If I have $100 dollars and spend $99.99 dollars, how much money do I have left?

The equations have no solution. Therefore, the two numbers does not exist.

There are two numbers. One number is twice the other number.

The difference of the smaller number and half the larger number is 20.

The equation that can be use to represent the situation can be represented as follows;

Hence,

let the two numbers be x and y.

2x = y

x - 1 / 2 y = 20

Note the smaller number is x

Therefore, using substitution,

x - 1 / 2 (2x) = 20

x - x  = 20

0 = 20

The value of x and y can't be solved from the equation formed.

Therefore, it has no solution.

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The variable that will be eliminated is variable y

It will be eliminated by adding the two equations

The reason it will be eliminated is because the

Therefore, to make the game fair, you should earn a profit of $3 when you win.

To determine the profit you should earn when you win in order for the game to be fair, we need to consider the overall expected value.

In this gambling game, you win 25% of the time and lose 75% of the time. Let's assume that when you win, you earn a profit of P dollars. When you lose, you lose $1.

The expected value can be calculated as follows:

Expected Value = (Probability of Winning * Profit) + (Probability of Losing * Loss)

Since the game should be fair, the expected value should equal zero. Thus, we can set up the equation:

0 = (0.25 * P) + (0.75 * (-1))

Simplifying the equation:

0 = 0.25P - 0.75

0.75 = 0.25P

P = 0.75 / 0.25

P = 3

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Answer:

2.8 liters

Step-by-step explanation:

So there are various ways to do this problem, this is just MY preferred way.

Since we are given 1/4th of a total value with 14 liters, we can actually make this 4/4 by multiplying our given value by 4. In this case, 14 liters for 25% becomes 56 liters for 100% antifreeze.

Since we know have a percent of 100%, we can proceed to take 10% increments, all the way up to 30%

10% is 5.6, multiplied by 3 is 16.8

While you might want to put 16.8 instantly, don't forget we are looking for how much is ADDED from 25%, not just how much there is.

In this case, subtract 14 from 16.8 to come out with a grand total of 2.8 liters added.

Answer: 5/8

\(m=\frac{-1-4}{-8-0}=\frac{-5}{-8}=\frac{5}{8}\)

Step-by-step explanation:

Answer:5/8

Step-by-step explanation:

Answer: it’s 9

Step-by-step explanation:

54 divined by 6 = 9

If Dmitry is making a recipe that uses 1 pound of wheat flour and 10 ounces of almond flour then he will require total 26 ounces of flour.

Given that Dmitry is making a recipe that uses 1 pound quantity of wheat flour and 10 ounces of almond flour.

We are required to find the total quantity of total flour that Dmitry uses.

Quantity or amount is basically a property that can exist as a multitude or magnitude,

We know that 1 pound is equal to 16 ounces.

Quantity of wheat flour=1 pound

In 1 pound of wheat flour=16 ounces of wheat flour.

Quantity of almond flour=10 ounces

Total requirement of flour=16+10

=26 ounces.

Hence if Dmitry is making a recipe that uses 1 pound of wheat flour and 10 ounces quantity of almond flour then he will require 26 ounces of flour.

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Answer:

2 2/3 or 24/9

Step-by-step explanation:

3 2/9 - 5/9 = 24/9 = 2 6/9

3*9+2 = 29/9

29/9 - 5/9 = 2 6/9

2 6/9 turns into 2 2/3

2 2/3 is equal to 24/9

Answer:

2 2/3

Step-by-step explanation:

What you do is make 3 2/9 into an improper fractions --> 9 * 3 + 2 = 29/9

29/9 - 5/9 = 24/9

So, now you're going to make 24/9 into a mixed number which is 2 6/9 --> 2 2/3

(a) If the mass of the object is 10 kg and it occupies the region bounded by the paraboloid z = x^2 + y^2 and the plane z = 9, then its density is 1 kg/m³. (b) To find the surface area of the object, we need further information or assumptions about its shape and characteristics.

(a) Given that the mass of the object is 10 kg and assuming it has constant density, we can determine its density by dividing the mass by the volume it occupies. Since the region is bounded by the paraboloid z = x^2 + y^2 and the plane z = 9, we need to calculate the volume of this region. However, without further information or assumptions about the shape of the object within this region, we cannot determine the volume or its density. Therefore, we cannot provide a specific value for the density in this case.

(b) The surface area of the object cannot be determined solely based on the given information. The surface area depends on the shape and characteristics of the object within the bounded region. Without specific details about the object, such as its shape or any additional equations or constraints, we cannot calculate its surface area. Additional information or assumptions would be needed to determine the surface area accurately.

The first paragraph summarizes the given problem and indicates that the density of the object is 1 kg/m³ based on the provided mass and assumption of constant density. It also mentions the need for further information to calculate the surface area.

The second paragraph explains the limitations in calculating the surface area due to the lack of specific information about the object's shape and characteristics. It emphasizes the need for additional details or assumptions to accurately determine the surface area.

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Answer:

The annual interest rate is 0.018, or 1.8%.

Step-by-step explanation:

Let r be the annual interest rate, t be the number of years the money was in the account, and I be the amount of interest earned. Since the interest is simple interest, the amount of interest earned is given by the formula I = Prt, where P is the principal, or initial amount deposited. In this case, we know that P = $3000, t = 3.5 years, and I = $262.50. Substituting these values into the formula, we get:

262.50 = 3000r * 3.5

r = 0.018

Thus, the annual interest rate is 0.018, or 1.8%.

The quadratic equation exists \($x^{2}+3 x+2=0$\).

If a quadratic equation exists \($a x^{2}+b x+c=0$\), the utilizing the quadratic equation the solutions for x will be given by

\($x_{1,2}=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$$\)

The solution for x exists

\($x=\frac{-3 \pm \sqrt{3^{2}-4(1)(2)}}{2(1)}\)

Comparing equations (1) and (2) we get, a = 1, b = 3 and c = 2.

Therefore, the quadratic equation exists \($x^{2}+3 x+2=0$\).

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Answer:

One guy said it was B. but I'm going with A.

Step-by-step explanation:

Ramiya is using the quadratic formula to solve a quadratic equation. her equation is x = startfraction negative 3 plus or minus startroot 3 squared minus 4(1)(2) endroot over 2(1) endfraction after substituting the values of a, b, and c into the formula. which is ramiya’s quadratic equation?

a) The probability of the second ball being drawn from Urn 2 is 2/3.

b) The probability that the second ball is black given that it is drawn from Urn 2 is 3/4.

c) The probability that the second ball is black is 11/24.

d) The probability that the second ball was drawn from Urn 1 given that it is black is 4/11.

e) The probability that the first ball drawn was red, given that the second ball drawn is black is 4/11.

f) The probability that both balls drawn are red is 1/6.

Given that Urn 1 contains two red balls and two black balls, the probability of drawing one ball is 1/2. Urn 2 contains one red ball and three black balls, the probability of drawing one ball is 1/4. Urn 3 contains two red balls and one black ball, the probability of drawing one ball is 1/3.

Let R1 and R2 represent the events of drawing a red ball from Urn 1 and Urn 2, respectively.

Also, let B1 and B2 represent the events of drawing a black ball from Urn 1 and Urn 2, respectively.

For this probability problem, we need to consider the three conditional events: drawing a second ball from Urn 2 if the first ball is red from Urn 3, drawing a second ball from Urn 1 if the first ball is black from Urn 3, and the overall probability of drawing a second ball that is black.

a) If the first ball is red from Urn 3, then there are two possible scenarios. Either the second ball is drawn from Urn 1, or it is drawn from Urn 2. The probability of the second ball being drawn from Urn 2 is 2/3, and the probability of it being drawn from Urn 1 is 1/3.

b) The probability that the second ball is black given that it is drawn from Urn 2 is 3/4.

c) If we consider all possible scenarios, the probability that the second ball is black is

(1/3)×(1/2)+(2/3)×(3/4) = 11/24.

d) The probability that the second ball was drawn from Urn 1 given that it is black is P(B1)×P(1|B1) / P(B),

where P(B1) is the probability of drawing a black ball from Urn 1, P(1|B1) is the probability of drawing from Urn 1 given that the first ball is black, and P(B) is the probability of drawing a black ball regardless of which urn it is drawn from. Plugging in the values,

we get (1/2)×(1/2) / (11/24) = 4/11.

e) The probability that the first ball drawn was red given that the second ball drawn is black is P(R1|B2) = P(B2|R1)×P(R1) / P(B2), where P(R1) is the probability of drawing a red ball from Urn 1, and P(B2|R1) is the probability of drawing from Urn 2 given that the first ball is red. Plugging in the values, we get (3/4)×(1/2) / (11/24) = 4/11.

f) The probability that both balls drawn are red is P(R1)×P(R2|R3) = (1/2)×(1/4) = 1/8.

Therefore, the probability of the second ball being drawn from Urn 2 is 2/3. The probability that the second ball is black given that it is drawn from Urn 2 is 3/4. The probability that the second ball is black is 11/24. The probability that the second ball was drawn from Urn 1 given that it is black is 4/11. The probability that the first ball drawn was red given that the second ball drawn is black is 4/11. The probability that both balls drawn are red is 1/6.

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Answer:

x = -1 or x = 4

Step-by-step explanation:

\(x^2-2x-1=x+3\)

subtract \(x\) from both sides:

\(\implies x^2-2x-1-x=x+3-x\)

\(\implies x^2-3x-1=3\)

subtract 3 from both sides:

\(\implies x^2-3x-1-3=3-3\)

\(\implies x^2-3x-4=0\)

factor:

\(\implies x^2+x-4x-4=0\)

\(\implies x(x+1)-4(x+1)=0\)

\(\implies (x-4)(x+1)=0\)

Therefore,

\(x-4=0 \implies x=4\)

\(x+1=0 \implies x=-1\)

To factor quadratics with leading coefficients other than 1, you can follow these steps:

Check your factoring by expanding the factored form to see if it simplifies back to the original quadratic equation.

Remember that factoring quadratics with leading coefficients other than 1 may involve more complex algebraic techniques, and in some cases, the quadratic equation may not factor easily. In such cases, you can resort to using the quadratic formula to find the roots of the equation.

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Answer:

x is 0.

9(0) - 7 = -7

Step-by-step explanation:

Answer: X=0

Step-by-step explanation:

Data: 9x-7=7

Step one, Add 7 to both sides

9x-7+7=-7+7=9x=0

The reason you do this is that your trying to isolate x so by adding 7, you get rid of the -7 right by 9x and since what you do to one side you do to the other, you add 7 to the other -7 as well to get 0

Step two, Divide by 9 on both sides

9x/9=0/9=x=0

The reason for this is that your trying to isolate x and by dividing by 9, you take out the 9 next to the x. However what you do to one side you have to do to the other so you divide 0 by 9 as well

Answer: X=0

I hope this helps!

Answer:

160

Step-by-step explanation:

If the scale factor is 4, we would have to multiply the height and width by 4

4*5=20

4*4=16

Now to find the area of the triangle using the formula (20*16)/2

That equals to 160

f(3) = 16

Function notation is used to express a rule in terms of x and f(x), where x is independent and f(x) is dependent.

Pronunciation of Function Notation

To use function notation it is important to know how to express the function in words.

The function "f(x) = 3x + 7" would be pronounced "F of X equals three X plus 7."

So, the function is "F of" whatever variable or value is within the parentheses.

Use of Function Notation

The function y=x is similar to the function f(x)=x. As a matter of fact, when graphed they both work the same way, but the function notation seen in the question allows us to see the value of x.

This is because the value in the parentheses is the value of x. So, in this situation, the question asks what is the value of the function when x equals 3.

Solving for f(3)

To solve this function, all we have to do is plug 3 in for x and evaluate.

First, multiple 3*3

Next, add 7

The future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

To find the future value of the fund on January 1, 2018, just after the third deposit, we can use the compound interest formula:

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

Where:

FV = Future Value

P = Principal amount (initial investment)

r = Annual interest rate (expressed as a decimal)

n = Number of times the interest is compounded per year

t = Number of years

Let's calculate the future value step by step:

First deposit:

P = $16000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 4.333 years (from September 1, 2010, to March 1, 2015)

\(FV_1 = 16000(1 + 0.072/12)^{(12*4.333)}\\= 16000(1 + 0.006)^{52}\\= 16000(1.006)^{52}\\= 20,296.43\)

Second deposit:

P = $13000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 2.917 years (from March 1, 2015, to January 1, 2018)

\(FV_2 = 13000(1 + 0.072/12)^{(12*2.917)}\\= 13000(1 + 0.006)^{35}\\= 15,618.04\)

Third deposit:

P = $12000

r = 7.2% = 0.072 (as a decimal)

n = 12 (compounded monthly)

t = 0.084 years (from January 1, 2018, to January 1, 2018)

\(FV3 = 12000(1 + 0.072/12)^{(12*0.084)}\\= 12000(1 + 0.006)\\= $12,072.00\\\)

Adding up the future values:

\(Total FV = FV_1 + FV_2 + FV_3\)

= $20,296.43 + $15,618.04 + $12,072.00

≈ $47,986.47

Therefore, the future value of the fund on January 1, 2018, just after the third deposit, is approximately $47,986.47.

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Answer:

36

Step-by-step explanation:

just divided 9 by 1/4 I think I may be wrong.

Answer:

169, 152, 135

Step-by-step explanation:

186-17=169

169-17=152

152-17=135

The jet airplane covers a distance of approximately 148.62 km in 14.0 minutes, given that it reached a speed of 637 km/h during the flight.

To find the distance covered by the jet airplane in 14.0 minutes, we need to use the formula:

distance = speed x time

First, we need to convert the speed from kilometers per hour to meters per minute, since time is given in minutes:

637 km/h = 637,000 m/h

1 hour = 60 minutes, so:

637,000 m/h ÷ 60 min/h = 10,616.67 m/min

Therefore, the speed of the airplane in meters per minute is approximately 10,616.67 m/min.

Now we can use the formula:

distance = speed x time

where time is given as 14.0 minutes:

distance = 10,616.67 m/min x 14.0 min

distance = 148,616.67 meters

To convert the distance to kilometers, we can divide by 1000:

distance = 148,616.67 m ÷ 1000 = 148.62 km

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Complete question is:

A jet airplane reaches 637. km/h on a certain flight. What distance does it cover in 14.0 min?

Let's start by setting up an equation to represent the problem.

Let's say Jake started with x amount of money.

After giving 1/3 to his wife, he has 2/3 left: (2/3)x

After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600

We can solve for x by isolating it:

(1/4)(2/3)x = $600

Multiplying both sides by 12/2 gives:

(2/3)x = $3600

Dividing both sides by 2/3 gives:

x = $5400

So Jake started with $5400.

To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:

(1/4)(2/3)($5400) = $900

So he gave his mother $900.

Step-by-step explanation:

x = original amount of money

the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.

x - (1/3)x - (1/4)x = 600

so let's bring every fractional term to .../12.

12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600

12x/12 - 4x/12 - 3x/12 = 600

5x/12 = 600

5x = 600×12

x = 600×12/5 = 120×12 = $1440

he gave to his mother

(1/4) × 1440 = $360

If the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairs of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

From the ΔABC ≅ ΔDEF we observe that the corresponding segment to BA in triangle DEF is ED.

Hence, if the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

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Answer:

a.y=6

b.-1/8

c.1/2

d.2800

e.-8

f.7.71

Step-by-step explanation:

Step-by-step explanation:

remember, when multiplying 2 expressions, you need to multiply every term of one expressing with every term of the other expression and then add the individual results together (while observing their signs, of course).

so, e.g. 5(x - 4) = 5x - 5×4 = 5x - 20

therefore,

1)

5x - 20 = 2x + 10

5x - 2x = 10 + 20

3x = 30

x = 10

2)

-12s - 6 = 6s + 30

-12s - 6s = 30 + 6

-18s = 36

s = -2

3)

12c - 21 = -2c + 7

12c + 2c = 7 + 21

14c = 28

c = 2

4)

-10p + 30 = -10

-10p = -10 - 30

-10p = -40

p = 4

5)

8x = -2x - 20

8x + 2x = -20

10x = -20

x = -2

6)

21 + 6a - 5 - 2a = 8

4a + 16 = 8

4a = -8

a = -2

Answer:

1436.8cm³

Step-by-step explanation:

Formula :

\( \frac{4}{3} \times \pi \times r ^{3} \)

\( \frac{4}{3} \times \pi \times 7^{3} \)

=1436.75504cm³

to 1dp

=1436.8cm³

a) Margin of error for 97% confidence: 2.55 years

b) 97% confidence interval: 18.45 to 23.55 years

c) Margin of error for 90% confidence: 1.83 years

d) 90% confidence interval: 19.17 to 22.83 years

e) The confidence intervals are different due to the variation in confidence levels.

f) Sample size required for 97% confidence interval with a margin of error of 2 years: at least 314.

a) To calculate the margin of error, we first need the critical value corresponding to a 97% confidence level. Let's assume the critical value is 2.17 (obtained from the t-table for a sample size of 35 and a 97% confidence level). The margin of error is then calculated as

(2.17 * 6) / √35 = 2.55.

b) The 97% confidence interval estimate is found by subtracting the margin of error from the sample mean and adding it to the sample mean. So, the interval is 21 - 2.55 to 21 + 2.55, which gives us a range of 18.45 to 23.55.

c) Similarly, we calculate the margin of error for a 90% confidence level using the critical value (let's assume it is 1.645 for a sample size of 35). The margin of error is

(1.645 * 6) / √35 = 1.83.

d) Using the margin of error from part c), the 90% confidence interval estimate is

21 - 1.83 to 21 + 1.83,

resulting in a range of 19.17 to 22.83.

e) The 97% and 90% confidence intervals are different because they are based on different levels of confidence. A higher confidence level requires a larger margin of error, resulting in a wider interval.

f) To determine the sample size required for a 97% confidence interval with a margin of error equal to 2, we use the formula:

n = (Z² * σ²) / E²,

where Z is the critical value for a 97% confidence level (let's assume it is 2.17), σ is the assumed population standard deviation (6), and E is the margin of error (2). Plugging in these values, we find

n = (2.17² * 6²) / 2²,

which simplifies to n = 314. Therefore, a sample size of at least 314 is needed to obtain a 97% confidence interval with a margin of error equal to 2 years.

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A one-to-one relationship between two tables is indicated by a primary key in one table being used as a foreign key in the other table. It means each record in one table corresponds to exactly one record in the other table.

In a one-to-one relationship between two tables, a primary key in one table is used as a foreign key in the other table. This relationship is established to ensure that each record in one table corresponds to only one record in the other table.

For example, in the "Customers" and "Orders" tables, each customer can have only one order, and each order can belong to only one customer. The primary key "CustomerID" in the "Customers" table would be used as the foreign key in the "Orders" table.

This indicates that each record in the "Orders" table is associated with a specific customer in the "Customers" table, creating a one-to-one relationship. For example, in the "Customers" and "Orders" tables, each customer can have only one order, and each order can belong to only one customer.

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Answer:

140°

Step-by-step explanation:

a° = 180°-(75°-35°) = 180°-40° = 140°

Answer:

54º.

Step-by-step explanation:

two angles that are complementary have to add up to 90º. therefore, 90º-36º=54º angle.