Find the maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane x+y+z=1.

The equation of the line is 2y+3x=-38

To find the equation of a line perpendicular to 3x= -20-2y that passes through the point (-6,-8), we can use the point-slope form of a line. The point-slope form of a line is[tex]y - y_1 = m(x - x_1)[/tex], where m is the slope of the line and [tex](x_1,y_1)[/tex] is an arbitrary point on the line. Since the given line has a slope of -2/3, the perpendicular line has a slope of 3/2. Therefore, the equation of the line can be written as y - (-8) = (3/2)(x - (-6)). Solving for y, we get 2y + 3x = -38. Therefore, the equation of the line is 2y + 3x = -38.

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Answer:

Step-by-step explanation:

The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.

An expression is a mathematical phrase that can contain numbers, variables, operators, and sometimes functions. Expressions are used to represent or calculate values, and they can be simple or complex. For example, "2 + 3" is a simple expression that can be evaluated to give the value 5, while "3x + 2y - 4" is a more complex expression that contains variables and can only be evaluated if values are assigned to the variables. Expressions can also be combined to form more complex expressions using operators like addition, subtraction, multiplication, and division.

To find the inverse function of g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)), we can follow these steps:

Step 1: Replace g(x) with y, so that the function becomes g'(x) = -y.

Step 2: Solve the equation for y in terms of x: y = - g'(x) = - (sqrt(x) + 6)/(1 - sqrt(x)).

Step 3: Interchange x and y: x = - (sqrt(y) + 6)/(1 - sqrt(y)).

Step 4: Solve for y in terms of x:

[tex]x = - (sqrt(y) + 6)/(1 - sqrt(y))\\x(1 - sqrt(y)) = -sqrt(y) - 6\\x - x sqrt(y) = -sqrt(y) - 6\\x + 6 = (x + 1) sqrt(y)\\(x + 6)/(x + 1) = sqrt(y)\\[/tex]

[tex]y = [ (x + 6)/(x + 1) ]^2[/tex]

Therefore, the inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is:g^-1(x) = [ (x + 6)/(x + 1) ]^2[/tex]

Note that this function is defined for all x except x = 1, where the original function g(x) is not defined. Therefore, g(x) is not invertible at x = 1.

Therefore, The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.

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Answer:

9.6$

Step-by-step explanation:

Answer: If 8 oranges cost 1.20, we can use a proportion to find the cost of 12 oranges:

8 oranges / 1.20 = 12 oranges / x

Solving for x, we can cross-multiply and get:

8 oranges * x = 1.20 * 12 oranges

8x = 14.4

x = 1.80

Therefore, 12 oranges would cost 1.80.

Based on this evidence and reasoning, it is reasonable to conclude that Brianna should get the credit card, as long as she uses it responsibly and pays off her balance in full every month to avoid paying interest charges.

Percent, denoted by the symbol "%", is a way of expressing a fraction or ratio as a portion of 100. It is commonly used in everyday life to express a part of a whole or to compare quantities. Percentages can be used in various contexts, such as in finance to calculate interest rates, in statistics to represent data, and in everyday life to express discounts, tax rates, and tips. It is important to understand percentages to make informed decisions and to effectively communicate information.

Here,

CER stands for Claim, Evidence, and Reasoning, which is a framework for presenting a persuasive argument. Using this framework, we can evaluate whether Brianna should get the credit card in question:

Claim: Brianna should get the credit card.

Evidence:

The credit card has an APR of 24.99%, which is high compared to other credit cards.

The credit card has a yearly fee of $150.00.

The credit card offers 1% cash back on most purchases.

Reasoning:

While the APR and yearly fee are high, Brianna can still benefit from using the credit card to build her credit.

The 1% cash back on most purchases can help offset the cost of the yearly fee and the interest charges if she pays off her balance in full every month.

By using the credit card, such as making payments on time and not carrying a high balance, Brianna can establish a positive credit history, which can help her in the future when she wants to apply for loans or other credit cards.

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The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.

The system of equations to find the smallest number of busses the orchestra can rent is,

The total number of buses :

b + v ≤ 6

The total number of passengers.

25b + 12v ≥ 111 - - - - (2)

Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.

It can be  estimated that 60 deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries.

We can deduct that  from  the sample of 80 deliveries, the Forest Park neighborhood received 24 deliveries.

We then  estimate how many deliveries will be to the Forest Park neighborhood if the driver makes 200 deliveries by applying  proportional reasoning:

In conclusion, the estimate is  that the driver will make 0.3 x 200 = 60 deliveries to the Forest Park neighborhood.

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Answer:

Step-by-step explanation:

1/2 x 1/8 : 1/24 =

1/16 x 24 =

24/18 =

3/2

The correct answer is: They are both 1 standard deviation away from their means, but in opposite directions. The first score is 1 standard deviation below mean, while second score is 1 standard deviation above the mean.

Standard deviation is a measure of the deviation or spread from the mean (mean) of a set of data values. 

More specifically, the standard deviation is calculated by taking the square root of the variance of the data. Variance is the mean square of the difference of each data point from the mean. 

The first score of 40 from a distribution with a mean of 50 and a standard deviation of 10 is 1 standard deviation below the mean, because it is (50-40)/10 = -1 standard deviation from the mean.

The second score of 45 from a distribution with a mean of 50 and a standard deviation of 5 is 1 standard deviation above the mean, because it is (45-50)/5 = -1 standard deviation from the mean.

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To find 20 percent of 30, you can multiply 30 by 0.2 (which is the decimal equivalent of 20 percent):

20% of 30 = 0.2 x 30 = 6

So, 20 percent of 30 is 6.

To divide 6 by 100, you can simply move the decimal point two places to the left:

6 ÷ 100 = 0.06

Therefore, if you want to find what is 20% of 30 and then divide that result by 100, the answer is 0.06.

Answer: 22 miles in one day

Step-by-step explanation:

To find how far Gianna hiked, we first need to convert the mixed number for Ethan and Rylee's hike into an improper fraction, and then multiply it by 3 3/4 to find the distance Gianna hiked.

Ethan and Rylee's hike (5 13/15):

(15 * 5) + 13 = 88

So, they hiked 88/15 miles.

Now, let's convert the mixed number 3 3/4 into an improper fraction:

(4 * 3) + 3 = 15

So, 3 3/4 = 15/4.

Next, we'll multiply the two improper fractions together:

(88/15) * (15/4) = (88 * 15) / (15 * 4) = 1320 / 60

Now, simplify the fraction:

1320 ÷ 60 = 22

So, Gianna hiked 22 miles in one day.

The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.

In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.

In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.

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The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ

What is congruent?

Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.

To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.

Given that T=​X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.

To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:

TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)

TU / TX = 1 (because T = X)

TX / XY = 1 (because U = Y)

Therefore, TU / XY = 1 * 1 = 1.

Similarly, we can compare the ratio of UV and YZ:

UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)

UV / UY = 1 (because U = Y)

UY / YZ = 1 (because T = X)

Therefore, UV / YZ = 1 * 1 = 1.

Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:

TUV ~ XYZ

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Answer:

The smallest number of cars that can tailgate in a straight line at a football game is 12.

Step-by-step explanation:

Smallest Tailgate Cars Number

This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.

This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.

Answer:

3

Step-by-step explanation:

basicly one car will be in the back one in the middle and one in the front. if I'm correct then it should be 3

The area of remaining sheet is 536 cm²

Since, we know that the area of circle [tex]=\pi \times r^2[/tex]

Area of bigger circle [tex]=\dfrac{22}{7} \times14\times14[/tex]

[tex]=44\times14[/tex]

[tex]=616 \ \text{cm}^2[/tex]

Thus, the area of bigger circle is 616 cm²

Similar way, the area of 2 smaller circles [tex]=2\pi r^2[/tex]

[tex]=2\times\dfrac{22}{7} \times3.5\times3.5[/tex]

[tex]=44\times0.5\times0.5[/tex]

[tex]=77 \ \text{cm}^2[/tex]

Thus, the area of 2 smaller circle is 77 cm²

[tex]\text{Area of rectangle}=\text{Length}\times\text{Breadth}[/tex]

[tex]=3\times1=3 \ \text{cm}^2[/tex]

Thus, the area of rectangle is 3 cm²

Now, remaining area of sheet = Area of bigger circle − Area of both smaller circle − Area of rectangle

[tex]=616-77-3=536 \ \text{cm}^2[/tex]

Hence, area of remaining sheet is 536 cm²

Using probability, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

What is probability?

Probability is a measure of the likelihood or chance that an event will occur. It is a numerical value between 0 and 1, where 0 represents an impossible event (i.e., an event that will never occur) and 1 represents a certain event (i.e., an event that will always occur).

Now,

To determine the percentage of people who test positive for the virus who actually have the virus, we can use Bayes' theorem.

Let A be the event that an individual has the virus, and B be the event that an individual tests positive for the virus. Then, we want to calculate the conditional probability of A given B, denoted as P(A|B), which is the probability that an individual has the virus given that they test positive.

Using Bayes' theorem, we can write:

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

where P(B|A) is the probability of testing positive given that an individual has the virus, P(A) is the overall probability of having the virus, and P(B) is the overall probability of testing positive.

We are given that the test returns a positive result for 99.5% of individuals who have the virus, so P(B|A) = 0.995. We are also given that the test returns a positive result for 0.5% of those who do not have the virus, so the probability of testing positive given that an individual does not have the virus is 1 - 0.005 = 0.995.

We are given that overall, 1% of people tested positive, so:

P(B) = 0.01

We can calculate the overall probability of having the virus as:

P(A) = (number of people with the virus) / (total number of people tested)

We do not have enough information to calculate these values directly, but we can use the fact that the test returns a positive result for 99.5% of individuals who have the virus to estimate the number of true positives.

Let n be the total number of people tested. Then, we can estimate the number of true positives as:

(number of true positives) = 0.995 * (number of people with the virus)

We know that overall, 1% of people tested positive, so:

(number of true positives) / n = 0.01

Substituting the estimate for the number of true positives, we get:

0.995 * (number of people with the virus) / n = 0.01

Solving for the number of people with the virus, we get:

(number of people with the virus) = 0.01 * n / 0.995

Substituting this into the expression for P(A), we get:

P(A) = (0.01 * n / 0.995) / n = 0.01005

So the overall probability of having the virus is approximately 0.01005.

Finally, substituting all the values into the expression for P(A|B), we get:

P(A|B) = 0.995 * 0.01005 / 0.01 ≈ 0.9985

Therefore, the percentage of people who test positive for the virus who actually have the virus is approximately 99.85%.

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The lateral surface area of the geometric shape formed by the given net is 3,780 sq in.

The lateral surface area is the sum of the areas of the trapezoidal faces and the rectangular faces.

The area of a trapezoid is given by the formula:

A = (1/2)h(b1 + b2)

where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides.

Area of trapezoid 1 = (1/2)(30 + 18)(48) = 972 sq in

Area of trapezoid 2 = (1/2)(18 + 18)(48) = 864 sq in

The area of each rectangular face is given by the product of the length and the width.

Area of rectangular face 1 = 30 x 18 = 540 sq in

Area of rectangular face 2 = 48 x 18 = 864 sq in

Area of rectangular face 3 = 30 x 18 = 540 sq in

The total lateral surface area is the sum of the areas of all the faces:

Lateral surface area = Area of trapezoid 1 + Area of trapezoid 2 + Area of rectangular face 1 + Area of rectangular face 2 + Area of rectangular face 3

Lateral surface area = 972 + 864 + 540 + 864 + 540

Lateral surface area = 3,780 sq in

Therefore, the lateral surface area of the geometric shape formed by the given net is 3,780 sq in.

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Answer:

2

Step-by-step explanation:

The equation has 2 terms in it which means 2 is the answer.

By answering the presented question, we may conclude that When y is 9 cuboid feet, the volume of the cube is 729 cubic feet.

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron with 8 vertices, 12 sides, and 6 rectangular faces. A cuboid is another name for it. A cube is a cuboid because it has six square faces. Objects found in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a cube are square and equal in size. Although the structures of the cube and cuboid are aesthetically similar, they differ significantly in terms of side length, diagonal, and area.

If you want to find the volume of a cube, the formula is:

Volume equals [tex]s^3[/tex]

where s is the length of one cube side.

If y = 9 feet and y indicates the length of one side of the cube, the volume of the cube may be determined as follows:

Volume = [tex]y^3 + 9^3 = 729 cu ft.[/tex]

When y is 9 feet, the volume of the cube is 729 cubic feet.

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Complete question -

Write and expression you can use to find the value of the cube then find the value if y=9 feet

As a result, this same current price index stands at about 481.2.

Amount offered or established as consideration again for sale of a certain item. the quantity of anything that is bought, requested, or bartered for another; also known as the price paid for something.

We may use the following formula to determine a current price index using 1975 price as reference value:

Price index: 100 multiplied by (Current market price / Reference price).

First, we must change the 56.7 cent price from 1975 to current currency:

Reference price is equal to 56.7 cents divided by $1.01 to get $0.567.

In the formula, we can then enter a current price oil $2.73 / gallon or the case the cost of $0.567 per gallon:

Price index equals ($2.73 | $0.567) x 100 ≈ 481.22

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the probability of getting red on at least one spin is 1 - 9/16 = 7/16 or 0.4375 in decimal form.

hope that helps!

Answer:

OP = 424: CE = 79,5

Step-by-step explanation:

I added a photo of my solution

7. True, 8. True, 9 No, because every name had an equal chance of being drawn from the jar, 10. False

Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.

7. True: Sampling bias: unequal chance of selection leading to unrepresentative samples.

8. True: Avoiding bias: random sampling, representative samples, and minimizing nonresponse bias.

9 No, because every name had an equal chance of being drawn from the jar.

10. False: Biased sample: unrepresentative sample due to factors like nonresponse or small sample size.

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law of contraposition = if p, then q. if not q, then not p.

example: if it's snowing, then there's no school. if there is school, then it's not snowing.

Answer:

There is no y intercept because the graph does not cross the y axis.

The x intercept is (-2,0)

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

3. 5.3 ft

4. 4.5 ft

Step-by-step explanation:

3.

Let's call the height of the connection point on the tree "h". We can use trigonometry to relate the angle and the length of the guy wire to "h". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the height "h", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:

sin(42) = h / 8

To solve for "h", we can multiply both sides by 8:

h = 8 sin(42)

Using a calculator, we get:

h ≈ 5.3 feet

So the height of the connection point on the tree is about 5.3 feet, to the nearest tenth of a foot.

4.

The ladder, the wall, and the ground form a right triangle, with the ladder being the hypotenuse. Let's call the height on the wall that the ladder reaches "x". We can use trigonometry to relate the angle and the length of the ladder to "x". Specifically, we can use the sine function:

sine of the angle = opposite / hypotenuse

In this case, the opposite side is the height "x", and the hypotenuse is the length of the ladder, which is 5 meters. So we have:

sin(65) = x / 5

To solve for "x", we can multiply both sides by 5:

x = 5 sin(65)

Using a calculator, we get:

x ≈ 4.5 meters

So the ladder reaches a height of about 4.5 meters on the wall.

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

Given that the current fridge

electricity charges= $60 monthly,

maintenance costs=$ 170

let the number of months be = x

and the total cost is y

the expression for the cost of the old fridge is

y=170+60x       ...say (1)

new fridge

electricity charges=$5

costs= $1140

let the number of months be x,

and the total cost be y'

the expression for the cost of the new fridge is

y'=1140+5x,       ... say(2)

For 10 year , there are 12*10=120 months

put x=120 in both equations,

y=170+60x  

y=170+60*120

y=170+7200

y=$7370

y'=1140+5*120

y'=1140+600

y'=$1740

Based on the analysis it will be less expensive to get the new fridge, hence buying the new fridge is worth it.

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Answer:

The best explanation for the steps to solve the pair of equations graphically is:

On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.

To solve the pair of equations graphically, you need to plot the two lines on the same coordinate plane and find the point where they intersect. To do this, you can use the slope-intercept form of the equations, which gives the y-intercept and the slope of each line. The y-intercept is the value of y when x equals 0, and the slope represents how steep the line is. Once you have graphed the two lines, the point where they intersect is the solution to the system of equations. In this case, the intersection point can be found by solving the system of equations, which is (x, y) = (2, -1).

Answer:

If the figure shows two rays ST and UT with a common endpoint U, then Malik's description is correct. When two rays share a common endpoint, they form an angle. The angle formed by rays ST and UT would be angle STU. So, if the figure matches this description, then Malik's statement is correct.