!) = 12

Three 1's and a 5; (⁴P₃/3!) = 4

Total = 116 numbers

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Answer:

Est: 4.62%

Step-by-step explanation:

The  Commutative property Associative property Identity property  property of addition states that the way addends are grouped does not affect their sum.

The commutative property of addition states that the sum is unaffected by the order of the addends. 2+3=3+3

Changing the order of the addends has no effect on the sum, according to the associative property of addition.

(2+3)+4=2+(3+4)

Identity of addition property: Any number is equal to the sum of 0 00 and that number. For instance 0+5=5

According to the commutative property of addition, altering the order of addends has no impact on the sum. 2+3 = 3+2

as 3 rules are there only

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The number of combinations that are possible for 4 cell phone models of 6 colors with 5 calling plans is  120 .

We have to find the total number of combinations of cell phone models, colors, and calling plans,

So , we multiply the number of choices for each category.

By Using the multiplication principle of counting:

⇒ Total number of combinations = (number of phone models) × (number of colors) × (number of calling plans) ;

⇒ 4 × 6 × 5

⇒ 120

Therefore, there are 120 possible combinations of cell phone models, colors, and calling plans from this particular cell phone company.

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The given question is incomplete , the complete question is

A particular cell phone company offers 4 models of phones, each in 6 different colors and each available with an one of 5 calling plans. How many combinations are possible ?

In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:  

In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.

Based on the given quantities' scale, we know that x, y, and z have a relationship where:

z = x/y

Then, the mathematical combinations that might be meaningful are:

- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.

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The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The system of linear equations is given below.

y = 9x + 14                ....1

y = 6x + 35              ....2

From equations 1 and 2, then we have

9x + 14 = 6x + 35

3x = 21

x = 7

The value of 'y' is given as,

y = 6 (7) + 35

y = 42 + 35

y = 77

The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

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Answer:

i) 84

ii) 7

iii) 47

iv) 16

v) 56

vi) 54

Step-by-step explanation:

The easiest way to understand this problem visually is to create a Venn diagram (See attached diagrams below to help you)

First, note that the total amount of people with each condition beside the relevant circle. Then, since 15 have all 3, write 15 in the center.

We're told 35 had arthritis and arteriosclerosis, and 15 had all 3, so the amount with arthritis and arteriosclerosis only is 25-25=20. So we write 20 in the crosssection between arthritis and arteriosclerosis that doesn't include loss of hearing.

We're told 33 had arthritis and loss of hearing, and 15 had all 3, so the amount with arthritis and loss of hearing but not arteriosclerosis is 33-15=18. So we write 18 in the crosssection between arthritis and loss of hearing that doesn't include arteriosclerosis.

We're told 31 had arteriosclerosis and loss of hearing, and 15 had all 3, so the amount with arteriosclerosis and loss of hearing only is 31-15=16. So we write 16 in the crosssection between arteriosclerosis and loss of hearing that doesn't include arthritis.

(see diagram A to see how this should look)

70 people have arthritis and (18+25+20=63) have arthritis and another condition, so the amount with only arthritis is 70-63=7

60 people have arteriosclerosis and (20+15+16=51) have arteriosclerosis and another condition, so the amount with only arteriosclerosis is 60-51=9

80 people have loss of hearing and (18+15+16=49) have loss of hearing and another condition, so the amount with only loss of hearing is 80-49=31

Marking in these figures completes the diagram (See diagram B to see how it should look)

i)

The total amount of people represented within the diagram (ie, the ones with conditions) is 7+20+9+18+15+16+31=116. If 200 were surveyed, this means the amount without these conditions is 200-116=84

ii)

Above, we found the amount with arthritis only was 7

iii)

7 have only arthrits, 9 have only arteriosclerosis, and 31 have only  loss of hearing , so the amount with only one ailment is 7+9+31=47

iv)

Above, we found that 16 had arteriosclerosis and loss of hearing but not arthritis

v)

The amount with arteriosclerosis or loss of hearing but not arthritis is equal to the amount with arteriosclerosis only plus the amount with loss of hearing plus the amount with both arteriosclerosis and loss of hearing: 9+31+16=56

vi)

Above, we found the amount with arthritis and arteriosclerosis only is 20, the amount with arthritis and loss of hearing but not arteriosclerosis is 18, and the amount with amount with arteriosclerosis and loss of hearing only is 16. So the total amount with exactly two conditions is 20+18+16=54

Let L be the length of the rectangular garden.

The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

Substituting the given values, we get:

328 = 2L + 2(67)

Simplifying the equation, we get:

328 = 2L + 134

2L = 328 - 134

2L = 194

L = 194/2

L = 97

Therefore, the length of the rectangular garden is 97 meters.

The probability that at least one is a boy, given that at least one is a girl is 0.823

To solve this problem, we can use conditional probability.

Let A be the event that at least one student is a boy, and let B be the event that at least one student is a girl.

We want to find the probability of A given B, denoted as P(A|B).

Let total student is,

Total girls (10) + Total boys (12) = 22

First calculating the probability of event B, which is probability that all three students are boys. This can be calculated as:

P(B) = 1 - (10/22)^3 = 1 - 0.214 = 0.906

The probability of event A intersecting B is then calculated, which is the probability that at least one student is a boy and at least one student is a girl. We can use the complement of this event, which is the likelihood that all three students are male or female:

P(A intersect B) = 1 - P(all girls) - P(all boys)

= 1 - (10/22)^3 - (12/22)^3

= 1 - 0.077 - 0.245

= 0.743

Finally, we use the formula for conditional probability to calculate P(A|B):

P(A|B) = P(A intersect B) / P(B)

= 0.743 / 0.906

= 0.822

Therefore, the probability that at least one student is a boy, given that at least one is a girl, is 0.862.

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The dimensions will be as follows;

width is 5cm while the length is 20cm.

Let width = w

Let length = 4w (according to question)

Perimeter = 50cm

Perimeter formula for a rectangle = 2 (l +w)

Substituting in the variables (width and length)

2(w + 4w) = 50

2(5w) = 50

10w = 50

w = 5

Remember that length = 4w

length = 4w

length = 4(5)

length = 20cm

Therefore, the dimensions of the rectangle are 5cm by 20 cm.

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For diagram A, the unsimplified equation represents the relationship between x and y is y = x + x/3.

For diagram B, the unsimplified equation represents the relationship between x and y is y = x + 2x/3.

For diagram C, the unsimplified equation represents the relationship between x and y is y = x - x/3.

For diagram D, the unsimplified equation represents the relationship between x and y is y = x - 2x/3.

Performing mathematical operations reduces an unsimplified equation to a simplified equation. A simplified equation is used for convenience.

Diagram A:

The value of x contains 3 congruent colored rectangles. The noncolored rectangle is 1. So, the value of the noncolored rectangle will be x/3.

Clearly, y will be the sum of x and x/3, that is, y = x + x/3.

Therefore, the obtained answer is y = x + x/3.

Diagram B:

The value of x contains 3 congruent colored rectangles. The noncolored congruent rectangles are 2. So, the value of the noncolored rectangles will be 2x/3.

Clearly, y will be the sum of x and 2x/3, that is, y = x + 2x/3.

Therefore, the obtained answer is y = x + 2x/3.

Diagram C:

The value of x contains 3 congruent colored rectangles. So, the value of 1 rectangle will be x/3.

Clearly, y will be the difference between x and x/3, that is, y = x - x/3.

Therefore, the obtained answer is y = x - x/3.

Diagram D:

The value of x contains 3 congruent colored rectangles. So, the value of 2 congruent rectangles will be 2x/3.

Clearly, y will be the difference between x and 2x/3, that is, y = x - 2x/3.

Therefore, the obtained answer is y = x - 2x/3.

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The probability of getting at least one nun in three spins of a dreidel is approximately 0.578

The probability is the ratio of number of favorable outcomes to the total number of outcomes

The probability of getting no nuns in a single spin is 3/4, since there are three non-nun letters (Gimel, Hei, Shin) and four total letters.

The probability of getting no nuns in three spins is then (3/4)^3, since the spins are independent and we can multiply probabilities of independent events.

So the probability of getting at least one nun in three spins is

= 1 - (3/4)^3

= 1 - 0.421875

= 0.578125

Therefore, the probability of getting at least one nun is 0.578

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The given question is incomplete, the complete question is:

A dreidel is a four-sided spinning top with the Hebrew letters nun, gimel, hei, and shin, one on each side. Each side is equally likely to come up in a single spin of the dreidel. Suppose you spin a dreidel three times. Calculate the probability of getting (a) at least one nun?

Sselecting A, B, and C is the same as selecting B, C, and A, so = 720/(3*2*1) = 120 combinations

When the decision's order is unimportant, a combination is a choice made in mathematics from among a group of distinct elements. A pear and an orange, an apple and an orange, or a trio of fruits—an apple, an orange, and a pear—can be paired into one of three pairs. An official definition of a k-combination of a set S is a subset of S's k unique items. Consequently, two combinations are considered to be same if and only if they both contain the same elements. If a collection contains n elements, a combination is any set of n objects taken k at a time without repetition.

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A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.

In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Complete Question

Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?

Answer:

100 dispenses

Step-by-step explanation:

To check the answer:

Gumballs: 200 - (1*100) = 100

Explanation: 200 gumballs - (1 gumball * 100 dispenses) = 100 gumballs left.

Chocolate Candies: 900 - (8*100) = 100

Explanation: 900 candies - (8 candies * 100 dispenses) = 100 candies left.

Answer:

  100

Step-by-step explanation:

Given a candy machine with 200 gumballs dispensed 1 at a time, and another with 900 chocolates dispensed 8 at a time, you want to know how many dispenses from each will result in equal counts left in the machines.

The number of remaining gumballs after d dispenses is ...

  g = 200 -d

The number of remaining chocolates after d dispenses is ...

  c = 900 -8d

The number remaining in each machine will be equal when ...

  g = c

  200 -d = 900 -8d . . . . . substitute the above expressions

  7d = 700 . . . . . . . . . . add 8d -200

  d = 100 . . . . . . . . . divide by 7

100 dispenses from each machine will make the number of candies in the machines equal.

Answer: First, we'll round the values of A and b:

A = 340 rounded to the nearest 10 = 340

b = 49.8 rounded to 1 decimal place = 49.8

Next, we'll find the product of A and b:

A × b = 340 × 49.8 = 16872

Finally, we'll find the minimum of A × b:

Minimum of A × b = 16872

So, the minimum value of A × b is 16872.

Step-by-step explanation:

The simplest form of the fraction equivalent to 0.7 is 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, to show the denominator of the fraction in the simplest form that is equal to 0.7

To convert 0.7 into a fraction, we have to write it in p/q form, where p and q are positive integers.

we can write .7 as 0.7/1

now to remove the decimal point we will multiply and divide by 10

therefore,

0.7/1 ×  10/10  = 7/10

Hence, the simplest form of the fraction equivalent to 0.7 is 7/10

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Answer:

Edit: it's actually translation, sorry about that.

Step-by-step explanation:

Answer: I think it might be translation

Step-by-step explanation:

Translation: A slide of a slide of a shape on a coordinate plane. We can move a shape upward, downward, leftward, or rightward.