gabriela is building wooden box that is 15 in. tall and has a rectangular base that is 18 in by 15 in

Answer:

y = 50e^(0.1t)

Step-by-step explanation:

This represents an exponential growth function. It models a quantity that increases or decreases by a constant factor over equal intervals of time. At any time t, the value of the function is given by 50e^(0.1t).

At time t=0, the value of the function is 50. As time increases, the value of the function increases exponentially at a rate of 0.1. For example, at time t=1, the value of the function is 50e^(0.1) = 63.1. At time t=2, the value of the function is 50e^(0.2) = 79.4, and so on.

1. The equation for the cost of adult tickets is:

$8.97 x number of adult tickets

The equation for the cost of child tickets is:

$6.79 x number of child tickets

The equation for the cost of renting out the theater is:

$190

2. Yes, you can get at least 5 adult tickets and 4 kids tickets.

3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.

4.  It would be a better deal to rent out the theater if you had more than 24 people.

You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.

The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.

Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.

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The equation of the given hyperbola is; x²/25 - y²/49 = 1

We are given;

Focus = (74, 0)

Asymptote; y = -⁷/₅x

Centered at origin

We are given that the general form of equation of a hyperbola is;

x²/a² - y²/b² = 1

Now, we know that the equations of the asymptotes are;

y = ±(b/a)x

Thus, comparing the above with our asymptote of y = -7/5x gives us;

a = 5 and b = 7

Thus, the equation of the given hyperbola is;

x²/5² - y²/7² = 1

⇒ The equation of the given hyperbola is;

x²/25 - y²/49 = 1

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Answer:

The answer is 5 and 7

Step-by-step explanation:

Answer:

7 hours

Step-by-step explanation:

810 - 180 = 630

630/ 90 = 7

Answer:

x = 7 h

Explanation:

First, we write the data of the problem.

Alex travels 810 miles away

Train - 90 miles / h

Alex covers 180 miles.

How many hours does Alex walk in the distance?

1. Calculate the distance Alex still has to travel.

 810 miles - 180 miles = 630 miles

2. We take into account the speed of the train to calculate how many hours Alex will cover the remaining distance.

90 miles .... 1 h

630 miles .... x h

x = 630 milesx1h / 90 miles

x = 7 h

The expression when evaluated is 17

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

a = 2, b = 3, c = 4 and d = 12

Also, we have

20 - 2b/a

Substitute the known values in the above equation, so, we have the following representation

20 - 2b/a = 20 - 2 * 3/2

Evaluate

20 - 2b/a = 17

Hence, the solution is 17

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Let's assume the number of adults who entered the cave is 'A' and the number of youths is 'Y'.We can use the substitution method or the elimination method.Therefore, 250 adults entered the cave.

The total number of people who entered the cave, which is 575, and the total amount collected, which is $5600.From this information, we can set up two equations. The first equation represents the total number of people: A + Y = 575. The second equation represents the total amount collected: 12A + 8Y = 5600.

To solve this system of equations, we can use the substitution method or the elimination method. Here, let's solve it using the substitution method.

From the first equation, we have A = 575 - Y. Substituting this value into the second equation, we get 12(575 - Y) + 8Y = 5600.

Expanding and simplifying the equation gives 6900 - 12Y + 8Y = 5600. Combining like terms yields -4Y = -1300.

Dividing both sides by -4, we find Y = 325.

Substituting this value back into the first equation, we can calculate A: A + 325 = 575, so A = 250.

Therefore, 250 adults entered the cave.

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Answer: +10/3

Step-by-step explanation:

first you must make the parenthesis, so whenever a number is next to a parenthesis it means that it is multiplied, in this case -5 multiplies the numbers inside the parenthesis = +10/3.

The completed table would look like this

Mass (kg)       12       24        36      48      60

Percentage   20%    40%   60%   80%   100%

The double number line represents Henrik's mass, which is 60 kg. The second tick mark on the Mass line corresponds to this value. The Percentage line ranges from 0% to 100%, representing the percentage of Henrik's mass. To complete the table, we need to calculate the different percentages.

To find a certain percentage of Henrik's mass, we locate the corresponding point on the Percentage line and draw a vertical line to intersect the Mass line. We can then read the mass value at that intersection point.

For example, to find 20% of Henrik's mass, we locate the point on the Percentage line labeled "20%." Drawing a vertical line from this point, it intersects the Mass line at a value of 12 kg. Therefore, 20% of Henrik's mass is 12 kg.

Similarly, for 40% of Henrik's mass, the vertical line intersects the Mass line at a value of 24 kg.

In summary, the completed table  would look like this

Mass (kg)       12       24        36      48      60

Percentage   20%    40%   60%   80%   100%

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To determine the number of receptacles required for the bathroom counter space, we need to refer to the electrical code guidelines. The specific requirements may vary depending on the country or region, as well as the local electrical codes in place.

In the United States, according to the National Electrical Code (NEC), at least one 20-ampere-rated branch circuit is required to serve the bathroom receptacles. The code specifies that this circuit should be dedicated solely to the bathroom receptacles and should not serve any other areas.

The NEC also states that at least one receptacle outlet is required on the bathroom countertop. This receptacle should be located within 3 feet of the outer edge of the countertop and should be installed above the countertop surface. This means that a receptacle needs to be placed within reach of the bathroom counter space.

Considering the given information that the bathroom counter space is seven feet, including the sink, we need to install at least one receptacle outlet on the countertop within 3 feet of the outer edge. Depending on the specific layout and size of the counter space, additional receptacles may be required to meet the code's requirements for accessibility and convenience.

To ensure compliance with local electrical codes and safety standards, it is advisable to consult with a licensed electrician or refer to the specific electrical codes applicable in your area. They will be able to provide accurate guidance based on the local requirements and regulations.

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Conditional probability is a key concept in probability theory that allows us to calculate the probability of an event occurring, given that another event has already occurred.

The formula for conditional probability is as follows:

P(A | B) = P(A and B) / P(B)

where P(A | B) represents the conditional probability of event A occurring given that event B has already occurred, P(A and B) represents the probability of both events A and B occurring together, and P(B) represents the probability of event B occurring.

It's important to note that the denominator, P(B), represents the background information that event B has already occurred. The numerator, P(A and B), represents the joint probability of both events A and B occurring. Dividing the joint probability by the background information gives us the conditional probability of event A occurring given that event B has already occurred.

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any function of the form y(x) = (A + D)*cos(x) + (B + C)*sin(x), where A, B, C, and D are constants, is a solution to the differential equation y'' + y = sin(x).

To determine the solutions of the differential equation y'' + y = sin(x), we need to find functions that satisfy this equation when differentiated twice with respect to x.

The differential equation is a second-order linear homogeneous differential equation. The general solution of this equation can be expressed as a linear combination of two linearly independent solutions.

To find these solutions, we can consider the complementary function, which is the solution of the homogeneous equation y'' + y = 0. The complementary function has the form y_c(x) = A*cos(x) + B*sin(x), where A and B are constants.

Now, we need to find a particular solution, denoted as\(y_p(x)\), that satisfies the non-homogeneous part of the equation, sin(x).

The particular solution can be of the form\(y_p(x) = C*sin(x) + D*cos(x)\), where C and D are constants.

Adding the complementary function and the particular solution gives the general solution\(y(x) = y_c(x) + y_p(x).\)

Therefore, the functions that are solutions of the given differential equation are:

1. y(x) = A*cos(x) + B*sin(x) + C*sin(x) + D*cos(x) = (A + D)*cos(x) + (B + C)*sin(x)

Here, A, B, C, and D are arbitrary constants.

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Answer:

\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)

Answer:

Step-by-step explanation:

Answer:

x = - 2 ± \(\sqrt{\frac{19}{3} }\)

Step-by-step explanation:

3x² + 12x = 7 ← factor out 3 from each term on the left side

3(x² + 4x) = 7

to complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 4x

3(x² + 2(2)x + 4 - 4) = 7

3(x + 2)² - 12 = 7 ( add 12 to both sides )

3(x + 2)² = 19 ( divide both sides by 3 )

(x + 2)² = \(\frac{19}{3}\) ( take square root of both sides )

x + 2 = ± \(\sqrt{\frac{19}{3} }\) ( subtract 2 from  both sides )

x = - 2 ± \(\sqrt{\frac{19}{3} }\)

The probability of it raining 5 days out of the week, given an average chance of rain of 36% each day, is approximately 0.036 or 3.6%.

To find the probability of it raining 5 days out of the week when the chance of rain each day is 36%, we can use the binomial probability formula.

The binomial probability formula is given by:

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

Where:

P(X = k) is the probability of getting exactly k successes

n is the number of trials

k is the number of desired successes

p is the probability of success in a single trial

(1-p) is the probability of failure in a single trial

In this case, we have:

n = 5 (number of days in the week)

k = 5 (desired number of rainy days)

p = 0.36 (probability of rain each day)

Using the formula, we can calculate the probability:

P(X = 5) = (5C5) * (0.36)^5 * (1-0.36)^(5-5)

Simplifying the equation:

P(X = 5) = 1 * 0.36^5 * 0.64^0

P(X = 5) ≈ 0.036

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The 7th term of the arithmetic sequence -3x+5, 2x+3, 7x+1, ... is: 27x-7.

To find the 7th term of the arithmetic sequence, we need to first determine the common difference between the terms. We can do this by subtracting the first term from the second term:

(2x+3) - (-3x+5) = 5x - 2

This means that the common difference between the terms is 5x - 2. Now, we can use the formula for the nth term of an arithmetic sequence:

aₙ = a₁ + (n - 1)d

Where an is the nth term, a₁ is the first term, n is the term number, and d is the common difference. Plugging in the values we have:

a₇ = (-3x+5) + (7 - 1)(5x - 2)

Simplifying the equation:

a₇ = -3x + 5 + 30x - 12

a₇ = 27x - 7

Therefore, the 7th term of the arithmetic sequence is 27x - 7.

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The total profit that the company earned last year is 1500000.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, each division earned a profit of $5 x 10 to the 5th power.

The profit will be:

= Number of division × Profit made

= 3 × (5 × 10^5)

= 3 × (5 × 100000)

= 3 × 500000

= 1500000

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Answer:

A.

Step-by-step explanation:

Your answer is A. because it crossed the x axis at (0,0) and it has a y-intercept of (1,-3)

Answer:

A shows the equation y = -3x

7)(3,8)

8)90 °

9)AZ is not a median

Explanation

Step 1

An altitude of a triangle is the perpendicular segment from a vertex of a triangle to the opposite side,so

in the graph, we would have

hence, th coordinate A is

Step 2

what is angle ZAX

due to the lines AZ and XY are perpendicular, the intersetion of the lines form an 90 ° angle

Step 3

b)Is AZ also a median? Justify your answer.

median is the line segment from a vertex to the midpoint of the opposite side. It is also an angle bisector when the vertex is an angle in an equilateral triangle or the non-congruent angle of an isoceles triangle.

therefore, the altitude is also the median ONLY for ISOSCELES TRIANGLES,

hence

AZ is not a median

I hope this helps you

A relation R on Z is an equivalence relation if and only if it is reflexive, symmetric, and transitive. Specifically, in this case, xRy if and only if x^2+y^2 is even.

Reflexive: for any x in Z, x^2+x^2 is even, thus xRx. So, R is reflexive.

Symmetric: for any x,y in Z, if xRy, then x^2+y^2 is even, which implies y^2+x^2 is even, thus yRx. So, R is symmetric.

Transitive: for any x,y,z in Z, if xRy and yRz, then x^2+y^2 and y^2+z^2 are both even, thus x^2+z^2 is even, thus xRz. So, R is transitive.

Therefore, R is an equivalence relation.

To describe the equivalence classes, we need to find all the integers that are related to a given integer x under the relation R.

Let [x] denote the equivalence class of x.

For any integer x, we can observe that xR0 if and only if x^2 is even, which occurs when x is even.

Therefore, every even integer is related to 0 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any even integer x.

Similarly, for any odd integer x, we can observe that xR1 if and only if x^2 is odd, which occurs when x is odd. Therefore, every odd integer is related to 1 under R, and we have:[x] = {y in Z: xRy} = {x + 2k: k in Z}, for any odd integer x.

In summary, the equivalence classes of R are of the form {x + 2k: k in Z}, where x is an integer and the parity of x determines whether the class contains all even or odd integers.

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There would be approximately 43,149 U.S. half dollars in a stack that is the same height as the Statue of Liberty.

To determine the number of U.S. half dollars that would be in a stack the same height as the Statue of Liberty, we need to convert the height of the statue from feet to millimeters and then divide it by the thickness of a single half dollar.

First, let's convert the height of the Statue of Liberty from feet to millimeters. We know that 1 foot is equal to 304.8 millimeters (rounded to the nearest tenth). Therefore, the height of the Statue of Liberty in millimeters is:

305 ft * 304.8 mm/ft = 92918 mm (rounded to the nearest whole number)

Next, we need to determine the thickness of a U.S. half dollar. Given that each half dollar is 2.15 mm thick, we can now calculate the number of half dollars in a stack that is the same height as the Statue of Liberty:

Number of half dollars = Height of stack / Thickness of a half dollar

Number of half dollars = 92918 mm / 2.15 mm

Number of half dollars ≈ 43149 (rounded to the nearest whole number)

Therefore, there would be approximately 43,149 U.S. half dollars in a stack that is the same height as the Statue of Liberty.

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The value of R expressed in standard form to an appropriate degree of accuracy as required in the task content is; 2.447 × 10⁶.

It follows from the task content that the equation given in the task content for R is;

R = x²/y.

Additionally, the values of x and y are given as; 3.8 × 10⁵ and 5.9 × 10⁴ respectively.

On this note, it follows from substitution that the value of R can be determined as follows;

R = (3.8 × 10⁵)²/(5.9 × 10⁴)

R = (3.8)² × (10⁵)²/5.9 × 10⁴

R = 14.44 × 10¹⁰/5.9 × 10⁴

It therefore follows from the quotient of powers law that we have;

R = (14.44/5.9) × 10⁶

R = 2.447 × 10⁶.

Therefore, the value of R expressed in standard form to an appropriate degree of accuracy as required in the task content is; 2.447 × 10⁶.

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Answer:

-49/10    or     -4 9/10

Step-by-step explanation:

-7/5 + -7/2 = -14/10 - 35/10 = -49/10 = -4 9/10

Answer:

x = - 18

Step-by-step explanation:

Let certain number = x

The difference between half of a certain number and seven

x/2 - 7

is the same as

=

with adding two to that number

x + 2

Find the number

x/2 - 7 = x + 2

x - x/2 = - 7 - 2

( 2x - x ) / 2 = -9

2x - x = -18

x = - 18

The variable data refers to the list [10, 20, 30]. After the statement data[1] = 5, data evaluates to [10, 5, 30]. A list is one of the compound data types that Python provides. Lists can contain items of different types, but they are usually all the same type.

Lists are mutable sequences, meaning that their elements can be changed after they have been created. Lists can be defined in several ways, including by enclosing a comma-separated sequence of values in square brackets ([ ]).

The elements of a list can be accessed using indexing, with the first element having an index of 0. The second element has an index of 1, the third element has an index of 2, and so on. To change the value of an element in a list, you can use indexing with an assignment statement.

For example, the statement `data[1] = 5` changes the second element of the `data` list to 5. Therefore, after this statement, the `data` list will be `[10, 5, 30]`.

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a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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Answer: 5

Step-by-step explanation: You have to multiply 1 2/3 and 3.

I hope this helps you out!

Answer:

5 Cups of Sugar

Step-by-step explanation:

1 * 3 = 3

2/3

2 * 3 = 6

6 / 3 = 2

2 + 3 = 5 Cups

there are 11 such valid strings.

To find the recurrence relation, let's consider the possibilities for the last digit of a valid bit string. It can either be 1 or 0. If it's 1, the remaining n-1 digits can be any valid bit string of length n-1. If it's 0, the second-to-last digit must be 1 to avoid having two consecutive 0s. In this case, the remaining n-2 digits can be any valid bit string of length n-2.

Therefore, the total number of valid bit strings of length n can be obtained by summing the number of valid strings of length n-1 (when the last digit is 1) and the number of valid strings of length n-2 (when the last digit is 0). This gives us the recurrence relation F(n) = F(n-1) + F(n-2).

For the initial conditions, we observe that F(1) = 2 because there are two valid bit strings of length 1: 0 and 1. Similarly, F(2) = 3 because there are three valid bit strings of length 2: 01, 10, and 11.

To find the number of valid bit strings of length five, we apply the recurrence relation iteratively. Starting with F(1) = 2 and F(2) = 3, we can compute F(3) = 5, F(4) = 8, and finally F(5) = 13. Therefore, there are 13 valid bit strings of length five.

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The graph has y-intercept (0,5) and increases with a constant ratio of 3.

A function in mathematics is a connection between a set of inputs (sometimes referred to as the domain) and a set of outputs (also referred to as the range). Each input value is given a different output value.

The y-intercept lies at (0, 5) because the value of the function at x=0 is 530 = 5. The 'constant ratio' is 3, meaning that any increment of 1 in x causes the function value to grow by a factor of 3. (That serves as the exponential term's foundation.)

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Missing parts;

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.

The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.

The graph has y-intercept (0, 3) and increases with a constant ratio of 5.

The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

Answer:

2) \(\frac{1}{\sqrt[6]m^{5}}\)

Step-by-step explanation:

As per the laws of indices:

\(\frac{x^{a} }{x^{b} } = x^{a - b} \\\\and \\ \\(x^{a})^b = x^{ab}\)

Therefore:

2-(1/3) = 5/3

So m ^(5/3)

5/3 multiplied by -1/2 = -5/6

so m^(-5/6)

Another law of indices:

\(x^{\frac{a}{y} } = \sqrt[y]{x^{a} }\)     and when there is something raised to a negative fraction do the reciprocal.