HELP PLEASE
An artist recreated a famous painting using a 4:1 scale. The dimensions of the scaled painting are 8 inches by 10 inches. What are the dimensions of the actual painting?

40 inches by 50 inches
32 inches by 40 inches
12 inches by 14 inches
2 inches by 2.5 inches

a. It is b. Permutation

b. Using permutation, the number of different codes is 3024 passcodes.

Permutation is the total number of ways of arranging n different objects in x ways ⁿPₓ  = n!/(n - x)! while combination is the total number of ways of selecting n objects x at a time ⁿCₓ = n!/x!(n - x)!

a. Since Sara is setting a new code for her garage. The key pad has the numbers 0-9 to choose from, and she needs to set a 4-digit passcode. Since no digit is to be repeated, it is a permutation since in permutation, we are looking for differnt arrangemnets of the objects.

So, it is b. Permuation

b. Since Sara the key pad has the numbers 0-9 to choose from, and she needs to set a 4-digit passcode and no digit is to be repeated. We have 9 digits permuted or arranged in 4 ways. So, our permutation is ⁹P₄ = 9 × 8 × 7 × 6

= 3024 passcodes

So, the number of different codes is 3024 passcodes.

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Therefore, the solution of the given IVP using Laplace transform is: y(t) = -e^(3t) + t e^(3t) + (t^2/2) e^(3t) u(t-3)

Taking the Laplace transform of both sides of the differential equation, we have:

L[y''(t)] - 6L[y'(t)] + 9L[y(t)] = L[e^(3t)u(t-3)]

Using the derivative property of the Laplace transform, we have:

s^2 Y(s) - s y(0) - y'(0) - 6[s Y(s) - y(0)] + 9Y(s) = e^(3t) / (s - 3)

Substituting y(0) = 0 and y'(0) = 0, we get:

s^2 Y(s) - 6s Y(s) + 9Y(s) = e^(3t) / (s - 3)

Simplifying, we get:

Y(s) = [e^(3t) / (s - 3)] / (s - 3)^2

Using partial fraction decomposition, we can write:

Y(s) = -1/(s-3) + 1/(s-3)^2 + 1/(s-3)^3

Taking the inverse Laplace transform of both sides, we get:

y(t) = -e^(3t) + t e^(3t) + (t^2/2) e^(3t) u(t-3)

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The initial number of white tokens in the bag is given as follows:

8.

The amount is obtained by a system of equations, for which the variables are given as follows:

A bag contains black and white tokens in a ratio of 3:2, hence:

x/y = 3/2.

2x = 3y

x = 1.5y.

8 black tickets and 2 white tokens are added to the bag. The ratio of black to white tokens are now 2:1, hence:

(x + 8)/(y + 2) = 2.

Replacing the first equation into the second, the initial amount of white tokens is given as follows:

(1.5y + 8)/(y + 2) = 2

2(y + 2) = 1.5y + 8

2y + 4 = 1.5y + 8

0.5y = 4

y = 8.

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The estimated quotient is $20, which corresponds to option D in the given choices. Thus, Rose estimated that she spent $20 per person on gifts.

Compatible numbers are numbers that are close in value and can be easily divided or multiplied mentally. These numbers are used to make estimation in mathematical calculations easier and quicker. By rounding numbers to compatible numbers, calculations become simpler, and  errors are minimized.

For example, if you need to divide 26 by 5, you can use compatible numbers by rounding 26 to 25 and 5 to 4. Then, you can easily divide 25 by 4 to get an estimate of the quotient as 6.25. Compatible numbers can also be used in multiplication, addition, and subtraction.

Using compatible numbers is particularly helpful when performing mental calculations or when there is no calculator available.

To estimate the quotient of 420 divided by 21 using compatible numbers, we can round 420 to 400 and 21 to 20. Then, we can divide 400 by 20 to get an estimate of the quotient:

420 ≈ 400

21 ≈ 20

400 ÷ 20 = 20

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Answer:

1 1/9

Step-by-step explanation:

Answer:

(a) Candy's initial sum as a terms of x is $6x

(b) x = $60

(c) $350

Step-by-step explanation:

The given parameters are;

The ratio in which Aliyah, Brenda and Candy share the sum of money = 3:5:6

The amount Candy later gives Aliyah = $100

The amount Candy later gives Brenda = $50

The new ratio of the sum of the shared money between Aliyah, Brenda and Candy = 2:3:3

(a) Whereby Aliyah has $3x at the start, we have;

Total sum of mony = Y

Amount of Aliyah's initial share = Y × 3/(3 + 5 + 6) = Y×3/14

Therefore, Y×3/14 = $3x

x = Y×3/14 ÷ 3 = Y/14

Amount of Candy's initial share = Y × 6/14

Therefore Candy's initial sum as a terms of x = $6x

(b) Given that Aliyah's and Candy's initial sum as a function of x are   $3x and $6x, therefore, in the ratio 3:5:6, Brenda's  initial sum as a function of x = $5x

Which gives;

Total amount of money = $14x

With

6x - 150, 3x + 100, and 5x + 50, the ratio =is 2:3:3

Therefore, we have;

14·x × 2/(2 + 3 + 3) = (6·x - 150)

14·x × 2/(8) = (6·x - 150)

14·x × 1/4 = (6·x - 150)

7·x/2 = (6·x - 150)

12·x - 300 = 7·x

12·x - 7·x = 300

5·x = 300

x = $60

(b) The final amount of money with Brenda = 5x + 50 = 5 × 60 + 50 = $350

The final amount of money with Brenda = $350.

The probability of picking 2 white balls and 1 black ball is 0.154

The given parameters are:

When each ball is selected, the total number of ball decreases by 1 and the type of ball also decreases.

So, the probability is represented as:

P(2 white and 1 black) = White/n * White - 1/n - 1 * Black//n - 2

Substitute known values

P(2 white and 1 black) = 12/20 * 11/19 * 8//18

Evaluate

P(2 white and 1 black) = 0.154

Hence, the probability of picking 2 white balls and 1 black ball is 0.154

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Emma used 1.86 pints of white paint to paint her bedroom walls

Emma used 9.3 pints of blue paint and white paint combined to paint her bedroom walls. Of this total amount, 4/5 is blue paint, which means 1/5 must be white paint.

To find the amount of white paint Emma used, we can calculate 1/5 of the total paint used.

1/5 of 9.3 pints = (1/5) * 9.3 = 1.86 pints

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The price of the car is, 28,750.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Now, To find the price of the car, you need to use the following formula:

Price of the car = Down payment / (down payment percentage / 100)

Hence, Plugging in the given values, you get:

Price of the car = 5,750 / (20 / 100)

Simplifying the expression, you get:

Price of the car = 5,750 / 0.2

Thus, The price of the car is, 28,750.

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Complete question is this,

Ms. D'Amico bought a car with a 20% down payment, which was 5,750. She will finance the rest of the car payments. What was the price of the car?

Answer:

Step-by-step explanation:

Hi

Using binomial probability, the probability of having exactly 4 dice on 4, 5 or 6 is 5/32.

Using binomial probability, we can calculate the probability that out of the 5 dice thrown, the probability of having exactly 4 dice on 4, 5 or 6 can be calculated as;

\(P(X=k) = C(n, k) * p^k * (1-p)^(^n^-^k^)\)

In the given data;

n = 5

k = 4

p = 3/6 = 1/2

Using the binomial probability formula, we can calculate:

P(X=4) = C(5, 4) * (1/2)⁴ * (1 - 1/2)⁵⁻⁴

P(X=4) = 5 * (1/2)⁴ * (1/2)¹

P(X=4) = 5 * (1/16) * (1/2)

P(X=4) = 5/32

Therefore, the probability that exactly 4 dice land on a 4, 5, or 6 when rolling five fair dice is 5/32.

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Recursive Formula

\(\begin{cases}a_1 = 8\\a_n = a_{n-1}-7\end{cases}\)

The top row says the first term is 8

The bottom row says that to get the nth term, we subtract 7 from the (n-1)th term. So basically we subtract 7 from each term to get the next term.

Note the subscripts tell us which term we're working with.

======================================================

Arithmetic Formula

We have a = 8 as the first term and d = -7 as the common difference.

a(n) = a + d(n-1)

a(n) = 8 + (-7)(n-1)

a(n) = 8 - 7n + 7

a(n) = -7n+15

The nth term arithmetic formula is a(n) = -7n+15

If you plug in n = 1, you should get a(n) = 8

If you plug in n = 2, you should get a(n) = 1

and so on.

=======================================================

Finding the 10th term

Plug in n = 10 to get

a(n) = -7n+15

a(10) = -7(10)+15

a(10) = -70+15

a(10) = -55

The 10th term is -55

cos(30)=x/8

Rewrite the equation as

x/8=cos(30)

Multiply both sides of the equation by

8

.

8

⋅

x/8=8⋅cos(30)

Simplify both sides of the equation.

Tap for more steps...

x=4√3

The result can be shown in multiple forms.

Exact Form:

x=4√3

Decimal Form:

x=6.9282032

Answer:

c

Step-by-step explanation:

c

If an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white ball is 3/5

The number of red balls = 2 balls

The number of white balls = 3 balls

Total number of balls = 2 + 3

= 5 balls

The probability = Number of favorable outcomes / Total number of outcomes

Number of favorable outcomes = Number of white balls = 3

Total number of outcomes = 5

The probability = 3/5

Hence, if an urn contains two red balls and three white balls and a ball is chosen at random, then the probability of getting white is 3/5

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The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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Answer: b

Step-by-step explanation:

Answer:

Step-by-step explanation:

ima a braintlest

Answer:

i think its 10

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Convert the 3 liters into milliliters and then divide it normally or in the fraction way

Answer:

The answer is B

Step-by-step explanation:

Step-by-step explanation:

Radius of the circle=8

We know that

\(\boxed{\sf Area=\pi r^2}\)

\( \sf \rightharpoondown \: area = \frac{22}{7} \times {8}^{2} \\ \sf \rightharpoondown \: \frac{22}{7} \times 64 \\ \sf \rightharpoondown \: \frac{22 \times 64}{7} \\ \sf \rightharpoondown \: \frac{1408}{7} \\ \sf \rightharpoondown \: 201.1units {}^{2} \)

\(\sf More\:to\:know\begin {cases}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Areas:-}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Breadth\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}p\sqrt {4a^2-p^2}\\ \\ \star\sf Parallelogram =Breadth\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {cases}\)

Answer:

\(-4x^{2} -4xy+6y^{2}\)

Step-by-step explanation:

(3x2 − 8xy + y2) − (7x2 − 4xy − 5y2)

First, we remove the parenthesses. We can just remove the first parnthesses because there isn't any sign before them. When removing the second ones, we will change the sign of every term in it. It becomes:

\(3x^{2} -8xy+y^{2} -7x^{2} +4xy+5y^{2}\)

Now we will combine the like terms. That means that we will subtract 7x2 from 3x2, add 4x to -8x etc.

\(-4x^{2} -4xy+6y^{2}\)

Answer:

-4xy - 8x + 12y

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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Answer:

9x50=450

Step-by-step explanation:

hope this helps

The given series converges to 4/3.

The given series is:

4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

We can rewrite this series as:

4(1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ...)

Now, we can use the alternating series test, which states that an alternating series converges if the absolute values of its terms decrease monotonically to zero.

In this case, the absolute values of the terms are:

|4/5|, |4/7|, |4/9|, |4/11|, |4/13|, ...

These terms do decrease monotonically to zero, so we can apply the alternating series test. Therefore, the series converges.

To find the sum of the series, we can use the formula for the sum of an alternating series:

S = a - a1 + a2 - a3 + ...

where S is the sum of the series, a is the first term, and ai is the ith term.

In this case, a = 4/5 and the common difference d = -2/5, since we are subtracting 2/5 from each term to get the next one. So, we have:

S = 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - ...

S = a/(1 + d) = (4/5)/(1 - 2/5) = 4/3

Therefore, the given series converges to 4/3.

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Answer:

The Answer is C. 50

Step-by-step explanation:

To pack 600 granola bars, 50 boxes are needed.

The correct option is C.

To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.

Number of boxes = Total granola bars / Granola bars per box

Number of boxes = 600 / 12

Number of boxes = 50

So, 50 boxes are needed to pack 600 granola bars.

The correct answer is option C: 50.

To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.

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Answer:

1/2 is the slope of a line with equation y.