Natalie has $20 $5 $1 $1 $1 and she needs two more bills to make $48 which bills will she need​

Finding the union of the sets A and C is the first step in solving P(A U C). Since set C only contains the number 6, the union of A and C has the elements 1, 2, 3, 4, and 6. A U C thus equals 1, 2, 3, 4, and 6.

The power set of A U C, which comprises all conceivable subsets of 1, 2, 3, 4, and 6, must then be located. If all conceivable subsets are listed, the power set of A U C, designated as P(A U C), will be discovered.

P(A U C) = { {}, {1}, {2}, {3}, {4}, {6}, {1,2}, {1,3}, {1,4}, {1,6}, {2,3}, {2,4}, {2,6}, {3,4}, {3,6}, {4,6}, {1,2,3}, {1,2,4}, {1,2,6}, {1,3,4}, {1,3,6}, {1,4,6}, {2,3,4}, {2,3,6}, {2,4,6}, {3,4,6}, {1,2,3,4}, {1,2,3,6}, {1,2,4,6}, {1,3,4,6}, {2,3,4,6}, {1,2,3,4,6}}.

There are 31 subsets in the power set P(A U C) that result from the union of sets A and C.

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Answer:

11

Step-by-step explanation:

You would start by subtracting $30 from $151 which is $121.

Then you would divide this by 11 which 121÷11=11

So 11 test were bought.

Answer:

triganometry is mathematics

Answer:

35

Step-by-step explanation:

Answer:

35

Step-by-step explanation:

Just multiply 7 by x and you'll get y.

Give brainliest if you want.

Answer:

She started with 10 candies.

Step-by-step explanation:

Answer:

She started with 10 pieces of candy.

Step-by-step explanation:

If she had 4 pieces for herself and then divided the rest of the candy amongst her 3 children, and they each recieved 2 pieces. (4 + 2 + 2 + 2)

Answer:

15x is the answer ihope this helps:j

The solution set of the inequality is B) x > -2.5.

What is inequality?

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

Here the given inequality is ,

=> 5.1(3 + 2.2x) > –14.25 – 6(1.7x + 4)

Now simplifying them then

=> 15.3+11.22x > -14.25-10.2x-24

=> 15.3+11.22x > -38.25 - 10.2x

=> 11.22x+10.2x > -38.25-15.3

=> 21.42x > -53.55

=> x> -2.5

Hence the solution set of the inequality is B) x > -2.5.

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The length of the rectangle is 7 cm and the width is 5 cm.

The whole distance covered by the rectangle's borders or its sides is known as its perimeter. As we know the rectangle will have 4 sides then the perimeter of the rectangle will be equal to the total of its four sides. And the unit will be in meters, centimeters, inches, feet, etc.        

The formula for the Perimeter of the rectangle is given by

Here we have

The length of a rectangle is 2cm greater than the width of the rectangle

And perimeter of the rectangle = 24 cm

Let x be the width of the rectangle

From the given data,

Length of the rectangle = (x + 2) cm  

As we know Perimeter of rectangle = 2(Length+width)

=> Perimeter of rectangle = 2(x+2 + x) = 2(2x +2)

From the given data,

Perimeter of rectangle =  24cm

=> 2(2x +2) = 24 cm

=> (2x +2) = 12     [ Divided by 2 into both sides ]

=>  2x = 12 - 2

=>  2x = 10

=>   x = 5         [ divided by 2 into both sides ]  

Length of rectangle, (x+2) = 5 + 2 = 7 cm

Therefore,

The length of the rectangle is 7 cm and the width is 5 cm.

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Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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Answer:

10 and 2

Step-by-step explanation:

10+2=12

10 is even

2*2=4  10-4+6

Hope this helps ! :)

The solution to the system of equations are (-4, 5), (2, 7), (3, -1), no solution, (-5, 8) and (7, -3)

System of equation can be solved using different method such as elimination method, substitution method and graphical method.

Question 1 and 2

See attachment for the graphs, where we have the solutions to be

System 1: (-4, 5)

System 2: (2, 7)

Question 3 and 4

Here, we solve the system of equation by substitution method.

So, we have

2x - 7y = 13

3x + y = 8

Make y the subject in (2)

y = -3x + 8

Let's substitute the value of y in equation (i)

2x - 7(-3x + 8) = 13

2x + 21x - 56 = 13

23x = 13 + 56

23x = 69

Divide both sides by 23

x = 69 / 23

x = 3

Let's find y

y = -3(3) + 8

y = -9 + 8

y = -1

For system (4), we have

x - 3y = 2

2x - 6y = 6

So, we have

x = 2 + 3y

By substitution, we have

2(2 + 3y) - 6y = 6

4 + 6y - 6y = 6

4 = 6

The system has no solution

Question 5 and 6

Here, we have

x + y = 3

x - 3y = -29

By eliminating x, we have

4y = 32

So, we have

y = 8

This means that

x + 8 = 3

x = -5

So, the solution is (-5, 8)

For system 6, we have

3y = 26 - 5x

6x + 7y = 21

So, we have

5x + 3y = 26

6x + 7y = 21

This gives

30x + 18y = 156

30x + 35y = 105

By elimination, we have

17y = -51

y = -3

This means that

6x + 7(-3) = 21

6x = 42

So, we have

x = 7

So, the solution is (7, -3)

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It will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

The lilypad doubles in size each day, which means that if it covers a certain fraction of the pond on day n, it will cover twice that fraction on day n+1. In other words, if the lilypad covers 1/2^k of the pond on day k, then it will cover 1/2^(k-1) of the pond on day k+1.

If we let n be the number of days it takes for the lilypad to cover the entire pond, then we can say that on day n-28, the lilypad covers 1/2 of the pond (since on day n-28, the lilypad will be half the size of what it is on day n). Therefore, we want to solve for n-28 when the lilypad covers the entire pond, which is equivalent to the lilypad doubling in size 28 times:

1/2 * 2^28 = 2^(28-n+28)

Simplifying, we get:

2^(n-28) = 2^28

Taking the logarithm base 2 of both sides, we get:

n-28 = 28

Solving for n, we get:

n = 56

Therefore, it will take 56 days for the lilypad to cover the entire pond. On day 28, the lilypad covers 1/2 of the pond, as we saw earlier.

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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The perfume bottle can hold a volume of \(= 108.9 \ cm^{3}\)

To calculate the volume of the perfume bottle, we need to find the volumes of the two components (right trapezoidal prism and right rectangular prism) and then sum them up.

1. Volume of the right trapezoidal prism:

The formula for the volume of a right trapezoidal prism is given by:

Volume = \((1/2) \times (base_{} + base_{2} ) \times height \times length\)

In this case, the bases of the trapezoidal prism are \(3\) cm and \(11\) cm, the height is \(3\) cm, and the length is \(3.3\) cm. Plugging in these values, we get:

Volume_trapezoidal = \((\frac{1}{2} ) \times (3 + 11) \times 3 \times 3.3\)

                  \(= 7 \times 3 \times 3.3\\= 69.3 \ cm^{3}\)

2. Volume of the right rectangular prism:

The formula for the volume of a right rectangular prism is given by:

Volume = \(length \times width \times height\)

In this case, the length is \(3.3\) cm, the width is \(3\) cm, and the height is \(4\) cm. Plugging in these values, we get:

Volume_rectangular = \(3.3 \times 3 \times 4\)

                  = \(39.6 \ cm^{3}\)

Now, we can calculate the total volume of the perfume bottle by adding the volumes of the two components:

Total volume = \(Volume\ of\ trapezoidal + Volum\ of\ rectangular\)

          \(= 69.3 + 39.6 \\ = 108.9 \ cm^{3}\)

Therefore, the perfume bottle can hold a volume of \(= 108.9 \ cm^{3}\)

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Answer:

10000000013.4 or 13.44+10^10

Step-by-step explanation:

1. move the left 10^5 and switch it with the 4.65

2. It should look like: (2.891 * 4.65) + (10^5 * 10^5)

3. Simplify: 13.44 + 10^10

4. Your answer should look like 10000000013.4 or 13.44 + 10^10. WooHoo! You just finished!

Please do Brainliest answer that would be appreciated!

Answer:

7.541 * 10^5

Step by step:

add 2.891 with 4.65

then add the 10^5

(This is an easy version on how to solve it. There is a more complex version but it’s too long.)

Answer:

27 glasses

Step-by-step explanation:

If one pitcher holds 9 glasses,

and

there are 3 pitchers,

multiply 9 by 3.

9×3 = 27

To determine if a set of vectors is linearly independent, we can calculate the determinant of the matrix formed by using these vectors as columns. If the determinant is non-zero, the vectors are linearly independent.

The determinant of a matrix provides information about its linear independence. If the determinant is non-zero, it indicates that the columns of the matrix are linearly independent. On the other hand, if the determinant is zero, it implies that the columns are linearly dependent.
In this case, we are given two vectors represented as columns of a matrix. Let's say the first vector is [8, 7] and the second vector is [a, b]. To determine if these vectors are linearly independent, we can form a 2x2 matrix with these columns: [[8, a], [7, b]].
The determinant of this matrix can be calculated as 8b - 7a. If this determinant is non-zero, it means that the vectors [8, 7] and [a, b] are linearly independent. However, if the determinant is zero, it indicates that these vectors are linearly dependent.
Therefore, to determine if the given set of vectors is linearly independent, we need to evaluate the determinant 8b - 7a and check if it simplifies to a non-zero value.

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Answer:

\(\frac{11}{20}\)

Step-by-step explanation:

2\(\frac{3}{4}\) ÷ 5

Convert mixed number fraction to improper fraction

\(\frac{11}{4}\) ÷ 5

To divide fractions we turn the second fraction (the one you want to divide by) upside down (this is now called a reciprocal) and we multiply

\(\frac{11}{4}\) × \(\frac{1}{5}\) = \(\frac{11}{20}\)

Surface area - The cost of medium popcorn will be $473.25.

What is surface area?

The surface area of a three-dimensional object is the space taken up by its outer surface.
For instance,
The surface area of a cube is what we need to calculate the amount of paint needed to paint it. It is consistently expressed in square units.

The surface area of the cylinder with the top open = πr(r + 2h)

we are given that,

r = 2in

h = 6in

taking π as 3.14, and substituting these vales in the above equation,

surface area = π x 2 (2 x 2 x 6)

= 3.14 x 2 (2 x 2 x 6)

= 1893in²

cost = 1893 x 0.25

= $473.25

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Answer:

8

Step-by-step explanation:

Reverse the steps and reverse the operations (divide to multiply, add to subtract)

Multiply 6 by 2 to get 12 and subtract 4 to get 8

We have the lease of a building is for 10 years with an annual rent of $48 000.

We first determine the 7.5% for the first 5 years, for that we add the cost of the rent for 5 years, that is:

In 5 years the rent will be of $240 000, now we find the 7.5%:

Her commision for the first 5 years is going to be of $18 000.

Now we determine the 5% for the next 3 years, for this we determine the rent for 3 years:

The rent for 3 years adds $144 000, now we determine the 5%:

From this we have that the commission for the next 3 years will be of $7200.

And finally, we determine the rent for the two remaining years:

We have that the last two years the rent will be of $96000, now we determine the 3.5% of her commission during that time:

From this we have her commission for the last two years will be of $3360.

Finally we add all of the values of the commissions she will get:

From this we have that the total commision money she will be getting during those 10 years will be $28 560.

As per the concept of counting problem, the reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

Counting Problems

Basically, counting refers the process of finding the number of elements of a finite set of objects.

Given,

Suppose you have a nickel, two dimes, and a quarter. One of the dimes was minted in 1976, and the other one was minted in 1992.

While we looking into the given problem,

For A) states that,  If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins. Let us label the dime as D, the penny as P, the quarter minted in 1976 as Q1 and the quarter minted in 1992 as Q2.

Here in this process if you choose one coin, you could choose either D, P, Q1, or Q2. This gives us 4 possible sets.

And If you choose two coins, you choose the following sets of coins: DP, DQ1, DQ2, PQ1, PQ2, Q1Q2. This gives us 6 possible sets.

Then If you choose three coins, you could the following sets of coins: DPQ1, DPQ2, DQ1Q2, PQ1Q2. This gives us 4 possible sets.

So, If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible set.

So, the total number of different sets of coins you can form is 4 + 6 + 4 + 1 = 15 different sets of coins can be formed.

Similarly, for b) If you choose at least one coin, this means you could choose 1, 2, 3 or 4 coins.

Then If you choose one coin you could choose either D, P, Q1, or Q2. However, since Q1 and Q2 give us the same sum, they are effectively the same set. This gives us 3 possible sums.

So, If you choose two coins, you could choose the following sets of coins : DP, DQ, PQ, Q1Q2.And this gives us 4 possible sums

Then If you choose three coins, you could choose the following sets of coins: DPQ, DQ1Q2, PQ1Q2. And this gives us 3 possible sums

Then If you choose four coins, you can only choose DPQ1Q2. This gives us 1 possible sum.

So, the total number of different sums of coins you can form is 3 + 4 + 3 + 1 = 11 different sums of money can be produced.

Finally, c) The reason that the answers in part (a) and part (b) are not the same is because Q1 and Q2 are treated as two different coins in part (a) whereas they are effectively treated as the same coin in part (b). And the reason they are treated as one coin is because they both contribute the same amount to the sum of money.

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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Answer:

  40.1 cm

Step-by-step explanation:

You want the perimeter of the triangle with altitude 8.4 cm dividing the side into segments 12 cm and 4.1 cm.

The lengths of the unknown sides can be found using the Pythagorean theoem.

  c = √(a² +b²)

  c = √(8.4² +12²) ≈ 14.65 . . . . . length of AC

and

  c = √(4.1² +8.4²) ≈ 9.35 . . . . . length of CD

Then the sum of side lengths is ...

  P = AC +CD +AD

  P = 14.65 +9.35 +(12 +4.1) = 40.1 . . . . cm

The perimeter of triangle ACD is about 40.1 cm.

Answer:

Step-by-step explanation:

For missing hypotenuse: \(\sqrt({a^{2} + b^{2})\)

Plug in the side lengths that are known to find the hypotenuse.

1. No, the angle is less than 18 degrees (closer to 15), so it is not safe

2. The length rounded to the nearest tenth is approximately 15.5 feet.

The value of a and b are 1 and -8 respectively.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given quadratic expression is x² + 2x - 7.

We have to write this in the form (x + a)² + b.

We have the algebraic identity a² + 2ab + b² = (a + b)²

x² + 2x - 7 = x² + 2x - 7 + 1 - 1

                 = (x² + 2x + 1) - 7 - 1

                 = (x + 1)² - 8, which is in the form (x + a)² + b.

a = 1 and b = -8

Hence the value of a is 1 and the value of b is -8.

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Activity 1: Obtain the differential equation of y = At^x, where A is a constant. To find the differential equation, we need to differentiate y with respect to t. Assuming A is a constant and x is a function of t, we can use the chain rule to differentiate y = At^x.

dy/dt = d(A\(t^x\))/dt

Applying the chain rule, we have:

dy/dt = d(A\(t^x\))/dx * dx/dt

Since x is a function of t, dx/dt represents the derivative of x with respect to t. To find dx/dt, we need more information about the function x(t).

Without further information about the relationship between x and t, we cannot determine the exact differential equation. The form of the differential equation will depend on the specific relationship between x and t.

Activity 3: Prove that y = \(4e^{(Ax + B)\), where A and B are constants, is a solution of the differential equation y'' - 25y = 0. To prove that y = \(e^{(Ax + B)\) is a solution of the given differential equation, we need to substitute y into the differential equation and verify that it satisfies the equation. First, let's calculate the first and second derivatives of y with respect to x:

dy/dx =\(4Ae^{(Ax + B)\)

\(d^2y/dx^2 = 4A^2e^{(Ax + B)\)

Now, substitute y, dy/dx, and \(d^2y/dx^2\) into the differential equation:

\(d^2y/dx^2 - 25y = 4A^{2e}^{(Ax + B)} - 25(4e^{(Ax + B)})\)

Simplifying the expression, we have:

\(4A^2e^(Ax + B) - 100e^{(Ax + B)\)

Factoring out the common term \(e^{(Ax + B)\), we get:

\((4A^2 - 100)e^{(Ax + B)\)

For the equation to be satisfied, the expression inside the parentheses must be equal to zero:

\(4A^2 - 100 = 0\)

Solving this equation, we find that A = ±5.

Therefore, for A = ±5, the function \(y = 4e^{(Ax + B)\) is a solution of the differential equation y'' - 25y = 0.

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