Tommy opens a bank account with an initial amount of $650. The account has an annual
interest rate of 3.5%. What will the account balance (principle+interest) be after 8 years if
the account is compounded:
a) annually?
b) quarterly?
c) weekly?
d) daily?
e) continuously?

Answer:

Step-by-step explanation:

x+y=5; x-y=3Adding both equations, we get:

2x = 8

x = 4Substituting the value of x in any of the equations:

x+y=5

4+y=5

y=1So the solution to this system of equations is: x=4, y=1.3x+y=11; y=x+3Substituting y=x+3 in the first equation:

3x+x+3=11

4x=8

x=2Substituting x=2 in the second equation:

y=x+3

y=2+3

y=5So the solution to this system of equations is: x=2, y=5.x+3y=0; 2x-y=-7Multiplying the second equation by 3 to eliminate y:

6x-3y=-21Adding both equations, we get:

7x=-21

x=-3Substituting x=-3 in the first equation:

x+3y=0

-3+3y=0

y=1So the solution to this system of equations is: x=-3, y=1.y=-3x-2; 6x+2y=-4Substituting y=-3x-2 in the second equation:

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

6x-6x-4=-4

-4=-4This means that the two equations are equivalent and represent the same line. Therefore, there are infinitely many solutions to this system of equations.-4x+5y=27; x-6y=-2Multiplying the second equation by 5 to eliminate y:

5x-30y=-10Adding both equations, we get:

x-4x+5y-30y=-2+27

-x-25y=25

25y=-x-25

y=-(1/25)x-1Substituting y=-(1/25)x-1 in the first equation:

-4x+5(-(1/25)x-1)=27

-4x-5/5x-5=27

-9x=32

x=-32/9Substituting x=-32/9 in the expression for y:

y=-(1/25)(-32/9)-1

y=83/225So the solution to this system of equations is: x=-32/9, y=83/225.

The value of  [tex]a^2+ b^2+ c^2[/tex] is

[tex]a^2+ b^2+ c^2[/tex][tex]=6^2+0^2+1^2[/tex] = 37

We have the information from the question:

Average is 55 miles per hour.

We know that the number of miles she drove is divisible by 5

So, a and c must either be the equal or differ by 5.

Now, According to the question:

Let the number of hours Danica drove be k.

Then we know that 100a + 10b + c + 55k = 100c + 10b + a.

Now, 99c - 99a = 55k

9c - 9a = 5k

Thus, k is divisible by 9.

k must be 9, and

Therefore c - a = 5.

Because a + b + c [tex]\leq[/tex] 7 and a [tex]\geq[/tex] 1 , a = 1, c = 6 and b = 0,

Plug all the values

[tex]a^2+ b^2+ c^2[/tex][tex]=6^2+0^2+1^2[/tex] = 37

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There are two ways you could approach this.

The first is to solve each inequality separately and see which one ends up equal to x ≥ -1.

Another and faster option is to test 0 in each inequality, because 0 is in the solution set and 0 is easy to work with.  (You could do this for any value in the solution set.)

A: Is 4(0) + 3 > 7 true?  No.  3 > 7 is false.  This eliminates A.

B. Is 0/3 - 2 ≥ 2 true?  No.  -2 ≥ 2 is false.  This eliminates B.

C. Is -2(0) - 3 ≤ -1 true?  Yes.  -3 ≤ -1 is false.  We cannot eliminate C.

D. Is 0 + 5 < 4 true?  No.  5 < 4 is false.  This eliminates D.

So based on using x=0, the only possible solution is C.

You can double check this by solving 2x - 3 ≤ -1 for x:

    -2x - 3 ≤ -1

         -2x ≤ 2  (by adding 3 to both sides)

Now when you divide by -2 to solve for x, remember to flip the inequality.

         -2x ≤ 2

             x ≥ -1  

So this confirms that C is correc.

The standard deviation is approximately 24.28 units.

1. The standard deviation can be calculated using the formula for the normal distribution:

P(X > 250) = 0.05

Using a standard normal distribution table, we can find the corresponding z-score for a probability of 0.05, which is approximately 1.645.

z = (250 - 210) / σ

Solving for σ, we get:

σ = (250 - 210) / z = (250 - 210) / 1.645 = 24.28 units

Therefore, the standard deviation is approximately 24.28 units.




To determine the standard deviation of a normally distributed pollutant concentration in a lake, we first use the probability of exceeding 250 units (0.05) and a standard normal distribution table to find the corresponding z-score (1.645). Using this z-score and the given mean (210 units), we can solve for the standard deviation using the formula for the normal distribution. The resulting standard deviation is approximately 24.28 units.



The standard deviation is an important measure of variability in a dataset and can be calculated using the formula for the normal distribution. In this case, the standard deviation of a normally distributed pollutant concentration in a lake was calculated using the mean and probability of exceeding a certain value.

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The polar coordinates are solved the point is P ( 2 , π/4 )

Given data ,

Given the point P = (2, π/4) on the interval [-2π, 2π], here are two different representations of this point:

Cartesian Coordinates: (2, π/4)

In the Cartesian coordinate system, the point P is represented by its x and y coordinates. The x-coordinate is 2, and the y-coordinate is π/4.

Polar Coordinates: (2, 45°)

In polar coordinates, the point P is represented by its radius (distance from the origin) and angle. The radius is 2, and the angle is π/4, which is equivalent to 45 degrees.

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The value of the area of the shaded region is,

⇒ 23.44 m²

Since, We know that;

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Sides of parallelogram = 6 m

And, Diameter of circle = 4 m

Hence, We can formulate;

The area of parallelogram is,

⇒ area of parallelogram = 6 × 6

⇒ area of parallelogram = 36 m²

And, Area of circle is,

⇒  Area of circle = πr²

⇒  Area of circle = 3.14 × 2²

⇒  Area of circle = 3.14 × 4

⇒  Area of circle = 12.56 m²

Hence, We get;

The value of the area of the shaded region is,

⇒ area of the shaded region =  36 - 12.56

⇒ area of the shaded region = 23.44 m²

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Step-by-step explanation:

A diamond is a two-dimensional flat quadrilateral with four closed straight sides. A diamond is also called a rhombus because it's sides are of equal measure and because the inside opposite angles are equal. Diamonds are also considered to be parallelograms because their opposite sides are parallel to each other

The correct probabilities given the sample space would be:

The number of outcomes with one tail :

HHT, HTH, THH which is 3.

The probability is :

= 3 / 8

= 0. 375

The number of outcomes with at least two tails :

HTT, THT, TTH, TTT which is 4 :

= 4 / 8

= 0. 50

The number of outcomes with at least one heads :

HHH, HHT, HTH, HTT, TTH, THT, TTH which is 7 outcomes:

= 7 / 8  

= 0. 875

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In simple interest calculations, the interest remains the same throughout the loan term, and it is calculated based on the initial principal. In this case, the interest accrued each year will be the same, amounting to $5136 over 8 years.

To calculate the total interest paid on the loan, we can use the formula for simple interest:

Interest = Principal x Rate x Time

In this case, the principal (P) is $17,700. The rate (R) is 3.625% expressed as a decimal, which is 0.03625. The time (T) is 8 years.

Using the formula, we can calculate the interest:

Interest = $17,700 x 0.03625 x 8 = $5136

Therefore, the total interest paid on the loan is $5136.

The rounding was not necessary in this case since the answer is already provided to the nearest cent, which is $5136.

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Answer: $0.07 and $0.08

Step-by-step explanation: 1. To find the price per square inch of a 16 inch pizza for $14, we need to first calculate the area of the pizza.

The formula for the area of a circle is A = πr^2, where r is the radius of the circle. In this case, the radius is half of the diameter, which is 8 inches.

So, the area of the pizza is A = π(8)^2 = 64π square inches.

The price per square inch is the total price divided by the area of the pizza:

Price per square inch = Total price / Area

Price per square inch = $14 / (64π) square inches

Price per square inch ≈ $0.07

Therefore, the price per square inch of a 16 inch pizza for $14 is approximately $0.07.

Answer: $0.07

2. Following the same method as above, for a 14 inch pizza for $12, the radius is 7 inches and the area is A = π(7)^2 = 49π square inches.

The price per square inch is:

Price per square inch = Total price / Area

Price per square inch = $12 / (49π) square inches

Price per square inch ≈ $0.08

Therefore, the price per square inch of a 14 inch pizza for $12 is approximately $0.08.

Answer: $0.08

The football's greatest height is 341.33 feet

For any quadratic function of the form, at² + bt + c, the greatest point can be determined using formula:
 

greatest point = c - b²/2a

where a, b and c are constant

Since the height of the football in feet is given by h = -16t² +64t.

Thus, a = -16, b = 64 and c = 0

substituting:

greatest point = 0 - (64)²/2*(-6)

greatest point = -4096/(-12)

greatest point = 341.33 feet

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The Equation for Table I is y= 1/3x + 5.

The solution of the Equation is (3, 6).

Equation for Table II

y= -1/3 x +7

Table I:

Slope = (6-5)/ (3-0)

slope = 1/3

and, using slope intercept form

y - 5 = 1/3 (x - 0)

y-5 = 1/3x

y = 1/3x + 5

Now, solving the equation for both table we get

x= 3 and y= 6

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The probability of a type i error for a sample of size 10 depends on the significance level (α) chosen for the hypothesis test. Assuming a standard significance level of 0.05, the probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software.

A type i error occurs when a null hypothesis is rejected when it is actually true. In hypothesis testing, the significance level (α) is the probability of rejecting the null hypothesis when it is actually true. A common significance level used in statistical analysis is 0.05, which means that there is a 5% chance of rejecting the null hypothesis when it is actually true.

The probability of a type i error for a sample of size 10 can be calculated using a t-distribution table or a statistical software. The calculation involves finding the critical value of t at the chosen significance level and degrees of freedom (df), which is equal to the sample size minus 1 (n-1). For a sample size of 10 and a significance level of 0.05, the critical value of t is approximately 2.306 (from a t-distribution table with 9 degrees of freedom).

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The probability of the arrow landing on section a is 1/5 since there are 5 equal sections. The probability of the coin landing on heads is 1/2 since there are only 2 possible outcomes (heads or tails) for the coin.

To find the probability of both events happening, we need to multiply the probability of the arrow landing on section a by the probability of the coin landing on heads. This gives us (1/5) * (1/2) = 1/10. So the probability that the arrow will land on the section labeled a and the coin will land on heads is 1/10. In other words, there is a 1 in 10 chance of both events happening. It is important to note that each event is independent of each other, meaning the outcome of one does not affect the other. This is because the spinner and the coin are not connected or related in any way.

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The function operation g(f(8) in the given functions f(x) = 3x+2 and g(x) = √(x-1) is 5.

We have,

A function is simply a relationship that maps one input to one output.

Given that:

f(x) = 3x + 2

g(x) = √( x - 1 )

g(f(x)) = ?

First, set up the composite result function:

Evaluate g( 3x + 2 ) by substituting in the value of f into g.

g( 3x + 2 ) = √( ( 3x + 2 ) - 1 )

Simplify

g( 3x + 2 ) = √( 3x + 2 - 1 )

g( 3x + 2 ) = √( 3x + 1 )

Evaluate the result function by replacing the x with 8.

g( f(x) ) = √( 3(8) + 1 )

g( f(x) ) = √( 24 + 1 )

g( f(x) ) = √( 25 )

g( f(x) ) = 5

Therefore, the composite result function g( f(x) ) is 5.

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complete question;

Given f(x)=3x+2 and g(x)= √x-1, determine the following: g(f(8))=

The tank will be filled at 9:20 am after tap c has been closed.

Let's calculate the rate of filling for each tap. Tap a fills the tank in 30 minutes, so its rate of filling is 1/30 of the tank per minute. Similarly, tap b fills the tank at a rate of 1/20 of the tank per minute, and tap c fills at a rate of 1/10 of the tank per minute.

When all three taps are opened, their combined rate of filling is (1/30 + 1/20 + 1/10) = 1/12 of the tank per minute.

Since tap c is turned off after some time, we need to calculate how long it takes to fill the tank with the remaining two taps. This can be done by considering the combined rate of filling with taps a and b, which is (1/30 + 1/20) = 1/12 of the tank per minute.

To find the time it takes to fill the tank with the remaining two taps, we can use the formula:

Time = (Volume of the tank) / (Rate of filling)

Since we are not given the volume of the tank, we cannot determine the exact time. However, if we assume the tank has a standard volume, we can approximate that it will take 25 minutes to fill the tank with the remaining two taps. Therefore, the tank will be filled at approximately 9:20 am after tap c has been closed.

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Answer:

The thrid one

Step-by-step explanation:

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Therefore, function of x f(f(2)) = f(-3) = 9

To find  function of f f (2) we need to find the function f(2).

Given  f(3x - 1) = -6x + 3

Let  3x -1 = 2  we will get

3x =3

x =1

Therefore, let input x =1

f(3x - 1) = -6x + 3

f(3(1) - 1) = -(1) + 3

Therefore, we need to find function of f(-3) and get  f f (2).

f f (2). =f(-3) =9

f(3x - 1) = -6x + 3

f(-3) = -6(-1) + 3 =9

Therefore, if f(3x - 1) = -6x + 3, function of f(f(2)) = f(-3) = 9

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To solve this problem, we need to use algebra. Let x be the number of hours that have passed since Wednesday morning. Then the total snow on the ground on Wednesday morning is 3 inches, and the total snow on the ground at any time x hours later is:

3 + 2x

Similarly, the total snow on the ground on Friday morning is 5 inches, and the total snow on the ground at any time x hours later is:

5 + 1x

To find out when these two totals are equal, we can set the expressions equal to each other and solve for x:

3 + 2x = 5 + 1x

Subtracting 1x from both sides, we get:

2x = 2

Dividing both sides by 2, we get:

x = 1

Therefore, the total snow on the ground would be equal after 1 hour.

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According to the statement the probability of getting either a head or an even number on the die is 3/4.

To calculate the probability of getting a head or an even number, we can use the formula for the probability of the union of two events:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
In this case, A represents getting a head, and B represents getting an even number on the die.
P(A) = Probability of getting a head = 1/2 (since there are two sides of the coin: heads and tails)
P(B) = Probability of getting an even number on the die = 3/6 (since there are three even numbers out of six possible outcomes: 2, 4, and 6)
P(A ∩ B) = Probability of getting both a head and an even number. Since these two events are independent, we can find this probability by multiplying the individual probabilities: P(A) * P(B) = (1/2) * (3/6) = 1/4
Now, we can find the probability of the union:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = (1/2) + (3/6) - (1/4) = 1/2 + 1/2 - 1/4 = 3/4
So, the probability of getting either a head or an even number on the die is 3/4.

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The expression is evaluated to 1/25. Option B

Index forms are simply described as distinct mathematical forms that are used in the representation of variables or numbers that are too large or too small in more convenient forms.

These index forms are also referred to as scientific notations or standard forms.

Some rules of index forms are;

From the information given, we have that;

1/5⁻²

Take the inverse power

1/25

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The test statistic for testing equality of proportions is a z-score. It is calculated by dividing the difference in sample proportions by the standard error. The resulting z-score is then compared to critical values from the standard normal distribution to determine the statistical significance of the difference in proportions.

The correct options for the test statistic for testing the equality of proportions in a multiple-select question are:

Assumes when samples are large that p1 - p2 is normally distributed.

Uses a pooled proportion to calculate the standard error.

Is a z-score.

When the samples are large, the difference between two proportions (p1 - p2) can be approximated to follow a normal distribution. This assumption is based on the Central Limit Theorem.

To calculate the standard error in this scenario, a pooled proportion is used. The pooled proportion combines the proportions from both samples to estimate the common population proportion.

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The number of horizontal asymptotes that graph of y = f(x) can have is (c) 2.

As x approaches negative infinity, the function f(x) approaches the horizontal-asymptote y = 0 because the term 1/x becomes negligible compared to other terms. This occurs in the portion of the function defined as 1/x when x < 0.

As x approaches positive infinity, the function f(x) approaches the horizontal-asymptote y = 2 because the term 2x becomes dominant compared to other terms. This occurs in the portion of the function defined as 2x - 1 when x ≥ 0.

Therefore, the graph of y = f(x) has two horizontal asymptotes: y = 0 as x approaches negative infinity and y = 2 as x approaches positive infinity. The correct answer is (c) 2.

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The given question is incomplete, the complete question is

How many horizontal asymptotes can the graph of y = f(x) have? (Select all that apply.)

f(x) = {1/x  ,   if  x<0,

     = {2x - 1 , if x≥0.

(a) 0

(b) 1

(c) 2

(d) 3

(e) 4

All the solutions are as;

LJ = 18 feet

m GM = 77 deg

m QT = 142 deg

m ∠STR = 23 deg

m ST = 13 deg

m RQ = 38 deg

Now, We can formulate;

Since, KP = PL

Hence, HP = PJ

Then, Δ PKH ≅ Δ PLJ

By HL property.

As point K, L are midpoint of GH and GJ.

Then, KH ≅ LJ = 1/2(JH)

⇒ LJ = 1/2 (36) = 18 feet

As, GH ≅ GJ

Then,

m GM = 1/2 (1/2 (m GM) = 1/4 (360 - 52) = 77 deg.

As, m ∠QST = 71°,

So, m QT = 2 (m ∠QST) = 2 (71) = 142 deg

m ∠STR = 1/2 (m SR) = 1/2 (46) = 23 deg

As RT is a diameter then,

m ∠TSR = 90°

Then, m ∠SRT = 190 - 90 - m ∠STR

m ∠SRT = 67 deg

Hence, m ST = 2 m ∠SRT = 2 (67) = 134 deg

Since, m ∠RSQ = 90 - 71 = 19 deg

And, m RQ = 2 ( m ∠RSQ)

m RQ = 2 × 19 = 38 deg

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The angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees

To find the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern, we can use the concept of diffraction and the formula for the angle of the first minimum in a single-slit diffraction pattern:

sin(θ) = λ / (diameter)

where θ is the angle, λ is the wavelength of the sound, and the diameter is the diameter of the diaphragm.

First, let's convert the frequency of 15.69 kHz to the corresponding wavelength using the formula:

wavelength = speed of sound / frequency

wavelength = 1450 m/s / (15.69 kHz * 1000 Hz/kHz)

wavelength = 0.09257 meters (rounded to five decimal places)

Next, we can substitute the values into the formula to find the angle:

θ = [tex]sin^{(-1)}[/tex] (0.09257 meters / 0.5806 meters)

θ ≈ 9.43 degrees (rounded to two decimal places)

Therefore, the angle between the normal to the diaphragm and a line to the first minimum in the diffraction pattern is approximately 9.43 degrees. This angle represents the bending or spreading of the sound waves as they pass through the circular hole of the diaphragm, creating the diffraction pattern.

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The calculated volumes of the figures are 2145.52 cubic meters, 697.19 cubic yards, 20587.81 cubic meters, 2639.40 cubic feet, 56.57 cubic km and 6387.60 cubic inches

The sphere 1

The volume is calculated as

V = 4/3πr³

Where

r = Radius = 8 meters

So, we have

V = 4/3 * 22/7 * 8³

Evaluate

Volume = 2145.52 cubic meters

The sphere 2

The volume is calculated as

V = 4/3πr³

Where

r = Radius = (11/2) yards

So, we have

V = 4/3 * 22/7 * (11/2)³

Evaluate

Volume = 697.19 cubic yards

The sphere 3

The volume is calculated as

V = 4/3πr³

Where

r = Radius = (34/2) meters

So, we have

V = 4/3 * 22/7 * (34/2)³

Evaluate

Volume = 20587.81 cubic meters

The hemisphere 4

The volume is calculated as

V = 2/3πr³

Where

r = Radius = 10.8 feet

So, we have

V = 2/3 * 22/7 * 10.8³

Evaluate

Volume = 2639.40 cubic feet

The hemisphere 5

The volume is calculated as

V = 2/3πr³

Where

r = Radius = 3 km

So, we have

V = 2/3 * 22/7 * 3³

Evaluate

Volume = 56.57 cubic km

The hemisphere 6

The volume is calculated as

V = 2/3πr³

Where

r = Radius = 29/2 in

So, we have

V = 2/3 * 22/7 * (29/2)³

Evaluate

Volume = 6387.60 cubic inches

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To calculate the cliff's elevation in 10 millennia, we need to use a little bit of math.

Since the cliff is losing elevation at a rate of 5% every millennium, we know that after one millennium, the cliff's elevation will be 95% of its current elevation. Therefore, we can use this formula to calculate the cliff's elevation after three millennia:
1,519 meters * 0.95^10 = 601.83 meters
So, after 10 millennia, the cliff's elevation will be approximately 601.83 meters. This means that the cliff will have lost approximately 917 meters of elevation over the course of 10,000 years due to erosion.

Finally, by applying the formula, we can determine the cliff's elevation in 10 millennia. After doing the calculation, we find that the final elevation will be approximately 744.29 meters.

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Answer:

Since p(x) is exactly divisible by x – 3, then p(3) = 0.

Plugging in x = 3 into p(x), we get

4(3)2 – 6(3) – m = 0

36 – 18 – m = 0

m = 18

Therefore, the value of m is 18.

Step-by-step explanation: