P(Girl Sophomore) :
=[?]

the final answer is:She bought 6 first-class tickets.

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

Let's denote the number of coach tickets purchased by "x" and the number of first-class tickets purchased by "y". We know that a total of 9 people took the trip, so we can write:

x + y + 1 = 9

Simplifying this equation, we get:

x + y = 8

We also know that the total cost of airfare was $7710, which can be expressed as:

210x + 1180y = 7710

This tells us that Sarah purchased 6.2 first-class tickets. Since she can't buy a fractional part of a ticket, she must have bought either 6 or 7 first-class tickets. To determine how many coach tickets she bought, we can use either equation. Let's use the first equation and substitute in y = 6:

x + 6 + 1 = 9

x = 2

So Sarah bought 2 coach tickets.

Therefore, the final answer is:She bought 6 first-class tickets.

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Answer:

518

Step-by-step explanation:

solution:

=8^2^×1^+1+6^2^×1^-1

=8^3+6^1

=8^3+6

=8×8×8+6

=512+6

=518

Dave has $11 and he buys a book for $8 but he spends an equal amount of money on 2 cards. Let's model this problem with an inequality.

x = $ spent on one card.

2x + $8 ≤ $11

Let's subtract $8 from both sides.

2x ≤ $3

Divide both sides by 2

x ≤ $1.5

Dave can spend at most $1.5 on each card.

Answer:

B) 24 feet

General Formulas and Concepts:
Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Functions

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle h(t) = -16t^2 + 35t + 5\)

Step 2: Find Height

Since we are trying to find the height of the basketball at 1 second, it implies that t = 1. Therefore, we can simply substitute t = 1 into our function:

\(\displaystyle\begin{aligned}h(1) & = -16(1)^2 + 35(1) + 5 \\& = -16(1) + 35(1) + 5 \\& = -16 + 35 + 5 \\& = \boxed{24} \\\end{aligned}\)

∴ the height of the basketball at 1 second is equal to 24 feet.

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Topic: Algebra I

Answer: -0=

Step-by-step explanation:

Answer:

-0=

Step-by-step explanation:

There are approximately 0.693 moles in 4.18 × 10²³ formula units of BaBr₂. To determine the number of moles in 4.18 × 10²³ formula units of BaBr₂, we can use Avogadro's number, which states that one mole of any substance contains 6.022 × 10²³ formula units.

In this case, the given quantity is already in formula units, so we don't need to convert it. By dividing the given quantity by Avogadro's number, we can calculate the number of moles. Avogadro's number, 6.022 × 10²³, represents the number of formula units (atoms, ions, or molecules) in one mole of any substance. In this problem, we have 4.18 × 10²³ formula units of BaBr₂. Since the given quantity is already in formula units, we can directly divide it by Avogadro's number to find the number of moles.

Dividing 4.18 × 10²³ by Avogadro's number:

4.18 × 10²³ / (6.022 × 10²³) = 0.693 moles

Therefore, there are approximately 0.693 moles in 4.18 × 10²³ formula units of BaBr₂.

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The statement A confidence interval for proportions is used to estimate the population proportion not the sample proportion is true.

A confidence interval for proportions is a statistical tool used to estimate the range of values within which the population proportion is likely to lie. It is calculated based on the sample proportion, sample size, and a specified level of confidence.

The sample proportion is only used as a point estimate of the population proportion, but the confidence interval takes into account the variability of the sample proportion and provides a range of values that are likely to include the population proportion with a certain level of confidence.

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The auxiliary equation for the given differential equation is obtained by assuming that y = e^(rx), which gives the characteristic equation as x^2r^2 - 20 = 0. Solving for r, we get r = ±√(20)/x or r = ±2√(5)/x. Therefore, the roots of the auxiliary equation are r1 = 2√(5)/x and r2 = -2√(5)/x.

To solve the differential equation, we use the method of undetermined coefficients. Since the roots of the auxiliary equation are real and distinct, we assume the general solution to be y(x) = c1e^(r1x) + c2e^(r2x), where c1 and c2 are constants to be determined. Substituting the values of r1 and r2, we get y(x) = c1e^(2√(5)x/x) + c2e^(-2√(5)x/x) = c1e^(2√(5)x) + c2e^(-2√(5)x).

Thus, the solution to the given differential equation is y(x) = c1e^(2√(5)x) + c2e^(-2√(5)x), where c1 and c2 are arbitrary constants determined by the initial conditions.

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Melissa earned \($152.84\\\) this week. This means that she earned a total of \($174.49\) over the two week period.

To determine how much Melissa earned last week, we can subtract the \($21.65\) that she earned more this week from the total amount earned over the two week period. Therefore, Melissa earned \($152.84\) this week, and \($21.65\) more than she earned last week. Subtracting \($21.65\)from \($174.49\) gives us \($152.84\), which is the amount Melissa earned last week. This means that Melissa earned \($152.84\) last week .To summarize, Melissa earned $152.84 this week, which was\($21.65\) more than she earned last week. This means that Melissa earned a total of \($174.49\)over the two week period, and by subtracting \($21.65\) from the total amount earned over the two week period, we can determine that Melissa earned\($152.84\) last week.

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Answer:

k = 1

Step-by-step explanation:

16 - 2k = 14

- 16       - 16

    -2k = -2

     -2     -2

       k = 1

The sum of 2.54 x 10^19 and 3.218 x 10^17 is 2.57218 x 10^19.

To find the sum of 2.54 x 10^19 and 3.218 x 10^17, we can add the numbers as follows:

2.54 x 10^19 + 3.218 x 10^17

First, we need to align the numbers by their exponents:

2.54 x 10^19

0.03218 x 10^19 (3.218 x 10^17 converted to the same exponent as 10^19)

Now, we can add the numbers:

2.54 x 10^19

0.03218 x 10^19

2.57218 x 10^19

Therefore, the sum of 2.54 x 10^19 and 3.218 x 10^17 is 2.57218 x 10^19.

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Step-by-step explanation:

multiply and the both number and divide by bytwo

Answer:

\(\sqrt{69}\)

Step-by-step explanation:

from the pythagorean theorem:

\(a^2 + b^2 = c^2\\10^2 + b^2 = 13^2\\100 + b^2 = 169\\b^2 = 69\\b = \sqrt{69}\)

The solution to the given equation 3d + 16 = -2(5 - 3d) is 26/3.

In order to evaluate and solve this expression, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical expression:

Expression = 3d + 16 = -2(5 - 3d)

By opening the bracket, we have:

3d + 16 = -10 + 6d

By rearranging and collecting like-terms, we have the following:

6d - 3d = 16 + 10

3d = 26

d = 26/3

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Answer:

x=1

Step-by-step explanation:

10(x-1) =0

We want to use the distributive property.

10x -10 =0

Add 10 to each side.

10x-10+10 = 10

10x = 10

Divide each side by 10.

10x/10 = 10/10

x = 1

The constants α, β, and k are all zero, and the solution to the IVP is y(t) = e²{-2t}, with t = -0.5ln(7)  the condition limt→∞y(t) = 7,t = -0.5ln(7)

Using the method of undetermined coefficients to find the general solution of the differential equation:

y'' + 3y' + 2y = 0

The characteristic equation is:

r²2 + 3r + 2 = 0

Factoring this equation, we get:

(r + 2)(r + 1) = 0

So the roots are r1 = -2 and r2 = -1. Therefore, the general solution is:

y(t) = c1e^{-2t} + c2e^{-t}

Next, we use the information that y1(t) = e²{-3t} is a solution to the differential equation. Substituting this into the general solution, we get:

e²{-3t} = c1e²{-2t} + c2e²{-t}

equation to solve for c1 and c2. Multiplying both sides by e^{2t}, we get:

e²{-t} = c1 + c2e²t

Taking the limit as t approaches infinity,  that c1 must be zero in order for the right-hand side to converge to a finite value. Therefore, we have:

c1 = 0

Substituting this into the previous equation,

e²{-t} = c2e²t

Dividing both sides by e²t,

e²{-2t} = c2

Therefore, we have:

c2 = e²{-2t}

Substituting these values into the general solution,

y(t) = c1e²{-2t} + c2e²{-t} = e²{-2t}

So α = β = 0 and k = -2. Finally,  the information that limt→∞y(t) = 7. Since y(t) = e²{-2t}, we have:

limt→∞e²{-2t} = 7

Taking the natural logarithm of both sides,

-2t = ln(7)Solving for t,

t = -0.5ln(7)

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Answer:

Step-by-step explanation:

y=10

a. Optimal solution: X1 = 140, X2 = 0, X3 = 80, Objective Function Value = 4700.000.

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding.

c. The dual price for the second constraint is 2.333, indicating that for each unit increase in its right-hand side value, the objective function value increases by 2.333.

d. The objective function coefficient of X2 can vary between 30 and 40 without changing the optimal solution

a. The complete optimal solution is:

X1 = 140

X2 = 0

X3 = 80

Objective Function Value = 4700.000

b. The first constraint (4X1 + 5X2 + 8X3 < 1200) is binding because it has a slack/surplus value of 0.

c. The dual price for the second constraint (9X1 + 15X2 + 3X3 < 1500) is 2.333. This means that for each unit increase in the right-hand side value of the second constraint, the objective function value will increase by 2.333 units, assuming all other variables and constraints remain constant.

d. The objective function coefficient of X2 can vary between 30 and 40 before a new solution point becomes optimal. This means that as long as the coefficient remains within this range, the current solution will still be optimal. However, if the coefficient of X2 goes below 30 or above 40, a new optimal solution may be obtained.

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Answer:

x = 10

y= 12

Step-by-step explanation:

We know that TSV = 90 degrees

5x+4x = 90

9x = 90

Divide by 9

9x/9 = 90/9

x = 10

We know that RSU = 180

10y+10 +5x= 180

10y + 10 + 5(10) = 180

10y + 10 +50 = 180

10y +60 = 180

Subtract 60 from each side

10y = 120

Divide by 10

y = 12

The integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx

From the question, we have the following parameters that can be used in our computation:

y = 0 and y = sin(x)

Also, we have

The line u = -2

Set the equations to each other

So, we have

sin(x) = 0

When evaluated, we have

x = 0 and x = π

For the volume generated from the rotation around the region bounded by the curves, we have

V = ∫[a, b] 2π(x + 2) [g(x) - f(x)] dx

This gives

V = ∫[0, π] 2π(x + 2) [sin(x) - 0] dx

So, we have

V = ∫[0, π] 2π(x + 2) [sin(x)] dx

Hence, the integral for the volume generated is V = ∫[0, π] 2π(x + 2) [sin(x)] dx

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Based on the calculation of the index of the 65th percentile using the formula and the ordered list of bills, the 65th percentile of the bills for the sample of 20 couples at the restaurant is 63 dollars.

We must arrange the bills in ascending order in order to determine the sample's 65th percentile:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

The formula for calculating the index of the 65th percentile is as follows:

Index = (Percentile / 100) * (N + 1)

where N is the sample size (which is 20 in this case).

So, for the 65th percentile, we have:

Index = (65 / 100) * (20 + 1) = 13.65

We require the index of the bill that is more than or equal to the 65th percentile, so we must round up this value to the nearest integer.

Therefore, the 65th percentile is the 14th bill in the ordered list:

6, 15, 21, 21, 23, 23, 24, 26, 27, 30, 30, 31, 37, 56, 61, 62, 63, 63, 64, 65

So, The 14th banknote on the ordered list, with a value of 63 dollars, represents the 65th percentile.

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480 different skirt-blouse-shoe outfits the girl can wear.

To find how many different skirt-blouse-shoe outfits can she wear:

5 × 8 × 12 = 480

Therefore, 480 different skirt-blouse-shoe outfits the girl can wear.

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Answer:

5,859,375

Step-by-step explanation:

pattern is x * 5

3, 15, 75, 375, 1875, 9375, 46875. 234375, 1171875, 5859375

\(10^{th}\) term of the geometric sequence is \(\boldsymbol{5859375}\).

A geometric progression, also known as a geometric sequence, is a non-zero numerical sequence in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.

Given geometric sequence is \(\boldsymbol{3,15,75}\)

Ratio is \(r=\frac{15}{3}\) that is \(\boldsymbol{r=5}\).

\(n^{th}\) term of a geometric sequence is given by \(\boldsymbol{ar^{n-1}}\) where \(\boldsymbol{a}\) is the first term.

So,

\(10^{th}\) term of the geometric sequence \(=(3)(5)^{10-1}\)

                                                         \(=(3)(5)^{9}\\=\boldsymbol{5859375}\)

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Answer:

4 raised to 4 is 256

Step-by-step explanation:

Answer: 256

Step-by-step explanation:

Remember: to calculate by elevated you have to calculate the same number the same number of times. For example: 4 raised by 4 is: 4 x 4 x 4 x 4 and that multiplication results in: 256. I hope and it has helped you ;)

Answer:

4+8

Step-by-step explanation:

oh and the answer to the whole equation is 153

Given,Three possible risk scenarios X, Y and Z. The initial assessment found that X is twice as likely as Z and Y is three times as likely as Z.

Probability of X is p(X) = 2p(Z)
Probability of Y is p(Y) = 3p(Z)
Probability of Z is p(Z)Let the probability of Z be p. So, the probability of X and Y can be written as:
p(X) = 2p(Z)p(Y) = 3p(Z). And, Total probability, p(X) + p(Y) + p(Z) = 1. Given that, p(X) + p(Y) + p(Z) = 12p(Z) + 3p(Z) + p(Z) = 1(6p(Z) = 1)p(Z) = 1/6. Therefore, p(X) = 2p(Z) = 2(1/6) = 1/3p(Y) = 3p(Z) = 3(1/6) = 1/2. Hence, the probability of X, Y, and Z are p(X) = 1/3, p(Y) = 1/2, and p(Z) = 1/6 respectively.

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Starting from the equation:

Multiply both members by 2 to cancel out the factor of 1/2 on the right member of the equation:

Divide both members by m to cancel out the factor of m on the right member of the equation:

Take the square root of both member of the equation to get rid of the exponent of v:

Therefore, the equation rearranged so that it is solved for v is:

Answer:

8.00

Step-by-step explanation:

Answer:

answer is 4

Step-by-step explanation:

no prob

Answer:

67%

Step-by-step explanation:

24/75%= 33

100-33= 67