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The exact dimensions of the rectangular prism are:

Width = [tex]((\sqrt{282} + \sqrt{1975})/3)/2[/tex]

Height = [tex](141 - (\sqrt{282} + \sqrt{1975})/3) / 2[/tex]

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The rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

To find the dimensions of the rectangular prism with a fixed surface area of 282 square units and maximum volume, we need to use the fact that the volume of a rectangular prism is given by V = lwh and the surface area is given by SA = 2lw + 2lh + 2wh. Since we want to maximize the volume, we can use the surface area formula to solve for one of the dimensions in terms of the other two, and then substitute into the volume formula to obtain a function of two variables.

We can then take the derivative of this function and set it equal to zero to find the maximum volume. Solving this equation, we obtain l = w = 9 and h = 14, which gives the desired dimensions.

Therefore, the rectangular prism with a fixed surface area of 282 square units and maximum volume has dimensions of 9 by 9 by 14 units.

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Inferences can be made for these types of plants, and the conclusion can be drawn that the fertilizer will help these types of plants grow taller.

A scientific experiment known as a randomised controlled trial (RCT) includes randomly allocating participants or subjects to various groups, often a treatment group and a control group. The intervention or therapy under test is administered to the treatment group while being withheld from the control group. Researchers can isolate the impact of the intervention on the desired outcome and reduce the impacts of confounding variables by randomly allocating individuals to these groups. To evaluate the effectiveness of therapies and treatments, RCTs are often employed in the medical, psychological, and other domains.

In the given experiment, the fertiliser appeared to be helpful in boosting plant development for this specific type of seedling since the plants that got it grew noticeably taller than the ones that did not.

Hence, option 4 is correct.

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The composite functions  are (A + B)(x) = x² + 2x + 4. and (AB)(x) = 2x³ - x² + 10x - 5.

To find (A + B)(x), we add the two functions A(x) and B(x):

(A + B)(x) = A(x) + B(x)

So, we have

= x² + 5 + 2x - 1 (substituting the given expressions for A(x) and B(x))

= x² + 2x + 4

Therefore, (A + B)(x) = x² + 2x + 4.

To find (AB)(x), we multiply the two functions A(x) and B(x):

(AB)(x) = A(x)B(x)

= (x² + 5)(2x - 1) (substituting the given expressions for A(x) and B(x))

= 2x³ - x² + 10x - 5

Therefore, (AB)(x) = 2x³ - x² + 10x - 5.

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This value of x doesn't satisfy the Equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

Let's start with the given information: we have two arc measures and an angle measure. We know that the sum of the arc measures is equal to the total circumference of the circle, which is 360 degrees. So, we can set up an equation:

59 + 2x = 360

Solving for x, we get:

2x = 301

x = 150.5

So, the value of x that makes one arc measure 2x and the other arc measure 59, and the angle measure 15, is 150.5.

Now, let's think about why this makes sense. The sum of the arc measures is equal to the total circumference of the circle, which means that the angle formed by those two arcs must be half of the central angle that intercepts them. In other words, the angle formed by the 59-degree arc and the 2x-degree arc is (59 + 2x)/2. We also know that the angle formed by the 15-degree angle and the same arc is equal to half of the angle formed by the two arcs. So:

(59 + 2x)/2 = (180 - 15)/2

59 + 2x = 165

2x = 106

x = 53

However, this value of x doesn't satisfy the equation we set up earlier (59 + 2x = 360). So, we must conclude that this value of x is incorrect, and the value we found earlier (x = 150.5) is the correct one.

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To find out how much Diana paid, we need to first calculate the total cost of the pizza, the chicken wings, the salad, the drinks, and the tip, and then divide that total by 2, since Diana is paying for half.

The total cost of the pizza, chicken wings, salad, and drinks is:

$13.02 (pizza) + $12.99 (chicken wings) + $6.25 (salad) + $3.25 (Diana's drink) + $3.25 (Carrie's drink) = $38.76

Adding the tip of $10.00 to this total gives:

$38.76 + $10.00 = $48.76

Half of this total is:

$48.76 / 2 = $24.38

Therefore, Diana paid $24.38 for her food, half the cost of the pizza, and half the tip.

Diana paid $19.65, which includes $9.02 for her share of the pizza, $5.00 for her share of the tip, $12.99 for chicken wings and $3.25 for a drink. Below is the working on the sketchpad.What is shown on the sketchpad?It is shown on the sketchpad below how Diana paid for her lunch at the restaurant.

The items that she paid for are indicated in the table below the sketchpad.What is the calculation for the amount Diana paid for lunch?Diana's share of the pizza is half of $13.02, which is $6.51. Adding $6.51 to the cost of the chicken wings and a drink gives a total of $22.75 for the cost of the lunch.

After adding the tip to the total cost of the lunch, we have $32.75 ($22.75 + $10.00 tip). To find the amount Diana paid, we need to find half of the total cost of the lunch and half of the tip.The following calculation shows the amount Diana paid:Her share of the cost of the lunch was $11.37 (($6.51 + $12.99 + $3.25)/2).Her share of the tip was $5.00/2, which is $2.50.The amount Diana paid for her food, plus her share of the cost of the pizza and tip is therefore $13.87 ($11.37 + $2.50).

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Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

A graph is a visual representation of data that is used to show the relationship between two or more variables. Graphs are commonly used in mathematics, science, engineering, and other fields to help visualize and analyze data.

There are many different types of graphs, each with its own unique features and applications. Some of the most common types of graphs include:

Line graphs: Line graphs are used to show the trend or change in a variable over time. They consist of a set of data points that are connected by straight lines.

Bar graphs: Bar graphs are used to compare data across different categories or groups. They consist of rectangular bars that are proportional in height to the values they represent.

Pie charts: Pie charts are used to show the proportion or percentage of each category within a larger whole. They consist of a circle that is divided into sections, with each section representing a different category.

If Leroy set the price at $3.99, then based on the given chart, Demand will be 1,500 units whereas Supply will be 500 units. Since Demand is higher than then supply at $3.99 price, hence, correct answer is Option (b).

Therefore, Correct answer is Option (b), The demand will exceed the supply.

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The complete question is:

The distance around the equator is 40,820 km, when the Earth's diameter is approximately 13000km. The distance around the Earth is the circumference.

The Earth is nearly a perfect sphere, but not quite. Astronomers utilized the diameter of the Earth as their primary measuring tool to gauge the extent of the solar system during the 18th and 19th centuries. Today's astronomers typically don't need to be aware of the Earth's size for their regular research tasks.

Nonetheless, the Earth's diameter continues to be the starting point for us, the inhabitants of this planet, in our quest to comprehend the cosmic distance scale. Eratosthenes measured the polar radius, and the number he obtained using the conversion of 0.15 km/stadium sits halfway between the polar and equatorial values.

Given:

Diameter = 13,000 km

Circumference = pi x diameter

Circumference = 3.14 x 13,000 = 40,820 km

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Answer:

A

Step-by-step explanation:

If bottles of soda are marked S, and one bottle costs $1,75

And slices of pizza - P, and one slice costs $3,5

Then the equation would be:

3,50p + 1,75s = 35,00

The area of the shaded region in this shape that has a rectangle and a circle within is 27.73 square cm.

The area of the rectangle can be found using the formula:

Area rectangle = length × width

Area rectangle = 8 cm × 7 cm = 56 square cm

The area of the circle can be found using the formula:

Area circle = π × radius^2

Given the radius is 3 cm, we have:

Area circle = π × (3 cm)^2 = 9π square cm  =  28.27 square cm

Now, to find the area of the shaded region (which is the rectangle minus the circle):

Area shaded = Area rectangle - Area circle

Area shaded = 56 square cm - 28.27 square cm = 27.73 square cm

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The probability that exactly two balls are of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 4/16 or 1/4.

There are three ways to draw two balls of the same color: two green balls and one of any other color, two red balls and one of any other color, or two yellow balls and one of any other color. Each of these ways can occur in 4 different orders (e.g. GGR, GRG, RGG, etc.) for a total of 12 possible outcomes. The probability of each of these outcomes is (1/4)^3 = 1/64. Therefore, the probability of exactly two balls being of the same color is 12/64 or simplified to 3/16, which is equivalent to 1/4.

Therefore, the probability of exactly two balls being of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 1/4.

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Answer:

The ladder is approximately 9.75ft from the building

Step-by-step explanation:

We can use Pythagoras theorem:

[tex]c^2=a^2+b^2[/tex]

where:

[tex]c =[/tex] it's the size of the ladder, 12ft

[tex]b=[/tex] it's the top of the ladder above the ground, 7ft

so:

[tex]c^2-b^2=a^2\\\implies a=\sqrt{c^2-b^2}\\ a=\sqrt{(12)^2-(7)^2}\\a=\sqrt{95}\\ a\approx 9.75ft[/tex]

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Answer:

The answer to your problem is, A semicircle is half of a circle

What is Semicircle?

If a circle is cut into half along the diameter, that half-circle is called a semicircle. The two halves are of equal measure. A semicircle can also be referred to as a half-disk and it represents a circular paper plate folded into halves. There is one line of symmetry in the semicircle that is considered as the reflection symmetry. Since the semicircle is the half of a circle which is 360°, hence the arc of the semicircle always measures 180°.

Or if you have no time imagine

You have an entire pizza you tell you other friend “ Lets half the pizza “ You do that next you can tell your friend that this is a semicircle and we both have semicircles your friend might not know but know they know . .

Interesting story I know but that is our answer.

Thus the answer to your problem is, A semicircle is half of a circle

Answer:

le demi-cerclec'est une figure plate délimitée par un diamètre de la circonférence et l'un des deux arcs de cercle plats déterminés par ledit diamètre. De cette façon, un demi-cercle est bordé par un demi-circonférence, qui se compose d'un arc de cercle plat et d'un segment droit qui joint les extrémités de l'arc de cercle plat.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The first number within the the x axis.

The second number is the y axis.

the point you're looking is where they both intersect,

Do that for the 3 points, and you get 3 dots.

Make a line connecting each other in order.

And you made a shape.

Happy Solving

Answer: a. x ≤7 b. x<6

Step-by-step explanation:

a. 6x-3≤4x+11

6x-4x≤11+3

2x≤14

x≤7

b. x<-x+12

x+x<12

2x<12

x<6

Answer:

Step-by-step explanation:

The probability that the part can be assembled in 7 minutes or less is 0.2592.

To solve the problem, we need to use the cumulative distribution function (CDF) of the exponential distribution. The CDF gives the probability that the random variable X (in this case, the time required to assemble the part) is less than or equal to a certain value x.

The CDF of the exponential distribution is given by:

F(x) = [tex]1 - e^{(-λx)}[/tex]

where λ is the rate parameter of the exponential distribution, which is equal to 1/mean. In this case, the mean is 14 minutes, so λ = 1/14.

To find the probability that the part can be assembled in 7 minutes or less, we plug x = 7 and λ = 1/14 into the CDF formula: F(7) = [tex]1 - e^{(-(1/14)*7)} \approx 0.2592[/tex]

So, there is a chance of about 25.92% (rounded to four decimal places) that the part can be assembled in 7 minutes or less.

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Answer:

Both are correct as we can transform one from the other.

Step-by-step explanation:

The equations describe the relation between the distance(m)  speed (9) and time (h),

distance = speed * time

m = 9h

Divide both sides by 9:

m/9 = h

h = (1/9) m

79 hours will it take for one person to harvest the entire strawberry patch.

The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.

Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.

The strawberry patch's measurements must first be changed from decameters (dam) to meters.

1 decameter (dam) = 10 meter

Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.

The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.

The strawberry patch's area is therefore:

Area of strawberry patch = length × width = 17 m × 14 m = 238 m²

We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:

= a number of hours needed to harvest the complete patch.

The total harvesting time is  = 79.33 hours nearly equal to 79

Therefore, it would take one person 79 hours to gather the complete strawberry patch.

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According to the solution we have come to find that, The equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

What is radius?

Radius is a straight line segment that joins the center of a circle to any point on its circumference. It is half of the diameter of the circle. The length of the radius is denoted by the letter "r".

The equation of a circle with center (a,b) and radius r is given by:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Substituting the given values, we have:

[tex](x - (-2))^2 + (y - 9)^2 = 8^2[/tex]

Simplifying, we get:

[tex](x + 2)^2 + (y - 9)^2 = 64[/tex]

Therefore, the equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]

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The surface area of the prism is [tex]169cm^{2}[/tex]

A measurement of an object's whole space is, in fact, its surface area. The total area around a three-dimensional form makes up its surface area.

The whole surface area of a three-dimensional shape is referred to as "surface area". By summing the areas from each face, it is possible to determine the surface area of a cuboid with six rectangular faces.

Alternatively, you may use the following formula to name this box's dimensions:

The surface area is made up of [tex]2lh, 2lw, 2hw[/tex]. (SA). The amount of space occupied by the surface of a three-dimensional shape is measured in terms of surface area.

Given

[tex]S_{1} = 7 cm, S_{2} = 7 cm, S_{3} = 9 cm[/tex]

[tex]base = 9 cm, h = 6 cm, l = 5 cm[/tex]

[tex]area = ( perimeter * length) + 2* base area\\[/tex]

[tex]perimeter= S_{1} +S_{2} +S_{3}[/tex]

[tex]P = 7 cm +7 cm+9 cm\\= 23 cm[/tex]

∴[tex]area= (Perimeter* l) +bh[/tex]

[tex]A = (23*5) +( 9*6)\\= 115 cm + 54cm\\= 169 cm^{2}[/tex]

Therefore the surface area of the prism is [tex]169cm^{2}[/tex]

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The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.

What is dice?

Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.

Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.

When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.

To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.

So, the probability of rolling a 5 and a 6 is

P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes

= 1 / 36

Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.

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The x and y intercepts are some of the features of the graph and their values are -7 and 6 respectively.

The graph of the function f(x) = 2log₂ (x + 8) has the following features:

Domain: The domain of the function is all real numbers greater than -8, because the argument of the logarithmic function must be positive.

Vertical asymptote: The graph has a vertical asymptote at x = -8, because the logarithmic function is not defined for x = -8.

X-Intercept: The function has an x-intercept at (-7, 0), which can be found by setting f(x) = 0 and solving for x.

Y-Intercept: The function has a y-intercept at (0, 2log₂ 8), which is 6.

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Answer:

8 cherries

Step-by-step explanation:

Let r represent the number of cherries Rua was given

24 - r - 5 = 1.5r - 1

Simplify and solve for r.

19 - r = 1.5r - 1

-2.5r = -20

r = 8

So Liz gave Rua 8 cherries at the start.

The 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation is (0.835, 0.866), option B.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts. So, it may be concluded that there is a 95% likelihood that the real value falls within that range if a point estimate of 10.00 is produced using a statistical model with a 95% confidence interval of 9.50 - 10.50.

Confidence intervals are used by statisticians and other analysts to comprehend the statistical significance of their estimates, conclusions, or forecasts. One cannot reasonably assert that a result from data produced by testing or experimentation is to be ascribed if a confidence interval involves the value of zero.

Confidence interval for Population Proportion is given as below:

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Where, p is the sample proportion, Z is critical value, and n is sample size.

We are given

x = number of items/observations of interest = 3010

n = sample size = 3539

Best Point Estimate = p = x/n

= 3010/ 3539

= 0.850522747

Confidence level = 99%

Critical Z value = 2.5758

(We can find this z-value by using R, excel, z-table, Ti-83/84 calculator, software, etc.)

[Excel command: =NORMSINV(1 - (1 - 0.99)/2)]

Confidence Interval = [tex]p \pm Z\sqrt{\frac{p(1-p)}{n} }[/tex]

Confidence Interval = [tex]0.850522747 \pm 2.5758 \sqrt{\frac{0.850522747(1-0.850522747)}{3539} }[/tex]

Confidence Interval = 0.850522747 ± 2.5758 x 0.0060

Confidence Interval = 0.850522747 ± 0.015

Lower limit = 0.850522747 - 0.015 = 0.835

Upper limit = 0.850522747 + 0.015 = 0.866

Confidence interval = (0.835, 0.866)

B. (0.835, 0.866).

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Complete question:

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities. Select one answer 10 points Suppose we take a poll (random sample) of 3539 students classified as Juniors and find that 3010 of them believe that they will find a job immediately after graduation What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation A. (0.839, 0.862) B.O(0.835, 0.866) C. (0.845, 0.857) D.O(0.841, 0.86)

the price per ticket that will give maximum revenue is $6.5, and the maximum revenue in dollars per ticket is $2.925.

As given,If club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend.

We need to determine the price that will give the maximum revenue for the show and the maximum revenue in dollars per ticket.

Let the number of $1 increases in price be x. Then the number of people attending will be (1000 - 100x), and the price per ticket will be $(3 + x).The total revenue will be:

Revenue = Price × Quantity= $(3 + x) × (1000 - 100x)= $3000 - $100(x^2 + 7x)

The revenue function is quadratic, with the coefficient of the x^2 term being negative. Hence the graph of the function is a parabola which opens downwards, with a maximum at the vertex of the parabola.To find the value of x that will give maximum revenue, we first find the x-coordinate of the vertex.

For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).In this case, a = -100, and b = -100(7) = -700. Therefore, the x-coordinate of the vertex is:x = -b / (2a)= 7/2= 3.5

Therefore, the value of x that will give maximum revenue is 3.5. Substituting this value of x in the revenue function, we get:Revenue = $3000 - $100(x^2 + 7x)= $3000 - $100(3.5^2 + 7(3.5))= $2925

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Answer:

Step-by-step explanation:

Therefore, the cost of the meal was $15.

Describe the dollar sign.

The dollar sign, also referred to as the peso sign, is a symbol that looks like a capital "S" crossed with one or two vertical strokes ($ or Cifro symbol ), and it's used to denote the unit of many different currencies around the world, including the majority of currencies denominated in "pesos" and "dollars." The Portuguese word for the specifically double-barred is cifro.

The sign is also present in a number of compound currency symbols, including those for the Nicaraguan córdoba (C$) and the Brazilian real (R$).

Let’s call the cost of the meal x.

Karen gave the waiter a tip of three dollars which is 1/5 of the total cost of the meal.

This can be written as:

3 = (1/5) * x

Multiplying both sides by 5 gives:

15 = x

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Answer: The length, breadth, and height of the rectangular prism are:

Length = 3x + y cm

Breadth = 2x + 2y cm

Height = 3y cm

The volume of the rectangular prism is given by the formula:

Volume = Length x Breadth x Height

Substituting the values, we get:

Volume = (3x + y) x (2x + 2y) x (3y)

Simplifying the expression, we get:

Volume = 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3

Therefore, the volume of the rectangular prism is 18x^2 y + 15xy^2 + 6x^2 y^2 + 6y^3 cubic cm.

Step-by-step explanation: