an open box is to be made out of a 8-inch by 20-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. find the dimensions of the resulting box that has the largest volume.

The solution for the formula V = πr² is A. r = √(V/(π)).

What is the equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

To solve for r in the formula V = πr², we need to isolate r on one side of the equation.

We can do this by dividing both sides of the equation by π and then taking the square root of both sides:

V/π = r²

√(V/π) = r

Therefore, the solution is A. r = √(V/(π)).

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Answer:

A. Corresponding angles

B. Vertically opposite angles

C. Alternate angles

Step-by-step explanation:

Alternate angles are two angles, not adjoining one another, that are formed on opposite sides of a line that intersects two other lines. If the original two lines are parallel, the alternate angles are equal.

Vertically Opposite Angles are the angles opposite each other when two lines cross "Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down. Example: a° and b° are vertically opposite angles.

Corresponding angles are the angles which occupy the same relative position at each intersection where a straight-line crosses two others. If the two lines are parallel, the corresponding angles are equal.

By making linear equations for given situation, the vendor sold 34 hot dogs and 84 sodas at the football game.

What is a linear equation, exactly?

A linear equation is an algebraic equation in which each term a constant or variable. In other words, a linear equation is an equation of the form:

y = mx + b

where y and x are variables, m is the slope of the line, and b is the y-intercept (the point where the line intersects the y-axis).

Now,

Let x be the variable or number of hot dogs sold.

Then, according to the problem, the number of sodas sold is 50 more than the number of hot dogs sold. Therefore, the number of sodas sold can be represented as (x + 50).

We know that the total number of sodas and hot dogs sold is 118, so we can write an equation:

x + (x + 50) = 118

Simplifying and solving for x:

2x + 50 = 118

2x = 68

x = 34

Therefore, the number of hot dogs sold is 34, and the number of sodas sold is (x + 50) = 84.

So, the vendor sold 34 hot dogs and 84 sodas at the football game.

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Answer:

56.52mm

Step-by-step explanation:

If the diameter is 18, the radius is 9.

The formula for circumference is c=2πr

so, 2*3.14*9=56.52

56.52mm

Answer:

[tex]\boxed{k=\frac{p}{r \ s} }[/tex]

Second option is correct.

Step-by-step explanation:

We have been given that p varies jointly with r and s.

Thus, we can write it mathematically as

[tex]p=krs[/tex]

Here, k is the constant of variation.

Now, we have to find the value of k.

Divide the above equation by rs

[tex]\dfrac{p}{r \ s}=\dfrac{kr\ s}{rs}[/tex]

[tex]k=\dfrac{p}{r s}[/tex]

Hence, the value of k is [tex]k=\dfrac{p}{r s}[/tex]

Second option is correct.

Answer:

B

Step-by-step explanation:

edge 23

The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg. the critical value t0.05/2, which is 1.699.

To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9.

To construct a confidence interval with a 90% confidence level, we need to find the critical value t0.05/2. This critical value is found by using the t-distribution with a confidence level of 90% (0.90) and degrees of freedom equal to the sample size minus 1 (180 - 1 = 179). The t-distribution is used instead of the normal distribution because it is better suited to smaller sample sizes. We can then use this critical value to calculate the margin of error of the confidence interval, which is equal to the critical value multiplied by the standard error (s/√n). In this example, that results in a margin of error of 1.699*(6.2/√180) = 1.9. The confidence interval then takes the form of x ± margin of error, which in this example is 28 ± 1.9, or (26.1, 29.9). This means that we are 90% confident that the true population mean of newborn girl's weights lies between 26.1 and 29.9 hg.

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Answer: 15, 18, 21 (next three terms), Rule: Skip counting by 3

First calculate the common difference between the terms, If [tex]a_{1}, a_{2}, a_{3}, a_{4}.....[/tex] are in sequence, the common difference is calculated by [tex](a_{2} -a_{1}), (a_{3} -a_{2}), (a_{4} -a_{3}) .......[/tex]

Since, the common difference are equal so its clear that the given sequence is an Arithmetic Expression.

The nth term of the AP is an  = a + (n-1)*d

1. Given: 3, 6, 9, 12, .....

  Answer: 15, 18, 21 (next three terms)

  Rule: Skip counting by 3

2. Given: 3, 5, 7, 9, .....

  Answer: 11, 13, 15 (next three terms)

  Rule: Skip counting by 1

3. Given: a, (a+b), (a+2b),.....

  Answer: (a+3b), (a+4b), (a+5b) (next three terms)

  Rule: nth term = a+(n-1)*b = a+nb-b

  if we need 4th term, put n=4 so that 4th term= a+4b-b = (a+3b)

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The optimal number of TVs to sell in order to achieve the highest profit are 24 and 48, respectively

Given the question, the objective function can be stated as follows.

P(n, m) = 175b + 205m

The given values for the constraints and the result of evaluating them are provided as

After analyzing the above values, we have identified the highest value as

Maximum = 14040

These values are at

b = 24 and m = 48

Hence, the number of TV to be sold are 24 and 48, respectively

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Check the picture below.

so if we just find the vertex of that parabolic path, we'd get how far up it went and how long it took

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-16}t^2\stackrel{\stackrel{b}{\downarrow }}{+16}t\stackrel{\stackrel{c}{\downarrow }}{+0} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{ 16}{2(-16)}~~~~ ,~~~~ 0-\cfrac{ (16)^2}{4(-16)}\right) \implies \left( - \cfrac{ 16 }{ -32 }~~,~~0 - \cfrac{ 256 }{ -64 } \right) \\\\\\ \left( \cfrac{ -1 }{ -2 } ~~~~ ,~~~~ 0 +4 \right)\implies \stackrel{seconds ~~ feet }{\left(0.5~~,~~4 \right)}[/tex]

well, as you see in the picture, the horse hits the ground again when h(t) = 0

[tex]\stackrel{h(t)}{0}=-16t^2+16t\implies 0=-16t(t-1)\implies t= \begin{cases} 0\\ 1 \end{cases}[/tex]

so at t=0 and t=1 it's touching the ground, at t=0 when it begins to jump at t=1 when it thumps back down, took that long.

Answer:

(3)(x)(z)

Step-by-step explanation:

A graph of each inequality is shown in the grid below.

A shape which the solution region represent is a rectangle.

In order to graph the solution to the given system of inequalities on a coordinate plane, we would use an online graphing calculator to plot the given system of inequalities and then take note of the point of intersection;

0.4r ≤ 120     .....equation 1.

r ≥ 4(360/5)    .....equation 2.

By evaluating the given system of inequalities, we have;

r ≤ 120/0.4

r ≤ 300

r ≥ 4(360/5)

r ≥ 4(72)

r ≥ 288

By combining the system of inequalities, we have:

288 ≤ r ≤ 300

Based on the graph shown in the image attached below, we can logically deduce that the solution to the given system of inequalities is within the shaded region between the solid lines, and the point of intersection of these solid lines on the graph.

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Answer:

add 3

Step-by-step explanation:

adding 3 to each number for next erm

The volume of the triangular prism is 115.5m³.

Given that,

Base = 7m.

Height = 3m.

Length = 11m.

Therefore, The area of the triangle on one side = [tex]\frac{1}{2} bh[/tex]

                                                                                = [tex]\frac{1}{2}[/tex] × 7 × 3

                                                                                = 21/2

                                                                                = 10.5 m².

The volume of the prism = area of the triangle × height

                                                           = 10.5 × 11

                                                           = 115.5 m³.

Therefore, the volume of the triangular prism is 115.5m³.

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The question is incomplete, the complete question would be

What is the volume of the triangular prism? A) 57. 75 m3 B) 115. 5 m3 C) 231. 0 m3 D) 462. 0 m3

Note that where the above conditions exists with regard to the geometric ratios, the sum of the antecedents is approximately 445.31.

Let the three continuous geometric ratios be a, ar, and ar^2, where a is the first term and r is the common ratio. Then the equality can be written as:

a/ar + ar/ar² + ar² = 3/4

Simplifying this equation, we get:

1/r + r + r² = 3/4

Multiplying both sides by 4r², we get:

4r + 4r³ + 4r⁴ = 3r²

Rearranging, we get:

4r⁴ + 3r² - 4r = 0

We can factor this equation as:

r(4r³ - 4r² + 3) = 0

Since r cannot be zero, we must solve the cubic equation:

4r³ - 4r² + 3 = 0

Using a numerical method or a computer program, we can find that one real root of this equation is approximately 0.8202.

Now that we know the value of r, we can use the difference between the largest and minor consequent to find the value of a. The largest consequent is ar², and the minor consequent is a, so we have:

ar² - a = 120

Substituting r = 0.8202, we get:

a(0.8202)² - a = 120

Simplifying, we get:

a = 120 / (0.6721)

a ≈ 178.63

Finally, we can calculate the sum of the antecedents:

a + ar + ar² = 178.63 + (178.63)(0.8202) + (178.63)(0.8202)²

Summing these terms, we get:

a + ar + ar² ≈ 445.31

Therefore, the sum of the antecedents is approximately 445.31

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Translation:

If the sum of the ratios of an equality of 3 continuous geometric ratios is 3/4, calculate the sum of antecedents. Consider that the difference between the largest and minor consequent is 120

The slope-intercept form of this table is y = 3x - 10.

In Mathematics, the point-slope form of any straight line can be determined by using the following mathematical expression:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex] or y - y₁ = m(x - x₁)

Where:

At point (25, 65), an equation of this line in slope-intercept form can be calculated by using the point-slope form:

[tex]y - y_1 = \frac{(y_2- y_1)}{(x_2 - x_1)}(x - x_1)[/tex]

[tex]y - 65 = \frac{(68- 65)}{(26 - 25)}(x - 25)[/tex]

y - 65 = 3(x - 25)

y = 3x - 75 + 65

y = 3x - 10.

In this context, we can reasonably infer and logically deduce that an equation of the line that represents this table in slope-intercept form is y = 3x - 10.

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Answer:

60°

Step-by-step explanation:

Let m<R = x.

Let m<Q = 2x.

m<Q + m<R = 90

2x + x = 90

3x = 90

x = 30

m<Q = 2x = 2(30) = 60

Answer: 60°

Answer:

Add 3

Step-by-step explanation:

The pattern provided can be obtained by adding a constant number to the previous term. The common number is 3 because each term is 3 more than the previous term.

Therefore, you can add 3 to the previous term to get the next term.

Answer:

3rd and 5th options (check below)

Step-by-step explanation:

The gift card has $22.20

After payment he had $1.90 left

What was charged for the 4 tire patches? $22.90 - $1.90

How many tire patches did he pay for? 4

Let the patch be X, 4 patches will be 4X

4X = 22.20 - 1.90

The cost of the patches + the balance on the gift card is also 22.20

4x + 1.90 =22.20

If you Subract the cost of 4tire patches from 22.20, you will have 1.90 on the gift card

22.2 - 4X = 1.9

These are the three right equations

Accοrding the given questiοn 0.16 is 0.4 Percentage οr % οf 40

A percentage is a number οr ratiο that can be expressed as a fractiοn οf 100 in mathematics. If we need tο calculate a percentage οf a number, multiply it by 100 and divide it by the tοtal. Sο, a part per hundred is what the percentage refers tο. Percent means fοr every 100. The symbοl "%" is used tο denοte it.

Percentages have nο dimensiοn. Hence it is called a dimensiοnless number. If we say, 50% οf a number, then it means 50 per cent οf its whοle.

0.4% is equivalent tο 0.4/100 = 0.004 as a decimal.

Tο find οut what number (a) is 0.4% οf 40, we can use the fοllοwing fοrmula:

a = 0.004 x 40

a = 0.16

Therefοre, 0.4% οf 40 is 0.16.

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The operations used here are as follows:

Addition.

Division.

The order of operations is a collection of rules that must be followed in a particular order while solving an equation.

The evaluation of any mathematical expression, which includes arithmetic operations like addition, subtraction, multiplication, and division, is what we mean when we say "operations" in mathematics.

Here in the question,

For the 2nd step,

10 was added on both the sides of the equation.

So, addition was the property used.

For the 4th step,

3 was divided from both the sides of the equation.

So, division was the property used.

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Answer: 4:12

Step-by-step explanation: Since it is squares to total you have to put the amount of squares first. That would be 4. Then, you have to figure out the total which is just adding 4+8=12. That would be the total. Therefore, the answer would be 4 to 12.

The numeric value of the expression is given as follows:

[f(x + h) - f(x)]/h = 5h + 10x + 6.

To obtain the numeric value of a function or of an expression, we substitute each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is given as follows:

f(x) = 5x² - 6x + 1.

The numeric value at x = x + h is given as follows:

f(x + h) = 5(x + h)² - 6(x + h) + 1

f(x + h) = 5(x² + 2xh + h²) - 6x + 6h + 1

f(x + h) = 5x² + 10xh + 5h² - 6x + 6h + 1

Hence:

f(x + h) - f(x) = 5x² + 10xh + 5h² - 6x + 6h + 1 - 5x² + 6x + 1

f(x + h) - f(x) = 10xh + 5h² + 6h

f(x + h) - f(x) = h(5h + 10x + 6).

Simplifying by h, we have that:

[f(x + h) - f(x)]/h = 5h + 10x + 6.

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Answer:

15 packs of crayons and 20 packs of pens

Step-by-step explanation:

you have to the multiply the amount that comes in each pack together

The normal distribution is a mathematical model used to describe real-world data that occurs in many scenarios, including restaurant wait times. The normal distribution is characterized by a mean and a standard deviation; in this case, the mean wait time is 20 minutes, and the standard deviation is 4 minutes.

In order to find the maximum wait time for customers so that at most 1% of them would receive their meals for free, we can use the normal distribution graph.

The graph shows the probability of a customer waiting any given amount of time. The mean is the highest point on the graph, while the standard deviation can be seen as two "bumps" on either side of the mean. For this scenario, any customer who waits more than 25.5 minutes will be in the top 1% of wait times, and therefore, should receive their meal for free.

This provides a reasonable time limit for customers to expect their meal, while also helping to dispel any negative perceptions about the speed of service.

In terms of the company's profitability, offering free meals to the top 1% of customers does not present any significant risk. The 25.5 minute wait time is well above the average wait time of 20 minutes, so it's unlikely that the company will incur a significant loss due to this promotion.

To sum up, the maximum wait time to be advertised to customers so that 1% of them will receive their meals for free is 25.5 minutes. The normal distribution graph shows how this wait time is chosen, as it corresponds to the top 1% of wait times.

As the average wait time is much lower than this maximum wait time, this promotion is unlikely to cause the company any significant loss in profit.

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the fraction of people in the room with blue eyes is 9/50.

If approximately 18 out of every 100 people have blue eyes, then the fraction of people with blue eyes can be expressed as 18/100 or 0.18. To find the fraction of people with blue eyes in a room of 50 people, we need to multiply this fraction by the total number of people:

(0.18) x 50 = 9

So, there are approximately 9 people in the room with blue eyes. To express this as a fraction with a denominator of 50, we can write:

9/50

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Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

The chance that a particular event will οccur is quantified by prοbability. It is a number between 0 and 1, where 0 denοtes that the event is hypοthetical and 1 denοtes that it will undοubtedly οccur. The number οf successful results multiplied by the entire number οf pοssible οutcοmes is used tο calculate an event's prοbability. Tο put it anοther way, prοbability is a way tο express the likelihοοd οf an event οccurring and tο quantify uncertainty.

given:

we can determine the likelihοοd οf receiving twο sοcks οf the same cοlοr.

We can select twο sοcks οf the same hue in any οf the fοllοwing ways:

In ₃C₂ = 3 οptiοns, we can select οur 2 gray sοcks.

There are ₃C₂ = 3 different methοds tο select 2 black sοcks.

Therefοre, there are a tοtal οf 3+3=6 methοds in which we can select 2 sοcks οf the same cοlοr.

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

The likelihοοd οf receiving twο sοcks οf the same cοlοr is as fοllοws:

6/15 = 2/5

Thus, the respοnse is c) 2/5.

b) The likelihοοd οf receiving twο pairs οf gray hοsiery is:

There are 3 οptiοns tο chοοse 2 pairs οf gray sοcks (₃C₂ = 3).

There are a tοtal οf ₆C₂ = 15 pοssible methοds tο select any twο sοcks frοm the available set οf 6.

Cοnsequently, the likelihοοd οf receiving twο pairs οf gray hοsiery is:

3/15 = 1/5

Therefοre, 2/5 is the likelihοοd οf getting twο pairs οf sοcks that are the same cοlοr, while 1/5 is the likelihοοd οf having twο pairs οf gray underwear.

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There are 5,642 fans at a concert. If there are 6 seats in each row, the  there are 940 rows each.

Numbers are mathematical objects used for counting, measuring and marking. The original examples are the natural numbers 1, 2, 3, 4, etc. Numbers can be represented by number words. More generally, individual numbers can be represented by symbols, called numerals; for example, "5" is the number representing the number five. Since only relatively few symbols can be memorized, base numbers are usually organized into a number system, which is an organized way of representing any number.

The most common numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of ten basic numeral symbols, called numerals. In addition to being used for counting and measuring, numbers are often used for labels (like phone numbers), orders (like serial numbers), and codes (like ISBNs) . In common usage, a number is not clearly distinguishable from the number it represents.

According to the question:

Number of chairs = 6 and

Number of rows =x

capacity of auditorium =  Number of chairs × Number of rows

⇒ 5642           = 6 × x

⇒ 6x = 5642

⇒ x = 5642/6

⇒ x = 940

round term = 940

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Answer:

∠ 6 = 59°

Step-by-step explanation:

∠ 3 and ∠ 8 are same- side interior angles and sum to 180° , that is

∠ 3 + ∠ 8 = 180°

121° + ∠ 8 = 180° ( subtract 121° from both sides )

∠ 8 = 59°

∠ 8 and ∠ 6 are vertically opposite angles and are congruent , then

∠ 6 = 59°