What is the maximum volume of a rectangular prism (or box) if the prism has a square base and a total surface area of 100 cm^2?

A) First, let x = the side length of the base and h = the height of the prism. Write and solve the equation for h.

B) Write a function for the volume of the box, V, in terms of x.

The appropriate measures of central location for interval data are Mode, median, and average

The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.

Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.

The data point in the middle of the data collection is known as the median.

It can be obtained by halving the data set, which will show where the median is located.

Simply put, mode refers to the data that occurs most frequently.

Each of these provides positional information on the data, as can be seen from the definition.

The one value that other values in the data center around is given by the mean.

Therefore, the correct options are Mode, median, and average

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Answer:

176 children and 105 adults.

Explanation:

Let's call x the number of children and y the number of adults.

If 281 people entered the park, we can write the following equation

x + y = 281

If they collected 684 dollars, we can write the following equation

1.5x + 4y = 684

because it cost $1.5 for children and $4 for adults.

Now, we have the following system of equations

x + y = 281

1.5x + 4y = 684

First, we need to solve the first equation for y, so

x + y = 281

x + y - x = 281 - x

y = 281 - x

Then, replace this expression on the second equation

1.5x + 4y = 684

1.5x + 4(281 - x) = 684

1.5x + 4(281) - 4(x) = 684

1.5x + 1124 - 4x = 684

-2.5x + 1124 = 684

Finally, we can solve the equation for x

-2.5x + 1124 - 1124 = 684 - 1124

-2.5x = -440

-2.5x/(-2.5) = -440/(-2.5)

x = 176

So, the value of y is equal to

y = 281 - x

y = 281 - 176

y = 105

Therefore, they admitted 176 children and 105 adults.

Answer:

39.3

but the 3 in the the tenths place is repeating

Step-by-step explanation:

Answer:

39.33...

Step-by-step explanation:

Using PEMDAS,

First, 0.33 / 0.9 = 0.366...

Second, 0.366... * 20 = 7.33...

Then, 6.4 / 0.2 = 32

Lastly, 7.33... + 32 = 39.33...

Data

Length = 15 ft

Width = 8 ft

Area

Answer:

Answer 1: Rajesh: 93/100 Sita: 82/100 (simplest form: 41/50) Rajesh earned more.

Answer 2: 11/100 more marks

Answer 3: Rajesh got an A, while Sita got a B-

Step-by-step explanation:

Put the 93 on top of 100, and do the same for 82.

Rajesh clearly earned more. Subtract 82 from 93 to find out Rajesh score 11 points more.

Since y varies directly with x then

So,

Then, 1/4 is the constant of proportionality. So that,

Answer:

==============================

[tex]\cfrac{ax+b}{4}=\cfrac{x+c}{3}[/tex]                                              Given

[tex]3(ax+b)=4(x+c)[/tex]                                     Cross-multiply

[tex]3ax + 3b=4x+4c[/tex]                                       Distribute

[tex]3ax-4x=4c-3b[/tex]                                       Collect terms with x

[tex]x(3a-4)=4c-3b[/tex]                                       Factor out x

[tex]x=\cfrac{4c-3b}{3a-4}[/tex]                                                   Divide both sides by 3a - 4

The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units , the correct option is (D)  .

If the equation of the circle is x² + y² + 2fx + 2gy + c = 0

then the center is (-f,-g)

and the radius is √(f²+g²-c)

In the question ,

it is given that the

equation of the circle is x² + y² + 14x + 2y + 14 = 0

So , on comparing it with the general form of equation , we get

2f = 14

f = 7

and 2g = 2

g = 1

hence, the center is (-7,-1) .

the radius is √(7² + 1² - 14)

= √(49 + 1 - 14)

= √(50 - 14)

= √36

= 6

Therefore , The coordinates for the center of the circle is (-7,-1) and the length of the radius  is 6 units .

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Answer:

3/4 or 0.75

Step-by-step explanation:

D

1) Taking the function g(x)= (x+1) (x-2) (x+5), as we can see this a 3rd degree ploynomial

g (x)= (x+1) (x-2) (x+5)

g(x) =x³+4x²-7x-10

As the coefficient is positive, then we'll have

Examining the options, we have as the roots S={-5,-1,2} So the answer is D

Answer:

0.1

Step-by-step explanation:

chance of pulling out a blue marble can be described as 8 equally probable outcomes (blue marbles) out of 20 equally probable outcomes (all marbles).

Similarly, the chance of pulling out a green marble is 5 out of 20.

In total, we have 8*5 (combinations of blue then green) outcomes out of 20*20 (any two marbles):

8*5 / (20*20) = 40 / 400 = 1/10 = 0.1

The length of the line segment will be 10 units.

What is Distance?

The distance between two points (x₁ , y₁) and (x₂, y₂) is defined as;

D = √( y₂ - y₁)² + (x₂ - x₁)²

Given that;

Two endpoints of the line segment are (6, -5) and (0, 3).

Now,

The length of the line segment is distance between two endpoints (6, -5) and (0, 3).

So, The distance between two endpoints (6, -5) and (0, 3) is calculated as;

D = √(0 - 6)² + (3 - (-5))²

D = √36 + 64

D = √100

D = 10 units

Thus, The length of the line segment will be 10 units.

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Answer:

1 ft   ≈   0.3048 m

1 ft2  ≈   0.09290304 m2

200 ft2   ≈   18.580608 m2

Step-by-step explanation:

The total surface area to paint  =  12 m  *  80 m   =   960 square meters

1 ft   ≈   0.3048 m

1 ft2  ≈   0.09290304 m2

200 ft2   ≈   18.580608 m2

And so one gallon of paint covers about  18.581  square meters.

960 m2  /  ( 18.581 m2 per gallon)  ≈   51.67 gallons

So  51  gallons would not be enough... it would take  52  gallons of paint to cover the wall.

Based on the length of the ribbon, and the length of the pieces Janice needs to make, the number of 3/8 foot pieces she can make would be

To find the number of pieces that Janice can get from the 7/8 foot ribbon, you need to divide this length by the length of each piece of ribbon.

The length of each of these pieces is 3/8 so the number of pieces of ribbon that Janice can get from the 7/8 foot ribbon is:

= 7 / 8 ÷ 3 / 8

= 7 / 8 x 8 / 3

= 56 / 24

= 2.33 ribbons

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Janice can make 2 pieces of ribbon from 7/8 feet of ribbon each measuring 3/8 feet.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Janice is cutting the ribbon to decorate a present. She has 7/8 feet of ribbon.

She needs to make pieces that are 3/8 feet each.

To obtain the no. of pieces we have to divide the total length of the ribbon by the length of each piece.

∴ (7/8)/(3/8).

= (7/8)×(8/3).

= 7/3 pieces.

But he can only make 2 pieces as pieces must be in integers.

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Answer:

$302.69

Step-by-step explanation:

399 x 30% = 119.7 # finding how much you save

399 - 119.7 = 279.3 # how much the item costs with the sale

279.3 x 8.375 = 23.39 # the sales tax for the discounted item

297.3 + 23.39 = 302.69 # adding sales tax to the discounted item

I think this is right. I was never that great at sales tax and discount.

Part A

Explanation: Count the number of leaves.

======================================================

Part B

Reason:

Look at the largest stem (9) and the largest leaf of this largest stem (5).

This forms the largest value of 95.

The smallest value is 41 since it corresponds to the smallest stem and smallest leaf.

The term "min" and "max" are often used here.

======================================================

Part C

Explanation:

The data set is

41, 52, 57, 58, 65, 66, 70, 75, 78, 80, 81, 95

There are n = 12 items in this set.

Splitting in half gets us n/2 = 12/2 = 6.

The item in slot 6 is 66, and the next item over is 70.

The midpoint of these values is the median. (66+70)/2 = 68.

This midpoint rule only applies if n is even.

To find the range, we subtract the largest and smallest items.

range = max - min = 95 - 41 = 54

======================================================

Part D

Reason:

The stem 8 doesn't have a leaf of 5 attached to it.

It only has the leaves 0 and 1 to form the numbers 80 and 81.

Given the equation:

You need to solve for "x" in order to find its value:

1. Apply the Addition Property of Equality by adding 0.03 to both sides of the equation:

2. Apply the Division Property of Equality by dividing both sides of the equation by 0.005:

Hence, the answer is:

Answer: [tex]m=\frac{360^{\circ}}{n}[/tex]

Step-by-step explanation:

This is a standard result.

The second option is the segment addition postulate.

The third option is the sum of the angles of a polygon with n sides.

The fourth option is the measure of each interior angle of a regular polygon with n sides.

The fifth option is the angle addition postulate.

C) x= -1/10

1) Evaluating the following expression

23x+2= 15x + 48x + 6 Add the like terms

23x +2 = 63x +6 Subtract 63x and 2 from both sides

23x -63x = 6 -2

-40x =4 Divide both sides by -40

x = -4/40 Simplify it by 4

x= -1/10

2) Hence, the answer is x= -1/10

The weight in pounds of the fourth dog, is 55 lbs.

What is weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

As given, Ben is walking with three dogs that weigh an average of 75 pounds each. Ben begins to walk with a fourth dog, and the average weight of the dogs decreases to 70 pounds.

The total weight of the first three dogs is 225 pounds.

This amount, plus the weight of the fourth dog, divided by total number of dogs, is the new average weight:

[tex]\frac{d+225}{4} = 70\\d + 225 = 280\\d = 280 - 225\\d = 55 lbs[/tex]

Therefore, the weight of the fourth dog is 55 lbs.

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The required equation of line would be 2y = 5x - 8 which is shown in the given graph.

The slope of a line is defined as the angle of the line.

According to the given figure,

We clearly see that the coordinates of the y-intercept would be (0, -4).

The value of the x-coordinate is 2 when y-coordinate is 1.

Here the line passes through the points (0, -4) and (2, 1).

Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x₂ -x]

x₁ = 0, y₁ = -4

x₂ = 2, y₂ = 1

⇒ y - y₂ = (y₂ - y₁)/(x₂ -x₁ )[x -x₂]

⇒ y - 1 = (1 - (-4))/(2 - 0 )[x -2]

⇒ y - 1 = 5/2[x -2]

⇒ 2y - 2 = 5[x -2]

⇒ 2y = 5x - 10 + 2

⇒ 2y = 5x - 8

Therefore, the required equation of line would be 2y = 5x - 8 which is shown in the given graph.

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Answer:

I don't know if you can use permutations but

(6P2-6)/6=4 ????

First, let's calculate the total amount of balls:

Since there are 2 white balls and 2 red balls, the number of white or red balls is 4.

So the probability is:

Correct option: A

The ratio term of given geometric progression is 3 and the 9th term of the GP is 6561.

What is Geometric Progression?

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. For instance, the geometric progression 2, 6, 18, 54,_ _ _ _ has a common ratio of 3.

Given in question,

first term of the GP is 1,

4th term of the GP is 27,

[tex]4^{th} term = ar^3[/tex]

[tex]ar^3 = 27[/tex]

Therefore, the ratio term of geometric progression, r = 3

We know that, [tex]a_n = ar^{n-1}[/tex]

[tex]a_9 = ar^8[/tex]

[tex]a_9 = 3^8[/tex]

a9 = 6561

Therefore, the 9th term of given geometric progression is 6561.

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Answer:

D. g(n)=2100(0.7)^nD. g(n)=2100(0.7)^

Explanation:

• The purchase price, i.e. the initial value of the computer = $2100.

• The rate at which its value reduces = 30%.

To determine the computer's value after n years of use, we use the depreciation formula below:

In this case:

• The Principal, P = $2100

• The rate, r = 30%

Substitute these values into the formula.

The function g(n) that represents the value of the computer after n years of use is Option D.

As per the given three coordinate of the triangle, the area of the triangle is 9.5 square units.

Area of triangle:

In the triangle ABC as with vertices or coordinates are A(x1, y1), B(x2, y2), and C(x3, y3), has the area,

Area(ΔABC) = (1/2){x1(y2 − y3) + x2(y3 − y1) + x3(y1 − y2)}

As the area is always positive.

Given,

Here we have the triangle VWX,

And their coordinates are V (-9,-7), W(-4,-5), and X(-6,-2).

Now we have to find the area of the triangle.

To find the area of the triangle, let us consider the coordinates (x1,y1) as v(-9,-7), (x2,y2) as W(-4,-5) and (x3,y3) as X(-6,-2).

Now, we have to apply the values on the formula, in order to get the area of the triangle,

=> A = 1/2 |(-9 [-5-(-2)] + (-4)[-2 - (-7)] + (-6)[-7 - (-5)]|

When we expand the terms, then we get,

=> A = 1/2 |(-9)[-3] + (-4)[5] + (-6)[-2]|

Further simplify the expression will gives you the following,

=> A = 1/2 |27 - 20 + 12|

=> A = 1/2 |19|

Therefore, the area of the triangle is 9.5 square units.

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We are given

Therefore the value of x can be gotten by simplifying the above equation

Given that x is 5, we can proceed to find the value of the expression.

This implies that

We will have the following:

Now, we corroborate with one of the expression, in our case we will analyze y = x^2:

So, the expression taht represents the value given is:

The system of inequalities that can be used to determine the number of each type of plant to be sold are :

x + y  ≥ 15

$150x + $125y  ≥  $2000

The first step is to determine the inequality signs that would be used in the system of inequalities:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is the greater than or equal to sign, ≥.

Two system of inequalities would be formed using the information provided in the question. The form of the system of inequalities would be:

number of Mediterranean palms sold + number of palmetto sold  ≥ least number of plants

(number of Mediterranean palms sold x cost of Mediterranean palms) + (number of palmetto sold x cost of palmetto sold   ≥ least number of sales

x + y  ≥ 15

$150x + $125y  ≥  $2000

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slope intercept equation is represented below

Therefore,