A box with an open top has vertical sides, a square bottom, and a volume of 108 cubic meters. If the box has the least possible surface area, find its dimensions.
Height = ?
Length of Base = ?

Probability to determine only two marbles are red is equal to 0.6.

As given in the question,

Total number of given red marbles in a bag = 4

Total number of given blue marbles in a bag = 2

Number of marbles selected simultaneously from the bag = 3

Condition : Only two marbles are red

Out of 3 marbles to be selected if 2 are red then 1 has to be  blue

Probability of taking out 3 marbles where only 2 are red

= ( ⁴C₂ × ²C₁ ) / ⁶C₃

= [4!/ (4-2)!2! ] × [ 2!/ ( 2- 1)!1! ] / 6! / (6-3)!3!

= ( 4 )( 3 ) / ( 5 )( 4)

= 12 / 20

= 0.6

Therefore, probability of selecting three marbles out of 6 with only 2 are red is 0.6.

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The interest rate if the simple interest on ​$4000 for 5 years is ​$​1,200  is 30%

The formula for calculating the simple interest is expressed as;

I = PRT/ 100

Where;

Now, let's substitute the values into the formula, we have;

$1200 = $4000 × R × 5/ 100

cross multiply

$120000 = $4000 × R

Divide both sides by the coefficient of R

R = $120000/$4000

R = 30%

Hence, the value is 30%

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The probability that a 3 will get any given times the dies is rolled is 0.17x

Total number of outcomes in one roll = 6

The favorable outcome = 3

The probability = Number of favorable outcomes / Total number of outcomes

Substitute the values in the equation

The probability of getting 3 in first roll= 1 / 6

Total number of times the die rolled = 11 times

The probability of getting 3 in all given times = (The probability of getting 3 in first roll )^ (Number of times the die rolled)

Consider the number of rolls as x

Substitute the values in the equation

The probability of getting 3 in all the given times = (1/6)^x

= 0.17x

Hence, the probability that a 3 will get any given times the dies is rolled is 0.17x

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Kayden has to work 3 hours the next week to earn $43.80.

We have given,

Kay Den worked 10 hours a week for his employer and took home $146. How many hours would he need to work the next week, at the same hourly rate, to make $43.80?

Kayden earned $146 for 10 hours.

If we calculate hourly wages,

Hourly wage of Kayden = [tex]\frac{146}{10}[/tex]

Hourly wage of Kayden = $14.6

If he is paid the same hourly wage,

We have to find, out how many hours will he have to work to earn $43.80

Let, him worked x hours.

14.6x = 43.80

[tex]x=\frac{43.80}{14.6}[/tex]

x = 3

Hence, it takes 3 hours.

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The planet that is closet to the sun is Mercury. Then it is Venus, Earth,Mars, Jupiter, Saturn, Uranus, Neptune.    

So likely it is 0% chance the earth is the closet planet to the sun.

The probability of an event occurring is intuitively understood to be the likelihood or chance of it occurring.

The higher the probability number or percentage of an event the more likely is that the event will occur is known as likelihood of an outcome.

We can use the following steps to calculate the probability of an event.

Step 1:- Identify an event with one result.

Step 2:- Identify the total number of results or outcomes and favorable outcomes that can occur.

Step 3:- Divide the number of favorable outcomes by the total number of possible outcomes.

Give question is incomplete.

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Third quartile Q₃ of the given data is 11

correct option is: b

What is the 75th percentile value?

0.675

For instance, the median represents the 50th percentile, the first quartile represents the 25th percentile, and the third quartile represents the 75th percentile.

What exactly is Q3?

Q3, the third quartile, is known as the 'upper quartile,' and represents the 75th percentile, which means that only 25% of the values in the set are greater than this value.

given data:

7,14,8,10,7,8,9,7,14,6.

In ascending, order data is 6,7,7,7,8,8,9,10,14,14.

number of terms N = 10

therefore, third quartile Q₃ = [tex]\frac{3}{4} (n + 1)[/tex]

Q₃ = [tex]\frac{3}{4} (10 + 1)[/tex]

Q₃ = 8.25th term

Q₃ = 8th term + 0.25 = 11

therefore, therefore, third quartile Q₃ of the given data is 10

correct option is: b

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The required value of of the given relation at x = 1.5 9 is 33.

Two qualities x and y are supposed to be directly proportional to one another when the proportion x:y consistently continues as before. Model : On the off chance that we purchase two pen for 50 Rs. It will cost us 100 Rs for four pen. Two qualities x and y are supposed to be conversely corresponding to one another when the proportion x:y1 consistently continues as before.

Let h(x) = kx where x is constant

Then, h(x)= 44, x=2

44 = 2k

k = 22

Now, the relation is h(x) = 22x

At x = 1.5, value of h(x)

h(x) = 22(1.5)

h(x) = 33

Thus, required value of h(x) is 33

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The circumference Of the circle with a radius is 70.336 inch

Describe circumference using an example.

A distance is covered by a boy if he starts jogging from point "A" and arrives at the same spot after going around the park once. The park's circumference, which is the length or limit that surrounds it and is shaped like a circle, is known. The boundary's length is its circumference.

What is the circumference measured in?

A circle's perimeter, or the distance encircling it, is known as its circumference. It has units of measurement like millimeters (mm), centimeters (cm), meters (m), or inches and is represented by the letter C in mathematical formulas. The following equations relate it to the radius,  , and pi: C = d. C = 2πr.

Given that:

Radius = 11.2 inch

Circumference = 2πr = 2 x 3.14 x 11.2 = 70.336 inch

Hence the Circumference is 70.336

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The distribution of the probability of each outcome is

P(X = 0) = 0.25

P(X = 1) = 0.5

P(X = 2) = 0.25

Given that,

A family consists of two kids. There are four alternative results if the genders of these kids are stated in the order they are born: bb, bg, gb, and gg. Assume that these results are equally probable. Let x be the proportion of girls among all children.

We have to find the complete part 1 of 2 by finding the probability distribution of x. part: 0 / 20 of 2 parts

We know that,

A probability is obtained by dividing the number of desired outcomes by the total number of outcomes.

The chance of each result is represented by the distribution, so

P(X = 0) = 1/4 = 0.25

P(X = 1) = 2/4 = 0.5

P(X = 2) = 1/4 = 0.25

Therefore, The distribution of the probability of each outcome is

P(X = 0) = 0.25

P(X = 1) = 0.5

P(X = 2) = 0.25

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Two rational expressions with the same denominator can be added or subtracted by adding or subtracting the numerators, then writing the result over the shared denominator.

There are four steps involved in adding or subtracting rational expressions:

For any value that renders either of the original rational expressions undefinable, the product of two rational expressions is, in general, undefinable.

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Answer: 30

Step-by-step explanation:

The gas used and miles are proportional for each scooter.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality .

Therefore, let's check whether the scooter A and scooter B shows proportional relationships.

Hence,

For scooter A:

y = kx

where

Therefore,

2 = 150 k

k = 2  /150

k = 1 / 75

Hence,

y = 1 / 75 x

From the table of scooter A, the ratio is constant, therefore, the relationships of gas used and distance covered is proportional for scooter A.

For the Scooter B the graph is also proportional because the ratios of the variables are constant.

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Equation in slope-intercept form that passes through a point and is parallel is y = mx + y1 - m(x1).

Given:

Let y = mx + b is a line and (x1,y1) be a point .

here slope = m

y - intercept = b

The line parallel to y = mx + b have same slope that is m.

parallel line slope = m

Passes through the point (x1,y1)

y1 = m(x1) + b

b = y1 - m(x1)

substitute b value in y = mx + b

y = mx + y1 - m(x1).

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The 95% confidence interval for the difference between the two population means is (-1,9).

The 95% confidence interval is a range of values that you can be 95% certain contains the true mean of the population. As the sample size increases, the range of interval values will narrow, meaning that you know that mean with much more accuracy compared with a smaller sample.

We have given that,

the point estimate of the difference between the means = 4,

the standard error = 5

and we need to find 95% confidence level for the difference between the two population means.

We know the formula of confidence interval, that is

CI = difference in mean ± error

⇒ CI = 4 ± 5

CI = 4 + 5 = 9

CI = 4 - 5 = -1

Therefore confidence interval for the difference between the two population means is (-1 , 9).  

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There will be 44 pages have exactly 7 stickers on each.

We know that Kory has a total of 314 stickers and he has to paste 7 stickers per page on a ticker book. So, for this, we have to divide the 314 stickers by the 7 per page. We can find the solution by using a simple Division Method. Given below is the calculation.

Let's suppose,
Total Stickers Available = x = 314
Stickers per page = y = 7
Total pages having 7 stickers = P =?

So we can find P by the following equation:

P = [tex]\frac{x}{y}[/tex]
P = [tex]\frac{314}{7}[/tex]

Total pages having 7 stickers = P = 44.86 Pages.
So, the Exact Pages having 7 stickers will be 44.

Also, we can see the remaining stickers by the given details.
Let's suppose,
Total Exact stickers to be pasted =  z
We can find Z by the given equation
z = P x y
  = 44 x 7
  = 308

Remaining Pages will be = x - z = 314 - 308 = 6
So, 308 pages would be pasted as 7 per page and the remaining stickers will be 6.

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The prime multiples of 5 is number 5

The multiples of 5 are 1, 5.

The prime numbers are the numbers who can be divided only by 1 and itselves.

First we need the multiplies of 8

And then find their factors, if the number of factors is exactly two( that is 1 and the number itself) then it is prime.

The factors of 1 is 1

The factors of 5 are 1 and 5

The numbers which have only two factors are prime.

5 [s the prime multiples of 5

Therefore, the number 5 is the only prime number multiple of 5

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The graph is in the image uploaded.

Given equation:

y = 3x-7

compare this with standard equation y =mx+b

so slope m = 3

y-intercept b = -7

so the point is (0,-7)

Table:

x        y

1        -4

0       -7

we can plot the graph with two points.

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The number of threads Marvin have left is 13 yards of thread

If  each spool thread is 10.5 yards 2 spools of thread will contain how many yards

= 10.5 * 2

= 21 yards

Marvin used 4 yards from each, hence Marvin used a total of 2 * 4 = 8 yards from the 2 spools of thread

The number of yards remaining is found by subtraction

= 21 - 8

= 13 yards

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The monthly rent during the 8th year of living in the apartment will be $2510

The cost of the apartment per month in the first year is $1600

The rent is set to go up by $130 per year

The monthly rent during the 8th year of living in the apartment

This can be calculated by using arthimetic progression

here a = 1600

d = 130

We need to caluclate a₈

a₈th = a + (8-1)d

= 1600 + 7 x 130

1600 + 910

= 2510.

Therefore, the monthly rent during the 8th year of living in the apartment will be $2510

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Expected payment for Rosaria is $202,020.

The Unitary Method is the process by which we first determine the value of a single unit and then the value of the necessary number of units.

In the question asked Rosaria has three expenses to pay,

Rosaria will be required to pay,

$36,259 in tuition for one year.

Room and board cost $12,258.

$1,988 is the cost of the books and lab.

Rosaria must therefore pay $50,505 each year, which is equal to $36,259 plus $12,258 plus $1,988.

Rosaria must pay $202,020 over the course of four years since 4 x $ 50,505 = $202,020.

Rosaria therefore expects to pay $202,020.

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Rosaria will pay $202,020.

The unitary method is used to find the value of a single unit from a given multiple. For example, if the price of 40 pens is Rs. 400, then how to find the value of one pen here? It can be done using the unitary method. Also, once we have found the value of a single unit, then we can calculate the value of the required units by multiplying the single value unit.

In this,

Rosaria has to pay

Tuition for one-year costs = $36,259.

Room and board cost = $12,258.

Books and lab costs = $1,988.

Rosaria must therefore pay $50,505 each year, as $36,259 + $12,258 + $1,988.

so for four years

4 x $ 50,505 = $202,020.

Rosaria will pay $202,020 for the course of four years.

Therefore expects to pay $202,020.

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Responses interval : (-1, -32) for the absolute minimum; (0, 0) for the relative maximum; (2, -32) for the absolute minimum; (+, +) for the absolute maximum (or "no absolute maximum")

Detailed explanation:

Extremes will occur at the domain interval's ends and at turns when the first derivative is zero.

It is the derivative.

h'(t) = 24t^2 -48t = 24t (t -2)

The extremes will be at t=0 and t=2, when there are zeros.

By evaluating the function at the endpoints of the interval and at the turning points, we can identify relative and absolute extrema.

h(-1) = 8(-1) (-1)

²(-1-3) = -32\s h(0) = 8(0)(0-3) = 0\s h(2) = 8(2²)(2 -3) = -32\s h(∞) = 8(∞)

³ = ∞

At t=-1 and t=2, the absolute minimum is found to be -32. The greatest value is, which is located at time t. At t=0, the relative maximum is zero, or 0.

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There are three main key terms here - Physical determinism, elitist-populist dilemma, and urban planning. They can be defined as done below.

First, we have at hand the term Physical determination which can be defined as the belief that physical objects and all physical causes can be described using terms and models of the physical sciences.

Secondly, the elitist-populist dilemma is a disagreement between two political factions. elitists are, of course, the socially and economically well-off sections of the population. The populist factions are the ones that cater to the general public and are at odds with the previous group.

Lastly, urban planning is the process of planning for development in urban areas.

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We will have obtuse-angled triangle if it has an obtuse angle which measures more than 90 degrees but less than 180 degrees

What are interior angles?

An Interior Angle is an angle inside a shape.

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90 degrees.

In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.

Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. Since, ∠A is 120 degrees, the sum of ∠B and ∠C will be less than 90° degrees.  

In the above triangle, ∠A + ∠B + ∠C = 180° (because of the Angle Sum Property)

Since ∠A = 120°, therefore, ∠B + ∠C= 60°.  

Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.

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Using Marked recapature formula for estimation on population size we get,

the estimate for total population size is 1200.

Marked recaputure Method :

first step is to capture and mark a sample of individuals. The assumption behind mark-recapture methods is that the proportion of marked individuals recaptured in the second sample represents the proportion of marked individuals in the population as a whole. In algebraic terms,

R/S = M/N

where R --> second time marked

S---> size of sample second time

N --> estimate population size

M ---> Marked in start point

We have given that ,

Total marked turtles by researchers (M) = 800

Second time total sample size (S) = 300

second time marked turtles(R) = 200

we have to find out estimate for total population size .

For this , Mark -Recapture method is very efficient to calculate estimate for total population size.

putting all known values in above formula we get, R/S = N/M

=> 200/300 = 800/N

=> 800× 300 = N× 200

=> N × 200 = 240000

=> N = 240000/200

=> N = 1200

so, the estimate for total population size is 1200.

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One way governments try to encourage growth is, the government can only promote growth by raising unemployment compensation.

Increased output of products and services is referred to as economic growth. Economic growth can be influenced by changes in capital goods, labour force, technology, and human capital. In general, there are two main factors that contribute to economic growth: an increase in the workforce's size and an increase in that workforce's productivity (output per hour worked). Both can expand the economy's total size, but only robust productivity growth can raise per capita GDP and income.

Given,

One way governments try to encourage growth is,

Out of the available alternatives, the government can only promote growth by raising unemployment compensation. Increased unemployment benefits will boost aggregate demand by giving laid-off workers their spending power back.

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The three sides of a triangle that is 3cm, 4cm, and 9cm not of the triangle.

Triangle:

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same

Here we have to find the given three sides of a triangle possible.

The three sides are 3cm, 4cm, and 9cm.

The property of a triangle is that the sum of two sides of a triangle is greater than the third side of a triangle.

The three sides are:

a = 3cm

b = 4cm

c = 9cm

a + b > c

3 + 4> 9

7> 9 which is incorrect

Therefore the three sides in not sides of a triangle.

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Answer:

1st: 2/4 or simplified to 1/2, 7th: 65/256

Step-by-step explanation:

the amount the numerator increases by doubles every time.

like +1, +2, +4, +8, +16, +32, etc

the denominator also doubles

The probability of getting the fewer than four twos is 0.5665.

       P(X = x) = C(n,x). p ˣ .(1 - p)ⁿ⁻ˣ

        C(n,x) = n!/x!(n-x)!

For the given question-

p is the likelihood that X will occur.

20 times of a die are rolled;

This indicates that; n = 20.

Six sides, one of which is two:

This indicates that; p = 1/6 = 0.1667.

Probability of having three or fewer twos:

Such is:

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

So,

P(X < 4) = C(n,x).  p ˣ .(1 - p)ⁿ⁻ˣ

P(X = 0) = C(20,0).  0.1667⁰ .(0.8333)²⁰

P(X = 0) = 0.0261

P(X = 1) = C(20,1).  0.1667¹ .(0.8333)¹⁹

P(X = 1) = 0.1043

P(X = 2) = C(20,2).  0.1667 ² .(0.8333)¹⁸

P(X = 2) = 0.1982

P(X = 3) = C(20,3).  0.1667³ .(0.8333)¹⁷

P(X = 3) = 0.2379

P(X < 4) = P(X = 0) +  P(X = 1) + P(X = 2) +  P(X = 3)

P(X < 4) = 0.0261 +  0.1043 + 0.1982 + 0.2379

P(X < 4) = 0.5665

Thus, the probability of getting the fewer than four twos is 0.5665.

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Excluding operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

We have to find out which of the following binary operations are associative.

(a) Subtraction of integers

(b) Division of nonzero rationals

(c) Function composition of polynomials with real coefficients

(d) Multiplication of 2 X 2 matrices with integer entries

Firstly, let us understand what do we mean by the associative property of binary operations. The associative property of binary operations states that in an expression if we restructure the parentheses, then there will be no change in the final answer.

Let us look into each of the binary operations given to us individually.

(a) Subtraction of integers

Let us consider a subtraction operation such as -

a-(b-c) = a-b-c

Now, if we change the parentheses in the above operation like (a-b)-c then also the operation will be given as -

(a-b)-c = a-b-c

So, the subtraction of integers operation is associative.

(b) Division of nonzero rationals

Let us consider a division operation such as -

3/(9/3) = 1

Now, if we change the parentheses in the above operation like (3/9)/3 then the operation will be given as -

(3/9)/3 = (1/3)/3 = 1/9

So, we see that there is change in the final answer when the parentheses is rearranged in the operation of division of nonzero rationals. Thus, the division of nonzero rationals operation is not associative.

(c) Function composition of polynomials with real coefficients

Let us assume that we have polynomials given by -

f, q, s: R→R

This implies that -

(f · (q · s))(x) = f((q · s)(x)) = f(q(s(x)))

Similarly,

((f · q) · s)(x) = (f · q)(s(x)) = f(q(s(x)))

We see that both the final results are same even if the parentheses are rearranged. So, (f · q) · s = f · (q · s)

So, the operations of function composition of polynomials with real coefficients is associative.

(d) Multiplication of 2 X 2 matrices with integer entries

Let us say that P, Q, R are three matrices. This implies that for any entries in the matrices, we can say that -

P(QR) =  ΣP( ΣQR)

=> P(QR) =  ΣΣPQR

Similarly,

(PQ)R = Σ( ΣPQ)R

=>  (PQ)R = ΣΣPQR

So, we see that P(QR) = (PQ)R

Thus, the operation of multiplication of 2 X 2 matrices with integer entries is associative.

Therefore, excepting the operation of division of nonzero rationals, all other binary operations i.e., subtraction of integers, function composition of polynomials with real coefficients, and multiplication of 2 X 2 matrices with integer entries are all associative.

Thus, option (a), (c), and (d) are associative while option (b) is not associative binary operation.

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