Find m<1
Not sure on this!

Base 3 logarithm of 81 equals 4 .The logarithmic form, written as log of "b" to base "a" is equal to "n," .

How many times must one "base" number be multiplied by itself in order to get another specific number is the subject of the mathematical expression known as a logarithm (or log). Mathematics includes both logarithms and logs. They share a connection with exponential functions. Logarithms are the opposite of exponentiation because they reveal the exponent (or power) required to create a given number. They were helpful in the past for splitting or multiplying huge numbers.

given

Base 3 logarithm of 81 equals 4 .

Therefore, the logarithmic form, written as log of "b" to base "a" is equal to "n," may be expressed in exponential form as  a = b.

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An equation that simplifies to the square root of -18 can be written as y = 3{√2}i.

The {i} in a complex number z = a + ib stands for -

i = [tex]$\sqrt{-1}[/tex]

i² = - 1

Given is the square root of -18.

An equation that simplifies to the square root of -18 can be written as -

y = √(- 18)

y = √(- 1) x √18

y = √(i)² x 3√2

y = 3{√2}i

Therefore, an equation that simplifies to the square root of -18 can be written as y = 3{√2}i.

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When 378 divided by 5 the quotient is 75 and the remainder is 3.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items.

Given that, dividend =378 and divisor =5.

Now, 378/5

5|378|75

  375

______

     3

Here, the quotient is 75 and the remainder is 3

Therefore, when 378 divided by 5 the quotient is 75 and the remainder is 3.

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Dwayne's percentage favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.

10% is a comparison number that means one tenth of any amount. The hundredth component, one percent (symbolized as 1%), is denoted by 100 percent, whereas 200 percent denotes double the quantity stated. In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100. If we want to calculate a percentage of a number, we should multiply the result by 100.

Dwayne's favorite eatery. Overall, the restaurant had 25 specials, with salmon filets accounting for 24% of those. The eatery served 6 salmon filets.

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It is 1/10 probable that two consecutive jellybeans will be red.

Simply put, the probability is the probability that something will occur. When we don't know how an event will turn out, we can discuss the probability or likelihood of several outcomes.

Biostatistics is the analysis of events that match a probability distribution.

So, the likelihood of receiving a red jellybean in two of the three trials will help you determine the likelihood of two jellybeans being red.

Keep in mind that you will require a likelihood of not turning red in one try.

1 - 4/10 (getting a red)

2 - 3/9 (getting a red)

3 - 6/8 (not getting a red)

The solution remains the same regardless of the order:

1 - 6/10 (not getting a red)

2 - 4/9 (getting a red)

3 - 3/8 (getting a red)

Add these up to calculate the likelihood:

4/10 x 3/9 x 6/8 = 1/10

Therefore, it is 1/10 probable that two consecutive jellybeans will be red.

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Answer:

2,112 [tex]ft^{3}[/tex]

Step-by-step explanation:

Volume of the cube

(12)(12)(12) = 1728

Volume of the pyramid

1/3(12x12x8) = 384

1728 + 384 = 2112

Adam will be paying by installment, and will pay the amount of $140 of his last payment if he pays the $10 minimum monthly payment up until the last payment.

Payment by installment is when one pay small sums of money at regular intervals over a period of time, rather than paying the whole amount at once.

Adam made a down payment of $100 out from the total amount of $1,670, so he will have to pay a balance of $1570 in 12 years.

The minimum monthly payment is $10, and he will have 144 months to pay up the balance.

If Adam pays $10 for 144 months, he will pay up a total of $1440 having a balance of $130 to pay after the deadline.

Therefore, if Adam makes the minimum monthly payment up until the last payment, he would have paid up $1430 which is $10 in 143 months and will pay the amount of $140 of his last payment.

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The fraction of the distance from Mrs. Thompson's house to the library that she biked was 2/3.

A fraction is a small part of a larger whole.

A fraction can represent a proportion of a larger number of units.

Fractions are quotients resulting from division operations.  Where the numerator is less than the denominator, it is called a proper fraction.  Otherwise, it is an improper fraction.  There are also complex fractions.

Fractions can be converted to decimals and percentages.

Total distance from Mrs. Thompson's house to the library = 3/4 kilometers

The distance biked by Mrs. Thompson = 1/2 kilometer

The fraction of the distance from the home to the library biked = 2/3 (1/2 ÷ 3/4)

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The 4 quadratic methods are factoring, completing the square, using the quadratic formula, and graphing.

Quadratic equations are a type of mathematical equation that can often be solved using a variety of methods. The four main methods used to solve quadratic equations are factoring, completing the square, using the quadratic formula, and graphing.

Factoring is a method that involves finding the factors of the quadratic equation in order to solve for the variables.

Completing the square is a method that involves rewriting the equation in the form of (x + a)² = b in order to solve for the variables. The quadratic formula is a method that involves using the formula ax² + bx + c = 0 to solve for the variables.

Finally, graphing is a method that involves plotting the equation on a graph and analyzing the graph in order to solve for the variables.

These four methods are the main ways to solve quadratic equations, and each method has its own set of advantages and disadvantages.

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The price of gasoline next year will be 4.575.

The function of the price of gasoline next year will be a function of the current price and the percentage increase.

Price of gasoline next year = (1 + percent increase/100) x current price

Price of gasoline next year = 3.75 x (1 + 22/100)

Price of gasoline next year = 3.75 x (1 + 0.22)

Price of gasoline next year = 3.75 x 1.22

Price of gasoline next year = 4.575

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The new coordinates of C is (-2, 2).

Reflection is a type of geometric transformation where the figure is flipped. In other words, a figure when undergoes reflection becomes it's mirror image.

The coordinate of C is (1, -2).

A point (x, y) when reflected over the X axis becomes (x, -y).

C becomes (1, 2) when reflected over the X axis.

Translation is done 3 units left.

Translation of a point towards left and right changes the x coordinate and translation towards up and down changes the y coordinate.

New coordinate of C is (1 - 3, 2) = (-2, 2).

Hence the coordinates of C is option B (-2, 2).

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1) The first step in construction of the parallel line is;  Construct another point Q different from point P that is not on the line.

2) The next step is; 4. With the compass opened to at least half of CD, draw arcs centered at C and D and label the point of intersection of the arcs E.

Parallel lines are defined as the lines that do not intersect or meet each other at any given point in a plane. This means that the lines are always parallel and equidistant from each other.
The steps to construct a parallel line passing through point P is as follows;

Step 1: Draw Line AB as shown in the figure.

Step 2: Take point P outside the line AB  as shown in the figure.

Step 3: From P to AB draw a perpendicular line PQ passing through AB.

Step 4: Now at point P, make an angle of 90 degrees and extend the line EF both sides of  P.

Step 5: EF is parallel line to AB passing through P

Looking at the options and comparing with the steps above, we can say that;

1) First step is option 2

2) Next step is option 4

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The friends does perry have could be 16.

What is linear equation ?

linear equation if the  highest degree of an equation is 1 , it is called as linear equation .

Given perry won 58 lollipops playing basketball .

He later gave three to each of his friends.

lets his number of friends could be x .

so,

58 - 3x  = 10

3x = 58 - 10

3x = 48

x = 16

Hence the friends does perry have could be 16

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The friends does perry have could be 16.

linear equation if the  highest degree of an equation is 1 , it is called as linear equation .

An equation is a mathematical statement that asserts the equality of two expressions. It typically consists of two parts, separated by an equals sign (=). For example, the equation 2x + 3 = 7 is a statement that the expression 2x + 3 is equal to the expression 7.

Given perry won 58 lollipops playing basketball .

He later gave three to each of his friends.

lets his number of friends could be x .

so,

58 - 3x  = 10

3x = 58 - 10

3x = 48

x = 16

Hence the friends does perry have could be 16

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The type of data expressed in the example is ordinal data.

This is an example of ordinal data, as it is data that is expressed on a scale from 1 to 5. Ordinal data is useful for comparing objects or ideas in relation to each other, and is often used to indicate levels of preference or satisfaction. In this case, the data is used to compare the reliability of two travel agents.

Ordinal data is a type of data where the values are ranked in order of magnitude. In the example given, the company has expressed their belief on a scale from 1 to 5, with higher numbers representing a higher level of reliability. Therefore, this type of data is considered ordinal.

The type of data expressed in the example is ordinal data.

Ordinal data is a type of data where the values are ranked in order of magnitude.

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(a) Expected number of repairs per year is 0.33 (b) Standard deviation of number of repairs per year is 0.749, (c) The mean and standard deviation of annual expense are $136.55 and $26.217 respectively.

Standard deviation is a measure in statistics which measures the amount of deviation a set of data has with respect to their mean.

(a) Expected number of repairs for the freezer per year is the sum of the product of number of repairs to their probability.

E(Repairs) = (0 × 0.80) + (1 × 0.11) + (2 × 0.05) + (3 × 0.04)

                 = 0.33

(b) Standard deviation of number of repairs per year can be calculated as,

SD(Repairs) = [tex]\sqrt{[(0 - 0.33)^{2}(0.8)]+[(1-0.33)^{2}(0.11)] + [(2-0.33)^{2}(0.05)]+[(3-0.33)^{2}(0.04)] }[/tex]

= √ (0.5611)

= 0.749

(c) Mean of the restaurant's annual expense with service contract is,

Mean = Expected cost = $125 + ($35 × 0.33) = $136.55

Standard deviation of the restaurant's annual expense with service contract is,

SD = [tex]\sqrt{35^{2}(0.5611) }[/tex] = 35 × 0.759 = 26.217

Hence the expected number of repairs is 0.33, standard deviation of number of repairs is 0.749, mean and standard deviation of annual expense is $136.55 and $26.217 respectively.

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The exponential decay model is found by solving for the time constant in the exponential decay equation.

The exponential decay equation is y(t)=y0e^{-kt}, where y0 is the initial value, k is the rate constant, and t is the time. The time constant is found by solving for t when y(t)=y0/2. This gives t=-ln(2)/k.

In mathematics, exponential decay refers to the process of decreasing an amount by a constant percentage rate over time. It can be expressed as y=a(1-b)x, where y is the final amount, an is the original amount, b is the decay factor, and x is the time elapsed.

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The value of [tex]b=6[/tex]

It is given that [tex]a[/tex] varies directly to [tex]b[/tex]

So, we can write [tex]a=kb[/tex]  ([tex]k[/tex] = constant)

We know that [tex]a=7[/tex] when [tex]b=2[/tex]

that is [tex]7= 2k[/tex]

          [tex]k=\frac{7}{2}[/tex]

so when [tex]a=21[/tex]

                    [tex]a=kb[/tex]

substitute the value of [tex]a[/tex] and [tex]k[/tex]

 that is     [tex]21=\frac{7}{2} b[/tex]

                    [tex]b=6[/tex]

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a) P20 is the 20th percentile, which separates the lowest 20% of the data from the highest 80%. To find P20, you would need to put the data in numerical order and find the value at the 20th percentile.

b) P67 is the 67th percentile, which separates the lowest 67% of the data from the highest 33%. To find P67, you would need to put the data in numerical order and find the value at the 67th percentile.

c) 34 is the 34th percentile, which separates the lowest 34% of the data from the highest 66%. It is the value at the 34th percentile

d) A boxplot is a graphical representation of a dataset that shows the minimum, first quartile, median, third quartile, and maximum of the data. To create a boxplot, you would need to put the data in numerical order, then calculate the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of the data. These values are then plotted on a graph, with the box representing the interquartile range (Q3 - Q1) and the whiskers representing the minimum and maximum values. The outliers(if any) will be plotted as dots

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Vectors V1=(22,15) and v2=(-2,4) are not orthogonal.

Two vectors are said to be orthogonal if they are perpendicular

to each other. i.e. the dot product of the two vectors is zero.

Given vectors are:

V₁ = (22,15)

V₂ = (-2,4)

Dot product of V₁ and V₂ = (22,15).(-2,4) = 22×-2 + 15×4

Part 1:

Multiplying x-coordinates of vectors-

(22×-2) = -44

Multiplying y-coordinates of vectors-

(15×4) = 60

Part 2: Adding the products = -44+60 = 16

Part 3: If the dot product of two vectors is zero, then the two vectors are orthogonal.

But the dot product from the above calculation is 16 means vectors are not orthogonal.

Hence, the two vectors are not orthogonal.

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Answer: The equation of the perpendicular bisector of AB is 3x+7y-77=0

A line equation is an algebraic representation of a set of points that together form a line in a coordinate system. Multiple points that together form a line on the coordinate axis are represented as a set of x,y variables to form an algebraic equation called a one-line equation.

Equation of line⇒[tex](y-y1)=\frac{(y2-y1)}{(x2-x1)} (x-x1)[/tex]

Midpoint of line⇒[tex]\frac{(x1+x2)}{2}, \frac{(y1+y2)}{2}[/tex]

Step-by-step explanation:

Line CD⊥AB

Equation of AB⇒ [tex]\frac{y+10}{x-4} =\frac{15-1}{10-4} \\[/tex]

                        ⇒ [tex]\frac{y+10}{x-4} =\frac{14}{6}[/tex]

                        ⇒ [tex]\frac{y+10}{x-4} =\frac{7}{3}[/tex]

                        ⇒ 3(y+10)=7(x-4)

                        ⇒ 3y+30=7x-28

                        ⇒ 7x-3y=30+28

                        ⇒ 7x-3y=58

Midpoint of AB⇒  [tex]\frac{4+10}{2} , \frac{1+15}{2}[/tex]

                         ⇒ [tex]\frac{14}{2}, \frac{16}{2}[/tex]

                         ⇒ (7, 8)

Slope of CD⇒  [tex]\frac{-1}{slope of AB}[/tex]

Slope of AB⇒ [tex]\frac{-7}{-3}[/tex]

                   ⇒ [tex]\frac{7}{3}[/tex]

Slope of CD⇒ [tex]\frac{-3}{7}[/tex]

Equation of CD⇒ [tex]y-8=\frac{-3}{7} (x-7)[/tex]

                        ⇒ 7(y-8)=-3(x-7)

                        ⇒ 7y-56=-3x+21

                        ⇒ 3x+7y-56-21=0

                        ⇒ 3x+7y-77=0

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Answer:

E = 102

Step-by-step explanation:

1) Write down what angles you already know

A = 38 (given)

D = 26 (given)

B = 90

2) Work out the angles in the triangle

A triangle has 180 degrees so...

3) Work out the angles on the straight line

From the previous calculation we know that C = 52 (as it was the remaining angle)

Angles on a straight line should add up to 180 and we are given that D = 26...

Hope this helps, have a great day!

Answer:

Step-by-step explanation:

In the figure, angle A measures 38

degrees and angle D measures 26

degrees. What is the measurement of angle E?

180 - 38 - 90 = 52° (Angle C)

180 - 52 - 26 = 102 (Angle E)

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

check

D + C + E = 180

26 + 52 + 102 = 180

180 = 180

the answer is good

The angle theta lies in quadrant I or III.

Hence, option (C) is the correct choice.

The coordinate system's two axes, the x-axis and the y-axis, constitute an area called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.

Cosθ=(1/Sinθ)

And, Secθ = (1/Cosθ)

As we know,

In the first Quadrant.

The value of Sinθ is positive, so the corresponding value of Cosθ will be also Positive.

As, In the second case the value of Secθ should be less than 0,

We know the value of Cosθ is negative in the third Quadrant.

So, the value of the Secθ will be less than 0 in the third quadrant.

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Yes, the given functions are inverses of one another.

Inverse function is represented by  with regards to the original function  and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function. The graph of the inverse function is obtained by swapping (x, y) with (y, x) with reference to the line y = x.

The given functions are f(x)=5x+2 and g(x)=(x-2)/5.

The function f(x)=5x+2 can be written as y=5x+2

Swap x and y positions, we get

x=5y+2

x-2=5y

y=(x-2)/5

Therefore, the function g(x) is the inverse function os f(x).

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The value of [tex]r[/tex] is [tex]7[/tex]

The given equation is

                        [tex]5(r-3)=20[/tex]

We will now open the bracket, [tex]5r-15=20[/tex]

Let's simplify,

                      [tex]5r=20+15\\5r=35\\r=\frac{35}{5} \\r=7[/tex]

The value of [tex]r=7[/tex]

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The area of the triangle in the image is 120 square centimeters.

The whole question is on the image at the end.

Remember that the area of a triangle of base B and height H is given by the equation:

A = B*H/2

On the image, we can see that the base of the triangle has a measure of 12 cm, so:

B = 12cm

And we know that the height H is 8cm more than that, then:

H = 12cm + 8cm = 20cm

Now that we know these values, we can replace them on the equation for the area, and we will get:

A = 20cm*12cm/2 = 120cm^2

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Answer:

A proportional graph is a straight line that goes through the origin (0,0).\

Based on this information, the only correct answers would be B and C.

Aiden can make up to 166 copies before his copy card balance reaches below $5.00 as each copy total costs $0.06.

1. 15.00 - 0.06x ≥ 5.00

2. Add 0.06x to both sides: 15.00 ≥ 0.06x + 5.00

3. Subtract 5.00 from both sides: 10.00 ≥ 0.06x

4. Divide both sides by 0.06: 166.67 ≥ x

5. Therefore, x ≤ 166.67, so Aiden can make a maximum of 166 copies.

Aiden's copy card balance is $15.00, and each copy he makes costs $0.06. To ensure that his card balance does not go below $5.00, he needs to calculate the max number of copies he can make. To do this, we set up an inequality, 15.00 - 0.06x ≥ 5.00, and solved it to get x ≤ 166.67, meaning Aiden can make a maximum of 166 copies.

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Therefore , the solution of the given problem of quadratic equation comes out to be  yields the final response. x=2 several roots.

The quadratic solution x = ax2 + foo + c=0 is a regression model for one variable equations. According to the First Theorem of Algebra, this polynomial only has one solution because of its second order. Both straightforward and complex solutions are viable options. The term "quadratic formula" refers to a formula with four variables. According to this, there can only be a single squared word present. Mathematical variables or variables a, b, and c are often used to represent the unknown variable "X" in the formula "ax2 + bx + c = 0," which is frequently used to solve arithmetic problems.

Here,

Use the quadratic formula to find the solutions.

−b±√b²−4(ac)/2a

Substitute the values

a=1, b=−4, and

c=4

into the quadratic formula and solve for

x.4±√(−4)²−4⋅(1.4) / 2⋅1

Simplify.

Simplify the numerator.

x=4/2⋅1

Multiply 2 by 1

x=4/2

Divide 4 by 2

x=2

The combination of the two solutions yields the final response. x=2 several roots.

Therefore , the solution of the given problem of quadratic equation comes out to be  yields the final response. x=2 several roots.

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Answer:

14.13

Step-by-step explanation:

Since we know the area of a circle is [tex]\pi r^2[/tex], we just need to divide it by 2 to get the semicircle's area ( [tex]\frac{\pi r^2}{2}[/tex] )

We know the radius is equal to half of the diameter, or in this case 3, and we're approximating pi to 3.14, so we just substitute on the formula:

[tex]\frac{(3.14)(3)^2}{2} = \frac{(3.14)(9)}{2} = \frac{28.26}{2} = 14.13[/tex]

The data represents the linear equation.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

We have the table:

x → y

-9 →  -71

-8 → -63

-7 → -55

-6 →  -47

-5 →  -39

To prove that the data represents in the tables are from the linear equation:

If a first difference of the table of values shows a constant rate of change,

then the function is a linear equation.

So,

y₂-y₁ = -63 + 71 = 8

y₃ - y₂ = -55 + 63 = 8

y₄ - y₃ = -47 + 55 = 8

y₅ - y₄ = -39 + 47 = 8

Here, 8 is the constant rate of change.

So, the data represents the linear equation.

Therefore, the data represents the linear equation.

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