If Julian starts a bank account with $10,000 and his bank compounds the interest quarterly at an annual interest rate of 8%, how much money does he have at the year's end?

After 5 years?

The correct equation to show the cost of meat per pound at Sam's Grocery Store is x = 2y, where x is the cost of meat per pound at Sam's Grocery Store and y is the cost of meat per pound at Lane Grocery Store.

This equation represents the fact that the cost of meat per pound at Sam's Grocery Store is twice the cost of meat per pound at Lane Grocery Store.

For example, if the cost of meat per pound at Lane Grocery Store is $5, then the cost of meat per pound at Sam's Grocery Store would be 2 * $5 = $10.

So, the equation x = 2y accurately shows the relationship between the cost of meat per pound at Sam's Grocery Store and the cost of meat per pound at Lane Grocery Store.

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Answer: Check the numbers that are already there.

Step-by-step explanation:

Example, what times 6 equals 24? then divided 24 by that number. Do this for all the numbers

The part of the whole brownies that Jiah eat will be 1/8.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Fractions help to distribute and judge the numbers easily and make the calculation faster. Instead of using decimal values, the representation of fractions looks simpler.

Jia's mom = 1/4

Jia's sister = 1/4

Jia's brother = 1/4

Jia's share = 1 - (1/4 + 1/4 + 1/4) = 1 - 3/4 = 1/4( of her share)

Jia's share in relation to the whole = 8/8 - 7/8 = 1/8

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$0.04  is the unit price (per ounce) for the sports drink.

A division is a process of splitting a specific amount into equal parts.

Given that  local grocery store is having a sale on sports drinks.

For a particular brand of sports drink, a 6 -pack of 20 -ounce bottles costs $4.96

We need to find the the unit price (per ounce) for the sports drink.

6×20

120 ounce bottles in total which cost $4.96.

Now 4.96/120 is the cost of each bottle

$0.04 is the unit price of the sport drink.

Hence, $0.04  is the unit price (per ounce) for the sports drink.

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Answer:

The solution to the system is (1.8, 7.6)

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.

Plot the lines:

y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.

y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.

Find the intersection point:

To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.

Substitute x from y = 2/3x + 4 into y = -x + 1:

-x + 1 = 2/3x + 4

Multiplying both sides by -3, we get:

3x - 3 = -2x - 12

Adding 2x to both sides, we get:

5x - 3 = -12

Adding 12 to both sides, we get:

5x = 9

Dividing both sides by 5, we get:

x = 1.8

Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:

y = 2/3x + 4

y = 2/3 * 1.8 + 4

y = 3.6 + 4

y = 7.6

So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.

Answer:

Step-by-step explanation:

If LP represented the height of the triangle, then the segment would be the vertical leg of a right triangle. This is due to the fact that the altitude of an isosceles triangle is perpendicular to the base MN.

Thus, by the Pythagorean Theorem, (1.3)^2 + (3.5)^2 = (3.7)^2 if and only if segment LP is the height of the triangle. Calculate for yourself whether this is true.

The fourth year increase in salary is 4.5 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Inka's starting annual salary was $55,600.

After her first year she received a 2% pay rise.

Now, 2% of 55,600

= 2/100 ×55,600

= 1112

So, salary of 2nd year is 55,600+1112=$56712

The next year she received a 3% pay rise.

Now, 3% of 56712

= 3/100 ×56712

= 1701.36

So, salary of 3rd year is 56712+1701.36=$58413.36

Last year she received an x% pay rise.

Now, x% of 58413.36+58413.36=61,042

x/100 ×58413.36=61,042-58413.36

584.1336x=2628.64

x=2628.64/584.1336

x=4.5%

Therefore, the fourth year increase in salary is 4.5%.

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Answer:

Below

Step-by-step explanation:

From mile 3 to mile 18 is 15 miles

   He needed   2 hrs - .75 hr  = 1.25 hr to run 15 miles

15 miles / 1.25 hr =  12 miles per hour    ( VERY fast !)

The graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

We know that the graph of the function f(x) = a|x| opens upwards if the value of a > 0 and it opens downwards for a< 0.

For the given function the value of a = -0.1 < 0.

So, the graph of f(x) opens downwards.

The coordinates of the graph are determined by substituting the value of y in the given function:

f(x) = -0.1 |x|

-10 = -0.1 |x|

x = -100 or x = 100

So, the two points are (-100, -10) or (100, -10).

Hence, the graph of f(x) = -0.1 |x| opens. The point (-100, -10) or (100, -10) is on the graph.

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Answer:

[tex]3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]3x^2 - 5x - 2[/tex]

To complete the square, factor out the coefficient of the leading term:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x-\dfrac{2}{3}\right)[/tex]

Add and subtract the square of half the coefficient of the term in x inside the parentheses:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\left(\dfrac{\frac{-5}{3}}{2}\right)^2-\dfrac{2}{3}\right)[/tex]

Simplify:

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\left(\dfrac{-5}{6}\right)^2-\left(\dfrac{-5}{6}\right)^2-\dfrac{2}{3}\right)[/tex]

[tex]\implies 3\left(x^2-\dfrac{5}{3}x+\dfrac{25}{36}-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Factor the perfect square trinomial formed by the first three terms inside the parentheses:

[tex]\implies 3\left(\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{36}-\dfrac{2}{3}\right)[/tex]

Distribute:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{75}{36}-\dfrac{6}{3}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-2[/tex]

Simplify:

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{25}{12}-\dfrac{24}{12}[/tex]

[tex]\implies 3\left(x-\dfrac{5}{6}\right)^2-\dfrac{49}{12}[/tex]

Answer:

y ≤ 3/4x-2

The 3/4 is the slope, and -2 is y intercept

The probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.

A corporate board refers to a governing body of a corporation, usually consisting of elected or appointed members, who are responsible for overseeing the management of the company and making important decisions related to its strategy, finances, operations, and other aspects. The board serves as a representative of the shareholders and is responsible for overseeing the actions of the CEO and other executives, ensuring that the company is run in a manner that benefits its stakeholders.

The probability that the committee will contain two accountants and three non-accountants can be calculated as follows:

The number of ways to choose 2 accountants out of 4 is 4 choose 2, or 4C2 = 6.

The number of ways to choose 3 non-accountants out of 8 (12-4) is 8C3 = 56.

The total number of ways to choose 5 people from 12 is 12C5 = 792.

Therefore, the probability that the committee will contain 2 accountants and 3 non-accountants is (6 × 56) / 792 = 6/66 = 3/33.

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The length of the rectangle is 8.2 feet.

Given area of the rectangle is 82 feet and width is 10 feet

let variable : length of rectangle

then the equation is 10x=82

x=82/10

x=8.2

x=length=8.2

Therefore the length of the rectangle is 8.2 feet.

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In light of this, Liam's earnings after six years will be roughly $47,139.92.

Profits from Liam's company have reached $43,200, and they are growing at a 1.2% annual rate.

We can use the compound interest calculation to calculate the number of profits after six years.

The formula is P = P0 *[tex](1 + r/100)^t[/tex], If t is the number of years, which is 6, P0 is the initial sum of $43,200, r is the yearly interest rate of 1.2%, and t is the number of years.

By substituting these values into the formula,

we can calculate the final amount as P = 43,200 * [tex](1 + 1.2/100)^6[/tex] = 43,200 * [tex]1.012^6[/tex] = 43,200 * 1.07711 = $47,139.92.

In light of this, Liam's profits after six years will be roughly $47,139.92.

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A geometric method is known as "stereographic projection" involves projecting a flat map of a sphere onto a three-dimensional surface with a point at its center.

This is one way to construct a sphere. The construction of geodesic domes, which gained popularity in the 1960s, is one example of an art and construction project that frequently makes use of this approach.

Using a solid material and carving it into the shape you want is another way to make a sphere. This can be accomplished using stone, clay, wood, and other materials. To produce a sphere with perfect symmetry, this method necessitates considerable skill and precision.

A third approach is to construct a sphere from numerous small, flat pieces. Paper or fabric can be used to accomplish this, with each piece being cut into a curved shape and glued together to form the sphere. Origami balls, for example, are a common decorative item made using this method.

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The required solution of the given equation is x = -7.

"Multi-step equation" means an equation that requires more than one step to be solved.

"Like terms" refers to terms that have the same variables raised to the same powers. In this equation, there are no like terms, so no simplification of the equation is needed in that regard.

"Negative coefficients" refers to the fact that some of the coefficients in front of the variables in the equation are negative. For example, in this equation, the coefficient of x is -3, and the coefficient of -9 is also negative.

To solve this equation, you can simplify both sides by combining like terms:

-9 + x -3x = 5

-9 - 3x + x = 5

-9 - 2x = 5

Next, isolate the variable on one side of the equation by adding 9 to both sides:

-9 - 2x + 9 = 5 + 9

-2x = 14

Finally, divide both sides by -2 to find x:

(-2x) / -2 = 14 / -2

x = -7

So the solution is x = -7.

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Answer:

Step-by-step explanation:

The two trains are moving apart from each other, so we can add their speeds to find their relative speed:

Relative speed = 75 + 95 = 170 miles per hour

We want to know how long it will take for the trains to be 204 miles apart. We can use the formula:

distance = rate × time

to solve for the time. Let t be the time in hours:

204 = 170t

Solving for t, we get:

t = 204/170

t ≈ 1.2 hours

Therefore, it will take approximately 1.2 hours for the two trains to be 204 miles apart.

Answer:

  314 yd²

Step-by-step explanation:

You want the area of a circle that has a diameter of 20 yards.

The usual formula for the area of a circle is ...

  A = πr² . . . . . . where r is the radius

The radius of the circle is half the diameter, so is (1/2)(20 yd) = 10 yd.

Using this value in the formula, we find the area to be ...

  A = 3.14(10 yd)² = 314 yd²

Answer:

Step-by-step explanation:

4(4y+5)=3(y+7)

16y+20=3y+21

13y=1

y=1/13

Answer:

y = 1/13

Step-by-step explanation:

 (4y + 5) : 3 = (y+7) :4

Product of extremes = (4y + 5) * 4

                                  = 4y *4 + 5*4

                                  = 16y + 20

Product of mean = 3*(y +7)

                            = 3*y + 3*7

                            = 3y + 21

Product of extremes = product of mean

          16y + 20 = 3y + 21

Subtract 20 from both sides,

                  16y = 3y + 21 - 20

                  16y = 3y + 1

Subtract 3y from both sides,

               16y - 3y = 1

                     13y = 1

                        [tex]\boxed{\bf y =\dfrac{1}{13}}[/tex]          

The  displacement x of the moving puck is; 0.43 meters

The displacement is defined as the change in position of an object. It is also called a vector quantity and has a direction and magnitude

The parameters given here are;

The polar coordinate initial velocity vector; U = 2.35 m/s, -22°

Final velocity vector; V = 6.42 m/s, +50°

This suggests to us that Cartesian x axis is parallel to angle 0° and y axis is parallel to +90°.

Change of velocity component parallel to +90° =  magnitude*sinθ,.

Thus, the change of that velocity

Δv = |V|sin(50) - |U|sin(-22)

Δv = 6.42sin(50) - 2.35sin(-22)

Δv = 4.9 - (-0.88)

Δv = +5.8 m/s

The equation for displacement is;

s = ut +1/2at^2

where acceleration time t = Δt = 0.215 s

initial velocity u = |U|sin(-22) = -0.88 m/s

acceleration parallel to u is a = Δv/Δt = +5.8/Δt

a = 5.8/t m/s^2

Thus;

s = -0.88t + ¹/₂* 5.8/t * t²

s = -0.88t +2.9t

s = 2.0t

s = 2.0 * 0.215

s = 0.43 m

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Answer:

120.010

Step-by-step explanation:

Based on the information from the sets, it can be inferred that the correct answer is: red, green (option C).

To identify the correct answer we must take into account the elements that are in each set. Once we identify this information, we must analyze the elements in common between the sets. In accordance with the above, we must take into account this:

Based on the above, the correct answer is red and green because these are the elements that have the sets A, B, and C.

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Event R: Drawing a Red Ballot, Event B: Drawing a Blue Ballot, Event Even: Drawing an Even Numbered Ballot, Event Odd: Drawing an Odd Numbered Ballot.

The general election is today, and volunteers are organizing the ballots. Depending on the part of the city in which a citizen lives, he or she receives a different ballot. The types of ballots consist of RED ballots numbered 1, 2, 3, 4 and BLUE ballots numbered 1, 2, 3, 4. First, the volunteers need to define the events of drawing a red ballot and drawing a blue ballot. This can be done by defining the events R and B, respectively. Next, the volunteers need to define the event of drawing an even numbered ballot and the event of drawing an odd numbered ballot. This can be done by defining events Even and Odd, respectively. The volunteers can then use these events to determine which ballots are being drawn by the citizens. For example, they can use the events R and Even to determine which citizens are drawing a red even numbered ballot.

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Answer:

i) 9

ii) 11

Step-by-step explanation:

First off, what is a "mode"?

The mode in a set of data is simply the most common answer/outcome;

Next, we need to understand the data;

In this case, families were asked about the number of cats they have;

The children answered 0, 1, 2 or 3;

8 families have 0 cats,

6 have 1,

10 have 2,

x have 3

So, the mode will be the most common answer to how many cats a family has;

As we can see from the data, the most common response was 2, i.e. 10 families have 2 cats, compared to only 8 with 0 cats and 6 with 1 cat;

If we know the mode is 2, the value of x has to be less than 10 as it is not the most common response;

The largest possible value will be 9.

If the mode is 3, then that means the x has to be the greatest number of responses;

Since the greatest number of responses to the other options is 10, then the number of responses to having 3 cats has to be at least 11;

The smallest possible value of x, if the mode is 3, will be 11.

The simple interest on a principal amount is the function on time t.

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Given here: Principal=$3200, Annual rate of interest =8% and time=5 years

Thus Simple interest is S.I= 3200×8×5 / 100

                                           =$1280

Which is equal to the interest given in the question.

Thus the the interest rate forms a linear function or

Simple Interest is calculated using the following formula: SI = P × R × T /100,

where r and P are constant then S.I can be written as the function of time t

SI(t)= P×r×t/100

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Answer: No, you can prove it

Step-by-step explanation:

It is a right angle at both triangles and the sides to points toward the vertex of the triangle have to be the same. So, the bottom side must be the same and the angles are the same. It is congruent.

Answer:

The answer is the equation for the function describing the movement of the buoy:

f(x) = 5 * sin(2 * pi * x / 16) + 8

Step-by-step explanation:

To graph the function, we need to find an equation that describes the buoy's movement. Since the buoy bobs up and down 5 meters from the ocean's depth, we can use the sine function. The amplitude of the function is 5, since the buoy moves 5 meters from the normal ocean depth. The period of the function is 16 seconds, since it takes 16 seconds for the buoy to go from its highest point to its lowest point.

Using this information, we can write the equation for the function as:

f(x) = 5 * sin(2 * pi * x / 16) + 8

where x is the time in seconds.

The first point on the graph would be (0, 8), since at x = 0 the buoy is at normal ocean depth. The second point would be either a maximum or minimum value on the graph closest to x = 0, which can be found by finding the derivative of the function and setting it equal to zero.

The graph of the function would look like a wave that oscillates up and down, with a maximum value of 5 meters above the normal ocean depth and a minimum value of 3 meters below the normal ocean depth.

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Answer:

Step-by-step explanation:

19?

Step-by-step explanation:

a row n adds the number n to the sum (= the first number from the right in row n-1), and therefore also n to the 3rd number from the right of row n-1.

in any case, the first number from the right is the result of

1 + 2 + 3 + 4 + 5 + ... + n-1 + n

that sum is

n(n+1)/2

for the row 20 that is

20×21/2 = 10×21 = 210

the 3rd number from the right in row 20 is then

210 - 2 = 208