Maya will spend more than $26 on gifts. So far, she has spent $15. What are the possible additional amounts she will spend?

Answer:

10+4x+11=x²-10+10 (add 10 both side)

21+4x-4x=x^2-4x  (substract 4x in both side)

21-21=x^2-4x-21 (substract 21 in both side)

x^2-4x-21=0

x^2+3x-7x-21=0(we can write -4x as (3x)+(-7x)=(-4x)

x(x+3)-7(x+3)=0 (get common factor)

(x+3)(x-7)=0 (get common factor which is (x+3) by both)

x=-3 or x=7

Step-by-step explanation:

The match can be scheduled in 900 different ways with the help of permutations and combinations.

Given,

Number of players from each school = 3.

Let, the players of the first school be A, B, and C.

Let, the players of the second school be X, Y, and Z.

The problem can be solved in two cases,

Case-1

According to the question,

Each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

Round 1 : AX BY CZ

Round 2 : AX BZ CY

Round 3 : AY BX CZ

Round 4 : AY BZ CX

Round 5 : AZ BX CY

Round 6 : AZ BY CX

In other words, we have to permutate these 6 rounds, i.e., 6! = 720 ways.

Case-2

Given,

Three rounds are played simultaneously in each round.

(a)

Round 1 : AX BZ CY

Round 2 : AX BZ CY

Round 3 : AY BX CZ

Round 4 : AY BX CZ

Round 5 : AZ BY CX

Round 6 : AZ BY CX

(b)

Round 1 : AX BY CZ

Round 2 : AX BY CZ

Round 3 : AY BZ CX

Round 4 : AY BZ CX

Round 5 : AZ BX CY

Round 6 : AZ BX CY

The total number of permutations for Case-2 will be twice of 6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Thus, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

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Answer:

999,960

Step-by-step explanation:

let x be a multiple of 120

120x ≤ 999,999

999,999 / 120 = 8333.325

8333 ≤ x ≤ 8334

8333(120) = 999,960

8334(1200) = 1,000,080  this is a 7-digit number

Therefore, the largest 6-digit number that is exactly divisible by 120 is 999,960

Answer:

1.5 miles.

Step-by-step explanation:

You can figure it out by dividing the yards by 1760.

Answer:

1.5 miles

Step-by-step explanation:

A mile is 1760 yards

2640 yds * 1 mil/1760 yds = 2640/1760 = 1.5 miles

The price of one senior citizen ticket is $6, and the price of one child ticket is $4.

To determine the price of each senior citizen ticket and each child ticket, we can set up a system of equations based on the information provided. Let's assume the price of one senior citizen ticket is x dollars and the price of one child ticket is y dollars.

From the first day of ticket sales, we know that 5 senior citizen tickets were sold, yielding a total of 5x dollars, and 8 child tickets were sold, resulting in 8y dollars. The total revenue from the first day is given as $70.

Similarly, on the second day, 10 senior citizen tickets were sold, generating 10x dollars, and 4 child tickets were sold, producing 4y dollars. The total revenue from the second day is given as $80.

Setting up the equations:

5x + 8y = 70 (equation 1)

10x + 4y = 80 (equation 2)

To solve this system of equations, we can use various methods such as substitution or elimination. By solving the equations, we find that x = 6 and y = 4.

Therefore, the price of one senior citizen ticket is $6, and the price of one child ticket is $4.

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Answer:

e = 2

Step-by-step explanation:

Plug in 2 as "f", then solve for e:

6e + 3f = 18

6e + 3(2) = 18

6e + 6 = 18

6e = 12

e = 2

So, e = 2

we have the function

Part a

For t=7

substitute in the given function

For t=14

For t=21

For t=28

For t=35

Observation: The values of E varies from -1 to 1, including the zero

Part B

Remember that

The Period goes from one peak to the next

so

Period=2pi/B

B=pi/14

Period=(2pi)/(pi/14)=2pi*14/pi=28

The value of the numerical expression 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1 will be 17,402.

The outcome of the expression corresponds to the outcome of the computation it represents when the pertinent elements and fundamental operations of a mathematical model are assigned values.

Making something a little less complicated while also making it simpler to accomplish or understand is the concept of easiness.

The numerical expression is written below.

⇒ 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1

Simplify the expression, then we have

⇒ 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1

⇒ 10,000 + 7,000 + 400 + 0 + 2

⇒ 17,402

The value of the numerical expression 1 x 10,000 + 7 x 1,000 + 4 x 100 + 0 x 10 + 2 x 1 will be 17,402.

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The complete question is given below.

Find the value of the expression.

1 x 10 000 + 7 x 1 000 + 4 x 100 + 0 x 10 + 2 x 1.

The first and third linear systems are possible and the second and the fourth have no solution.

(a) A linear system of 3 equations and 3 unknowns can have infinitely many solutions if the equations are linearly dependent or if the system represents a plane intersecting a line or three planes intersecting at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0  0 |  3 ]

[ 0  1  0 | -2 ]

[ 0  0  0 |  0 ]

(b) A linear system of 3 equations and 4 unknowns cannot have exactly one solution. This is because there are more unknowns than equations, which leads to an underdetermined system. Therefore, there will be infinitely many solutions or no solutions at all.

(c) A linear system of 3 equations and 2 unknowns can have exactly one solution if the equations represent three lines that intersect at a single point. An example of an augmented row-reduced echelon matrix that satisfies this description could be:

[ 1  0 |  2 ]

[ 0  1 | -3 ]

[ 0  0 |  0 ]

(d) A linear system of 3 equations and 2 unknowns cannot have a unique solution. This is because there are more equations than unknowns, resulting in an overdetermined system. Therefore, there will be either infinitely many solutions or no solutions at all.

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Value of X6 = N6 - N5. From the given realization of the Bernoulli counting process, N5 = 3 and N6 - N5 = X6. Hence, X6 = N6 - N5 = 5 - 3 = 2. The value of S is the largest value of n for which Nn = 3. From the given realization of the Bernoulli counting process, N3 = 1, N4 = 2, N5 = 3, and N6 = 5. Hence, the value of S is 5.

The value of T2 is the time at which the second success occurs. From the given realization of the Bernoulli counting process, N2 = 1. Hence, the time at which the second success occurs is T2 = 2.d) P{N2=1, Ns=3, N7-4} = P{N2=1} × P{Ns-N2=2} × P{N7-Ns=1} × P{No=4}.Using the Bernoulli counting process, the probability of a success is p = 0.2 and the probability of a failure is q = 1 - p = 0.8. Therefore, P{N2=1} = pq, P{Ns-N2=2} = p²q, P{N7-Ns=1} = pq², and P{No=4} = p³.Thus, P{N2=1, Ns=3, N7-4} = (0.2)(0.8)(0.2²)(0.8)(0.2)(0.8²)(0.2³) = 0.0016384. A Bernoulli counting process is a stochastic process that consists of a sequence of independent and identically distributed random variables, where each random variable takes the value 1 or 0 with probability p and q = 1 - p, respectively. The Bernoulli counting process is often used to model the arrival times of events that occur randomly over time. The Bernoulli counting process has many applications in areas such as reliability theory, queueing theory, and inventory management.In this question, we are given the realization of a Bernoulli counting process, and we are asked to find various quantities associated with this process. We are first asked to find the value of X6, which is the number of successes that occur between times 5 and 6. We are then asked to find the value of S, which is the largest time at which three successes have occurred. We are also asked to find the value of T2, which is the time at which the second success occurs. Finally, we are asked to find the probability of a specific sequence of events occurring, given that the success probability is p = 0.2.To find the value of X6, we simply subtract the value of N5 from the value of N6. Similarly, to find the value of S, we look for the largest time at which Nn = 3. To find the value of T2, we look for the time at which N2 = 1. Finally, to find the probability of a specific sequence of events occurring, we use the probabilities of success and failure to calculate the probability of each event occurring, and then multiply these probabilities together. Thus, we have found the value of X6, the value of S, the value of T2, and the probability of a specific sequence of events occurring.

In conclusion, the Bernoulli counting process is a powerful tool for modeling the arrival times of events that occur randomly over time. By using the probabilities of success and failure, we can calculate various quantities associated with this process, such as the value of X6, the value of S, the value of T2, and the probability of a specific sequence of events occurring. The Bernoulli counting process has many applications in areas such as reliability theory, queueing theory, and inventory management.

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a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

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

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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First we need to determine how many days they have lived in 26 years

26 years * 365.25 days / year = 9496.5 days

Now we can figure out how many hours they have lived because there are 24 hours in 1 day

9496.5 days * 24 hours / day =227916 hours

Now we can figure out how many minutes they have lived because there are 60 minutes in 1 hour

227916 hours * 60 minutes / 1 hour = 13674960 minutes

They have lived 13674960 minutes

Answer:

A) Ray

Step-by-step explanation:

Because I know maths!

Given data;

The given inequality is 9>x.

The all values of x for which x is less than 9.

Thus, x=2 and x=5 are the solution of the given inequality.

The Probability that Robert randomly pulls out a black sock is 1/5  .

In the question ,

it is given that

Total number of socks in sock drawer = 30 socks

number of white socks in the drawer = 16 socks

number of black socks in the drawer = 6 socks

number of red socks in the drawer = 2 socks

number of yellow socks in the drawer = 6 socks

So , the probability that he randomly pulls out a black sock = (number of black socks in the drawer) / ( total number of socks in the drawer )

= 6 / 30

= 1/5

Therefore , The Probability that Robert randomly pulls out a black sock is 1/5  .

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let's firstly get the EQUATion, of the graph before we get the inequality.

so we have a quadratic with two zeros, at -6 and 8, hmmm and we also know that it passes through (-2 , 10)

\(\begin{cases} x = -6 &\implies x +6=0\\ x = 8 &\implies x -8=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +6 )( x -8 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=10 \end{cases}\)

\(a ( -2 +6 )( -2 -8 ) = 10\implies a(4)(-10)=10\implies -40a=10 \\\\\\ a=\cfrac{10}{-40}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{1}{4}(x+6)(x-8)=y\implies -\cfrac{1}{4}(x^2-2x-48)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12=y \end{array}}~\hfill\)

now, hmmm let's notice something, the line of the graph is a solid line, that means the borderline is included in the inequality, so we'll have either ⩾ or ⩽.

so hmmm we could do a true/false region check by choosing a point and shade accordingly, or we can just settle with that, since the bottom is shaded, we're looking at "less than or equal" type, or namely ⩽, so that's our inequality

\({\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12\geqslant y \end{array}}\)

Answer:

3

Step-by-step explanation:

was

Answer:

4

Step-by-step explanation:

Answer: It has no solutions.

(Hope this helps!)

Answer:

e=-2

Step-by-step explanation:

9e-7e=-11+7

2e=-4

e=-2

Answer:

100 minutes

Step-by-step explanation:

This is because it takes 5 minutes to fry 24 wantons, so we can write 5/24. Now we need to find out how long it takes to fry 40 dozen wantons, or 480 wantons. We can rewrite this as x/480. Since the time should be proportional, we get the following:

5/24 = x/480

We can now cross multiply. 24x=5x480. Therefore, 24x = 2400. If we divided each side by 24, we would get 100. Therefore, it takes 100 minutes to fry 40 dozen wantons, or about 1  2/3 hours.

Answer:

100 minutes (1 hour & 40 minutes).

Step-by-step explanation:

5 minutes = 2 dozen, which means it takes 2.5 minutes to cook 1 dozen.

2.5 minutes x 40 dozen = 100 minutes...

The expression for the cost in dollars of a pounds of apples and p pounds of pears is (0.9a + 1.07p) dollars.

Let's write an expression for the cost in dollars of a pounds of apples and p pounds of pears.

Cost of apples = 90 cents/pound

Cost of pears = 1.07 dollars/pound

To convert the cost of apples to dollars, we divide it by 100 since there are 100 cents in a dollar.

Cost of apples (in dollars) = 90 cents/pound / 100 cents/dollar = 0.9 dollars/pound

Now we can write the expression for the cost of a pounds of apples and p pounds of pears:

Cost = (0.9 dollars/pound) * a + (1.07 dollars/pound) * p

Therefore, the expression for the cost in dollars of a pounds of apples and p pounds of pears is (0.9a + 1.07p) dollars.

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To determine the number of units that need to be sold to achieve an operating profit target of K500,000, we need additional information such as the contribution margin per unit and the fixed costs.

To calculate the number of units required to achieve an operating profit target, we need to consider the contribution margin per unit, which is the difference between the selling price per unit and the variable cost per unit. The contribution margin represents the amount available to cover fixed costs and contribute towards the operating profit.

Let's assume that the contribution margin per unit is C. The formula to calculate the breakeven point, where the operating profit is zero, is as follows: Breakeven Point (in units) = Fixed Costs / Contribution Margin per Unit To achieve an operating profit target of K500,000, we need to calculate the breakeven point and then add the desired profit to determine the total number of units that need to be sold. Let's assume the breakeven point is B and the desired profit is P. The formula to calculate the required sales volume is as follows:

Required Sales Volume (in units) = Breakeven Point + (Desired Profit / Contribution Margin per Unit) By plugging in the appropriate values, we can calculate the required number of units that need to be sold to achieve the operating profit target of K500,000. It's important to note that this calculation assumes a linear relationship between sales volume and profitability and does not take into account other factors such as market demand, pricing strategies, or potential economies of scale. Additionally, it's crucial to consider the accuracy and reliability of the available data used in the calculation to ensure the results are meaningful and actionable.

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Hello! I'd be happy to help you evaluate the integral ∫sin³(t)cos(t)dt using the substitution u = sin(t). Let's follow the steps:

1. Substitute: Replace sin(t) with u, so sin³(t) becomes u³. To find the differential, take the derivative of the substitution equation: du/dt = cos(t).

2. Rewrite integral: Multiply both sides of the equation du/dt = cos(t) by dt to get du = cos(t)dt. Now, the integral becomes ∫u³du.

3. Evaluate the integral: To evaluate ∫u³du, use the power rule for integration, which is ∫u^n du = (u^(n+1))/(n+1) + C. In this case, n = 3, so we have:

∫u³du = (u^4)/4 + C.

4. Resubstitute: Replace u with the original expression, sin(t), to obtain the final answer:

∫sin³(t)cos(t)dt = (sin^4(t))/4 + C.

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To evaluate the integral ∫sin3 t cos t dt by making the substitution u = sin t, we need to follow these steps:

1. First, we need to express sin3 t in terms of u. Using the identity sin^2 t = 1 - cos^2 t, we can rewrite sin^3 t as sin t * sin^2 t = sin t * (1 - cos^2 t) = sin t - sin t * cos^2 t. Since u = sin t, we can substitute sin t = u and cos t = √(1 - u^2) to get sin^3 t = u - u * √(1 - u^2).

2. Next, we need to find the derivative of u with respect to t, which is du/dt = cos t. We can solve for dt in terms of du by rearranging to get dt = du/cos t. Since we have cos t = √(1 - sin^2 t) = √(1 - u^2), we can substitute cos t = √(1 - u^2) and dt = du/√(1 - u^2).

3. Now we can substitute u and du/√(1 - u^2) into the integral to get: ∫(u - u * √(1 - u^2)) * √(1 - u^2) * (du/√(1 - u^2)).

4. Simplifying the expression gives us: ∫(u√(1 - u^2) - u^3) du.

5. Integrating this expression gives us: (1/2) * (1 - u^2)^(3/2) - (1/4) * u^4 + C, where C is the constant of integration.

6. Finally, we need to substitute back u = sin t to get the final answer in terms of t: (1/2) * (1 - sin^2 t)^(3/2) - (1/4) * sin^4 t + C.

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\(\huge\boxed{6.37500}\)

Explanation...

Let's divide the numerator by the denominator.

\(\boxed{3\;Divided\;by\;8=0.375}\)

Now, lets add the whole number (6) to 0.375.

\(\boxed{6+0.375=6.37500}\)

That's your final answer. (Above)

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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The Monotonicity Fairness Criteria means that as voters move a candidate up or down in their rankings, the winner must remain the same. It is an important criterion for many voting systems since a failure of this criterion can cause a candidate to lose their election despite being more favored by voters.

To satisfy Monotonicity, if a candidate wins an election, they should still win if the ballots are changed in their favor (or not against them) and no other candidate should win as a result. Here is an example of the Montonocity Fairness Criteria being violated.

When the votes are counted and the candidate with the fewest votes is eliminated, their votes are transferred to the next-choice candidate on each ballot. This process is repeated until one candidate has a majority of the votes.

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Answer:

-11

Step-by-step explanation:

Answer:

No the Answer is 24

Step-by-step explanation:

The number (x) in: "9 more than three times a number is 24" is what we are solving here. In other words, you are looking for a number (x) that if you multiply it by three (same as three times) and then add 9, you get 24.