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 distance (d) between two points is computed as follows:

where (x1, y1) and (x2, y2) are the points of interest. In this case, the points are (7, 8) and (-1, 0). Replacing into the equation:

We are given that the length of a rectangle is 3 inches greater than the width.

Let us draw a rectangle and label the width and length.

Part A:

Let the width of the rectangle is x inches.

Then the length of the rectangle is (x + 3) inches.

Now recall that the area of a rectangle is given by

Where L is the length and W is the width of the rectangle.

Therefore, the above polynomial represents the area of the rectangle.

Part B:

We are given that the width is 4 inches.

Substitute the width (x = 4) into the equation of the area that we found in part A.

Therefore, the area of the rectangle is 28 square inches.

The car will need 6 gallons of gasoline to travel 102 miles

Given that the car travels 442 miles on 26 gallons of gasoline.

Because the more the distance, the more the volume of gasoline used, this is a direct proportion.

So, we have:

It will need 6 gallons.

The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2

The graph represents the given parameter

From the graph, we have the following function types

Using the options as a guide, we have the equations to be

Next, we calculate the domain

The quadratic function stops at x = 2 with an open circle

So, the domain is x < 2

The linear function starts at x = 2 with a closed circle

So, the domain is x ≥ 2

Hence, the graphed function is (a)

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Answer:

the subtraction property of equality

Step-by-step explanation:

trust

Answer:

Subtraction

Step-by-step explanation:

The total area of the figure is 298.17 ft².

For the given question;

Let divide the given the figure in three parts;

The dimensions of the rectangle is;

Length = 26 - 9 = 15 ft

Breadth = 9 ft

Area = length x breadth

Area = 15 x 9

Area = 135 ft²

The dimension of the triangle is-

Base = 9 ft

Height = 15 - 7 = 8 cm

Area = (1/2) base x height

Area = (1/2) x 9 x 8

Area = 36 ft²

The dimension of semi circle is -

Radius = 9 ft

Area = πr²/2

Area = 3.14 x 9² / 2

Area = 127.17 ft²

Total area = rectangle +triangle + semicircle

Total area = 135 + 36 + 127.17

Total area = 298.17 ft²

Thus, the total area of the figure is 298.17 ft².

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Simplified version of the given radical expression would be...

[tex]5x^2\sqrt{7x}[/tex]

Hope this helps!

We are given a two-way probability table

Part a)

If one of the vehicles is selected at random, determine the probability that the vehicle is a car.

From the table, we see that the total number of cars are 1441

Also, the total number of vehicles is 2420

Then the probability of selecting a car is

Therefore, the probability that the vehicle was a car is found to be 0.5955

Part b)

If one of the vehicles is selected at random, determine the probability that it used the electronic toll pass, given that it was a car.

This is a conditional probability problem.

The conditional probability is given by

From the table, we see that,

So, the probability is

Therefore, the probability that it used the electronic toll pass, given that it was a car is found to be 0.3727

The probability that the randomly chosen vehicle is a car is  59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is  61.94%.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

The probability that the randomly chosen vehicle is a car is the total no of cars divided by the total no. of vehicles which is,

= 1441/2420.

= (1441/2420)×100%.

= 59.54 %.

The probability that the randomly chosen vehicle is a car given that it used the toll pass is the total no. of cars that used the toll pass divided by the no. of vehicles that used the toll pass which is,

= (537/867)×100%.

= 61.94%.

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Answer:

1 hour and 40 minutes

Step-by-step explanation:

60 minutes in an hour

we have 100 minutes

100 - 60 = 40

in 100 minutes we already have 1 hour

now we have 40 minutes left

can 40 minutes make another 60?

No.

so 100 minutes make

Answer: The perimeter of the triangle is 69 cm.

Step-by-step explanation:

Let us consider the side of the triangle be 3x ,4x and 5x.

According to the question,

The longest side of the triangle be 30 cm.

. 5x=30cm

x=6 cm

So the side of the triangle are 18cm ,24 cm and 30 cm.

The perimeter of the triangle is the sum of sides of the triangle.

so perimeter is =15+24+30=69 cm



Answer:

Explanation:

Here, we want to get the dimensions of the rectangle

Let us represent the length by l and the width by w

From the question:

The length of the rectangle is 3 m less than double the width

Mathematically:

The product of the two represents the area

Now, let us substitute the first equation with the second:

Solving the quadratic equation, we have:

Recall:

If the chi-square test's expected frequencies rule is broken, either the row or the column is combined to provide a higher frequency that can be used to run the independence test.

Generally speaking, if more than 20% of the anticipated frequencies have a value of less than 5, Chi-Square should not be used (it does not matter what the observed frequencies are).

Both the chi-square test and Fisher's exact test are inappropriate if the sampled values' independence is broken. This presumption will be broken if the same subject results in more than one observation in the contingency table.

There are distinct assumptions for each non-parametric test as well. The data in the cells should represent frequencies or counts of cases rather than percentages or other data transformations, according to the Chi-presumptions. square's The variables' levels are mutually exclusive.

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Answer:

Step-by-step explanation:

First, graph your first point at (-1,3) Then, take your slope which is 1/2 and use rise over run. So from your point of (-1,3) go up 1 in your y coordinate, and 2 in your x coordinate. So your next point should be at (1,4)

We are to solve an inequality and give the answer in graph form.

The inequality is:

Let's solve for n in order to be able to answer the question.

we start by trying to isolate n on one side of the inequality symbol. So first combine 6-5 = 1 and re-write the inequality:

Now, subtract 1 from both sides, and you get the final answer:

n must be larger than or equal to 17. WHich agrees with the first answer option provided by the problem.

Answer:

Step-by-step explanation:

0 mixed berry smoothies and 70 milkshakes

Answer:

Step-by-step explanation:

Let the cost of stone sphere is s and stone cylinder is c.

According to question we have equation:

Solve it for s:

Substitute the value of c:

By properties of perpendicular lines and algebra properties, the slope of the line perpendicular to line ℓ is represented by m' > 1.

Let m be the slope of a line, in accordance with analytic geometry, the slope of line perpendicular to the first one is equal to m' = - 1 / m. The statement can be summarized by the following inequality:

0 < m < 1

Then, by algebra properties for inequalities we find that that slope for the perpendicular line is:

0 < m · m⁻¹ < m⁻¹

0 < 1 < m⁻¹

1 < m⁻¹

- m⁻¹ > 1

- 1 / m > 1

m' > 1

The slope of the line perpendicular to line ℓ is represented by m' > 1.

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For the graduation party, Nathan and Sydney should order  pieces of 70 fried chicken ,  11 pounds of meats  and 36 pounds of lasangnia .

In the question ,

it is given that

there are 15 drop in guests , and drop in guests are counted as half a guest .

So , the number of half guests = 15/2 = 7.5

number of guests for the party = 40 guests

So , total number of guests = 40+7.5 = 47.5

From the table , we can see that

19 party guests need 28 pieces of fried chicken .

So , 1 party guests will need 28/19 pieces of fried chicken .

so, 47.5 guests will need [tex]47.5*\frac{28}{19}[/tex] pieces of fried chicken

[tex]47.5*\frac{28}{19}[/tex] = 70

hence , 70 pieces of fried chicken is needed .

From the table , we can see that

19 party guests need [tex]4\frac{1}{3}[/tex] = 13/3 pounds of meats  .

so, 1 party guests will need 13/(3*19) pounds of meats .

So, 47.5 guests will need [tex]47.5*\frac{13}{3*19}[/tex] pounds of meats .

[tex]47.5*\frac{13}{3*19}[/tex] = 10.833

≈ 11

hence , 11 pounds of meats is needed .

From the table , we can see that

19 party guests need [tex]10\frac{3}{4}[/tex] = 43/3 pounds of lasangnia .

So , 1 party guests will need 43/(3*19) pounds of lasangnia .

So, 47.5 guests will need [tex]47.5*\frac{43}{3*19}[/tex] pounds of lasangnia .

[tex]47.5*\frac{43}{3*19}[/tex] = 35.8333

≈ 36

hence , 36 pounds of lasangnia is needed .

Therefore , For the graduation party Nathan and Sydney should order 70 pieces of fried chicken , 11 pounds of meats  and 36 pounds of lasangnia .

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Answer:

y= x/(n-9)

Step-by-step explanation:

Move 9 to the right side to get n-9

Take y over to get x=y(n-9)

Then shift n-9 over to other side to get y= x/(n-9)

Answer:

x = 11,2 inchs

Step-by-step explanation:

I infer that the units are in inches.

8-3 = 5

Then:

By the Pythagorean Teorem:

x² = 10² + 5²

x² = 100 + 25

x² = 125

√x² = √125

x = 11.18

to the nearest tenth:

x = 11.2 inches

0.895 with 95 repeating on and on as a simplified fraction can be re-written as 887/990.

By critically observing the given number, we can reasonably and logically deduce that it has three (3) repeating digits. Since this number has three (3) repeating digits, we would have to multiply n by 1000 as follows:

1000n = 0.895

1000n = 895.95        .......equation 1.

10n = 8.95            .......equation 2.

Subtracting equation 2 from equation 1, we have:

1000n - 10n = 895.95 - 8.95

990n = 887

Dividing both sides by 990, we have:

n = 887/990

Simplified fraction, n = 887/990.

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Complete Question:

Write 0.895 with 95 repeating on and on as a simplified fraction.

Step-by-step explanation:

For the first family, 5 out of the total ratio = 5/63

For the second family, 12 out of the total ratio = 12/63

For the third family, 2 out of the total ratio = 15/63

For the fifth family, 29 out of the total ratio = 29/63

a) The first family = 5/63 of the money, $630

we can therefore say the money they received is

= 5/63 ×630

= $50

b) The last family = fifth family = 29/63 of the money, 630

= 29/63 × 630

= $290

recall that the first family received $50 , the positive difference between the money received by both the first and last family

= $290 - $50

= $240

c) Since another family joins in, the total number of families become 6

we can't find the average without knowing what the second, third, and fourth family received out of that money

the second family = 12/63 ×630

= $120

the third family = 2/63 × 630

= $20

the fourth family = 15/63 × 630

= $150

in this case, we were told the average became $140

which means that

sum of money received by the families/ the number of families involved in the sharing = $140

($630+n)/6= $140

now the plan would be to make n subject of formula

$630+n = $840

take $630 to the other side, it becomes -$630

n = $840-$630

n = $210

therefore the newly added family received $210

I honestly hope I explained it properly...thank you

The arithmetic says we should subtract find the difference between 86.89 and 56.389.

Notice we have to put a place holder of 0 at the ending of 86.89 to do the subtraction. Then we have to borrow 1 from the hundredth term(9) of 86.890 to make 0 ten . so ten minus 9 should be 1. Then the difference of the hundreth term(8 - 8) is 0. 8 minus 3 is 5. 6 minus 6 is zero and finally 8 minus 5 is 3.

The answers are B and D

It would take 9 Teenagers to finish a very large pizza in $15$ minutes.

From the knowlegde of Propotional method/ subject formular in mathematics;

From the questions:

12 Teens finished a very large pizza in $20$ minutes.

The number of teens to finish a very large pizza in $ 15 minutes would calculate thus,

12 Teens=$20$ minutes.

x Teens=$15$ minutes.

then we cross multiply:

x Teens × $20$ minutes =$15$ minutes × 12 Teens

making  x Teens subject of the formula we have;

x Teens=$15$ minutes × 12 Teens/$20$ minutes

x Teens=9 Teens

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EXPLANATION

We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:

Perimeter = 40 cm = 4x + 2x + 2 + x + 3

Adding like terms:

40 = 7x + 5

Subtracting 5 to both sides:

40 - 5 = 7x

Adding like terms:

35 = 7x

Dividing both sides by 7:

35/7 = x

Simplifying:

Then, by the obtuse triangle theorem, the following relationship should be fulfilled.

Answer:

9 + 7 + 7.2 = 23.2

23.2 x 2 = 46.4

Step-by-step explanation:

The all possible zeros predicted by the Rational Zero Theorem individually and separated by commas are  ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.

P(x) = 11x³ + 2x² + x + 10

The factors of the constant term 10 is  ±1, ±2, ±5, ±10 (=p)

The factors of leading coefficient are ±1, ±11 (= q)

The possible rational zeros are p/q : ±1/1, ±1/11, ±2/1, ±2/11, ±5/1, ±5/11, ±10/1, ±10/11.

After simplification the possible roots are  ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11.

Therefore, ±1/1, ±1/11, ±2, ±2/11, ±5, ±5/11, ±10, ±10/11. are the all possible zeros predicted by the Rational Zero Theorem individually and separated by commas.

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Answer

Check Explanation

Explanation

a ≡ b (mod n)

This means a and b have the same remainder when they are divided by n

So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.

1) 67 × 73 ≡ 1 × 3 (mod 5)

4891 ≡ 3 (mod 5)

So, to check,

(4891/5) = 978 remainder 1

(3/5) = 0 remainder 3

The remainders are different.

So, this equation is wrong and does not work.

This equation is false.

2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

Noting that it is the units digit that determines the remainder

3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer

5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer

So, using these numbers,

83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)

81 ≡ 625 (mod 17)

(81/17) = 4 remainder 13

(625/17) = 36 remainder 13

The remainders are the same.

So, this equation is correct and it works.

This equation is true.

Hope this Helps!!!

Answer:

Step-by-step explanation:

y=-3x+24

(0,24)