Andy, Bert, and Charles have 20 pieces of chocolate. Some of the chocolates have nuts, some are plain, and some are filled with caramel (they are split in a ratio of 1:2:2, respectively). Neither Andy nor Charles can eat nuts, and Charles will always take caramels over plain chocolates if he can (the others are indifferent to plain or caramels). If Andy, Bert, and Charles split the chocolates among themselves in a ratio of 3:1:1, respectively, in a way that makes each person as happy as possible, how many pieces of chocolate with caramel does Andy receive?

A. To represent the value of the car as a function of time, we can use the formula for exponential decay:

Value = Initial Value * (1 - Rate)^(Time)

In this case, the initial value is $18,000 and the rate of depreciation is 1.2% or 0.012. The function can be written as:

Value = $18,000 * (1 - 0.012)^(Time)

Using technology, such as a calculator or spreadsheet software, you can estimate the number of years it will take for the value to reach each given amount by solving for Time in the above equation. Simply substitute the given value for Value and solve for Time.

B. To find the number of years it will take for the value to reach $17,000, solve the equation:

$17,000 = $18,000 * (1 - 0.012)^(Time)

C. To find the number of years it will take for the value to reach $15,000, solve the equation:

$15,000 = $18,000 * (1 - 0.012)^(Time)

D. To find the number of years it will take for the value to reach half of the starting value ($9,000), solve the equation:

$9,000 = $18,000 * (1 - 0.012)^(Time)

E. To find the number of years it will take for the value to reach one-third of the starting value ($6,000), solve the equation:

$6,000 = $18,000 * (1 - 0.012)^(Time)

G. To find the number of years it will take for the value to reach $10,000, solve the equation:

$10,000 = $18,000 * (1 - 0.012)^(Time)

By solving these equations using technology, you can estimate the number of years it will take for the car's value to reach each given amount based on the given rate of depreciation.

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Answer:

Step-by-step explanation:

A is the answer

Answer:

A

Step-by-step explanation:

Random explanation so ya dont judge me dobt listen to my answers

Answer:

A

Step-by-step explanation:

mah brotha cuz I said so

Answer:

= 1/c

Step-by-step explanation:

Apply the sum/Different Rule: ( f + g ) ' = f ' + g'

= d/dx (x/c) + d/dx (b)

d/dx (x/c) = 1/c

d / dx (B) = 0

= 1/c + 0

Simplify = 1/c

Answer:

To be clear, do u want the angle of M?

Answer:

secM = \(\frac{17}{15}\)

Step-by-step explanation:

secM = \(\frac{1}{cosM}\)

cosM = \(\frac{adjacent}{hypotenuse}\) = \(\frac{MN}{LM}\) = \(\frac{15}{17}\) , then

secM = \(\frac{1}{\frac{15}{17} }\) = \(\frac{17}{15}\)

Answer:

8

S-by-step explanation:

Answer:

There are three 2's common to both numbers, so 2*2*2 = 8 is the "greatest common factor" (GCF) of 16 and 24.

Answer:

x = 0, y = -2

Step-by-step explanation:

\(\left \{ {{-10x-6y=12} \atop {4x+7y=-14}} \right. = \left \{ {{-10x=12+6y} \atop {4x+7y=-14}} \right. = \left \{ {{x=\frac{12+6y}{-10} }(1) \atop {4x+7y=-14}} \right\)

Replace x from formula (1) to formula (2), we got:

\(4*\frac{12+6x}{-10}=-14 <=> \frac{-2}{5}(12+6y)+7y=-14 <=> \frac{-24}{5} + \frac{-12}{5}y+7y=-14 <=> \frac{23}{5}y = \frac{-46}{5} <=> y = -2\\=> x= \frac{12+6*(-2)}{-10} = 0\)

Answer:

$4.56

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The four properties of parallelogram are:

i) Opposite sides are parallel & equal.

ii) Sum of adjacent interior angles is 180°

iii) Opposite angles are equal.

iv) Diagonals bisect each other.

The quadrilateral with two pairs of parallel sides is known as a parallelogram. Equal in length and width on both sides is required. Four vertices make up a parallelogram, which also has four edges.

A parallelogram is a two-dimensional (2D) shape that has two matching pairs of opposite sides that are parallel and equal in length. The angles inside the two sides of the shape must add up to 180 degrees, which means that all of the angles must add up to 360 degrees.

A rectangle that has been pushed over slightly is all that a parallelogram really is. Because of this, finding the area of a parallelogram can be done using the same formula as finding the area of a rectangle.

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Answer:

\(\sqrt{3} - \frac{\pi}{2}\)

Step-by-step explanation:

Firstly, you connect the three origins, and then a triangle form, the triangle is certainly an equilateral triangle.

The three sides of the triangle are all 2cm because the radius of the three coins are 1cm, it's very easy to understand.

Now, using the Pythagorean theorem (of you have a right triangle with two sides a, b and the hypotenuse c, you can see that\(\sqrt{a^{2} +b^{2} }=c\), \(\sqrt{c^{2}-b^{2} } =a\)and \(\sqrt{c^{2}-a^{2} } =b\)), we can get the area of the equilateral triangle by calculating the two right triangles in it (you can get the two triangles by drawing a line connecting the point of one angle to the middle point of its opposite side)

The area of one of the two small right triangles is: \(\frac{1*\sqrt{2^{2}-1^{2} }}{2}=\frac{\sqrt{3} }{2}\), and the sum of the area of the two right triangles, which is also the area of the equilateral triangle is: \(2*\frac{\sqrt{3} }{2}=\sqrt{3}\)

We calculate all this because we need to use the area of the equilateral triangle to subtract the area of the three sectors in it, and the result will be the area of the shaded area.

Now, to calculate the area of the three sectors, we need to know the angles of them, which is 60 degrees(because they are in an equilateral triangle). And then, the area of one of the three sectors(they are completely the same) are \(1^{2} \pi *\frac{60}{360} =\frac{\pi }{6}\), so the sum of the three sectors are \(\frac{\pi }{6}*3=\frac{\pi}{2}\).

Then, the shaded area of the area of the equilateral triangle subtract the area of the three sectors, which is\(\sqrt{3} -\frac{\pi}{2}\)

If you want the result in decimals, you can use a calculator.

Hope this will help:)

P.S. Typing this rly took me  a LONG time >_<

Answer:

The larger angle is 143

Step-by-step explanation:

x + y = 180 (This is the meaning of supplementary. Two angles make up 180 degrees)

4x - 5 = y

x + (4x - 5) = 180            Remove the brackets.

x + 4x - 5 = 180

5x - 5 =  180                  Add 5 to both sides

5x - 5 +5 = 180 + 5       Combine

5x = 185                        Divide by 5

5x/5=185/5

x = 37

y = 4*37 - 5

y = 148 - 5

y = 143

Answer:

2.18

Step-by-step explanation:

Answer:

x = 8

y = 3

Step-by-step explanation:

11x - 20y = 28

3x + 4y = 36

11x - 20y = 28

11x = 20y + 28

x = \(\frac{20}{11}\)y + \(\frac{28}{11}\)

3x + 4y = 36

3 ( \(\frac{20}{11}\)y + \(\frac{28}{11}\) ) + 4y = 36

\(\frac{104}{11}\)y = \(\frac{312}{11}\)

y = 3

x = \(\frac{20}{11}\)y + \(\frac{28}{11}\)

x = \(\frac{20}{11}\) ( 3 ) + \(\frac{28}{11}\)

x = 8

Answer:

-33/56

Step-by-step explanation:

suppose: A,B are the 2 angles of a triangle

we have: A = arcsin\(\frac{-4}{5}\)

               B = arctan \(\frac{5}{12}\)

=> sin A = \(\frac{-4}{5}\) => cos A = \(\sqrt{1-\frac{(-4)^{2} }{5^{2} } } =\frac{3}{5}\) (because A is in quadrant IV)

    tan B = \(\frac{5}{12}\)

have:

\(1+ cot^{2}B=\frac{1}{sin^{2}B } => 1+\frac{1}{tan^{2} B}=\frac{1}{sin^{2}B } \\=> 1+\frac{1}{\frac{5^{2} }{12^{2} } } =\frac{1}{sin^{2}B }\\ => sin^{2}B=\frac{25}{169}\)

because B is in quadrant III => \(sin B=-\sqrt{\frac{25}{169} }=\frac{-5}{13}=>cosB=-\sqrt{1-\frac{5^{2} }{13^{2} } }=\frac{-12}{13}\)

tan(arcsin(-4/5)+arctan(5/12)) = tan( A + B)

but A,B are the 2 angles of a triangle => tan(A + B) = \(\frac{sin(A+B)}{cos(A+B)}\)

have: sin(A+B) = sinA.cosB + cosA.sinB = \(\frac{-4}{5}.\frac{-12}{13} +\frac{3}{5}.\frac{-5}{13}=\frac{33}{65}\)

cos(A + B) = cosA.cosB - sinA.sinB =\(\frac{3}{5}.\frac{-12}{13}-\frac{-4}{5}.\frac{-5}{13}=\frac{-56}{65}\)

=> tan(A + B) = \(\frac{33}{65}:\frac{-56}{65}=\frac{-33}{56}\)

Answer:

pie/6

Explaniation:

just took the test on k12

Answer:

X= -1

Step-by-step explanation:

•Remember PEMDAS

•exponents: X^2

•Square root/x^2-6x-2

= x-2.4x-1.4=0

•Add 1.4 to 0

x-2.4x=1.4

•Combine like terms

-1.4x=1.4

•divide by -1.4 on each side to get x by itself

-1.4x/-1.4= 1.4/-1.4

X=-1

Answer: I hope you understand, just mutiply whatever x is by 11 to get Y

Step-by-step explanation:

x = unknown number

9x+2x= 11x

Y=11x

Dahila's Child and Dependent Care Credit in 2022 would be $6,000.

The Kid and Ward Care Credit is a tax cut that can assist with balancing the expenses of really focusing on qualified youngsters and wards. How much the not entirely set in stone by the person's changed gross pay (AGI) and the sum they spend on care? In the event that the AGI is underneath $125,000, the individual can get a credit equivalent to half of their childcare costs.

In 2022, Dahila brought about $12,000 in kid care expenses and has an AGI underneath $125,000, so her Kid and Ward Care Acknowledge would be determined as follows:

$12,000 x 50% = $6,000

Therefore, Dahila's Child and Dependent Care Credit in 2022 would be $6,000.

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Answer: the answer is like it is

Step-by-step explanation:

You just round the number in the tenths 0 is closer to 0 then to 10!

Answer:

V ( 4,-5)

Step-by-step explanation:

-7( X -4 )²= y+5

( X - 4)² = -1/7 (y+5)

Compare with ( X - h)² = -4p ( y-k)

Therefore, h = 4, k = -5

Vertex, V = (h,k)

V (4,-5).

(a) A point estimate for p is 0.2 and a 95% confidence interval is (0.0896, 0.3104). (b) The minimum sample size needed to estimate the population proportion p with 95% confidence is 615 patients.

(a) To find a point estimate for p, we need to calculate the sample proportion of patients who suffered serious side effects. The formula for the sample proportion is:

Sample proportion (p-hat) = (Number of patients with serious side effects) / (Total number of patients)

p-hat = 10 / 50 = 0.2

Now, we'll construct a 95% confidence interval for p using the sample proportion. The formula for the confidence interval is:

Confidence interval = p-hat ± Z * sqrt((p-hat * (1 - p-hat)) / n)

where Z is the Z-score corresponding to the desired confidence level (1.96 for 95%), n is the sample size, and p-hat is the sample proportion. Plugging in the values, we get:

Confidence interval = 0.2 ± 1.96 * sqrt((0.2 * 0.8) / 50)

Confidence interval = 0.2 ± 0.1104

The 95% confidence interval for p is approximately (0.0896, 0.3104).

(b) To find the minimum sample size needed to estimate the population proportion p with 95% confidence and within 0.01 of p, we will use the following formula:

n = (Z^2 * p-hat * (1 - p-hat)) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level (1.96 for 95%), p-hat is the sample proportion, and E is the desired margin of error (0.01). Plugging in the values, we get:

n = (1.96^2 * 0.2 * 0.8) / 0.01^2

n = 614.656

Since we cannot have a fraction of a person in a sample, we will round up to the nearest whole number. Therefore, the minimum sample size needed is 615 patients.

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Answer:

7.065 about

Step-by-step explanation:

Area= 3.14 r squared r=3/2

3.14 x 1.5 squared=7.065

Answer: 4 hours

Step-by-step explanation:

First, set up an equation. We know that Bob spent $30 on playing paintball so we use that as our 'answer.' We need to find how many hours Bob played so we need to use x, a variable to find it. We also add 16 because we need to account for the entry fee.

3.50x + 16 = 30

Secondly, solve for x. Move 16 across the equal sign(=). Every time you move across the =, you're going to want to change the sign (if it's addition or subtraction). Since it was +16 and we're moving it, it's now -16.

3.50x = 30 - 16

Calculate 30 - 16 = 14.

Now we have

3.50 x = 14.

To calculate x, we're going to need to divide 3.50 from x. Since we multiplied by x we need to do the opposite across the =.

x = 14 / 3.50

x = 4

Bob spent 4 hours playing paintball.

You can plug it in to check answers as well

3.50 (4) +16 = 30

Answer:

Triangle A

Step-by-step explanation:

Because in the picture it shows the grid and if you look closely you can see the points on the x and y axis, (3,2) (4,7) and (5,6) are the three points formed to make triangle A.

Answer:

Step-by-step explanation:

520 miles

The function g(x) is defined as follows: g(x) = 9x for x < 0, and g(x) = 2x for x > 0. We need to evaluate g(10) - g(-x).

To evaluate g(10), we substitute x = 10 into the respective piece of the function. Since 10 > 0, we use the second part of the definition, g(x) = 2x. Therefore, g(10) = 2 * 10 = 20.

To evaluate g(-x), we substitute x = -x into the first part of the definition, g(x) = 9x. This gives g(-x) = 9 * (-x) = -9x.

Now we can calculate g(10) - g(-x). Substituting the values we found, we have 20 - (-9x), which simplifies to 20 + 9x.

Therefore, g(10) - g(-x) is equal to 20 + 9x.

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Answer:

2 cos (x + pi/2)

Step-by-step explanation:

Of the choices given, this looks like a cos curve that is shifted to the Left by pi / 2  and   multiplied to give an amplitude of 2

Answer:

2 : 1 : 3

Step-by-step explanation:

14 : 7 : 21 ( divide each part of the ratio by 7 )

2 : 1 : 3

Answer:

2:1:3

Step-by-step explanation:

To simplify you find the greatest common factor and divide all the numbers by it, in this case 7 is the largest number that goes into all the numbers.

14 divided by 7 =2

7 divided by 7 = 1

21 divided by 7 = 3

Answer:

Step-by-step explanation:

If the solutions are x = -3 and x = -1, then (x - 3) (x - 1) will give us our answer. Using the FOIL method,

(x - 3) (x - 1)

x^2 - x - 3x + 3

x^3 - 4x + 3 = 0

Your answer is 3