Mr. and Mrs. kinkaid open a certificate of deposit account that pays 1.45% interest compounded daily. How much interest will the account earn in 5 years on their deposit of $8,500? SHOW ALL WORK FOR CREDIT.

Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

Answer:

www.imsorryineedpoints.org

The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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Answer:

Multiplication

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

The gradient = rise/ run

= (0-6)/(3-0)

= -6/3

= -2.

A)  The gradient of line AB is -2.

B) The gradient of a line perpendicular to AB is 1/2.

C) The equation of the line passing through point A and perpendicular to AB is \(x - 2y + 12 = 0\).

A) The slope of line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Gradient of line \(= \frac{0-6}{3-0}\)

\(=-2\)

Therefore, the gradient of line AB is -2.

B) The gradient of a line perpendicular to AB can be determined by taking the negative reciprocal of the gradient of AB.

Negative reciprocal of -2 = 1/2

Therefore, the gradient of a line perpendicular to AB is 1/2.

C) To find the equation of the line passing through point A (0,6) and perpendicular to AB, we can use the point-slope form of a linear equation:

\(y - y_1= m(x - x_1)\)

Substituting the values:

\(x_1 = 0\)

\(y_1 = 6\)

\(m = \frac{1}{2}\)

\(y - 6 = \frac{1}{2}(x - 0)\)

\(y - 6 = \frac{1}{2}x\)

Multiplying both sides by 2 to eliminate the fraction:

\(2y - 12 = x\)

Rearranging the equation:

\(x - 2y + 12 = 0\)

Therefore, the equation of the line passing through point A and perpendicular to AB is \(x - 2y + 12 = 0\).

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Answer:

Step-by-step explanation:

Slope of the line:

\(m = \frac{y-y1}{x-x1} \\\)

Given:

slope = -3/4

point (x1,y1) = (2, -1)

Substitute and solve

\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)

1/2 is the y-intercept

(0,1/2)

Since we have 2 points already, we can then graph the line.

(2, -1) and (0, 1/2)

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:

Mean of Connors 3 card is 9

Step-by-step explanation:

Solution

Minimum of 3cards is 6

range is 7

max -min=7

max=min+7

max=7+6

max=13

Mean=6+13+8/3=27/3=9

Answer:

Mean of Connors 3 card is 9

Step-by-step explanation:

Solution

Minimum of 3cards is 6

range is 7

max -min=7

max=min+7

max=7+6

max=13

Mean=6+13+8/3=27/3=9

Answer:

The equation for the line is y = 2/5x + 24/5

Step-by-step explanation:

If you need the exact points, go to m4thway and plug that equation in.

Answer:

13 packages

Step-by-step explanation:

We need to find the highest common factor, in order to solve this problem.

So, we have to find the highest common factor of 39 and 13.

We find the highest common factor of 39 and 13 because it says in the problem” Tim has 39 pairs of headphones and 13 music players.”

And than you just find the highest common factor, after you find the highest common factor... YOU ARE DONE SOLVING THE PROBLEM!

The highest common factor will be 13

13: 1,13

39:1,3,13,39

ANSWER:13

Hope this helps!

Answer:

13

Step-by-step explanation:

Greatest number of packages Tim can make =

H. C. F of 39 and 13

Factors of 39 = 13 * 3 * 1

Factors of 13 = 13 * 1

H.C.F = 13

Therefore, Greatest number of identical packages Tim can make is 13.

Answer:

The probability that exactly 2 out of the first 10 customers buy a magazine

=

1.92%

Step-by-step explanation:

The Proportion of customers who buy a magazine = 9.6%

If 2 out of the first 10 customers buy a magazine, the proportion is given as  2/10 or 20%.

Therefore, the probability that exactly 2 out of the first 10 customers will buy a magazine is equal to the proportion of customers who buy a magazine multiplied by the proportion of the first 10 customers who buy a magazine

= 9.6% * 20%

= 1.92%

The solution has been explained below.

We will use the following equation, x² + y² = 81, where x and y are the pool's dimensions in feet, to determine the necessary estimations for the pool project.

1. Calculate the pool's diameter and radius:

We can infer that the radius of the pool is equal to the square root of 81 because the equation depicts a circle. As a result, r = 81 = 9 ft.

The pool's diameter is simply equal to twice its radius, or d = 2r = 18 feet.

2. Calculate the amount of water in the pool:

Since the pool is 4 feet high, we can determine its volume by multiplying the area of its circle-shaped base by the height.

The formula A = πr² can be used to calculate the area of the pool's base,

Therefore, V = Ah = πr²h = 1017.87 cubic feet represents the volume of water in the pool.

3. Determine the pool's total material cost:

There are 7.48 gallons in a cubic foot and a gallon of water costs $0.22.

As a result, Cw = V × 7.48 × 0.22 = 1017.87 × 7.48 × 0.22 = $1,619.72 is the entire cost of water for the pool.

If the radius of the pool is $185 per foot, then the cost of the materials is Cm = r × 185 = 9 × 185 = $1,665.

4. Calculate the pool's total labour hours:

A pool's construction is estimated to take 2.5 hours for every foot of its radius.

So, L = r × 2.5 = 9 × 2.5 = 22.5 hours of labour would be needed to complete this pool.

5. Calculate the total cost of labour for the project:

If you pay someone $19 per hour, Cl = L × 19 = 22.5 × 19 = $427.5.

6. Find the project's overall cost:

The project's overall cost is the product of its labour and material costs:

Cost as a whole equals Cm + Cw + Cl, which is 1,665 + 1,619.72 + 427.5, or $3,712.22.

In conclusion, the pool has an 18-foot diameter and a 9-foot radius according to the supplied equation. There are roughly 1017.87 cubic feet of water in the pool. Water and building supplies are included in the pool's projected material cost of $3,284.72. 22.5 hours of labour in total are needed, with a labour cost estimate of $427.5. Consequently, $3,712.22 is the expected final cost of the pool renovation.

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Answer:

5

Step-by-step explanation:

You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.

Answer:

(c) n = 100, p = 0.2

Step-by-step explanation:

To approximate to use the normal distribution for a binomial, we need that:

\(np \geq 10, n(1-p)\geq 10\)

So, for each option

(a) n = 10, p = 0.5

\(np = 10*0.5 = 5 < 10\)

So not appropriate

(b) n = 40, p = 0.88

\(np = 40*0.88 = 35.2 > 10\)

\(n(1-p) = 40*0.12 = 4.8 < 10\)

So not appropriate.

(c) n = 100, p = 0.2

\(np = 100*0.2 = 20 > 10\)

\(n(1-p) = 100*0.8 = 80 > 10\)

So appropriate

(d) n = 100, p = 0.99

\(np = 100*0.99 = 99 > 10\)

\(n(1-p) = 100*0.01 = 1 < 10\)

So not appropriated

(e) n = 1000, p = 0.003

\(np = 1000*0.003 = 3 < 10\)

So not appropriate

A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.

Given that,

Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.

We have to determine,

In which of the following situations would it be appropriate to use a normal distribution to approximate probabilities for a binomial distribution with the given values of n and p.

According to the question,

Probabilities for a binomial distribution with the given values of n and p.

(a) n = 10, p = 0.5

(b) n = 40, p = 0.88

(c) n = 100, p = 0.2

(d) n = 100, p = 0.99

(e) n = 1000, p = 0.003

To approximate to use the normal distribution for a binomial is given as,

\(np\geq 10 , \ n(1-p)\geq 10\)

        \(= np \geq 10\\\\= 10 \times 0.5 = 5<10\)

The normal distribution is less than 10 so, this not appropriate.

        \(= n.p \geq 10\\\\= (40).(0.88) \geq 10\\\\= 35.2\geq 10\\\\Then,\\=n(1-p) = 40(1-0.88) \geq 10 \\\\= 40\times 0.12 \geq 10 = 4.8\leq 10\)

The normal distribution is less than 10 so, this not appropriate.

        \(= n.p \geq 10\\\\= (100).(0.2) \geq 10\\\\= 20\geq 10\\\\Then,\\=n(1-p) = 100(1-0.2) \geq 10 \\\\= 100\times 0.8\geq 10 = 80\geq 10\)

The normal distribution is greater than 10 so, this appropriate.

        \(= n.p \geq 10\\\\= (100).(0.99) \geq 10\\\\= 99\geq 10\\\\Then,\\=n(1-p) = 100(1-0.99) \geq 10 \\\\= 100\times 0.01\geq 10 = 1\leq 10\)

The normal distribution is less than 10 so, this not appropriate.

        \(= np \geq 10\\\\= 1000 \times 0.003 = 3<10\)

The normal distribution is less than 10 so, this not appropriate.

Hence, A Normal distribution to approximate probabilities for a binomial distribution with the given values of n = 100 and p = 0.2.

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Answer:

It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients

For the circular cover we have:

A) The area is 379.94 ft²

B) The length of the rope must be 68.2 ft

Remember that the area of a circle of radius R is given by the formula:

\(A = pi*R^2\)

Where pi = 3.14

In this case, the diameter of the pool is 20ft, then the radius is:

R = 20ft/2 = 10ft

And it must extend 12 inches beyond, then the radius of the cover must be:

R = 10ft + 12in

Now, we know that 1ft = 12 in, then we can rewrite the radius as:

R = 10ft +1ft = 11ft

Then the area of the cover is:

\(A = 3.14*(11ft)^2 = 379.94 ft^2\)

B) now we want to get the length of the rope, we know that the rope runs along the cover, then the length of the rope must be equal to the circumference of the cover.

Remember that the circumference of a circle of radius R is:

\(C = 2*pi*R\)

Then the length of the rope will be:

\(C = 2*3.14*11ft = 68.2ft\)

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Option A) is correct

There is only one solution: x = 1. The solution x = 3 is an extraneous solution.  

Solution :

Given Equations:

\(\frac{1}{x} +\frac{1}{1-x} =\frac{x-2}{y-3}\)

solving The given Equation have :

\(\frac{1}{x}+ \frac{1}{x-3} =\frac{x-2}{y-3}\)

\(\frac{2x-3}{x(x-3)} =\frac{x-2}{y-3}\)

\(2x-3=x^{2} -2x\)

\(x^{2} -4x+3=0\)

\(x^{2} -x-x3+3=0\)

\(x(x-1)-3(x-3)=0\\x-3)(x-1)=0\\x=1,x=3\)

Extraneous solutions:

Due to its exclusion from the original equation's domain, an auxiliary solution is not a root of the original equation.

We may get this conclusion, but we cannot accept it as a conclusion since it is insufficient.

However, x = 3 cannot be a solution to the preceding equation because it produces a denominator of zero when used in the provided equation.

As a result, the following equation's solution is x = 1, while its superfluous solution is x = 3.

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Step-by-step explanation:

The height of the coin, after t seconds, is given by the following equation:

How long will it take the coin to reach the stream?

The stream is the ground level.

So the coin reaches the stream when h(t) = 0.

Multiplying by (-1)

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

This polynomial has roots  such that , given by the following formulas

In this question:

So

Time is a positive measure, so we take the positive value.

It will take 5.61 seconds for the coin to reach the stream.The height of the coin, after t seconds, is given by the following equation:

Answer:

B. 7.73 square units

Step-by-step explanation:

The area of the shaded region = area of the square - area of the inscribed circle

Radius of the circle (r) = 3 units

Side length of the square (s) = diameter of 2*radius of the inscribed circle = 6 units

Area of square = s² = 6² = 36 square units

Area of inscribed circle = πr² = π3² = 28.27 square units

Area of shaded region = 36 - 28.27 = 7.73 square units

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

4, -4, 36

Step-by-step explanation:

a) a*2 = -2*-2 = 4

b) a^2 = -2^2 = -4

c) a*3^2= 3*-2^2 = -36

a. The missing value in the table 0.03

b. The mean is 4.18

c. The variance is 3.23 and standard deviation is 1.80

d.  The larger the standard deviation, the greater the spread of the probability distribution.

A random variable is a variable that can take on different values depending on the outcome of a random event. In this case, the random variable X represents the number of calls per hour to a call center in the last month.

a. The missing value in the table is the number of calls per hour for the probability 0.03. From the table, we see that the number of calls per hour is 7.

b. The mean, also known as the expected value, is a measure of the center of the probability distribution. It is calculated by taking the sum of the product of each possible value of X and its corresponding probability. In mathematical terms, the mean of X is given by:

E(X) = 1 * P(1) + 2 * P(2) + 4 * P(4) + 5 * P(5) + 6 * P(6) + 7 * P(7)

E(X) = 0.01 + 0.2 + 1.04 + 1.65 + 1.08 + 0.21 = 4.18

So, the mean number of calls per hour to the call center in the last month is 4.18.

c. The variance of X is a measure of the spread of the probability distribution. It is calculated by taking the sum of the squared differences between each possible value of X and the mean, multiplied by the corresponding probability. In mathematical terms, the variance of X is given by:

Var(X) = (1 - 4.18)² * P(1) + (2 - 4.18)² * P(2) + (4 - 4.18)² * P(4) + (5 - 4.18)² * P(5) + (6 - 4.18)² * P(6) + (7 - 4.18)² * P(7)

Var(X) = 3.23

The standard deviation is the square root of the variance, and it is also a measure of the spread of the probability distribution. In mathematical terms, the standard deviation of X is given by:

=> SD(X) = √(Var(X)) = √(3.23) = 1.80

d. Interpretation:

The mean of 4.18 calls per hour represents the average number of calls to the call center in the last month.

The standard deviation of 1.80 indicates that the number of calls per hour deviates from the mean by approximately 1.80 calls on average.

This means that about 68% of the time, the number of calls per hour will be between 2.38 (4.18 - 1.80) and 6.08 (4.18 + 1.80).

Complete Question:

The random variable X represents the number of calls per hour to a call center in the last month. The probability distribution for X is below.

x 1 2 4 5 6 7

P(x) 0.01 0.10 0.26 0.33 0.18 0.06 0.03

a. What is the missing value in the table?

b. Find the mean.

c. Find the variance and standard deviation.

d. Interpret your results.

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Answer:

Step-by-step explanation:

Given triangle QRS with:

Use the law of sines to solve:

Answer:

29.5

Step-by-step explanation:

original had 29.3 which is not an option. 29.5 is right.

Answer:

1)

7+9-15 = add 7 and 9, then subtract 15

2)

15-(7+9) = The sum of 7 and 9 subtracted from 15

3)

15-(7+9) =  subtract 7 from 15, then add 9

Step-by-step explanation:

Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient

Answer:

positive

Step-by-step explanation:

Answer:

Answer: Positive

Step-by-step explanation:

Answer:

my answer -C

Step-by-step explanation:

White,Red,and Green.

Answer:

slope: 5

y-intercept: -4