How much would $100 invested at 8% interest compounded continuously be
worth after 15 years? Round your answer to the nearest cent.
A (t) = P*e^rt

Answer:

Step-by-step explanation:

Given points are P(-1,4) and Q(-4,-2)

we know that slope m between two points (x1,y1) and (x2,y2) is m=y2-y1/x2-x1

so,slope m between points P and Q is m=-2-4/-4-(-1)

m=-6/-3

m=2

Now,we know that equation of line

with slope m having points (x1,y1) and (x2,y2) is y-y1=m(x-x1)

so equation of line between P and Q is y-4=2(x+1)

y-4=2x+ 2

y=2x+6

The hare can afford to nap for a maximum time of 3,690 seconds without losing the race if his speed is 15 m/s.

After running for 7 seconds, the hare has covered a distance of:

[tex]distance = speed \times time\\distance = 15 \times 7\\[/tex]

distance = 105m

The hare is now 895 m away from the starting line and 100 m away from the finish line.

The hare needs to cover a distance of 100 m to reach the finish line, while the tortoise needs to cover a distance of 895 m.

calculate the time it would take the tortoise to reach the finish line:

[tex]time = \frac{100}{0.27}[/tex] = 3704 seconds

The maximum speed of the hare is 15 m/s, which means the time it would take the hare to cover the distance is:

[tex]time = \frac{100}{15}[/tex] = 6.67 seconds

so, the time hare have to nap so that he does not lose race = 3704 - (7+6.67) ≅3690 seconds

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Answer:

Jennifer raised $25

Rebecca raised £50

Derek raised $37.50

Matthew raised $75

Step-by-step explanation:

J: 50% = dividing by 2, 50/2= 25

R: 50 is 100%, because that was the total

D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50

M: We add another 25% onto 50 so 25+50=75.

(hope this works!!)

Answer:

[tex]8[/tex]

Step-by-step explanation:

[tex]x^2+12x+44=(x^2+12x+36)+8=(x+6)^2+8[/tex]

In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.

We can approach this problem using the principle of inclusion-exclusion.

First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:

8P₃ = 8 x 7 x 6 = 336

Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃  = 4 x 3 x 2 = 24 ways.

Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃  = 4 x 3 x 2 = 24 ways.

However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.

There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.

Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃  = 4 x 3 x 2 = 24 ways.

Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:

336 - 24 - 24 + 2 + 24 = 314 ways.

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The required value of the x for the missing lengths of the side triangle is given as 28.6 ft.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

here,
As the triangles are similar,
The ratio of corresponding sides is equal,
So
13/5 = x/11
x = 13 × 11 / 5
x = 28.6

Thus, the required value of the x for the missing lengths of the ais given as 28.6 ft.

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Answer:

8√57/57

Step-by-step explanation:

a² + b² = c²

a² + 8² = 11²

a² + 64 = 121

a² = 57

a = √57

For angle Θ, opp = 8, adj = √57, hyp = 11.

tan Θ = opp/adj = 8/√57 = 8√57/57

Answer: 7,000,000

By the way: How do we have almost the same name?

Answer:

the answer is 7,000,000

Step-by-step explanation:

6,000,000+1,000,000=7,000,000

There are 6 grams of sugar in 3/4 of a liter of the sports drink. when There are 4 grams of sugar in 1/2 of a liter of a new sports drink.

To find out how much sugar is in 3/4 of a liter of the sports drink, we need to first calculate the total amount of sugar in 1 liter of the drink. Since there are 4 grams of sugar in 1/2 of a liter, then in 1 liter, there would be 4 x 2 = 8 grams of sugar.

Now that we know there are 8 grams of sugar in 1 liter, we can calculate how much sugar there is in 3/4 of a liter: 8 x (3/4) = 6 grams.

Therefore, there are 6 grams of sugar in 3/4 of a liter of the sports drink.

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The equation of the quadratic curve are:

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex for curve 1

v (h, k) = (-5, 4)

h = -5

k = 4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x + 5)² + 4

Using (-3, 0) to solve for a

y = a(x + 5)² + 4

0 = a(-3 + 5)² + 4

-4 = a (2)²

a = -1

The equation is y = -(x + 5)² + 4

The vertex for curve 2

v (h, k) = (5, -4)

h = 5

k = -4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x - 5)² - 4

Using (3, 0) to solve for a

y = a(x - 5)² - 4

0 = a(3 - 5)² - 4

4 = a (-2)²

a = 1

The equation is y = (x + 5)² + 4

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When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the mean, we call the new value a Z-Score.

In statistics, each mathematical formula and each element has an internationally recognised name. This is to ensure that everyone in the world understands what every researcher has to say in every letter. A statistic that tells the number of standard deviations a data value is above or below the mean is called a z-score. And its formula is, Z = (X − μ)/σ

where, μ--> population mean,

σ --> population standard deviation and

x --> the raw-score.

Hence, when a data value is converted to a standardized scale, new value, Z-Score is representing the number of standard deviations the data value lies from the mean.

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The angles that are corresponding angles:

∠1 and ∠3

∠5 and ∠7

∠6 and ∠8

We know that when a transversal intersects parallel lines or non-parallel lines then the angles formed at the same relative position at each intersection are nothing but the corresponding angles.

If a transversal intersects parallel lines, then the corresponding angles formed have equal measure.

Wheras if a transversal intersects non-parallel lines, then the corresponding angles formed doesn’t have any relation with each other.

In the following figure we can observe that line p and line q are non-parallel lines and are intersected by transversal r.

From definition of corresponding angles, the pair of corresponding angles:

∠1 and ∠3

∠5 and ∠7

∠6 and ∠8

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Find the complete question below.

For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.

When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".

The species of bacteria follow an exponential growth pattern.

The exponential growth is given as:

[tex]A(t) = A_0e^{kt}[/tex]

Where, A₀ is the initial population = 4000

k = constant

t = time = 30 minutes = 1/2 hour.

The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.

Substituting the values in the equation:

[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]

Takin ln on both sides of the equation:

ln(2) = 1/2 k

2(ln(2)) = k

k = 1.38

The number of bacteria present after 3 hours:

[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]

A(t) = 256000

Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.

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The solution to the given quadratic equation formed is; y = -9/4 and y = -1

The given equation is expressed as;

(3 + 2y) = √(-y)

Taking the square of both sides gives us;

(3 + 2y)² = √(-y)]²

→ 9 + 12y + 4y² = -y

4y² + 13y + 9 = 0

Factoring the expression gives us;

4y² + 4y + 9y + 9 = 0

4y(y + 1) + 9(y + 1) = 0

Thus;

(4y + 9) = 0

(y + 1) = 0

y = -9/4

y = -1

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To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.

The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:

1. Simplify any expressions inside parentheses.

2. Evaluate any exponents.

3. Perform multiplication and division, from left to right.

4. Perform addition and subtraction, from left to right.

Let's follow these steps to simplify the expression,

1. Simplify any expressions inside parentheses.

There are two sets of parentheses in the expression: (4x + 3) and (x - 3).

We can use the distributive property of multiplication over addition to eliminate the parentheses:

2(4x + 3) + (x - 3) = 8x + 6 + x - 3

2. Evaluate any exponents,

There are no exponents in the expression.

3. Perform multiplication and division, from left to right.

There is no multiplication or division to perform.

4. Perform addition and subtraction, from left to right.

We can now simplify the expression by combining like terms:

8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3

Therefore, the simplified expression is 9x + 3.

In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.

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Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

Based on the information in the graph, it can be inferred that Josephine must have painted 1/4 of the painting.

To find the amount (fraction) of the paint, Josephine should have painted the section marked on the image. To know how much that section is equivalent to, we must take as a reference that the entire painting would be 1.

So, if we divide the painting in half, it would be 1/2, that is, we paint 1 of 2 possible parts. However, in the case of Josephine there are 4 possible parts and she only painted one. From the above, what she should have painted was 1/4.

Note: This question is incomplete. Here is the complete information:

question:

Approximately what portion of the painting was Josephine supposed to paint?

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PLEASE GIVE BRAINLIEST!

thank you and have a good day ;)

Answer:

-11/2

Step-by-step explanation:

Multiply both sides by a polynomial to clear functions

x + 1 = 3(x +4)

x + 1 = 3x + 12

x - 3x = 12 -1

-2x = 11

x = -11/2

I hope this helps

Answer:

The answer can be written in multiple forms

Fraction Form:   [tex]x=-\frac{11}{2}[/tex]

Decimal Form:   [tex]x=-5.5[/tex]

Step-by-step explanation:

Given

[tex]\frac{x+1}{x+4}=3[/tex]

Lets solve for [tex]x[/tex].

Eliminate the fraction by multiplying each side of the equation by [tex]x+4[/tex].

[tex]x+1=3(x+4)[/tex]

Simplify the right side by applying the distributive property.

[tex]x+1=(3*x)+(3*4)[/tex]

[tex]x+1=3x+12[/tex]

Subtract [tex]3x[/tex] from both sides of the equation.

[tex]x+1-3x=12[/tex]

Add [tex]x[/tex] and [tex]-3x[/tex].

[tex]-2x+1=12[/tex]

Subtract [tex]1[/tex] from both sides of the equation.

[tex]-2x=11[/tex]

Divide each side of the equation by [tex]-2[/tex].

[tex]x=-\frac{11}{2}[/tex]

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The p-value of the test statistic is 0.0401, which is less than the commonly used significance level of 0.05.

In statistical analysis, hypothesis testing is an essential method used to make inferences about population parameters using sample data. In this case, a hospital director wants to test a claim that the percentage of insured patients is less than the expected percentage.

The alternative hypothesis is that the percentage of insured patients is less than the expected percentage. To test this hypothesis, the director will use a one-tailed z-test for proportions. The test statistic is calculated as:

z = (p - P) / √(P(1-P) / n)

where p is the sample proportion, P is the expected proportion under the null hypothesis, and n is the sample size.

In this case, the sample proportion is 115/230 = 0.5, and the expected proportion is not specified. However, since the null hypothesis is that the percentage of insured patients is equal to the expected percentage, we can use the observed percentage of 55% as a reasonable estimate of the expected percentage. Thus, P = 0.55.

Plugging in these values, we get:

z = (0.5 - 0.55) / √(0.55 * 0.45 / 230) = -1.74

p-value = -1.74/0.069 = 0.0401

Trough this one we have identified that the test statistic's p-value is 0.0401, indicating that it is below the widely accepted significance level of 0.05.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true.

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The average rate of change of the function is 1.6

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

The graph

The interval is given as

−4≤x≤1.

From the graph, we have

f(-4) = -4

f(1) = 4

The average rate of change at this interval is calculated as

Rate = Change in function values/Change in x values

So, we have

Rate = (-4 - 4)/(-4 - 1)

Evaluate

Rate = 1.6

Hence, the rate is 1.6

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The complete expression in the blank is cos (56°) = sin(34°)​

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

cos (56°) = sin(°)​

The blank expression can be calculated as

When x + y = 90;

sin(x) = cos(y)

Using the above as a guide, we have the following:

Blank + 56 = 90

Evakuate the like terms

Blank = 34

So, we have

cos (56°) = sin(34°)​

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the solution is where they intercept; (2,-4)

The value of the function f(-1) is -4

A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.

From the information given, we have the function;

f(x)=4x^2+9x+9

To determine the value of f(-1)

substitute the value of x as- 1, we get;

f(-1) = 4(-1)² + 9(-1) + 9

expand the bracket, we get;

f(-1) = -4 -9 + 9

Add or subtract the values, we have;

f(-1) = -4

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Answer:

The down payment that Jordan made on the house was $300,000 x 10% = $30,000. So, he financed $300,000 - $30,000 = $270,000.

where

M = monthly payment

P = loan amount ($270,000)

r = monthly interest rate (3% / 12 months = 0.003)

n = number of payments (30 years x 12 months/year = 360)

This comes out to a monthly payment of approximately $1,173.38.

To simplify

The loan amount is- $270,000

Her monthly payment will be- $1,173.38

The amount of interest she will pay is- $8,100

The total number of hours that Jane studied for her two tests were 8 ¹¹ / ₁₂ hours

To find the number of hours that Jane studied, you first need to convert the hours studied for history and math, from mixed fractions to improper fractions.

4 ² / ₃ hours :

= ( 4  x 3 + 2 ) / 3

= 14 / 3 hours

4 ¹ / ₄ hours :

= ( 4 x 4 + 1 ) / 4

= 17 / 4 hours

Add up both hours by using a common denominator of 12 :
= ( ( ( 12 / 4 ) x 17 ) + ( ( 12 / 3 ) x 14 ) ) / 12

= ( 51 + 56 ) / 12

= 8 ¹¹ / ₁₂ hours

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The full question is:

Last weekend Jane studied 4 2 3 hours for her history final and 4 1 4 hours for her math exam. How many hours in all did Jane study for the two tests?

Answer:

[tex]-1[/tex]

Step-by-step explanation:

[tex](x+y)+(3x-y)=4 \implies 4x=10 \implies x=2.5 \\ \\ 2.5+y=6 \implies y=3.5 \\ \\ \therefore x-y=2.5-3.5=-1[/tex]

Answer:

speak Spanish

Step-by-step explanation:

I"m sorry

to help