How do you solve exponential functions with different bases?

The mean of the given data set is 21.7 and the sample proportion of numbers less than the mean is 60%.

Consider the given data set (in the image attached to this answer). We have to find the mean of the data set is, and the sample proportion of numbers. We have been told that any non-integer answers should be entered as decimals, rounded to the tenth place. The means is the average of any data set.

Here, mean = (20.5 +24.2 +18.3 + 1.3 +27+25.5 +21+19.8+27.3+18·4 + 20.5+17-6 +25.5 +23.4 +20.2)/15

Mean = 325.5/15 =21.7

The sample proportion of numbers less than

Mean = 9/100 * 15 %

Answer: 21.7 60%

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Exponential form of 12 is 2. 2. 3. It is based on the prime factorization of the number.

Exponential form is a mathematical operation written as [tex]a^{n}[/tex] involving the base a and an exponent n. In the case where n is a positive integer, exponentiation corresponds to repeated multiplication of the base, n times.

[tex]a^{n}[/tex] =  a × a × a.... n times

In order to write the exponential form we have to write the prime factorization of that number. Prime factorization of the number is that number written as a product of prime numbers or as a product of powers of prime numbers. The exponential form is an easier way of writing repeated multiplication involving base and exponents.

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Answer:

I believe the answer is D

Answer:

  D.  (2x +1)(x -6)

Step-by-step explanation:

You want the expression that is equivalent to 2x² -11x -6.

There are a couple of ways to go at this. One way is to eliminate the answers that make no sense: A and C. We say these are nonsense because they have an overall factor of 2. The coefficient -11 is not a multiple of 2, so there cannot be such a factor.

If you were to examine the remaining choices (after eliminating A and C), you would find the x-term of the product to be ...

  B: 2x(-2) +3(x) = -4x +3x = -x

  D: 2x(-6) +1x = -12x +x = -11x . . . . . the expression we're looking for

If you were to factor this equation, you would look for factors of 2·(-6) = -12 that have a sum of -11. Of course, those are -12 and 1. This means we can rewrite the equation as ...

  2x² -11x -6 = 2x² -12x +x -6

  = 2x(x -6) +1(x -6) . . . . . . . factor by grouping (pairs of terms)

  = (2x +1)(x -6) . . . . . . . . . . matches choice D.

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Answer:

100 should be added as 8100 is square root of 90 ...

In Y=3/4x+3 the Slope is 3/4, the Y-intercept is (0,-3) and the usual form is 3x4y=12. , which does not have a conic section. as opposed to asymptotes.

Use the slope and y-intercept, or two points, to graph the line. 3 / 4 of a slope; y-intercept: (0,-3) Write in formal language. 3 x-4 y=12         Discover the negative reciprocal of the original line's slope.

[tex]$$m_{\text {perpendicular }}=-\frac{4}{3}$$[/tex]

In order to identify the periods during which the equation is increasing or decreasing, graph it. Continued Growth There are no asymptotes since the equation Y=3/4x+3 is not a reasonable expression. There are no asymptotes. Any conic section's form is not compatible with the equation. Not a Conic Section.This subject can't be explored any further. Please double-check the supplied phrase or select a different subject.

[tex]$$y={3}/{4} x-3$$[/tex][tex]$$y={3}/{4} x+3$$[/tex]

Identify the y-intercept = b , y = mx + b. Plot the y-intercept. The focus will be (0, b). Calculate the slope=m of the equation y = mx + b. Create a single step utilizing the rise and run from the slope. Connect those two places with your line.

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Answer:

Skills Practice. Multiplying a Polynomial by a Monomial. Find each product. 1. a(4a + 3). 2. -c(11c + 4). 4a2 + 3a. -11c2 - 4c. 3. x(2x - 5). 4. 2y( y - 4).

Step-by-step explanation:

Double prime is called by different names as per the topics used in Mathematics :

Inches in length , second order derivative in differentiation, conjugate points, transformed coordinates etc.

As given in the question,

Therefore, the double prime is known by many names such as inches in length, second order derivative, conjugate points, transformed coordinates etc.

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A line of best fit can be described by the equation y=mx+b, where m denotes the slope and b the y-intercept. For a better understanding of the idea of approximating the equation of a line of best fit and making predictions, we will look at two examples that show a scatter plot with a line of best fit.

What is a line, exactly?

Having only length and no width, a line is a one-dimensional figure. A line is created from a collection of points that are endlessly stretched in the opposing directions.

                  A two-dimensional plane's two points serve as its determining factors. Collinear points are two points that are located on the same line.

What is the equation for a straight line?

. A straight line has the equation y=mx+c, where c is the height at which the line crosses the y-axis, also known as the y-intercept, and m is the gradient.

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Answer: 3 = 12 , 4 = 2 , 2 = 22
             

Step-by-step explanation: Since t represents the number of tickets purchased, we need to plug that into our equation.

d = -10t + 42

d = -10(3) + 42

We know that d is the balance of the bank account, so if we plug in the number of tickets purchased, we will solve to get the balance of the bank account.

d = -10(3) + 42

d = -30 + 42

d = 12

In this equation, If we purchase 3 tickets, the balance of the bank account would be 12 dollars.

Let's do the last 2 equations using d = -10t + 42.

d = -10(4) + 42

d = -40 + 42

d = 2

In this equation, If we purchase 4 tickets, the balance of the bank account would be 2 dollars.

d = -10(2) + 42

d = -20 + 42

d = 22

In this equation, If we purchase 2 tickets, the balance of the bank account would be 22 dollars.

Answer:16

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

For this question, the x represent the question mark.

8 + (-4) = x

Since positive plus negative equals negative, we subtract.

8 - 4 = x

x = 4

Breanna was biking at a constant rate of 14 miles per hour.

A rate can be defined as the speed at which something happens or changes or the amount or number of times it happens or changes in a particular period.

The formula that describes the relationship between distance (d), rate (r), and time (t) is d = rt.

Now, we will solve for r. From d = rt. Our r will equals to:

= d/t.

Now we compute the rate at which Breanna was biking.

= 84 miles/6 hours

= 14.

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The  pascal’s triangle to expand (3s+2)⁵ is 243s⁵ +810s⁴ + 1080s³ + 720s² + 240s + 32.

What is the expanded form of an expression?

Expanded form, also known as expanded notation, is a method of writing numbers that allows you to see the math value of individual digits. When numbers are separated into individual place values and decimal places, a mathematical expression can be formed.

Most people are introduced to Pascal's triangle via a seemingly arbitrary set of rules. Begin with a 1 on top and 1s running down both sides of a triangle. Each new number is located between and below two other numbers, and its value is the sum of the two numbers above it. The theoretical triangle is infinite and continues indefinitely downward, but only the first six lines are shown in figure 1. More rows of Pascal's triangle are shown in the article's final figure. Another way to look at the triangle is to imagine the first line as an infinite sequence of zeros with the exception of a single 1.Add every adjacent pair of numbers and write the sum between and below them to get successive lines. Pascal's triangle is the non-zero part.

Pascal 's triangle is

1

1,1

1,2,1

1,3,3,1

1,4,6,4,1

1,5,10,10,5,1

The expanded form of (3s+2)⁵ is

= 1×(3s)⁵×2⁰ + 5×(3s)⁴×2¹+ 10×(3s)³×2² +10×(3s)²×2³ + 5×(3s)¹×2⁴+ 1×(3s)⁰×2⁵

=243s⁵ +810s⁴ + 1080s³ + 720s² + 240s + 32

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Perimeter of a semi circle = ñr + d(2r),ñ=22/7,r=?, d=2r

54=22/7 × r +2r

54=3.142r +2r

54=5.142r

r=54/5.142

r=10.5

d=2r

d=2×10.5017

d=21.00cm

======================================================

Explanation:

You are correct in thinking you'll set two things equal to one another. This type of thing happens often in algebra. The question you probably have is: what two things do I set equal?

The key term is "isosceles" which tells us we have two non-parallel sides equal in this trapezoid. In other words, we ignore the parallel sides.

The non-parallel sides of a trapezoid are known as the legs.

The legs in this case are

Set those expressions equal to one another and solve for the variable y.

AB = CD

7y-4 = 8y-18

-4+18 = 8y-7y

14 = y

y = 14 is the final answer

----------------------

Check:

Both legs AB and CD are 94 units long to confirm this trapezoid is indeed isosceles. The answer is confirmed.

Side note: as mentioned earlier, we completely ignore BC = 4y-6. It was probably put in there as a distraction.

The  number of times you would expect to roll a 5 if you rolled a fair die 300 times is B. 50.

We should note that that a fair die has a  six sided cube and the number that is on the die faces start from 1 to 6 .

Since each of the die  faces consists of a probability of 1/6 now let find the number of times to roll a die.

Expected number of times = 300 × 1/6

Expected number of times = 50

Therefore we can conclude that the expected number of time to rolled the die is B. 50 times.

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Answer: (5, -2)

Step-by-step explanation:

They give you two equations with two variables. You can solve this using elimination or substitution. However, it seems as though the problem wants you to do it through elimination. On the right, you have the equation

    6x + 10y = 10

+  -6x - 24y = 18

After add these equations, you get -14y = 28. By dividing both sides by -14, you get y = -2. You can plug y = -2 back into either one of the original equations, and solve for x.

x = 5.

So your answer is (5, -2)

[tex]s=a+b+c[/tex] solve for b

Flip:

[tex]a+b+c=s[/tex]

Add -a to both sides:

[tex]a+b+c+-a=s+-a[/tex]

[tex]b+c=-a+s[/tex]

Add -c to both sides:

[tex]b+c+-c=-a+s+-c[/tex]

[tex]\fbox{b = -a - c + s}[/tex]

Answer:

S - c - a = b or b = S - c - a ( same answer just written differently)

Step-by-step explanation:

S = a + b + c move the unwanted exponents to the other side

S = a + b + c / - c

S - c = a +b / - a

S - c - a = b

The rules for substitution are, first simplify the given equation, solve one of the equations for any unknown value, substitute the step 2 solution in another equation, solve the new equation, and finally solve the equation to find the second variable.

The substitution method is the algebraic method to solve different linear equations. In this method, the value of one variable from either of the equation is substituted in the other equation.

The following steps of rules are used to solve an equation by substitution method:

Step 1. Simplify the given equation by removing the parenthesis.

Step 2. Solve one of the equations for any unknown value.

Step 3. Substitute the step 2 solution in the other equation.

Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.

Step 4. Finally, solve the final equation for the second variable.

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The percent of the dresses that are for films set in the 1700s or during the civil war era is; 75%

Percentage is normally calculated by dividing the value by the total value, and then multiplying the result by 100. It is given by the expression; Percentage = (value / total value) * 100%

Now, we are told that;

Number of movie dresses kept = 240 dresses

Fraction used for  movies that take place in the 1700s = 3/5

Percentage used for movies in the civil war era = 15%

Thus;

Number of dresses in the 1700 = 3/5 * 240 = 144

Number of dresses for the civil era = 15% * 240 = 36

Thus;

Total for civil era and in the 1700s = 144 + 36 = 180

Thus;

Percentage for either period = 180/240 * 100% = 75%

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The quadratic equation has two solutions, x1 = 3.44 and x2 = 0.56

Quadratic equations are the ones with degree 2. The standard form of a quadratic equation with variable x is ax2 + bx + c = 0, where a ≠ 0. These equations can be solved by splitting the factorisation, completing the square, or by quadratic formula method.

2x²-8x+8 = -3

2x²-8x+8+3 = 0

2x²-8x+11=0

Using the quadratic formula

x = (- b ± √(b² - 4ac)) / 2a

where a = 2

b = -8

c = 11

x = (-(-8) ± √(11² - 4(2)(11))) / 2(2)

x = (8 ± √(121 - 88)) / 4

x = (8 ± √(33))/4

x 1 = (8 + √(33))/4

x1 = (8 + √(33))/4

x1 = (8 + 5.75)/4

x1 = 13.75 / 4

x1 = 3.44

x2 = (8 - √(33))/4

x2 = (8 - 5.75)/4

x2 = 2.25/4

x2 = 0.56

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The slope of ef and gd can be found by using the formula: slope = (y2 - y1) / (x2 - x1) where ef = (x1, y1) and gd = (x2, y2) are the coordinates of the points e and g.

       - The two bases (the parallel sides) are congruent.

       - The two legs (the non-parallel sides) are congruent.

       - The diagonals of the trapezoid bisect each other.

       - The midpoints of the legs are congruent, since the legs are congruent.

       - The midpoints of the bases are congruent, since the bases are congruent.

       - The segments joining the midpoints of the legs and the bases are congruent, since they are both the same distance from the midpoint of the bisected diagonal.

        The slope of ef and gd can be found by using the formula: slope = (y2 - y1) / (x2 - x1) where ef = (x1, y1) and gd = (x2, y2) are the coordinates of the points e and g.

the slope of ef = -1/slope of gd.

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The quadrant of the given point (2,3) is given A I ( that is first quadrant ).

As given in the question,

Given point is equal to :

Point ( 2, 3 )

Conditions of the quadrant in the coordinate plane is given by :

Let ( x ,y ) be the coordinates in the coordinate plane.

In the first quadrant :  ( x , y ) both x and y are positive.

In the second quadrant :  ( -x , y )  x is negative and y is positive.

In the third quadrant :  ( -x , -y ) x is negative and y is negative.

In the fourth quadrant :  ( x , -y )  x is positive and y is negative.

Here in the given point ( 2,3 ) both x and y are positive.

Given point lies in the first quadrant.

Therefore, the quadrant of the given point (2,3) is equal to A I ( that is first quadrant ).

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Prior to selecting an input value range, create the table. Replace each input value with its equivalent in the supplied equation's left-hand column.

Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.

given

Prior to selecting an input value range, create the table.

Replace each input value with its equivalent in the supplied equation's left-hand column.

The output value can be found by analyzing the equation in the middle column.

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The graph of function y = -1.5x, for x = -3, 4, 5, and 6 is shown.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
y = -1.5x.

Substitute the value of x = -3, 4, 5, and 6.

x = -3
y = -1.5(-3)
y = 4.5

Similarly,
x = 4   ;y = -6

x = 5  ;y = -7.5
x = 6  ;y = -9

Thus, the graph for the value of has been shown,

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The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

f(x) = 4 - x² and g(x) = 6

The function (g - f)(x) will be given as,

(g - f)(x) = 6 - 4 + x²

(g - f)(x) = 2 + x²

The value of the function (g - f)(x) at x = 3 will be give as,

(g - f)(x) = 2 + (3)²

(g - f)(x) = 2 + 9

(g - f)(x) = 11

The value of the function (g - f)(x) = 6 - 4 + x² at x = 3 will be 11.

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The circumference of the jar is 56.57cm.

The radius of the jar is 9 cm.

A cylinder is a three-dimensional object. It is a prism with a circular base.

The curved surface area of a cylinder = 2πrh

Where:

1584 = 2 x 3.14 x 28 x r

r = 1584 / (2 x 3.14 x 28)

r = 9 cm

Circumference = 3.14 x diameter

diameter = 2 x radius

3.14 x 2 x 9 = 56.57cm

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Answer:

0.011

Step-by-step explanation:

To convert a percentage into a decimal, simply divide by 100;

Some examples are:

1% = 0.01

5% = 0.05

10% = 0.1

50% = 0.5

N.B. finding a percentage of a number is multiplying by the decimal form, so, e.g. 1.1% of 1000 is:

1000 × 0.011 = 11

Answer:

0.011

Step-by-step explanation:

To convert a percentage to a decimal, you must divide the percentage by the number 100.

Therefore, 1.1% / 100 = 0.011.

(If the question was the other way around and you wanted to turn a decimal into a percentage. All you have to do is the opposite. When you have a decimal multiply it by 100 to get a percentage.)

Hope this helped you!

The end behavior of a graph with an odd degree and a positive leading coefficient is that the graph will tend to increase infinity as x approaches positive infinity and decrease to negative infinity as x approaches negative infinity.

This end behavior of a graph is due to the fact that when the degree is odd, the leading coefficient acts as a multiplier for the highest degree term, making its contribution to the graph’s y-value the largest and most dominant. For example, if the equation of the graph is y = 4x^3 + x^2 – 7x + 5, then the end behavior of the graph will be increasing to positive infinity as x approaches positive infinity and decreasing to negative infinity as x approaches negative infinity. To calculate this, we can use the equation y = 4x^3. When x = 1000, y = 4,000,000,000. As x increases, y will continue to increase to positive infinity. When x = -1000, y = -4,000,000,000. As x decreases, y will continue to decrease to negative infinity.

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