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The equivalent expression to the given expression is 3⁶/9¹⁵.  

A mathematical expression made up of variables, coefficients, constants, and operations like addition, subtraction, multiplication, and division is called an algebraic expression.  

Equivalent expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are entered into the formula.    

Here we have

=> [tex][ \frac{9^{-3} }{ 3^{-2} 9^{2} } ]^{3}[/tex]  

We can solve the above expression as follows

=> [tex][ {9^{-3} \times3^{2} \times 9^{-2} ]^{3}[/tex]  

=> [tex][ {9^{-5} \times3^{2} ]^{3}[/tex]  

=> [tex][ {9^{-15} \times3^{6} ][/tex]  

=> [tex]\frac{ 3^{6}}{9^{15} }[/tex]    

Therefore,

The equivalent expression to the given expression is 3⁶/9¹⁵.  

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Answer: (- 1, 3 )

Step-by-step explanation:

The function f(x) = x² is called  as the quadratic function.

In math the term function is called as the relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Here we need to identify the function type of the given function f(x) = x².

As we all know that the polynomial function with one or more variables in which the highest exponent of the variable is two is known as quadratic function.

The general form of the quadratic function is written as,

=>  f(x) = ax² + bx + c

where the value of a ≠ 0.

Based on the general form we have identified that the given function

=> f(x)  = x²

is known as the quadratic function.

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Answer:

In this algebraic expression, "Negative x" represents a term with a coefficient of -1, and "x" represents a variable. "10.2" represents a constant term. The "+" sign represents addition.

Step-by-step explanation:

"minus one-half x" represents a term with a coefficient of -0.5 and variable "x". "+ y" represents a term with variable "y" and a coefficient of 1.

Simplifying the expression by combining like terms:

-x - 0.5x = -1.5x

Negative x + 10.2 - one-half x + y = 10.2 - 1.5x + y

Rebecca and Mohammed sold 16 shirts and 6 hats.

To solve this problem, we can write an equation on the information provided. Let x be the number of shirts sold and y be the number of hats sold. Such that:

x + y = 22 {the total number of pieces sold}

12x + 9y = 350 - 125 {the total profit, including the savings they started with}

We can solve for one variable in terms of the other using the first equation:

x = 22 - y

Then we can substitute this expression into the second equation:

12(22 - y) + 9y = 350 - 125

Simplifying this equation:

264 - 12y + 9y = 350 - 125

y = 6

Therefore, Rebecca and Mohammed sold 6 hats and 16 shirts

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Answer:

The geometric sequence is 15, 9, 27/5, 81/25, 243/125

Step-by-step explanation:

The probability that bin 1 contains exactly 3 balls would be 0.015. Probabilities can be expressed as fractions, decimals, or percentages, and they can be used to make predictions or to quantify uncertainty.

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain. For example, if the probability of it raining tomorrow is 0.3, it means that there is a 30% chance of it raining tomorrow. In addition, probability theory is a branch of mathematics that studies the probability of events, and it plays an important role in many areas such as statistics, finance, and science.

The probability that bin 1 contains exactly 3 balls out of the 10 balls placed is given by the binomial probability mass function with parameters n = 10 and k = 3, and probability of success p = 1/20. Therefore, the probability is given by:

(10 choose 3) * [tex](1/20)^3[/tex] * [tex](19/20)^7[/tex] = 120 * (1/8000) * [tex](19/20)^7[/tex] = 120/8000 = 0.015

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The solution of the equation in the interval [0, 2π] is π or 180.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given the equation;

Sinx = cosx + 1

Then Square both sides of the equation;

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms;

1-1-cos²x-cos²x-2cos x  = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = 180 degrees

Hence, the value of x = π

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Answer:

15, 80

Step-by-step explanation:

Angle of triangle=180 degrees

180-85=95

3x+16x=95

19x=95

x=95/19

x=5

3x=15

16x=80

Yes, it is possible to form a triangle with side lengths 3, 4 and 5 units and we can form a right triangle.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Given that, a triangle with side lengths 1, 5 and 3 units

The properties of the triangle are:

1) Here, 5-1>3

No, we can not form a triangle with 1, 5 and 3.

2) A triangle with side lengths 3, 4 and 5 units

Here, 5-3<4

It is possible to form a triangle.

Now, c²=a²+b²

5²=3²+4²

25+25

With side lengths 3, 4 and 5 units right angle triangle can be formed.

Yes, it is possible to form a triangle with side lengths 3, 4 and 5 units and we can form a right triangle.

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The number of students who liked cake batter frozen yogurt is 135.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

From the given diagram the sum of all the percentages except the Cake batter is (28.5 + 21.5 + 13 + 10)% = 73%.

Therefore, The percentage of students who liked Cake batter is,

= (100 - 73)%.

= 27%.

So, The number of students who liked cake batter is,

(27/100)×500.

= 27×5.

= 135.

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It would take a car 5 hours to cover 200 km at a speed of 40 km/h.

The car moves at a constant speed of 40 km/hr.

The car has to travel a total distance of 200 km.

As we know the formula of speed is distance/time,

Hence, s = d/t km/hr

So t = d/s hr

Let speed, distance and time be s, d, t respectively.

So by putting the values,

time t = 200/40 = 5 hours

Hence it can be said that the car would cover 200 km at the speed of 40 km/hr in 5 hours.

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The value of k if one root of the quadratic equation x²+kx-8=0 is-4 is 2.

The equation x^2+kx-8=0 is a quadratic equation and of the form

ax^2 + bx + c ;where a =1 , b=k and c= -8.

Now, we know that the sum of the roots of a quadratic equation = -b/a

and the product of the roots is = c/a.

Now, let the other root of this equation be y.

Then , by above properties,

(-4) + y = -k/1 =-k ..... (1)

And, (-4)y = -8/1=-8....(2)

From 2, we get y = 2.

Putting this value in (1), we get -

(-4) + 2=-k

So, k = 2.

Thus, if one of the roots of this equation -4 , then the other root must be 2 and so , the value of k is 2.

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The complete question is:

Which of the following is the value of k,if one root of the quadratic equation X2+kx-8=0 is-4? a) 0 b) 4 c) 0 or 4 b) 2

Answer: The value of x is 43 degrees

The solution set for the given system of equations is (1, 5).

Given is the system of equations as -

4x + 3y = 19

- 3x + y =2

The given system of equations is -

4x + 3y = 19

- 3x + y =2

Now, we can write -

- 3x + y = 2

y = 2 + 3x

Then, the equation 4x + 3y = 19, will become -

4x + 3(2 + 3x) = 19

4x + 6 + 9x = 19

13x = 13

x = 1

Then, the value of {y} will be -

y =2 + 3

y = 5

Therefore, the solution set for the given system of equations is (1, 5).

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The current age of Sam is 30 years and Harry is 10 years.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign. It shows the relationship of equality between the expression written on the left side with the expression written on the right side. In every equation in math, we have, L.H.S = R.H.S (left hand side = right hand side). Equations can be solved to find the value of an unknown variable representing an unknown quantity. If there is no 'equal to' symbol in the statement, it means it is not an equation. It will be considered as an expression.

Let Sam's age be y years and Harry's age be x years.

Sam is currently three times harry's age.

The equation formed: y = 3x

Sam's age is also 10 more than twice harry's age.

The equation formed: y = 2x + 10

Substitute the value of y from first equation in second equation:

3x = 2x + 10

x = 10

Put the value of x in first equation:

y = 3x = 3*10 = 30

Thus, the current age of Sam is 30 years and Harry is 10 years.

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The equation that models the problem is given as follows:

s = 120/1.5.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

For this problem, the variables are given as follows:

Hence the equation used to obtain the number of stripes that Murphy will paint is given as follows:

1.5s = 120

s = 120/1.5

s = 80. (solution).

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An estimate of the total number of televisions that would need repairing in Clover City is A. Between 546,000 and 972,000 televisions.

Thanks to the research by the local television repair shop, we know that on average, 2.53 ± 0.71 per family will need to be fixed.

The lower bound of this mean range would be:

= ( Mean - error ) x Number of households

= ( 2. 53 - 0. 71 ) x 300, 000

= 546, 000 televisions

The upper bound of the mean range is:

= ( 2. 53 + 0. 71 ) x 300, 000

= 972, 000 televisions

The estimate for televisions to be repaired is therefore between 546,000 and 972,000 televisions.

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The number of students who chose football exists 38.5.

A ratio is a tool for comparing like-kind quantities or illustrating relationships between them. To compare similar items, we employ ratios.

It's crucial to keep in mind that the ratio of one value to another is the same as the real value in relation to the other when calculating values using supplied ratios.

The percentage of students that chose rugby and tennis is listed as 8:17, which means that out of every 25 students (8 + 17), 8 chose rugby and 17 chose tennis. The ratio of 17 would now be replaced by the value 51 as the total number of students who picked tennis was 51. Although we do not yet know the total number of people that choose rugby, we can draw down an equation as shown below;

17/25 = t/x

Where t is the number of tennis players as represented by ratio 17 and x is the total number of both tennis and rugby players as represented by 25.

By cross multiplication we now have

17 × x = 25 × 51

x = (25 × 51)/17

Simplifying the above equation, we get

17x = 1275

x = 75

If 84 students participate in both rugby and tennis, but only 57 of them play tennis, the number of rugby players is calculated as follows.

Let the equation be r = x - t

simplifying the equation, we get

r = 75 - 51

r = 24

Given that 25 students participated in rugby and that the proportion of football players to rugby players is 3:2, the relationship can be mathematically stated as follows;

3/5 = r/y

Where r is the total number of rugby players and y is the total number of both football and rugby players

2/5 = 25/y

By cross multiplication you now have

y = 62.5

If the total number of football and rugby players is 63 and out of these 27 play rugby only, then the number of football players is derived as;

f = y - r

f = 62.5 - 24

f = 38.5

Therefore the number of students who chose football is 38.5.

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The conclusion sum of the measures of the angles 4, 5 and 11 is equal to 180 degrees not be accurate to the drawing.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Supplementary angles are those angles that sum up to 180 degrees

so angle 1 and 4 are supplementary angles.

Congruent angles are two or more angles that are identical to each other

so angles 10 and 1 are congruent.

angles 5 and 7 are congruent.

The three interior angles of a triangle will always have a sum of 180°.

The sum of the measures of the angles 4, 5 and 10 is equal to 180 degrees.

The sum of the measures of the angles 4, 5 and 11 is not equal to 180 degrees.

Hence, the conclusion sum of the measures of the angles 4, 5 and 11 is equal to 180 degrees not be accurate to the drawing.

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Answer:

60, pi/2, 2pi

Step-by-step explanation:

Q4: pi/3 * 180/pi = 180/3 = 60 degrees

Q5: 90/1 * pi/180 = pi/2 = 1.5708

Q6: The formula of the central angle is theta = S/r

so it is 2pi.

To find the domain of the function F(x) = - √x—5 +10, we need to find the set of x-values for which the expression inside the square root is defined. The expression inside the square root is x - 5. For the square root of a real number to be defined, that number must be non-negative, so x - 5 ≥ 0, or x ≥ 5. Therefore, the domain of the function is x ≥ 5.

What is an example of a domain and range?

Think about the relationship (0,7,0,8,(1,7,(1,8,(1,9),(2,10)). The relation is shown in this case as a set of sorted pairs. The set of x -coordinates, 0, 1, and 2, and the set of y -coordinates, 7, 8, 9, and 10, define the domain and range, respectively.

To find the range of the function F(x) = - √x—5 +10, we need to find the set of y-values that the function can output. The function starts with the square root of x-5, which is always non-negative, and then subtracts it from -5 and adds 10. Therefore, the range of the function is all real numbers y, such that y ≥ 10.

So the domain of the function F(x) = - √x—5 +10 is x ≥ 5 and the range of the function is y ≥ 10.

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An ensemble approach called bagging combines the predictions from all models after fitting each one to a distinct portion of a training dataset.

When the standard deviation is low, the data tend to cluster around the mean; when it is large, the data are more spread. Calculated using the standard deviation, the data's divergence from the mean value is determined. It is useful for contrasting data sets with possibly the same mean but a distinct range. For instance, the mean of the two following numbers is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. But it's clear that the second is more diffused. The standard deviation shows how erratic the data is. It conveys the difference between each observed value and its mean.

given

An variation of bagging called random forest additionally randomly chooses the subsets of features that are applied to each data sample.

With the addition of splitting on a random subset of characteristics, random forest outperforms bagging by decorrelating the trees.

As a result, the model only takes into account a small subset of its properties at each branch in the tree rather than all of them.

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The unit price is $6.55 per pair of pants

Kristen's dry cleaning charge a fee of $32.75 for 5 pairs of pants

The unit price of the pants can be calculated as follows

32.75= 5

x= 1

Cross multiply both sides

5x= 32.75

x= 32.75/5

x= 6.55

Hence the unit price of the pants is $6.55

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The unit price for the cleaning fee is $6.55 per pair of pants

An equation shows the relationship between numbers and variables in an expression.

Unit rate is the ratio of two quantities. The denominator of a unit rate is always equal to one.

Kristen's dry cleaning fee was $32.75 for 5 pairs of pants. Hence:

Unit price = total cleaning fee / number of pants

Substituting values gives:

Unit price = $32.75/5 pairs of pants = $6.55 per pair of pants

The Unit price is $6.55 per pair of pants

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The probability of selling at least 30 widgets is 0.0468.

The problem is asking us to use a binomial distribution to estimate the probability of selling at least 30 widgets given the information provided.

A binomial distribution is a probability distribution of the number of successes in a fixed number of trials.

Where n = 200 (number of customers arriving and purchasing a widget from the store each day) and

p = 0.1667 ( probability of a customer buying a widget)

We are looking for the probability of selling at least 30 widgets, which is equivalent to finding the probability of selling 30 or more widgets.

This can be calculated using the cumulative probability formula for a binomial distribution:

P(X >= 30) = 1 - P(X < 30) = 1 - Σ (nCx)(p^x)(1-p)^(n-x) from x=0 to 29

We can use a calculator or a software to calculate this probability. The result is 0.0468 rounded to 4 decimals.

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Answer: C

Step-by-step explanation:

cube root of 8x^6y^12

equals 2x^2y^4

The graph that displays the altitude of a skydiver as he is taken up in a plane and then jumps:

A graph has time on the x-axis and altitude on the y-axis.

The correct option is A.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Given:

We have a graph.

The graph is given in the attached image.

From the graph;

A graph has time on the x-axis and altitude on the y-axis.

Therefore, x-axis shows the time and y-axis shows altitude.

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Answer:

c

Step-by-step explanation:

(5x + 2) and (3x + 18) are vertically opposite angles and are congruent, so

5x + 2 = 3x + 18 ( subtract 3x from both sides )

2x + 2 = 18 ( subtract 2 from both sides )

2x = 16 ( divide both sides by 2 )

x = 8

Similarly

(5y + 68) and (3y + 96) are vertically opposite angles and are congruent, so

5y + 68 = 3y + 96 ( subtract 3y from both sides )

2y + 68 = 96 ( subtract 68 from both sides )

2y = 28 ( divide both sides by 2 )

y = 14

Answer: (y-6)/3

Step-by-step explanation:

6x = 2y - 12

x = (2y - 12)/6 = (y-6)/3

(I can only put x in terms of y because you only provided one equation)