inverse function
[tex]f(4) = 7 {f}^{ - 1} = ?\ \textless \ br /\ \textgreater \ [/tex]
​

Answer:

A

Step-by-step explanation:

Answer:

40.2°

Step-by-step explanation:

The new expression is written as a single logarithm with a coefficient of 1 is [tex]\log\left(\frac{125u^3v^6}{w^9}\right)[/tex] .

A mathematical formula known as a logarithm determines how many times the base, or initial number, must be multiplied by itself in order to arrive at the desired result. This indicates that the exponent to which b is raised to obtain a number x is the logarithm of x to the base b.

The property of the logarithm used to calculate the given expression is

[tex]\log a^b=b\log a[/tex]

Then, the new expression is written as,

[tex]\begin{aligned}3\log \left(\frac{5 uv^2}{w^3}\right)&=\log\left(\frac{5 uv^2}{w^3}\right)^3\\&=\log\left(\frac{125u^3v^6}{w^9}\right)\end{aligned}[/tex]

In the above expression, the coefficient is 1. Therefore, the required answer is found to be [tex]\log\left(\frac{125u^3v^6}{w^9}\right)[/tex].

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The number of cones that can be made with 5 pounds of ice is calculated to be 30

From the given information, we have the following parameters that can be employed in our computation:

3 snow cones = 0.5 pounds of ice

For 5 pounds of ice, we have the following representations;

(cones, 5)

Using the above information as a guide, we have the following:

Cones : Pounds of ice = Ratio

Substituting the known values in the above equation as follows;

Cones : 5 = 3 : 0.5

Now multiplying the second ratio by 10

So. we have

Cones : 5 = 30 : 5

By comparison, we determine the number of cones as follows;

Cones = 30

Hence, the number of cones is calculated to be 30

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Answer:
1.80

Step-by-step explanation:

Answer:

Volume of a cylinder (v) = πr²h

Step-by-step explanation:

Given V = 5m³

r = 0.7m and π = 3.14

h= ?

using V = πr²h

5 = 3.14 x 0.7² x h

5 = 3.14 x 0.49 xh

5= 1.5386h

divide both side by 1.5386

5/1.5386 = h

h= 3.24970

h= 3.25m ( nearest hundredth)

Answer:

194 minutes

Step-by-step explanation:

First you subtract $7 from $20.58 because that was the start fee and get 13.58. Then divide 13.58 by 0.07, and get 194.

By using the squeeze theorem, we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]

Limit of a function, Squeeze Law:

The squeeze theorem states that if f(x) ≤ g(x) ≤ h(x) for all numbers, and at some point x=k we have f(k)=h(k), then g(k) must also be equal to them. We can use the theorem to find tricky limits like sin(x)/x at x=0, by "squeezing" sin(x)/x between two nicer functions and ​using them to find the limit at x=0

We say that a function f(x) approaches a limit L approaches a, or, [tex]$\lim _{x \rightarrow a} f(x)=L$[/tex]

if, for every number [tex]$\epsilon > 0$[/tex], however small, such that [tex]$|f(x)-L| < \epsilon$[/tex],

there always exists a number δ>0 such that

[tex]|x-a| < \delta \text {. }[/tex]

The Squeeze Law:

Suppose that g(x) ≤ f(x) ≤h(x) in some neighborhood of a and also that

[tex]$$\lim _{x \rightarrow a} g(x)=L=\lim _{x \rightarrow a} h(x)$,[/tex]

then,

[tex]$$\lim _{x \rightarrow a} f(x)=L .$$[/tex]

We have to find the limit of f(x) as x approaches to x.

Let [tex]$b-|x-a|=g(x)$[/tex] and [tex]$b+|x-a|=h(x)$[/tex].

Then we have the inequality, g(x) ≤ f(x) ≤h(x)

Let us see what happens to g(x) and h(x) as [tex]$$x \rightarrow a$.[/tex]

[tex]$$\begin{aligned}g(x) & =b-|x-a| \\\\lim _{x \rightarrow a} g(x) & =\lim _{x \rightarrow a} b-|x-a| . \\& =b\end{aligned}$$[/tex]

Similarly,

[tex]$$\begin{aligned}h(x) & =b+|x-a| \\\lim _{x \rightarrow a} h(x) & =\lim _{x \rightarrow a} b+|x-a| . \\& =b\end{aligned}$$[/tex]

We have the conditions required by the Squeeze law,

[tex]$$\lim _{x \rightarrow a} g(x)=b=\lim _{x \rightarrow a} h(x)$$[/tex]

so we conclude that, [tex]$$\lim _{x \rightarrow a} f(x)=b .$$[/tex]

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Answer:

a 22950

b 4590

Step-by-step explanation:

7.5% of 306,000 is 22950

20% of 22950 is 4590

y=x is the equation of line parallel to y=x-8 which passes through (7, 7).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We need to find the equation of line parallel to y=x-8 and assing through the point (7, 7).

The slope of parallel lines is same.

So the slope is 1.

Now let us find the equation of the parallel line.

To find this we need to find the y intercept.

7=7+b

b=0

The equation of line is y=x

Hence, the equation of line parallel to y=x-8 and passing through (7, 7) is y=x.

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The exponential equation of the given statement will be equal to, 1262 ×[tex](2)^x[/tex].

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given information in the question,

Total number of downloads initially = 1,262

Let the number of months be x.

Then, the equation will be,

y = 1262[tex](2)^x[/tex]

Here, y is the total number of songs.

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The expression for the total amount earned in t hours is 24t.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Amount earned per hour = $12

Amount earned in t hour = 12t

The amount is double.

The amount earned per hour.

= 2 x 12t

= 24t

Thus,

The total amount earned in t hours is 24t.

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The statement that is true about the proportional relationship of the graph is;

C: Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

We are told that the equation c equals one fourth times s. This is expressed as;

c = ¹/₄s

Where;

c is the number bags of cements

s is the number of bags of sands required to make concrete.

We can see that the number of bags of cements is directly proportional to the number of bags of sands required to make concrete.

In this question, the number of bags of sand is the independent variable while the number of bags of cement is the dependent variable.

From the graph attached, we see that the number of bags of sand is on the y-axis, while the number of bags of cement is on the x-axis.

Hence, the correct statement is option (C) Bags of Sand should be on the x-axis, and Bags of Cement should be on the y-axis.

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The expression represent a trinomial polynomial with three terms. The constant term is 1 , the leading term is 5, and the leading coefficient is 1 / 7.

A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using operations such as addition, subtraction, multiplication and division.

Trinomials are the algebraic expressions with three unlike terms.  Trinomial has three terms.

A constant term is a term in an algebraic expression that does not contain any variables and therefore is constant.

The leading term is the term with the highest power of x.

The leading coefficient of a polynomial is the coefficient found with the variable that has the largest exponent.

Therefore, the expression is a trinomial polynomial. This means it has 3 terms.

The constant term of the polynomial is 1 ,

The leading term is 5, and the leading coefficient is 1 / 7.

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Answer:

(-1,5), (0,4), and (-6,7)

Step-by-step explanation:

One may enter each point in both equations and solve matematically to find which points satisfy both equations.  But with access to a free, and easy, online graphing utility, it is more illuminating to plot both inequalites to identify the region containing mutual points (faster, also).  The attached plot illustrates the result.  Each inequality adds a shaded area showing the points satisfying the equation.  The color is darkest where the solution areas overlap, as seen in the upper left of the graph.  All points in this area satify both inequalities.  They are:

(-1,5)

(0,4), and

(-6,7)

Of the remaining three, only (2,-3) satifies neither equation.

Answer:

(-1,5), (0,4), and (-6,7)

Step-by-step explanation:

The variables (x, y) have the solution (1, -3) in the system of linear inequality

A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system.

In the question given

y ≥ -x + 2 ...eq(i)

y > -5x - 2 ...eq(ii)

Plotting this on a graphing calculator to find the point of intersection which will determine the solution of the graph;

The solutions to the variables (x, y) in the linear inequalities are (1 , -3)

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The radical part for both given expressions are √6 and √2

A radical expression is an expression containing a square root.

Given are two expressions, 3√54 and 3√128, we need to find the radical parts for bot,

1) 3√54=

= 3x√9x6

= 3x3√6

= 9√6

2) 3√128 =

= 3√2x2x2x2x2x2x2

= 3x2x2x2√2

= 24√2

The radical parts are the number under square roots.

Hence, The radical part for both given expressions are √6 and √2

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Yes, your answer is correct.

First Guess:

I believe that it would be correct

Final Answer:

Your answer is correct

Step-by-step explanation:

How to calculate the average:

     In order to find the average, you need to add a group of numbers and then divide by how many numbers there is.

      (((For example: 2, 3, 3, 5, 7, 10 -- That equals 30. Then to find the average, you need to divide (30) by how many numbers there is (6). 30/6=5. The average of this is 5)))

This set of numbers is 63, 53, 20, 10. The current average is 36.5.

Adding 9 to that number makes it equal 155. To find the average, we now have to divide 155 by 5(because thats how many numbers there is.

155/5=31

(Please give brainliest I worked hard)

Answer:

$41.00

Step-by-step explanation:

To determine the total price of the phone including taxes, we need to first calculate the amount of sales tax by multiplying the price of the phone by the sales tax rate:

Sales tax = Price of phone * Sales tax rate

Sales tax = $39 * 5%

Sales tax = $1.95

Next, we can calculate the total price of the phone including taxes by adding the amount of sales tax to the price of the phone:

Total price including taxes = Price of phone + Sales tax

Total price including taxes = $39 + $1.95

Total price including taxes = $40.95

Rounded to the nearest cent, the total price of the phone including taxes is $41.00.

formula: y = mx + b

current points we know:

m = 1/2

x = 10

y = 0

so we solve for the b value.

0 = 1/2 (10) + b

0 = 5 + b

(inverse operation we subtracted 5 on both sides)

-5 = b

so the equation for a line with slope 1/2 passing through the point (10,0) is

y = (1/2)x + (-5) or y = (1/2)x - 5

(not sure if this is correct...)

Answer: WIth the discount: $3.56, you do not have enough money, and are $0.56 short.

Step-by-step explanation:

Find 20% of 4.45

(4.45*0.2)= 0.89

Subtract the 20% from 4.45.

4.45-0.89=3.56

$3.56 is more than the $3 you have.

Subtract the $3 you have from the discounted price.

3.56-3.00=0.56

you are $0.56 short.

Answer: The two expressions that represent the perimeter of the rectangular pool include the following:

A. x + 3x + 1 + x + 3x + 1

E. 8x + 2

How to calculate the perimeter of a rectangle?

Mathematically, the perimeter of a rectangle can be calculated by using this equation;

P = 2(L + x)

Where:

P represents the perimeter of a rectangle.

L represents the length of a rectangle.

x represents the width of a rectangle.

Since the length is 1 more than 3 times the​ width, we have;

Length, L = 3x + 1

Therefore, the two expressions for the perimeter of this rectangle is given by:

P = 2(3x + 1 + x) = x + 3x + 1 + x + 3x + 1

P = 2(4x + 1) = 8x + 2

Next, we would determine the total cost as follows;

P = 8x + 2

P = 8(20) + 2

P = 162 feet.

Total cost = 1.86 × 162

Total cost = $301.32

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Complete Question:

A hotel manager is adding a tile border around the​ hotel's rectangular pool. Let x represent the width of the​ pool, in feet. The length is 1 more than 3 times the​ width, as shown. Find two expressions that represent the perimeter of the pool. Use the expressions to describe two ways to find the perimeter. The length of each tile is 1 foot. If the width of the pool is 20 ​feet, and each tile costs ​$1.86​, what would be the total cost of the tile for the​ border?

A. x + 3x + 1 + x + 3x + 1

B. x + 3x + 1

C. 2x + 3x + 1

D. 8x + 1

E. 8x + 2

F. 4x + 1

Step-by-step explanation:

By comparing the speeds of all the people, Bob picked apple the fastest.

Speed is generally the change in distance per unit time. In this case instead of distance we can use the number of apples.

For this question, speed of picking apples = no of apples / time (in minutes). For Bob, speed = 15/8 = 1.88 apples/minute

For Mary, speed = 16/16 = 1 apples/minute

For Suie, speed = 10/19 = 0.526 apples/minute

This shows that Bob picked apples the fastest.

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Answer:

11 cm

Step-by-step explanation:

2x+x+6+x+4=30

4x+10=30

   -10.  -10

4x=20

/4.  /4

x=5

now we find each length to find the longest

2(5)

10 cm

5+6

11 cm

5+4

9 cm

11 is the biggest one

Hopes this helps have a wonderful day

y= x² - 4 is the function symmetric about the point (0,3).

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

We need to find the  function's graph is symmetric about the point (0,3)

You want a parabola with a vertex at the point (0,3) so that is symmetrical on each side of that point.

Using the point (0,3),

The equation for a parabola in vertex form and then simplify:

Vertex = (h,k)

Vertex = (0,3)

y = (x - h)² + k

= (x - 0)² +3

y= x² - 4

Hence, y= x² - 4 is the function symmetric about the point (0,3).

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The total cost of the skateboard if Loui has to pay a state sale tax of 6. 25% is 72.26.

As per the given data, Loui wants to buy a skateboard that has an original price of 79.91, will be discounted 12 %, and will have a sales tax of 6.25 %.

When performing the calculations, remember to convert percent to decimal form and if needed, round to two decimal places since money must be rounded to the nearest cent.

First, we need to find the amount of the discount and then find the sale price (the price after the discount):

Sale price:

Original price - Amount of discount = 79.91 - 11.9 = 68.01

Now that we have the sale price, we can find the amount of tax and then the total cost:

Amount of tax  = ( sale price) × (sales tax percent)

[tex]$$\begin{aligned}& =\ 68.01 \times \ 0.0625 \\& \approx \ 4.25 \end{aligned}$$[/tex]

Total cost = sale price + amount of tax

= 68.01 +  4.75

= 72.26

Therefore the cost is 72.26.

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Based on the correlation coefficient from the technology data given, the data has a strong negative association.

The correlation coefficient is defined as a statistical measure of the strength of a linear relationship that exists between two variables.

The possible range of values for correlation coefficient is from -1.0 to 1.0. This tells us that the values cannot be more than 1.0 nor be less than -1.0.

Thus, a correlation coefficient of -1.0 shows a perfect negative correlation, while a correlation coefficient of 1.0 shows a perfect positive correlation.

We are given a correlation coefficient of r = -0.9478.

Now, the closer the negative correlation is to -1 indicates a strong negative correlation while the farther it is from -1 indicates a weak negative correlation.

Thus, we can conclude that in this case where the  negative correlation is closer to -1 than farther, it can be said to be a strong negative correlation.

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Answer: 39 mm

Step-by-step explanation:

1 cm = 10 mm

3.9 cm = 39 mm

I just need to take 3.9 times 10 and you will get 39 mm

The train does not always go the same distance each minute.

Predicted amount of time to travel 30 kilometers is equal to 47.52 minutes.

In order to determine a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).

In this scenario, the time (in minutes) would be plotted on the x-axis of the scatter plot while the distance (km) would be plotted on the y-axis of the scatter plot.

On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the distance (km) and time (in minutes), a linear equation for the line of best fit is given by:

y = 1.40x + 5.52

Next, we would determine the predicted amount of time to travel 30 kilometers:

y = 1.40(30) + 5.52

y = 42 + 5.52

y = 47.52 minutes.

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Answer:

$102.72

Step-by-step explanation:

If the mp3 player typically costs $120 and was on sale for 20% off, then the sale price would be 120 * (1 - 0.2) = $96.

If Siddhu had to pay 7% sales tax on the sale price, then the total tax he paid would be 96 * 0.07 = $6.72.

Therefore, Siddhu paid a total of 96 + 6.72 = $102.72 for the mp3 player when it was on sale with the sales tax included.

Option (d) is correct. Heteroscedasticity of residuals in regression suggests that there is a non constant variation in the error.

Heteroscedasticity means unequal scatter. In regression analysis, we talk about heteroscedasticity in the context of the residuals or error term. Heteroscedasticity is a systematic change in the spread of the residuals over the range of measured values. Heteroscedasticity is a problem because ordinary least squares regression assumes that all residuals are drawn from a population that has a constant variance that is heteroscedasticity. the residuals should have a constant variance. Heteroscedasticity is also called as heteroskedasticity. It occurs more often in datasets that have a large range between the largest and smallest observed values. This explains Heteroscedasticity.

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The correct answer is (C) Prediction values are meaningful only for X-values in (or close to the range of the original data.

A regression line is a statistical model that is used to make predictions about the value of a dependent variable (Y) based on the value of an independent variable (X). The regression line is based on a sample of data, and it is typically used to make predictions about the population from which the sample was drawn.

The validity of the predictions made using a regression line depends on the assumptions that were used to create the model. One of these assumptions is that the relationship between X and Y is linear, which means that the predictions are only meaningful for X-values that are within (or close to) the range of the original data. If the X-value is outside this range, the prediction may not be accurate because the model may not accurately represent the underlying relationship between X and Y.

Therefore, to provide meaningful predictions for Y, the values of X should be within (or close to) the range of the original data.

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