What is the domain of a square root?.

The dimension of the Box is equal to 3×6×6 where the Height = 3m and the length of base = 6m

We have the volume of the box as

V= 108 cubic meters

Let 'a' be the height of the box and 'b' be the one side of the base of the box.

Therefore the formula for volume is

Volume = ab²

108 =  ab²

=> a = 108/b²    ....(1)

Now the surface area of the box is,

S = b² + 4ab   ....(2)

From equations (1) and (2) we get,

Sa = b² + 4× (108/b²) × b

Sa = b² + 432 / b²  ....(3)

Now for the least possible surface area differentiate equation (3) we get,

d(Sa)/db = 2b - 432/b²   ....(4)

Now put the equation (4) equal to zero we get,

2b - 432/b² = 0

2b = 432/b²

b³ = 216

b = 6

Now put the value of b in equation (1) we get,

a = 3 m

Therefore the dimension of the box is 3 × 6 ×6

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Answer:

Shelly walked farther by 0.0666666666 or 0.07

Step-by-step explanation:

1 divided by 3 = 0.333333333

4 divided by 15 = 0.266666666

0.33 is greater than 0.26, so Shelly walked farther by 0.33 - 0.26 = 0.07

Answer:

[tex]x = -2[/tex]

Step-by-step explanation:

This is a vertical line. The equation for a vertical line is:

[tex]x = \textrm{constant}[/tex]

where the constant is the x-coordinate of every point on the line.

In this case, the x-coordinates given are -2, so the equation for this line is:

[tex]x = -2[/tex].

The total Drake feed his horse this week is 58.22 pound or 58[tex]\frac{11}{50}[/tex] pound.

Let's break it down,

day 1 = 12 pound

day 2 = 12 pound

day 3 = 12 pound

day 4 = 11[tex]\frac{2}{5}[/tex] pound

day 5 = 10.82 pound

First to answer in decimal, change all value to decimal. Since only day 4 value is not decimal, so we only change day 4 value.

day 4 = 11 + (2 ÷ 5) = 11.4 pound

Total pound = 12+12+12+11.4+10.82

= 58.22 pound

Next, to answer in fraction, we only change the result in decimal to fraction. So,

58.22 = 58 + (22 ÷ 100)

= 58[tex]\frac{22}{100}[/tex]

simplified

= 58[tex]\frac{11}{50}[/tex]

Thus, this week Drake feed his horse 58.22 pound of hay or equal to 58[tex]\frac{11}{50}[/tex] pound of hay.

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Answer:

[tex]f(3) = 5x - 2[/tex]

[tex]f(3) = 5(3) - 2[/tex]

[tex]f(3) = 15 - 2[/tex]

[tex]f(3) = 13[/tex]

Step-by-step explanation:

f(3)=f(x)

it means x=3

and we we use it to find f(3)

The solution for p(-2) in the function when the function p(n) = 2n is -2

From the question, we have the following equation that can be used in our computation:

p(n)=2n

To make the equation legible, we need to rewrite it

So, we have the following representation

p(n) = 2n

Also from the question, we have

p(-1)

This means that the value of n is -1, and we calculate p(n) when n = -1

Substitute the known values in the above equation, so, we have the following representation

p(-1) =  2 * -1

So, we have the following equation

p(-1) =  2 * -1

There is no constant to add or subtract to both sides of the equation

So, we have the following representation

p(-1) =  -2

Hence, the solution is -2

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The first 8 prime numbers that occur are as given below in the lis

The prime numbers can be referred to or concentrated as such numbers, which are whole number s but are divisible only by 1 and the number itself. The list given above contains the numbers which are not only prime but are also divisible only by one and the number themselves. The list given above contains such numbers which are divisible as per the conditions of prime numbers.  Therefore, the significance regarding prime numbers has been aforementioned in the given list.

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The area covered by fire in 20 hours time is 1311 square meters

13% increment represents increment by a factor of 1.13

The rate at which the fire increases is 13% per hour, hence in 20 hours the area will be covered by a factor of 22.6 solved as shown below:

= 20 * 1.13

= 22.6

The area covered by fire in 20 hours time

= 22.6 * 58 m^2

= 1310.8 m^2

= 1311 m^2

Using the rate of the fire coverage which is 13% per hour in 20 hours the fire will cover 1311 square meters

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When organisms are crossed, there are only two possible phenotype outcomes, and they each have a 50/50 chance of emerging, which is known as a 1:1 phenotypic ratio.

In the given question we have to explian about 1:1 phenotypic ratio.

The phenotypic ratio is the relationship between the proportion of children that will exhibit a particular trait or a combination of features. This ratio is often obtained by performing a test cross, noting how frequently a characteristic or combination of traits will be manifested based on the genotype of the offspring, and using the information from that cross.

When organisms are crossed, there are only two possible phenotype outcomes, and they each have a 50/50 chance of emerging, which is known as a 1:1 phenotypic ratio.

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Having $21,000 after investing 11 years with an annual simple interest rate of 4.5% means that the principal amount that Cindy's mom invested when Cindy turned 10 years old was $14,046.82

Simple interest rate is calculated by multiplying the interest rate given in a period of time with the principal without any compounding, and multiply it by the period of time that the principal is invested.

Given that the interest rate is at 4.5% annually, we will need to convert the percentage into a decimal with the following calculation:

4.5/100=0.045

The principal is invested when Cindy was 10 years old and by the time Cindy turned 21 years old the total investment accumulated is $21,000 within 11 years. We will then need to figure out the initial amount invested with the following formula:

P = A / (1 + rt)

Where P is the principal amount, A is the total amount of principal including the interest, r is the interest in decimal, and t is the number of years the money is invested.

P = 21000/(1+(0.045×11))

P = 14,046.82

The original amount of investment was $14,046.82

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Given that f might either be 29 or 31, both of which are greater than 23, and thus n follows, sufficient conditions for n is divided by positive integer d.

According to Statement A, 900 divided by f yields a remainder of m = 1. This provides no information about n or D; Insufficient

According to Statement B, the remainder n = x if N is divided by D = 23. This provides no information about r or d; Insufficient

Putting A and B together, since 900/f gives r = 1, d is a factor of 899.

The challenging part: 899 factors equal 29*31

Consequently, f might either be 29 or 31.

Since R can't be more than 23 based on B, D=23, and R is the reminder, so,

23 => n < 23

Thus, given that f might either be 29 or 31, both of which are greater than 23, and thus n follows, sufficient.

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The resulting polynomials include,

y = 2x³ + 4x² - x + 5

y = -3x² + 4x + 9

Given function,

2x³ + 4x² - x + 5 = -3x² + 4x + 9

A function with zeroes that are equal to the roots of a polynomial equation which system of equations can you use to find the roots,

For the polynomial function the roots are equal to the zeroes;

The obtained polynomials are,

y = 2x³ + 4x² - x + 5

y = -3x² + 4x + 9

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a) The proportion of heads that  is represented in this sample is [tex]\bar{p}[/tex]=0.583.

It is a parameter that describes a percentage number connected with a population. For example, the 2010 United States Census revealed that 83.7% of the American population was identified as not being Hispanic or Latino; the figure of.837 is a population proportion. In general, the population proportion and other population metrics are unknown. A census can be undertaken to establish the true value of a demographic metric, although it is generally impractical due to the expenses and time required.

A population proportion is typically computed using an unbiased sample statistic derived from an observational study or experiment.

Given that,

A coin is flipped 120 times, the number of heads we get are 70

a) The sample proportion is,

[tex]\bar{p}[/tex]=No. of heads/No. of times the coin is flipped

[tex]\bar{p}[/tex]=70/120

[tex]\bar{p}[/tex]=0.583

The proportion of heads that  is represented in this sample is [tex]\bar{p}[/tex]=0.583

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Yes, AAA Theorem is a valid theorem for congruency when used along with two more theorems to prove congruency of triangles.

AAA (Angle-Angle-Angle) Theorem states two corresponding angles of a triangle are equal to that of the second triangle if and only if the two corresponding sides containing the angles are proportional. Then the triangles are similar.

The AAA Theorem is valid for congruency of triangles if it follows the above given conditions along with the fact that two more theorems such as SSS or AAS.

As congruency in triangles is the condition in which both the given triangles are proven to be of the same shape and size.

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The circle's center is located at (-4 -5i).

Given data,

A circle has a diameter with endpoints at -2 + i and -6 -11i.

(x₁, x₂) = (-2, -6)

(y₁, y₂) = (i, -11i)

To find what is the center of the circle;

It can be calculated by,

Add the two 'x' coordinates together and average, and the two 'y' coordinates together and average.

Now,

(x₁ + x₂)/2 = (-2 -6)/2

               = -8/2

               = -4

(y₁ + y₂)/2 = (i - 11i)/2

                = -10i/2

                = -5i

Hence, the center of the circle is at (-4 -5i).

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72 is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 54.

We know that the sum of all the angles of any triangle is 180

We have to use the above property in order to find the measurement of the vertex angle.

Now our triangle is isosceles , that is the two equal sides will be containing equal angle. One of them is given as 54

And hence the other will also be 54.

Let the vertex angle be x

180=54+54+×

180=108+×

x=180-108

x=72

Hence the vertex angle is 72

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The score at 35th percentile is 469.6 marks according to standard deviation and mean.

What is standard deviation?

Standard Deviation could be a measure that shows what quantity variation (such as unfold, dispersion, spread,) from the mean exis

Main body:

Given:

mean of μ = 500  and standard deviation of σ = 80

To answer this, we must find the z-score that is closest to the value 0.35 in the z table. This value turns out to be -0.38:

We can then plug this value into the percentile formula:

Percentile Value = μ + zσ

35th percentile = 500 + (-0.38)*80

35th percentile = 469.6

the score at the 15th percentile weighs about 469.6 marks.

Hence marks at 35th percentile is 469.6

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Answer: The answer is -1.525 which you don't have as an answer choice.

Step-by-step explanation:

−6.475+4.95

=−6.475+4.95

=−1.525

Hope this helps!!! :)

The probability when the sum dots are greater than 8 is 0.277.

when two dice are thrown then total probability for 2 dice, Here ,two dices are thrown. Therefore total possible outcome is  (6)2  = 36 and sum is greater than 8 , so favorable outcome is = 10

Probability is the department of arithmetic regarding numerical descriptions of ways in all likelihood an occasion is to occur, or how in all likelihood it's miles that a proposition is true. The possibility of an occasion is a range of among zero and 1, where, kind of speaking, zero shows impossibility of the occasion and 1 shows certainty.") For example, the possibility of flipping a coin and it being heads is ½, due to the fact there's 1 manner of having a head and the overall variety of viable effects is 2 (a head or tail). We write P(heads) = ½ .

favorable possible result:

(3,6)

(4,5)

(4,6)

(5,4)

(5,5)

(5,6)

(6,3)

(6,4)

(6,5)

(6,6)

Therefore the required probability is =  10/36

probability=  5/18 = 0.277 .

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When testing for significance among three or more groups, it may be difficult to determine where the significant differences are in a dataset. An Analysis of Variance (ANOVA) can pinpoint the difference(s). The correct option is B.

Analysis of variance is a collection of statistical models and the estimation procedures that go with them that are used to analyze the differences between means. Ronald Fisher, a statistician, invented ANOVA. ANOVA is a method for determining whether the means of two groups differ. Inferential statistics uses samples to infer population properties. Statistical tests such as ANOVA assist us in determining whether sample results are applicable to populations.

The null hypothesis in ANOVA states that there is no difference between group means. The ANOVA will report a statistically significant result if any group differs significantly from the overall group mean. ANOVA is a statistical method that divides observed variance data into different components for use in additional tests. For three or more groups of data, a one-way ANOVA is used to learn about the relationship between the dependent and independent variables.

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A) The y-intercept of the given is 43.13 and coordinates is,

[tex](x_1,y_1)=(45,37.25)\\(x_2,y_2)=(118,40.90)[/tex]

B) The y-intercept represent the constant variable.

What is y-intercept?

 In mathematics, the intersection point is the point on the y-axis through which the slope of the line passes. The y-intercept is where the line or curve intersects or touches the y-axis. This is the vertical, often dark line in the middle of the chart. The y-intercept of a chart is the point where the chart intersects the y-axis. Y-INTERCEPT means the y-coordinate of the point where the line, curve, or surface intersects the y-axis.

in given problem take number of text represent as x coordinate and cost of month represent y coordinate , then

[tex](x_1,y_1)=(45,37.25)\\(x_2,y_2)=(118,40.90)[/tex]

Now using slope formula ,

slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = 3.65/73 = 0.05

Now using equation formula ,

[tex]y-y_1=m(x-x_1)[/tex]

=> y-45 = 0.05(x-37.25)

=> y-45 = 0.05x-1.8625

=> y= 0.05x+45-1.8625

=> y = 0.05x+43.13

Here we know that equation general form is y = mx+b ,  where b is

y intercept.

Therefore y intercept is 43.13 and it represent the constant variable.

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Answer:

[tex]12x+36[/tex] in²

Step-by-step explanation:

The area of the inner square is [tex]x^2[/tex] in².

The area of the whole square is [tex](x+6)^2[/tex] in².

Taking the difference, [tex](x+6)^2-x^2=(6)(2x+6)=12x+36[/tex] in².

Answer:

[tex]\huge\boxed{\sf 12x + 36 \ in.^2}[/tex]

Step-by-step explanation:

Length = x in.

So,

Area = (x)²

Area = x² in.²

Length of the whole rug = 3 + x + 3 = x + 6

So,

Area = (x + 6)²

Area = x² + 12x + 36 in.²

= Area of the whole rug - Area of the inner part

= x² + 12x + 36 - x²

= x² - x² + 12x + 36

[tex]\rule[225]{225}{2}[/tex]

There is no sufficient evidence at the 0.05 level of significance that the percentage is not 58%.

What is percentage?

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

Given percentage = 98%

alpha = 0.05

First we will design the null hypothesis.

null hypothesis: p greater than or equal to 0.58

and alternate hypothesis: p is less than to 0.58

The null hypothesis shows that 58% or more readers owns a Rolls Royce.

The alternative hypothesis shows less than 58% of the readers own a rolls Royce.

Thus, the null hypothesis is selected.

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There will be 90 games for 10 teams to play each other twice

There are ten teams in total.

Team 1 will play the match with rest of the 9 teams.

There will be 9 matches in total.

Similarly, team 2 will play rest of 8 teams as team 1 had already played with.

There will be 8 matches.

This will go like:

9 + 8+ 7 + 6 + 5 + 4 + 3 + 2 + 1

This series is a arthimetic progression with common difference is 1

The sum of a  a(a + 1)/2

9(9 + 1)/2

= 45

45.

Since each match will happen twice, there will be 90 matches.

Therefore, The 10 teams to play each other twice so there will be 90 matches in total.

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The required value of x for the given condition g(x) = f(2) is x = 2.

This relationship is regularly represented as y = f(x) — which is expressed "f of x" — and y and x are connected with the end goal that for each x, there is an extraordinary worth of y. That is, f(x) can not have more than one incentive for a similar x. To utilize the language of set hypothesis, a capability relates a component x to a component f(x) in one more set.

f(x) = 3x - 1 and g(x) = 2x - 3

To find value of x for g(x) = f(2)

Then, f(2) = 3(2) - 1 = 6 - 1 = 5

So, g(x) = 2x - 3 = 5

2x = 8

x = 4

Thus at x = 4   g(x) = f(2).

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Answer:

n - 5

Step-by-step explanation:

n is a variable

less mean to subtact so n - 5

A solution to a system of equations is a value that, when substituted for unknown variables, causes the equations to be true.

A system of linear equations is made up of two or more linear equations made up of two or more variables, and all equations in the system are considered at the same time.

The set of all values that, when substituted for unknowns, make the equations true is referred to as the solution of a system of equations.

To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that simultaneously solves all of the equations in the system.

Some linear systems have no solution, while others have an infinite number of solutions.

There are three types of two-variable linear equation systems and three types of solutions.

As a result, a solution to a system of equations is a value that, when substituted for unknown variables, causes the equations to be true.

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The measure of [x] in the triangle will be 61°.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle as shown in the image attached.

The given triangle is a isosceles triangle. So, we can write -

[x] + [x] + 58 = 180

2x + 58 = 180

2x = 122

x = 61

Therefore, the measure of [x] in the triangle will be 61°.

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Answer:  The answer is b = -28 (type -28 in the box)

Step-by-step explanation:

The equation of this line in y=mx+b format is:

y=-6x-28

Solution to the system of linear inequalities 2x - 3y <12, graph plotted below.

What is inequality ?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

In this case, the inequality 2x - 3y <12

Related formula: 2x - 3y = 12.

Having x-intercept means

y = - intercept

Also, 2(0) - 3(0) < 12.

Hence the inequality 2x - 3y <12 holds good and the graph is plotted below.

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