Write 256 as a product of primes.
Use index notation when giving your answer.

The answer of 1 more than 12 is 13.

The answer of 1 more than 12 is 13 which can be derived using simple mathematical calculations.

To find 1 more than 12, you can add 1 to the original number 12.

1 + 12 = 13

It's a simple arithmetic operation where you add a specific number, in this case 1, to the original number.

An arithmetic operation is a mathematical process that combines two or more numbers to produce a new number. The most basic arithmetic operations are addition, subtraction, multiplication, and division.

Addition: It is the process of combining two or more numbers to find their sum. For example, 2 + 3 = 5 is an addition operation.

Subtraction: It is the process of finding the difference between two numbers. For example, 5 - 3 = 2 is a subtraction operation.

Multiplication: It is the process of finding the product of two or more numbers. For example, 3 x 4 = 12 is a multiplication operation.

Division: It is the process of finding the quotient of two numbers. For example, 12 ÷ 3 = 4 is a division operation.

Therefore, The answer of 1 more than 12 is 13.

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By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x

Given, the linear equations are y = x and y = -x

We have to draw the graphs of the equations on the same cartesian plane.

Considering the equation y = x

We need a few points to plot on the graph.

For x = 1, y = 1

For x = 4, y = 4

Therefore, the points of the equation are (1, 1) and (4, 4)

By plotting the points (1, 1) and (4, 4) on the graph and joining the points we get a straight line which is the graph of y = x

Considering the equation y = -x

We need a few points to plot on the graph.

For x = 3, y = -3

For x = -4, y = 4

Therefore, the points of the equation are (3, -3) and (-4, 4)

By plotting the points (3, -3) and (-4, 4) on the graph and joining the points we get a straight line which is the graph of y = -x.

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Answer:

To evaluate 0.5^3 and 0.5^-3 as fractions, you can use the Decimal to Fraction Calculator. 0.5^3 is equal to 1/8 and 0.5^-3 is equal to 8/1. your welcome

Answer:

1/8 and 8.

Step-by-step explanation:

0.5^3

= (1/2)^3

= 1/ 2^3

= 1/8.

0.5^-3

= 1 /0.5^3

= 1 / 1/8

= 8.

Answer:

16

Step-by-step explanation:

Simplify the following:

(-4)^2

(-4)^2 = 16:

Answer: 16

As per the given coordinates (-2, 3), the mirror image is (2,3)

In math the term coordinate is defined as  a set of values which helps to show the exact position of a point in the coordinate plane.

Here we have given the coordinates as (-2,3) and we need to find the mirror image on y axis.

The general term for the mirror image on y axis is written as,

=> (x, y) = (-x, y)

Which the rule defines that the sign of x coordinate is changed when we calculate the mirror image on y axis.

Therefore here we have to change the sign of x coordinate that is -2, then we get the mirror image as,

=> (-2,3) = (2,3)

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The value of the expression is 4√3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, [tex]\sqrt{8}\cdot\sqrt{6}[/tex]

On solving we get

[tex]\sqrt{8}\cdot \sqrt{6}= \sqrt{48\\} \\=\sqrt{48} \\\\= \sqrt{16.3} \\\\=4 \sqrt{3}[/tex]

Hence, the value of the expression is 4√3

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The sum of 11 of the interior angles of a regular dodecagon is 1650°.

The formula (180n-360)/n is used to determine the interior angle of a regular polygon. n=11 for an undecagon.

The interior angle of a regular dodecagon is 150°.The sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.

The interior angles of a dodecagon are a bit harder. You can use this generic formula to find the sum of the interior angles for an n-sided polygon (regular or irregular).Sum of interior angles = (n-2)\times 180°(n−2)×180°

Sum of interior angles = 10\times 180°=1800°10×180°=1800°

Therefore, the sum of 11 of the interior angles of a regular dodecagon is 150* 11 = 1650°.

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The value of y in equation 2x-3y=-6 is y = (2x+6)/3

Let us proceed to solve the equation 2x - 3y = -6

We take the term 3y to the right-hand side of the equation which gives 2x = -6 + 3y

Now we bring 6 to the left side of the equation 2x + 6 = 3y

And lastly, we bring the 3 also to the other side of the equation thus dividing the term (2x-+6) by 3 which ultimately gives us the value of y.

(2x + 6) /3 = y

Thus, The value of y in equation 2x-3y=-6 is y = (2x+6)/3

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it is 21

Step-by-step explanation:

The angle 67.5 degrees is 3 times its complement

Let us assume that the complement of the angle be p degrees.

Given that the measure of the angle is three times its complement.

So, the measure of the angle = 3p

We know that two angles are complementary when their measures add to 90 degrees.

The sum of complementary angles is 90 degrees.

So we get an equation, p + 3p = 90

We solve this equation to find the value of p.

p + 3p = 90

4p = 90

p = 90/4

p = 22.5 degrees

so, the measure of complement of the angle is 22.5 degrees.

And the required angle would be, 3 × 22.5 = 67.5 degrees

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The equation pair cannot be solved if the lines are parallel.

Although a system of linear equations typically has a single solution, it occasionally may have infinite or no solutions (parallel lines) (same line). When the graphs cross at a particular point, a system of linear equations has a single solution.

When the graphs are parallel, an equation system with linear components cannot be solved. The graphs of a system of linear equations have an infinite number of solutions. The lines must connect since the slopes differ. The system of equations that the lines represent has just one solution since the lines intersect at a specific place.

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Answer:

27 minutes

Step-by-step explanation:

Convert 45% to a fraction

45% = 45/100 = 9/20  (divide numerator and denominator by 5)

1 hour = 60 minutes

45% of 1 hour = 9/20 x 60 = 27 minutes

The degree of the polynomial 2x² 5x³ 7 is 5.

A polynomial is described as an expression that consists of variables, constants, and exponents, which might be mixed with the use of mathematical operations along with addition, subtraction, multiplication, and department (No division operation by a variable).

In arithmetic, a polynomial is an expression that includes indeterminates and coefficients, that entail best the operations of addition, subtraction, multiplication, and fine-integer powers of variables. An instance of a polynomial of an unmarried indeterminate x is x² − 4x + 7.

Polynomials are sums of phrases of the form k⋅xⁿ, in which okay is any wide variety and n is a positive integer. for example, 3x+2x-5 is a polynomial. advent to polynomials.

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Complete Question:

What is the degree of the polynomial 2x² 5x³ 7?

All possible solutions for the inequalities are from 2.5 to infinity.

Option F is the correct answer.

All possible solutions for the problem situation are 2.5 to 8.

Option D is the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

27 ≤ 12 + 6x

Solve for x.

27 - 12 ≤ 6x

15 ≤ 6x

x ≥ 15/6

x ≥ 5/2

x ≥ 2.5

This means,

x values can be 2.5 and more.

Now,
For x = 8,

12 + 6 x 8

= 12 + 48

= 60 gallons (possible)

For x = 9,

12 + 6 x 9

= 12 + 54

= 66 gallons (not possible)

Since the maximum gallon the pool can contain is 60 gallons.

Thus,

All possible solutions for the inequalities are from 2.5 to infinity.

All possible solutions for the problem situation are 2.5 to 8.

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The equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

The equation y = 2x - 4 can be written in slope-intercept form as y = 2x + b, where b is the y-intercept. To find the slope and y-intercept of the equation, we need to solve for b.

The y-intercept is the point where the line crosses the y-axis. To find the y-intercept, we can set x equal to 0 in the equation to get y = 2(0) - 4. This simplifies to y = -4, so the y-intercept is -4.

The slope is the rate at which the line rises. To find the slope, we can take the coefficient of x, which is 2. So the slope of the equation y = 2x - 4 is 2.

In summary, the slope of the equation y = 2x - 4 is 2 and the y-intercept is -4. We can write the equation in slope-intercept form as y = 2x - 4, where 2 is the slope and -4 is the y-intercept.

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complete question : what is the slope and y-intercept of the equation

y = 2x - 4 ?

The future value of $2000 at a 3% interest rate compounded annually for 3 years would be $2185.40.

The future value of $2000 at a 3% interest rate compounded annually for 3 years can be calculated using the formula:

FV = PV * (1 + r)ⁿ

where PV is the present value, r is the annual interest rate, and n is the number of compounding periods.

In this case:

FV = $2000 * (1 + 0.03)³

FV = $2000 * 1.03³

FV = $2000 * 1.0927

FV = $2185.40

So, the future value of $2000 at a 3% interest rate compounded annually for 3 years would be $2185.40.

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If the variance is unknown and the sample size is small, then the t-test statistic is appropriate to use.

The t-test is a statistical hypothesis test used to identify whether an unknown population mean is different from a particular value. A t-test is appropriate to use when there is a small random sample collected from some statistical population and the sample is required to be compared with the mean from the sample to another value. Also, the variance of the sample is not known.

Thus, a t-test is appropriate to be used when the population variance or standard deviation is not known, and a sample size is less than 30.

"

Correct question:

If the variance is unknown and the ample size is small, which test statistic is appropriate?

"

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The number of words that can be formed with PATI is a total of 24 words.

Expressed mathematically, we can use the Permutations method.

The Permutation allows us to symbolically express the number of words that we can form and order with just one.

A permutation is defined as the variation of the position of the elements belonging to a given set.

The PATI permutation:

We see how many elements are in the word: 4 elements.

[tex] \: \: \: \: \: \: \: \: \: \: \begin{gathered} \bold{4 ! = 4 \times 3 \times 2 \times 1} \\ \bold{ 4! = 12 \times 2 \times 1 }\\ \bold{4! = 24 \times 1 }\\ \bold{4! = 24}\end{gathered}[/tex]

[tex]\therefore[/tex] The number of words that can be formed with PATI is a total of 24 words.

An equation that has two variables which the formula Ax + By = C.

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1.

So, an equation that has two variables which the formula Ax + By = C.

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Answer:

y = 10x + 20.

Step-by-step explanation:

Slope of the line = (60-30) / (4 - 1)

                            = 30/3

                            = 10

y-intercept = 20

Formula is y = mx + c where m = slope and c = y-intercept

So, the answer is y = 10x + 20.

Answer:

Ryan's answer: 8m - 6

Jane's answer: 4m - 3

Ryan is correct. By factoring out the greatest common factor from the expression, we get:

32m - 24 = (8m - 6) (4m - 2)

Jane's answer 4m-3 is not factor of the given expression.

The expression 32m - 24 can be written as (8m-6)(4m-2) but not as (4m-3)

So Ryan is correct.

Step-by-step explanation:

a) The probability distribution of X

X P(X)

0 022667

1 0.4073511

2 0.27452

3 0.082223

4 0.0093252

b) The most likely value for X is one.

c) The probability that at least two of the four selected have earthquake insurance is 0.3660.

We have, some parts of California are particularly earthquake-prone.Suppose that in one metropolitan area, 31% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random.

Let X denote the number among the four who have earthquake insurance. The probability that the homeowner are insured against earthquake is 0.31. Let S denote a homeowner that has insurance and F denote a homeowner that does not has insurance.

a) For X = 0, {FFFF}

The probability of X = 0

= 0.69x0.69x0.69×0.69

= 0.22667

For X = 1, {SFFF, FSFF, FFSF, FFFS}

P( X = 1) = (0.31 x0.69x0.69×0.69) *4)

= -0.40735116

For X = 2,{SSFF, SFSF, SFFS, FSSF, FSFS, FFSS}

P(X= 2) = (0.31x0.31x0.69×0.69)*6

= -0.27451926

For x = 3,{SSSF, SSFS, SFSS, FSSS}

= (0.31x0.31x0.31x0.69) *4

= -0.08222316

For X = 4, {SSSS}

P(X= 4) = (0.31 <0.31 x0.31x 0.31)

= 0.00923521

Hence, the probability distribution of X

X P(X)

0 022667

1 0.4073511

2 0.27452

3 0.082223

4 0.0093252

(b) The most likely value for X is X = 1, since it has large probability comparing with other values.

(c) We have to calculate the probability that at least two of the four selected have earthquake insurance, P(X ≥2)= P(X=2)+ P(X=3) + P(X=4)

= 0.27452+0.082223+0.0093252

P(X ≥2)=0.3660

Hence, the required probability is 0.3660.

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The values of p is 5 and q is 2 in the solution of the given system .​

Given that,

px + qy = −26 -----(1)

qx − py = 7 ------(2)

Multiplying  (1) by  y and (2) by  x

pxy+qy^2=−26y -----(3)

qx^2−pxy=7x -------(4)

Then adding  equation (3) and  (4), we get,

pxy+qy^2+qx^2−pxy=−26y+7x

qy^2+qx^2=−26y+7x

q(y2+x2)=−26y+7x

q=−26y+7xy^2+x2 --------(5)

Substitute x= -4 and y= -3  into the given system to solve it for "p" and "q". Hence, using  x=−4,y=−3 in  (5)

q = −26(−3) + 7(−4)(−3)^2 + (−4)2

q = 78 −289 + 16 = 5025 =2

And then, putting  q=2 in (2) we get,

2x−py=7⇒2x−7=py

2x−7y=p⇒2(−4)−7(−3)=p

After putting values of x and y, we get  2(−4)−7(−3)=p

−8−7−3=p⇒−15−3=p

p=5

Therefore, the values of p=5 and  q=2

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Answer:

5.196152421cm

Step-by-step explanation:

tan= opposite(perpendicular)/adjacent(base)

tan60=9/x

1.732050808=9/x

1.732050808x=9

x=9/1.732050808

x=5.196152421

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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The total volume of ice cream served per cone V=256πcm³

The volume of a cone defines as the space or the capacity of the cone. It is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called an apex or vertex.

Given that radius of a cone is r=4 centimeters.

Ice Cream serves 3 scoops of ice cream in its signature cone.

To calculate the total volume of ice cream cones we have a formula:

V=4/3πr³.

Substitute the radius we get:

V=4/3π(4)³*3

V=4/3π(64)*3

V=256π

Therefore, the total volume of ice cream served per cone V=256π

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The portion of the diagram that illustrated the set A ∪ B ∩ C is given on the  image presented at the end of the answer.

The union operation, symbolized by U, is composed by the elements that belong to at least one of the sets.

The intersection operation, symbolized by ∩, is composed by the elements that belong to all the sets.

Hence, for the set A ∪ B ∩ C, the requirements are given as follows:

The shaded region corresponding to the operation is given at the end of the answer.

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Answer:

Step-by-step explanation:

It is Linear