Colton is going to invest $76,000 and leave it in an account for 15 years. Assuming the interest is compounded daily, what interest rate, to the nearest hundredth of a percent, would be required in order for Colton to end up with $155,000?

Answer:

135

Step-by-step explanation:

Hello There!

Remember the exterior angle of a triangle rule:

An exterior angle of a triangle is equal to the sum of its opposite interior angles

so x = the sum of its opposite interior angles (58 and 77)

58 + 77=135

so x = 135

Answer: x=135°

Step-by-step explanation:

Angles in a triangle always add up to 180° so to find the corner of the missing side next to x you need to do 58+77=135 then do 180-135=45°

So then, now we have the angle inside the triangle, we can now work out what x is.

Angles on a straight line always add up to 180° so you do 180-45=135° so x=135°.

Hope this helps :)

Answer:

Income $500, Fixed exp. $100, Living Expenses $300

The sum $a b c$ is 11760 if the ratio of the areas of two squares is  \($\frac{32}{63}$\).

Let the side length of the first square be x and the side length of the second square be y. Then we have:

\(\frac{Area of first square}{Area of second square} = \frac{x^2}{y^2} = \frac{32}{63}\)

By cross multiplying, we get:

63 x² = 32 y²

And then by rearranging:

\(\frac{x}{y} = \frac{4\sqrt{7} }{9}\)

Now, rationalizing the denominator, we get:

\(\frac{x}{y} = \frac{4\sqrt{7} }{9} . \frac{\sqrt{7} }{\sqrt{7} } = \frac{28\sqrt{7} }{63}\)

Thus, a.b.c = 28.7.63 = 11760.

Therefore, the value of the sum $a b c$ is 11760.

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Answer:

168 in

Step-by-step explanation:

Pythagoras says:

b² + 56² = 70²

so

b² = 70² - 56²

b = √1764 = 42

so the perimeter is 70+56+42 = 168

Ozone can be both harmful and beneficial to health, depending on its location in the atmosphere and the levels at which it is present.

In the stratosphere (the layer of the atmosphere that is located about 10-50 kilometers above the Earth's surface), ozone is a beneficial gas that protects life on Earth by absorbing harmful ultraviolet (UV) radiation from the sun. However, at ground level, ozone can be harmful to health, particularly for people with respiratory problems such as asthma.

Exposure to high levels of ozone can irritate the respiratory system and cause coughing, throat irritation, and chest pain. It can also worsen bronchitis, emphysema, and other lung diseases. Ozone can also reduce lung function and inflame the linings of the lungs, leading to more serious health problems.

It is important to note that ground-level ozone is not emitted directly into the air, but is formed when pollutants from sources such as vehicle exhaust, power plants, and industrial facilities react with sunlight and heat.

Therefore, Ozone can be both harmful and beneficial to health.

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a. In total 1820  many different jury selections are possible

b. The probability that a majority of the jury members will be men if the choice is made randomly is 0.172. 

a. The number of diverse jury determinations conceivable can be found utilizing combinations:

The number of distinctive jury choices = (Add up to the number of combinations of 12 individuals from 16) = 16C12 = (16!/(12!4!)) = 1820.

In this manner, there are 1820 distinctive jury choices conceivable.

b. Let X be the number of men chosen within the jury.

Since each choice is autonomous and the likelihood of selecting a man is rise to the likelihood of selecting a lady, X takes after a binomial dispersion with parameters n=12 and p=0.5.

The likelihood that a lion's share of the jury individuals will be men is the entirety of the probabilities of selecting 7, 8, 9, 10, 11, or 12 men:

P(X>=7) = P(X=7) + P(X=8) + P(X=9) + P(X=10) + P(X=11) + P(X=12)

Utilizing the binomial likelihood equation, we will discover each of these probabilities:

P(X=k) = (12 select k) * \(0.5^12\)

Hence,

P(X>=7) = [(12 select 7) + (12 select 8) + (12 select 9) + (12 select 10) + (12 select 11) + (12 select 12)] * \(0.5^12\)

Employing a calculator, we are able to assess this expression to induce:

P(X>=7) = 0.171875

Hence, on the off chance that the choice is made arbitrarily, the likelihood that a larger part of the jury individuals will be men is around 0.172. 

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The line a and line c are perpendicular to each other.

Lines are known if they are parallel or perpendicular by there slopes.

Therefore, parallel lines have the same slopes and perpendicular have slopes that are negative reciprocals of one another.

The slope of a line is the change in the dependent variable to the change in the independent variable.

Therefore, let's find the slopes of each line.

line a:

slope = -3 - 1 / 6- 0  = - 4 / 6 = - 2 / 3

line b:

slope = -2 - 0 / 3 + 3 = - 2 / 6 = - 1 / 3

line c:

slope = 7 + 2 / 2 + 4 = 9 / 6 = 3 / 2

Therefore, line a and c are perpendicular

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The only cardinal number whose letters are in alphabetical order in English is "forty". This word meets the criteria because its letters appear in alphabetical order: "f", "o", "r", "t", "y".
To find the cardinal number with letters in alphabetical order, we need to examine each number individually. Starting from zero, we can see that "zero" does not have letters in alphabetical order. Similarly, "one" and "two" do not meet the criteria. The word "three" has letters in alphabetical order, but it is not a cardinal number. Continuing our search, we find that "forty" is the first and only cardinal number where the letters are arranged in alphabetical order.
In English, the only cardinal number whose letters are in alphabetical order is "forty".

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Therefore, the derivative of 5^(4x) is 20ln(5) * 5^(4x).

To calculate the derivative of 5^(4x), we can use the chain rule of differentiation. The chain rule states that if we have a function f(g(x)), then its derivative is given by f'(g(x)) * g'(x).

In this case, we can let f(x) = 5^x and g(x) = 4x. Then we can write the original function as f(g(x)) = 5^(4x).

Now we can calculate the derivative as follows:

f'(x) = 5^x * ln(5)     (the derivative of 5^x is 5^x times the natural logarithm of 5)
g'(x) = 4              (the derivative of 4x is 4)

Using the chain rule, we obtain:

(5^(4x))' = f'(g(x)) * g'(x)
         = 5^(4x) * ln(5) * 4
         = 20ln(5) * 5^(4x)

Therefore, the derivative of 5^(4x) is 20ln(5) * 5^(4x).
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Answer:

A i think ( Sorry if am wrong.)

Step-by-step explanation:

Comparing the articles I, II, and III of the constitution, in the descending order of length and detail, the articles are ranked as I, II, and III. Article I is the longest.

Article I of the constitution created the legislative branch, article II of the constitution created an executive branch, and article III of the constitution created a judicial constitution. Article I is the longest and more detailed part of the constitution as the powers and the duties of the legislative branch are much more varied than the executive branch. Additionally, the legislative branch is composed of more individuals than the executive branch.

Article 1 is the longest as founding fathers believed that a legislative branch is very important in a government that represents the citizens. Article 3 is the shortest part of the constitution as the founding fathers did not expect the judiciary to play a large role.

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Answer:

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

Step-by-step explanation:

At Lawson Middle School, Mr. Hernandez asked 90 randomly selected students from each grade level for their favorite subject.

   90 randomly selected students from each grade level for their favorite subject, and 28 chose social studies as their favorite.

so, the percent of students who love social studies is given by:

28/90 x 100=31.11%

   He used this data to draw the inference that out of the 250 middle school students, about 20% prefer social studies.

No, Mr. Hernandez’s sample is random, not biased, large enough compared to the population, but 28 is not 20% of 90.

Answer:

C on EDG

Step-by-step explanation:

Answer:

Step-by-step explanation:  V= Voltage

                                               I= Current

                                               R= Resistance

Ohm's Law Mathematically expressed as: I= V/R or V= IR or R= V/I

V= 500

I= ?

R= 250

I= V/R

I= 500/250

I= 2 amps

Answer:

I know it know!!!!

Step-by-step explanation:

Answer:

6.2 < x < 26.6

Step-by-step explanation:

The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.

16.4 - 10.2 = 6.2

16.4 + 10.2 = 26.6

Let x = length of third side.

6.2 < x < 26.6

The percent of attendance figures that differs from the mean by 1500 persons or more is 6.68%.

From the question above, Mean μ = 10,000

Standard Deviation σ = 1,000

The formula for z-score is :

z = (x-μ) / σ

Where, x = observation

z = z-score

Mean μ = 10,000

Standard Deviation σ = 1,000

From the above formula, let's calculate z-score for x = 11,500

z = (x-μ) / σ

z = (11,500 - 10,000) / 1000

z = 1.5

Now, find the probability of attendance figures that differs from the mean by 1500 persons or more.

P(z ≥ 1.5) = 0.0668

To find the percentage, we need to multiply the above value by 100.

P(z ≥ 1.5) × 100 = 0.0668 × 100 = 6.68%

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Mia would have to work 26.1 hours (approx. 26) to earn $124.00

4.75x=124

divide 4.75 by 4.75 and divide 124 by 4.75

x=26.1

Answer:

Square A is 4 times greater than Square B

Step-by-step explanation:

Square A is 12 feet x 12 feet = 144

Square B is 6 feet x 6 feet = 36

144 ÷ 36 = 4

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

good i think

Step-by-step explanation:

The total number of gold and blue squares are 18 and 13 respectively.

Here, we are given that Megan is making a quilt from squares of material.

The quilt has 9 rows and each row has 6 squares.

There are 4 corner squares in the quilt which will be white. Around 1 corner square there will be 3 squares that share a side with the white square.

Thus, there will be a total of 12 gold square around the 4 corner squares.

Further, there are two center squares in the middle row that are white.

Around these 2 center white squares there will be 6 squares that share a side with them. Hence, these 6 square will also be gold.

Therefore, the total number of gold squares will be-

6 + 12

= 18

Now, the white squares = 4 + 6 = 10

and gold squares = 18

and the total number of squares = 9 × 6 = 54

Thus, the number of remaining squares = 54 - 18 - 10

= 26

Out of these remaining 26 squares half will be blue and half pink.

Thus, the number of blue squares will be-

26/2

= 13

Hence, we find that the total number of gold and blue squares are 18 and 13 respectively.

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The expression that represents the value of the stock after two years in terms of x is 1.6144x

After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -

x + 0.39x = 1.39x

After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -

1.39x - 0.16(1.39x) = 1.16(1.39x)

Simplifying this expression, we get,

1.16(1.39x) = 1.6144x

Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.

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The complete question is -

Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.

Change your group will get back from a $100 cost bill = $4

Me and my three friends are going to wonderland water park. Our group decided to ride each water ride two times.

The coaster cost = $4.50

The slide cost = $4.00

The drop cost = $3.50

Number of people = you + your friends = 1+3 =4

Cost of all three rides = The coaster cost + The slide cost + The drop cost

= $4.50 + $4.00 + $3.50 = $12.00

Four people takes all the rides = $12.00 x 4 = $48.00

If they take all rides twice = $48 x 2 = $96

Change will your group get back from a $100 bill = $100 - $96

Change your group will get back from a $100 bill = $4

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Answer: 13

Step-by-step explanation:

The step that is missing for Jimmy to draw a 50° angle is "He finds 50° on the protractor and draws a mark on the paper" (option B).

According to the process described, Jimmy has already draw the first ray that is going to work as the baseline for him to draw the angle he requires. After this, he will need to line up his protactor with this ray (step 1).

Then the next step would be to use a pencil or similar material to make a mark in the 50°, this is an important step as it guarantees the angle is correct before he draw the line.

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The conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To find the conditional probability that the size of the family is less than 6 given that it is at least 3, we need to use the formula for conditional probability.

Let's denote A as the event that the size of the family is less than 6, and B as the event that the size of the family is at least 3.

The conditional probability of A given B, denoted as P(A|B), is calculated as follows:

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

First, we need to find P(B), the probability that the size of the family is at least 3. Since the family is selected at random, we can assume that all possible family sizes have an equal chance of being selected.

Let's assume the total number of possible family sizes is n. The probability of selecting a family with at least 3 members is the sum of the probabilities of selecting a family with exactly 3 members, exactly 4 members, and exactly 5 members.

P(B) = P(3) + P(4) + P(5)

Next, we need to find P(A and B), the probability that the size of the family is both less than 6 and at least 3. Since any family size less than 6 is also at least 3, P(A and B) will be the same as P(B).

Finally, we can substitute the values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = P(B) / P(B) = 1

Therefore, the conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

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Answer:

Assuming

\(y = -2x + 6x - 1\\y = 4x - 1\)

Step-by-step explanation:

See Graph

The area of each polygon in this problem is given as follows:

a) 252 square units.

b) 65 square units.

For item a, we have a rectangle of dimensions 12 and 21, hence the area is the multiplication of the dimensions, as follows:

A = 12 x 21 = 252 square units.

For item b, we have a triangle with base 13 and height 10, hence the area is half the multiplication of the base by the height, as follows:

A = 0.5 x 13 x 10 = 65 square units.

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Answer:

15x²y + 21xy²

Step-by-step explanation:

Given

3xy(5x + 7y) ← distribute by 3xy

= 15x²y + 21xy²

Answer:

15x^2+21x^21x

is your ans I hope it helps mate

#Captainpower:)

have a great day

(a) The number of ways to choose 5 colors without replacement from 15 distinct colors, where the order of the choices is not relevant, is given by the combination formula. This is denoted as "15 choose 5," or 15C5, which is equal to 3,003.

(b) If the order of the choices is relevant, then the number of ways to choose 5 colors without replacement from 15 distinct colors is given by the permutation formula. This is denoted as "15 permute 5," or 15P5, which is equal to 3,003,600.

In part (a), we use the combination formula because we want to know the number of ways to choose 5 colors from 15 distinct colors without regard to the order of the choices. This formula is given by nCr = n!/(r!(n-r)!), where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15C5 = 15!/(5!(15-5)!) = 3,003.

In part (b), we use the permutation formula because we want to know the number of ways to choose 5 colors from 15 distinct colors, where the order of the choices matters. This formula is given by nPr = n!/(n-r)!, where n is the number of items to choose from, and r is the number of items to choose. In this case, n = 15 and r = 5, so we have 15P5 = 15!/10! = 3,003,600.

Overall, the key difference between part (a) and part (b) is whether or not the order of the choices matters. If the order doesn't matter, we use the combination formula (nCr), and if the order does matter, we use the permutation formula (nPr).

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Answer:

The slope is \(\frac{-1}{3}\).

Step-by-step explanation:

Math Vocabulary            Values

Vertical Change                 -1

Horizontal Change             3

Slope                                   \(\frac{-1}{3}\)