.
Choose correct way to write three dollars and seventeen cents using the dollar symbol.
$31.07
3.17 ¢
$3.17¢
$3.17

Therefore , the solution of the given problem of interest comes out to be

$4,962.93 money more made by Alexander.

Simple interest is calculated by dividing the principal by the borrowing cost, the remaining time, and other elements. The simple return formula in marketing is principal + interest plus hours. Utilizing this method is the simplest way to calculate interest. As a percentage of the principle sum is the most frequent way to calculate income. For instance, he will only pay his portion of the 100% cost if he borrows $100 from a friend and agrees to pay the loan back with 5% interest.. You have to pay interest on money you borrow, and you have to charge interest on money you lend.

Here,

Given :

Luke :

Principal amount = $86,000

and rate of interest =  5 ⅛ % or 41/8% or 5.125%

Alexander :

Principal amount = $86,000

rate of interest = 5 ⅝ % or 45/8% or 5.625%

To find the amount of money after time =8 years.

So ,

using compound formula :

=> A = P\((1 + r/n)^{nt}\)

For luke = P=86000\((1 + 41/8*1)^{1*8}\) = $42,276.33

For  Alexander =   P=86000\((1 + 45/8*1)^{1*8}\) = $47,239.26

The amount made by Alexander by luke

=> 47,239.26 - 42,276.33 = 4,962.93

Therefore , the solution of the given problem of interest comes out to be

$4,962.93 money more made by Alexander.

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The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The mode of the data in the line plot is the data with the highest number of marks

The mode of the data is 8

From the line plot, we have the following frequency table:

Number        Frequency

5                       2 marks

6                       4 marks.

7                        3 marks

8                        6 marks

9                         2 marks

10                         4 marks

11                         2 marks

The number with the highest mark is 9

Hence, the mode of the data is 8

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Answer: The mode is 8

Step-by-step explanation: Mode means the number that shows up must in the graph and since 8 is the highest that goes the mode is 8. Also I did the k12 quiz.

Answer: -1 and 5

Step-by-step explanation:

You see you know in f(x) that become f(5) that means x=5 so in the graph you have to find the line of the x ( it is written) and then just see where the the curve is “ cutting” the graduation 5 of the line of the x . Sorry if you don’t understand, have an amazing rest of you day :)

Copper would weigh 105g in the jar of the chemical

the comparison of two quantities by the method of division is very efficient. We can say that the comparison or simplified form of two quantities of the same kind is referred to as a ratio. This relation gives us how many times one quantity is equal to the other quantity. In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones.

The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things. The sign used to denote a ratio is ‘:’.

If zinc to copper is 3 : 19

Then total shares = 3 + 19 which is 22

Let the total weight of the jar be x

so that for copper's weight = 19/22 * x  gives 665

19/22 * x = 665

19x = 665 x 22

19x = 14630

x = 14630/19

x = 770g

weigh of zinc = 770 - 665 which is 105g

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To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

What is a polynomial?

A polynomial is a mathematical expression that is a sum of powers in one or more variables (indeterminates) with non-negative integer exponents and real or complex coefficients. The degree of a polynomial is the highest power of the variable. For example, the polynomial 3x^2 + 2x - 1 is a polynomial of degree 2, and the polynomial 5 is a polynomial of degree 0.

To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

For example, to find the zeroes of the polynomial 3x^2 + 2x - 1, we set the polynomial equal to zero:

3x^2 + 2x - 1 = 0

Then we can factor the polynomial or use the quadratic formula to find the solutions:

x = (-2 +/- sqrt(2^2 - 43(-1)) ) / (2*3) = (-2 +/- sqrt(4 + 12))/6 = (-2 +/- sqrt(16))/6 = (-1 +/- sqrt(4))/3 = (-1 +/- 2i)/3

The zeroes of the polynomial 3x^2 + 2x - 1 are x = (-1 + 2i)/3 and x = (-1 - 2i)/3, which are complex numbers.

Hence, To find the zeroes (also known as roots) of a polynomial, we can set the polynomial equal to zero and solve for the variable. The solutions to the equation are the zeroes of the polynomial.

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Answer:

JKM = 36 degrees

JMK = 54 degrees

Step-by-step explanation:

Subtract right angle ( 90) from the 54 degress known and then you get 36 for JKM.  

The Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

Accοrding tο the Pythagοrean theοrem, the square οf a right triangIe's hypοtenuse (the side οppοsite the right angIe) equaIs the sum οf its οther twο sides' squares.

Outside waII's Iength and width are equaI if it is a square. Let's caII this Iength "x"

Using the Pythagοrean theοrem, we can find the Iength οf the diagοnaI οf the square:

diagοnaI² = height² + width²

Since the height is 9 ft and οne side οf the square is 12 ft, we can write:

diagοnaI² = 9² + 12²

diagοnaI² = 81 + 144

diagοnaI² = 225

Taking the square rοοt οf bοth sides, we get:

diagοnaI = √(225)

diagοnaI = 15 ft

Therefοre, the Iength οf the diagοnaI οf the square exteriοr waII shοuId be 15 feet.

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The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

\(\huge{ \mathfrak{  \underline{ Answer }\:  \:  ✓ }}\)

The given triangle is a right angled triangle,

therefore, by using trigonometry :

\( \boxed{ \cos(45) = \frac{6}{x} }\)

_____________________________

\(\mathrm{ ☠ \: TeeNForeveR \:☠ }\)

Answer:

The ratio of blue to red marbles is 3 to 8.

Hope this helps :) have a good day!

To calculate the average speed of the lap record, we need to know the distance covered and the time taken.

Distance = 5.303 km

Time = 1 minute and 24 seconds = 84 seconds

To convert seconds to hours, we divide by 3600 (the number of seconds in an hour):

\( \frac{84 \: seconds \:}{3600} = 0.02333 \: hours\)

Now we can calculate the average speed:

\(Average \: speed = \frac{d}{t} = \frac{5.303km}{0.02333} \)

Average speed = 227.59 km/h

For the given data, the range, variance, and standard deviation is 1.47, 0.1716, and 0.414, respectively.

To find the range, subtract the minimum value from the maximum value in the set of data. The minimum value is 0.48 and the maximum value is 1.95, so the range is: 1.95 - 0.48 = 1.47.

To find the sample variance, follow these steps.

1. Calculate the mean of the data set.

2. Subtract the mean from each value in the data set.

3. Take the summation of the squares of the result.

4. Divide the sample size minus 1.

Upon calculation, the sample variance is 0.1716.

Lastly, to find the sample standard deviation, take the square root of the sample variance: √0.1716. = 0.414.

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The value of the cosine X is 0.724

We need to know the different trigonometric identities.

These identities are written as;

From the information given, we have that;

Z=90°, XZ = 20, YX = 29, and ZY = 21.

The ratio for the cosine identity is;

cos θ = adjacent/hypotenuse

Adjacent side = XZ = 20

Hypotenuse side; YX = 29

then, we have;

cos X  = 21/29

cos X = 0.724

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A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer:

Step-by-step explanation:

Area of circle = 49π m^2

Area of rectangle = 14π*11 = 154π m^2

Surface area = 2*49π + 154π = 252π m^2 = 792 m^2

By adding 3 to both sides of the equation (6+3)-3=9-3, this demonstrates the addition property of equality. This results in the equation being simplified to 6+3=9.

The properties of equality describe the relationship between two sides of an equation and state that the two sides remain equal even after the same arithmetic operation is performed on each side. a = a, according to the reflexive property of equality. For example, 5 = 5, because the number's value is equal to itself.

As per the addition property of equality, when we add the same number to both sides of an equation then the two sides remain equal. This can be written as, if a = b, then a + c = b + c.

Translated question "Draw a line from each equation to the property of equality it illustrates. (6+3)−3=9−3 Addition Property of Equality"

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Answer:

Step-by-step explanation:

You could do this 2 ways (NOT including going to a calculator and punching it in and getting the answer!). The first way is to use Newton's Method (which will give you an EXACT answer); the second is to use differentials (which will only approximate the answer). We'll do both here, beginning with Newton's Method. The formula for Newton's Method is

\(x_{1}-\frac{f(x_{1})}{f'(x_{1})}\) where x1 is your initial input.

Let x = \(\sqrt{38}\) so

\(x^2=38\\x^2-38=0\) with a derivative of 2x. Fitting this into the formula with an initial input of 6, since 6-squared is 36 and that's pretty close.

\(6-\frac{6^2-38}{2(6)}=\frac{37}{6}\)  and use that answer in the next iteration:

\(\frac{37}{6}-\frac{\frac{37}{6}^2-38 }{2(\frac{37}{6}) }=\frac{2737}{444}\) and use that answer in the next iteration:

\(\frac{2737}{444}-\frac{\frac{2737}{444}^2-38 }{2(\frac{2737}{444}) }=6.164414003\) and use that answer in the next iteration:

\(6.164414003-\frac{.164414003^2-38}{2(6.164414003)}=6.164414003\)

Since we got the same number after that last iteration, the exact value of the square root of 38 is 6.164414003. Check your calculator for accuracy.

The next method is by differentials. the formula is

f(x + Δx) ≈ f(x) + f'(x)dx

We will let f(x) = √x with x = 36 and dx = 2 (36 is a perfect square and adding 2, the dx value, gets you back to 38, our number in question).

Filling in the formula:

f(x + Δx) ≈ √x + \(\frac{1}{2\sqrt{x} }\) dx

f(x + Δx) ≈ \(\sqrt{36}+\frac{1}{2\sqrt{36} }(2)\) and simplifying a bit:

f(x + Δx) ≈ 6 + \(\frac{1}{6}\)  which gives us 6.166666

Not quite as accurate as Newton's Method, but it works for mere approximations.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

slope= -1

y-intercept is 6

Step-by-step explanation:

slope = y2-y1/ x2-x1

slope = 6-8/ 0-(-2) = -1

y-intercept is 6 because of (0,6), where the points cross y-axis

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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Answer:

The answer is C. 4,300

Answer explanation :

Answer: C. 4,300

Steps:

64,500 / 15 = 4,300

Check:

15 * 4,300 = 64,500

64,500 = 64,500 ✅

I would appreciate the brainliest if this was helpful and correct! :)

Greetings from Brasil...

In a linear function, the rate of change is given by M (see below).

M = rate of change

N = linear coefficient

The Function 2 has M = 4, cause

F(X) = 4X + 1

(M = 4 and N = 1)

For Function 1 we have a rate of change equal to zero, becaus it is a constant function... let's see:

M = ΔY/ΔX

M = (3 - 3)/(4 - 0)

M = 0/4 = 0

So, the Function 2 has 4 times more rate of change than the first

Your answer is two!!

Answer:

360 km^2

Step-by-step explanation:

To find the area after 10 years, we would have to decrease 4500 by 8%. We would convert 8% to decimal form, which is 0.08, and multiply it by 4500, which is 360 :)

The answer choice which correctly draws a comparison between the end behaviors of the functions is; Choice C; They have the same end behavior as x approaches -∞ and same end behavior as x approaches ∞.

As given in the task content; the graph of the exponential function passes through (-4, 9), (0, 1), (1, 0), and (5, -2).

It therefore follows that as; x reduces (approaches -∞), the y value increases.

And, as x -increases (approaches +∞), the y-value decreases.

For the table, the values can be written as coordinates as follows; (-1,2), (0,4), (1,6), (2, 0), (3,-2).

Consequently, as x reduces (approaches -∞), the y- values decrease.

And, as x increases (approaches +∞), the y-values decrease.

Ultimately, the two functions in discuss can be concluded to have; Choice C.

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Answer:

\(Amount = \frac{10}{3}L\)

Step-by-step explanation:

Given

\(Water = \frac{4}{3}L\)

\(Plants = \frac{2}{5}\)

Required

Amount of water for the whole plants

The amount of water for the whole plants is calculated as:

\(Amount = \frac{Water}{Plants}\)

This gives:

\(Amount = \frac{4}{3}L/\frac{2}{5}\) --- The division equation

Convert division to multiplication

\(Amount = \frac{4}{3}L*\frac{5}{2}\) --- The multiplication equation

Solving further:

\(Amount = \frac{4*5}{3*2}L\)

\(Amount = \frac{20}{6}L\)

Simplify:

\(Amount = \frac{10}{3}L\)