The expression log1/3/log2 is the result of applying the change of base formula to a logarithmic expression. Which could be the original expression? ​

Answer:

The standard deviation of the data set is 5.7 to the nearest tenth

Step-by-step explanation:

* Lets explain how to find the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 3 , 17 , 18 , 15 , 12 , 21 , 9

∵ Their sum = 3 + 17 + 18 + 15 + 12 + 21 + 9 = 95

∵ They are seven

∴ The mean = 95 ÷ 7 = 13.6

# Step 2: subtract the mean from each data and square the answer

∴ (3 - 13.6)² = 112.36

∴ (17 - 13.6)² = 11.56

∴ (18 - 13.6)² = 19.36

∴ (15 - 13.6)² = 1.96

∴ (12 - 13.6)² = 2.56

∴ (21 - 13.6)² = 54.76

∴ (9 - 13.6)² = 21.16

# Step 3: find the mean of these squared difference

∵ The mean = the sum of the data ÷ the number of the data

∵ The sum = 112.36 + 11.56 + 19.36 + 1.96 + 2.56 + 54.76 + 21.16 = 223.72

∴ The mean = 223.72 ÷ 7 = 31.96

# Step 4: the standard deviation is the square root of this mean

∴ The standard deviation = √(31.96) = 5.6533 ≅ 5.7

* The standard deviation of the data set is 5.7 to the nearest tenth

- 3 + 3x = 2x – 13

Bring -3 to the right side of the equation by adding 3 to both sides

(- 3 + 3) + 3x = 2x – 13 + 3

0 + 3x = 2x - 10

3x = 2x - 10

Bring 2x to the other side by subtracting 2x to both sides

3x - 2x = 2x - 2x - 10

x = -10

Check:

-3 + 3(-10) = 2(-10) - 13

-3 + (-30) = -20 - 13

-33 = -33

Hope this helped!

~Just a girl in love with Shawn Mendes

The function f(x) = 4.34 is a constant function, which means it does not change regardless of the value of 'x'. Thus, none of the options provided (A: Decreasing linear, B: Exponential growth, C: Increasing linear, D: Exponential decay) correctly describe the function.

The function represented by f(x) = 4.34 is a constant function.

This is because no matter what value of 'x' you put into the function, the output is always going to be 4.34.

Looking at the options provided:

A. Decreasing linear - This indicates that the function should decrease as 'x' increases, which is not the case here.

B. Exponential growth - This would mean the function increases at an increasing rate, which also does not apply to a constant value.

C. Increasing linear - This suggests that the function's value should increase as 'x' increases, which is not true for a constant function.

D. Exponential decay - This implies the function's values decrease at a decaying rate, which, again, does not match a constant value.

Therefore, none of the options accurately describe f(x) = 4.34.

The function is neither increasing nor decreasing and it is not an exponential function.

Answer:

Table B

Step-by-step explanation:

we know that

A relationship between two variables, a, and b, represent a proportional variation if it can be expressed in the form [tex]b/a=k[/tex] or [tex]b=ka[/tex]

In this problem the table B shows a proportional relationship because

For a=20, b=25 -----> b/a=25/20=1.25

For a=24, b=30 -----> b/a=30/24=1.25

For a=32, b=40 -----> b/a=40/32=1.25

The constant of proportionality k is 1.25

Answer:

Im pretty sure its B :)

Step-by-step explanation:

[tex]A(7,0)\Longrightarrow\boxed{A'(-7,0)}[/tex]

Hope this helps.

r3t40

Answer:

(- 7, 0)

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y )

Hence

(7, 0 ) → (- 7, 0 )

Answer: 14x-7u+14

Step-by-step explanation:  multiply parenthesis by -7

Answer:

14x -7u+14

Step-by-step explanation:

-7(-2x+u-2)

Multiply -7 by each term in the parentheses

-7*-2x + -7*u + -7*-2

14x -7u+14

There are a few ways to do it; the easiest is just to follow the pattern of taking away two from the average.

The next lines of the table are

6 to 7  -13

7 to 8   -15

8 to 9   -17

Answer: C. -17

Let's find the equation and do it that way.

We have a vertex at (0,3) so we can fill out the vertex form a bit.  In general for vertex (p,q) it's

y = a(x-p)^2+q

We have

f(x) = ax^2 + 3

f(1) = 2

a+3 =2

a = -1

So we found our equation,

y = -x^2 + 3

Let's check it at x=5, y=-5^2+3=-25+3=-22, good

We want the rate of change from 8 to 9, which is

[tex]r = \dfrac{f(9)-f(8)}{9-8}=f(9)-f(8)=-9^2 - -8^2 = -17[/tex]

Answer: -17 again, that checks

The average rate of change for the interval from x=8 to x=9 is -17.

The correct option is (C)

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

We have a vertex at (0,3).

In general let us take vertex (p,q) then

y = a(x-p)²+q

We have,

f(x) = ax² + 3

as x=1, f(x)=2

so,

f(1) = 2

a+3 =2

a = -1

Now, the equation

y = -x² + 3

Thus, the rate of change from 8 to 9

= f(9)-f(8)/9-8

= -9²-(-8)²

=-81+64

=-17

Hence,  the average rate of change for the interval from x=8 to x=9 is -17.

Learn more about this concept here:

https://brainly.com/question/14372714

#SPJ2

Answer:

5.80

Step-by-step explanation:

How much was the total profit

1412 -1006

406

She sold 70 puppets

The profit per puppet is the profit divided by the number of puppets

406/70

5.80

Answer:

Table 3 and Table 5

Step-by-step explanation:

y = 3/5 x

The slope is 3/5

3/5 = .6

We want a slope that is lower

We want to find the slope for each table

Slope is found by

m = (y2-y1)/(x2-x1)

Table 1

    = (12-4)/(9-3) = 8/6 = 4/3 =1.33

Table 2

   = (12-4)/(15-5) = 8/10 = 4/5=.8

Table 3

   = (54-18)/(93-31) = 36/62=18/31=.58

Table 4

= (33-11)/(54-18) = 22/36 = 11/12=.92

Table 5

 = (21-7)/(36-12) =14/24 = 7/12 =.58

Answer:

g(x)=40x+4x^2

Step-by-step explanation:

[tex]g(x) = 40x + 4 {x }^{2} [/tex]

Answer:

9

Step-by-step explanation:

The small triangle on the left, the larger triangle on the right, and the overall triangle all have the same angles, and therefore are similar.

Writing a proportion:

4 / 6 = 6 / a

a = 9

Answer:

C. 9 (third option)

Step-by-step explanation:

A proportion sets two ratios equal to each other.

For example of proportion: ⇒ [tex]x*6=y[/tex]

Another example of proportion: ⇒ [tex]\frac{y}{x}=\frac{6\div 2}{2\div2}=\frac{3}{1}=3[/tex]

6/4=4/a

=9 is the correct answer.

Answer:

169

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

The slope of a line passing through points (a,b) and (c,d) is given by :-

[tex]m=\dfrac{d-b}{c-a}[/tex]

From the given graph , the line is passing from points (6,33) and (15,15).

Now, the of a line passing through points (6,33) and (15,15) is given by :-

[tex]m=\dfrac{15-33}{15-6}=\dfrac{-18}{9}\\\\\Rightarrow\ m=-2[/tex]

Hence, the slope of the line = -2

Answer:

1. A

2. C

Step-by-step explanation:

H in the parent function equations are always negative and k is always positive.

Ex:

[tex]f(x)=2^(x-h)+k[/tex]

So that means when we're adding 4 to the exponent, we're actually subtracting, therefore moving the graph 4 units to the left.

Then, since k is positive, and we're adding 8, we move the graph 8 units up.

Answer: the answer is C. Range :D

Step-by-step explanation:

Answer:

$9.00

Step-by-step explanation:

4x + 12 = 48         - First, subtract 12 from each side of the equation.

4x = 36                 - Then, divide each side by 4 to get x by itself.

x = 9                     - After dividing by 4, we are left with x = 9, so 1 ticket costs

                              $9.00

For this case we have the following equation:

[tex]4x + 12 = 48[/tex]

Where the variable "x" represents the cost of a performance ticket.

Clear "x" of the equation to know the cost of a ticket.

Subtracting 12 on both sides of the equation:

[tex]4x = 48-12\\4x = 36[/tex]

Dividing between 4 on both sides of the equation:

[tex]x = \frac {36} {4}\\x = 9[/tex]

So, the cost of a ticket is $ 9.00

Answer:

Option C

Answer:

13 inches

Step-by-step explanation:

Your formula for a right circular cylinder's volume is

[tex]V=\pi r^{2} h[/tex]

All you have to do is plug in your variables. Since we know that the volume is 2028pi and the height is 12 inches, we can set up the equation as follows:

[tex]2028\pi =\pi r^{2} 12[/tex]

Next, we simplify. First, we have to divide both sides by pi.

[tex]2028=12r^{2}[/tex]

Once we've divided both sides by pi, we can divide both sides by 12.

[tex]169=r^2[/tex]

Now, to find the radius, we have to find the square root of both sides. This is because the square root of r squared is r.

[tex]13=r[/tex]

Your radius is 13 inches.

In the context of Mathematics, it involves utilizing the volume formula of a right circular cylinder (V = πr²h) and rearranging it to solve for radius. Then, we substitute given values (volume and height of the cylinder) into the rearranged formula to calculate the value of the radius.

The subject of this question is Mathematics. Specifically, it involves using the formula for calculating the volume of a right circular cylinder to determine the radius when given the volume and height. The formula for the volume, V, of a right circular cylinder in terms of its radius, r, and its height, h, is V = πr²h.

To solve this problem, we need to rearrange the formula to solve for r which turns out to be r = √(V/(πh)). Substituting the given details, r becomes √(2028/(3.142*12)), which will give us the value of the radius. This involves use of algebra and geometry concepts.

https://brainly.com/question/16136732

#SPJ2

Answer:

Step-by-step explanation:

2 - 3y + 3t = -x - 2yz

I don't think you can actually solve the equation. You are not given any information about the letters (variables).

Answer:

y=-2/5x^2-3x+63

Step-by-step explanation:

Use y=mx+b

Answer:

-3+4

Step-by-step explanation:

if it's put in parentheses it needs to be done first

Answer:

y=-2x+14

Step-by-step explanation:

If we are looking for a line parallel to 2x+y=5.

Then we are looking for an equation with the same slope as the equation 2x+y=5.

To obtain the slope of equaiton 2x+y=5 I will put it in slope-intercept form.

Luckily there is only one step which is to subtract 2x on both sides.

y=-2x+5

The slope of this line is -2

The slope of parallel line will also be -2.

So we know our equation is in the form y=-2x+b

To find b we will just use the point (x,y)=(5,4) we know is on the line.

Plug in and solve for b.

4=-2(5)+b

4=-10+b

14=b

So the equation that is parallel to 2x+y=5 and goes through (5,4) is y=-2x+14

Answer:

If two chords intersect each other in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

x² = 12

x = 2√3

The formula x = r0 is used to calculate the length of a circular arc 'x', given the radius 'r' and an angle '0' in radians. For example, for a radius of 0.15m and an angle of 75.4 radians, we find x = 11m.

The problem revolves around the relationship between the radius r and an angle in radians 0, given by the formula x = r0. This applies to questions involving the measurement of a circular arc, where 'x' is the length of the arc. An example calculation would be, if we had a radius of 0.15m and an angle of 75.4 radians, we would multiply these to find 'x', giving us x = 11m. Similarly, for a radius of 0.0450m and an angle of 220 radians, x = 9.90m. Notice that the unit of 'x' will always be in the same unit as the radius (in this case, meters).

https://brainly.com/question/32035879

#SPJ12

Answer:

4

Step-by-step explanation:

4 - 2 = 4 + -2 = -2 + 4

Final answer:

To find the quotient of x + 4x² divided by 2x, divide each term inside the numerator by the denominator. Simplify the expression by dividing each term by 2x.Simplifying further, we get: 1/2 + 2x

Explanation:

To find the quotient of x + 4x² divided by 2x, we divide each term inside the numerator by the denominator.

This gives us: (x + 4x²) ÷ 2x

Next, we can simplify the expression by dividing each term by 2x:

x ÷ 2x + 4x² ÷ 2x

Simplifying further, we get: 1/2 + 2x

Answer:

one solution: (2.5, 0)

Step-by-step explanation:

y = 2x – 5  

–8x – 4y = –20

Solve the second equation for y

Add 8x to each side

–8x+8x – 4y =8x –20

-4y = 8x-20

Divide by -4

-4y/-4 =8x/-4 -20/-4

y = -2x+5

The two equations are

y = 2x-5

y = -2x+5

Both equations are solved for y so set them equal

2x-5 = -2x+5

Add 2x to each side

2x+2x-5 = -2x+2x+5

4x-5 = 5

Add 5 to each side

4x-5+5 = 5+5

4x=10

Divide by 4

4x/4 = 10/4

x = 2.5

y = 2x-5

Substitute x=2.5 in

y = 2(2.5) - 5

y=5-5

y=0

There is one solution (2.5,0)

Answer: B (2.5, 0)

B: - One solution: (2.5, 0)                  

Step-by-step explanation:

Given : Two linear equation -

Equation 1 -  

Equation 2 -  

To find : How many solutions does this linear system have?

Solution :

We solve the given equations,

Substitute the value of y from equation 1 in equation 2

Now, put value of x in equation 1

There is one solution (x,y) = (2.5, 0)

B is correct.

Answer:

1.56666

Step-by-step explanation:

3.5/2.25=1.555

Answer:

as a decimal its 0.125 as a fraction its 1 5/9

Step-by-step explanation:

All you have to is first change both into a mixed number so 7/2 divided by 9/4 then do keep change flip (KCF) so 7/2 * 4/9 which equals 28/18 and it simply to 1 5/9.

Answer:

x=0, x=-6

Step-by-step explanation:

Answer: -33

Step-by-step explanation:

Answer:

Step-by-step explanation:

Recall any base that is raised to a negative power is simply the reciprocal of the base.

i.e [tex]x^{-1}[/tex] = [tex]\frac{1}{x}[/tex]

Using this knowledge, we can start simplifying the equation (see attached)

Answer:

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]  

Step-by-step explanation:

Given : Expression [tex]\frac{a^3b^2}{a^{-1}b^{-3}}[/tex]

To find : Multiply or divide as indicated. Leave your answer with no factors in the denominator.

Solution :

We know when two same term are in divide then their power get subtracted.

So, [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]

Applying in the expression,

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{3-(-1)}b^{2-(-3)}[/tex]

Solve the power,

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{3+1}b^{2+3}[/tex]

[tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]

Therefore, The solution is [tex]\frac{a^3b^2}{a^{-1}b^{-3}}=a^{4}b^{5}[/tex]

The number 0.58 produces a rational number when added to 0.42.

A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. It can be expressed as a whole number or in the fractional format.

Let us find the nearest rational number which can be expressed in the whole number format.

For 0.42, the nearest rational number is 1 .

Thus the number added to 0.42 is (1 - 0.42) = 0.58 .

Therefore, the number 0.58 produces a rational number when added to 0.42.

To learn more about rational number, refer -

https://brainly.com/question/12088221

#SPJ2