3. A function f has the following verbal description: “Subtract 2, then cube the result.”
(a) Find a formula that expresses f algebraically.
(b) Make a table of values of f, for the inputs -1, 0, 1, 2, 3, and 4.
(c) Sketch a graph of f, using the table of values from part (b) to help you.
(d) How do we know that f has an inverse? Give a verbal description for f^-1 .
(e) Find a formula that expresses f ^-1
algebraically.

Answer:

The 3 in the tens place is worth 10 times the 3 in the ones places.

Step-by-step explanation:

Have a great day :)

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The number of times the students on your floor order pizza in a week, population.

A population is a complete set of individuals or objects that share common characteristics. It is an entire group of people, animals, plants, or objects that can be studied. A population can also be a group of people living in a certain geographical area.

A sample is a subset of a population. It is a smaller group of individuals or objects drawn from the population that are used to make inferences about the population as a whole.

A sample is used in statistical analysis to estimate population characteristics, such as mean, median, and variance. The accuracy of the estimates depends on the size and representativeness of the sample.

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The complete question is:

Determine whether the statement describes a population or a sample. The number of times the students on your floor order pizza in a week, ___.

Answer:

(0,1)

(-2,0)

(2,2)

Step-by-step explanation:

Uri paid a total of $85.47 for the landscaping service including tax and tip.

Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.

Given that company charged $74 for the service plus 5% tax.

The tax is 5%, that is:

Tax = 5% of $74 = 0.05 x $74 = $3.70

Cost after tax = $74 + $3.70 = $77.70

Now, tip is 10%:

Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77

Total cost = $77.70 + $7.77 = $85.47

Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.

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The function:

The domain of this function always is going to be for the values when:

So, the domain is for all values of x equal or greater than -3/12

Domain= R>=-3/12

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

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a. The answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. The answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

a. To represent 20 longs in base seven, we need to find the fewest number of multibase blocks required.

In base seven, we have the following conversions:

1 long = 1 unit

1 flat = 10 units

1 block = 10 flats

To represent 20 longs, we can use 2 flats (each flat representing 10 units) and 0 units since there are no remaining units.

So, the fewest number of multibase blocks required would be 2 flats.

Therefore, the answer is: The fewest number of multibase blocks required to represent 20 longs in base seven is 2 flats.

b. To represent 10 longs in base three, we need to find the fewest number of multibase blocks required.

In base three, we have the following conversions:

1 long = 1 unit

1 flat = 3 units

1 block = 3 flats

To represent 10 longs, we can use 3 flats (each flat representing 3 units) and 1 unit since there is one remaining unit.

So, the fewest number of multibase blocks required would be 3 flats and 1 unit.

Therefore, the answer is: The fewest number of multibase blocks required to represent 10 longs in base three is 3 flats and 1 unit.

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The change in the graph is the y-intercept would remain the same but the slope would increase.

What is a graph?

⇒ The link between lines and points is described by the mathematical network model known as a graph. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is a name for each element in a graph.

What is the slope of a graph?

⇒ A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

Calculation:

An initial $24.00 membership fee is required to join the music club. Each CD costs $8.50.The graph shows the cost of belonging to the club as a function of CDs purchased.

The number of CD is listed on the x-axis of the graph, while the total cost is listed on the y-axis.

⇒ This equation is: y = 8.50x + 24.

We will now raise the price of the CD by $1.00.

The total fee would then rise as well.

Then, the slope would rise but the y-intercept would stay the same.

⇒ The revised formula is y = 9.50x + 24.

Hence, The change in the graph is the y-intercept would remain the same but the slope would increase.

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Disclaimer: The question was given incorrectly on the portal here is the correct question.

Question: A music club charges an initial joining fee of $24.00. The cost per CD is $8.50. The graph shows the cost of belonging to the club as a function of CDs purchased. How will the graph change if the cost per CD goes up by $1.00?

True, While "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

The statement "-1000 2/3 is not a real fraction" is true. A real fraction is a mathematical expression that represents a ratio of two real numbers. In a fraction, the numerator and denominator are both real numbers, and they can be positive, negative, or zero.

In the given statement, "-1000 2/3" is not a valid representation of a fraction. The presence of a space between "-1000" and "2/3" suggests that they are separate entities rather than being part of a single fraction.

To represent a mixed number (a whole number combined with a fraction), a space or a plus sign is typically used between the whole number and the fraction. For example, a valid representation of a mixed number would be "-1000 2/3" or "-1000 + 2/3". However, without the proper formatting, "-1000 2/3" is not considered a real fraction.

It's important to note that "-1000 2/3" can still be expressed as an improper fraction. To convert it into an improper fraction, we multiply the whole number (-1000) by the denominator of the fraction (3) and add the numerator (2). The result would be (-1000 * 3 + 2) / 3 = (-3000 + 2) / 3 = -2998/3.

In conclusion, while "-1000 2/3" is not a real fraction, it can be represented as the improper fraction -2998/3.

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All the points (20, -2), (-2, 2), (4, 2), (8, 1), (-8, 5), and (16, -1) lie on the same line.

To determine which points lie on the same line passing through (-4, 4) and (12, 0), we can use the equation of a line.

First, we find the slope (m) of the line using the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of the two given points.

m = (0 - 4) / (12 - (-4)) = -4 / 16 = -1/4.

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1),

where (x1, y1) is any point on the line.

Let's check which points satisfy this equation:

(20, -2):

-2 - 4 = (-1/4)(20 - (-4)),

-6 = (-1/4)(24),

-6 = -6.

The equation is true, so (20, -2) lies on the same line.

(-2, 2):

2 - 4 = (-1/4)(-2 - (-4)),

-2 = (-1/4)(2),

-2 = -2.

The equation is true, so (-2, 2) lies on the same line.

(4, 2):

2 - 4 = (-1/4)(4 - (-4)),

-2 = (-1/4)(8),

-2 = -2.

The equation is true, so (4, 2) lies on the same line.

(8, 1):

1 - 4 = (-1/4)(8 - (-4)),

-3 = (-1/4)(12),

-3 = -3.

The equation is true, so (8, 1) lies on the same line.

(-8, 5):

5 - 4 = (-1/4)(-8 - (-4)),

1 = (-1/4)(-4),

1 = 1.

The equation is true, so (-8, 5) lies on the same line.

(16, -1):

-1 - 4 = (-1/4)(16 - (-4)),

-5 = (-1/4)(20),

-5 = -5.

The equation is true, so (16, -1) lies on the same line.

In summary, all of the given points: (20, -2), (-2, 2), (4, 2), (8, 1), (-8, 5), and (16, -1) lie on the same line passing through the points (-4, 4) and (12, 0).

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Note the complete question is

A line passes through the points (-4, 4) and (12, 0) . Which points lie on the same line? Select all that apply: (20_ -2) (-2, 2) (4, 2) (8, 1) (-8, 5) (16, -1)

Answer:

First, we need to calculate Michael's daily interest rate:

0.1199 / 365 = 0.0003282

Then, we can calculate his daily finance charge:

327.50 x 0.0003282 = 0.1075

To find his monthly finance charge, we multiply his daily finance charge by the number of days in a month:

0.1075 x 30 = 3.225

So Michael's monthly finance charge will be $3.23 (rounded to the nearest cent).

Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

The value of the infinite series expression \(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) is -30.

Given information:

\(\sum^{124}_{i = 1}a_i = -10\)  and \(\sum^{124}_{i = 1} b_i = -20\).

The required series form can be rearranged as,

\(\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i\)

Substitute the provided values of \(\sum^{124}_{i = 1}a_i = -10\)  and \(\sum^{124}_{i = 1} b_i = -20\).

We get,

\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = 29(-10) - 13(-20)

\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = -290+ 260

\(\sum^{124}_{i = 1}(29a_i - 13b_i) \\\) = -30.

As a result, the required value is -30.

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1) We were told to simplify this expression. So, we'll do it using the properties from the exponents.

2) Let's write it down:

Note that in this case, we've got to distribute the exponents over each variable, so that will lead to this:

Note that we did this by multiplying each exponent by the outside exponent.

Answer:

the answer is 40 hope this helps you

According to the angles between intersecting secant and tangent, the value of

angle DF is 52 degrees

angle PQR = 49 degrees

The value of angle DF is solved using the angles of intersecting secant out side the circle

The theorem give the formula in the form

44 = 1/2 (140 - DF)

88 = 140 - DF

DF = 140 - 88

DF = 52 degrees

Using intersection of tangents, for the second figure

exterior angle = 1/2 (major arc - minor arc)

major arc = 360 - 131 = 229

PQR = 1/2 (229 - 131)

PQR = 49 degrees

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Answer:

112 cm

Step-by-step explanation:

14 x 8 = 112

Answer:

D) 32

Step-by-step explanation:

Given;

series: 56, 54, 50, 38, 34, ....

find the difference between successive numbers;

56         54        50             38            34             x

     2            4             12              4             2            

The highest difference between the numbers is  12, after which it decreases to 4 and finally back 2.

The next number "x" is calculated as;

34 - 2  = x

34 - 2 = x

32 = x

Therefore, the next number should be 32.

The next number that should come next in the series is 32.

Sequence is an arrangement of two or more things in a successive order.  Series is the cumulative sum of a given sequence of terms.

Given the numbers in the series: 56, 54, 50, 38, 34, . . ..

The difference is 2, 4, 12, 4, 2

The highest difference between the numbers is  12, after which it decreases to 4 and finally back 2. Hence:

The next number = 34 - 2 = 32

The next number that should come next in the series is 32.

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Answer:

x=0.107

Step-by-step explanation:

First we distribute 13 to x and 15. That gives us 13x+15x=3. Now we add 13x and 15x, that gives us 28x=3.  Now we divide by 28 on both sides. That gives us x=0.107

For the graphed function, we have:

Domain:  (-1, 1) U (3, 5)

Range: (5, 2)

For any function y = h(x) we define the domain as the set of the inputs while we define the range as the set of the outputs.

To find the domain we need to look at the horizontal axis, we can see that the function is graphed on the intervals (-1, 1) and (3, 5), so the domain is:

D: (-1, 1) U (3, 5)

For the range we need to look at the vertical axis, the two intervals are (-4, 2) and (-5, 0), the union of these intervals gives:

(-4, 2) U (-5, 0) = (5, 2)

Then the range is R: (5, 2)

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do they give the whole amount of both trails together? then someone would be able to answer this so pls add that

Answer:

The relationship between the number of faces, vertices, and edges of a three-dimensional object is described by Euler's formula, which states that for any polyhedron (a solid object bounded by flat faces), the number of faces (F), vertices (V), and edges (E) satisfy the equation F + V - E = 2. This formula is true for any convex polyhedron, such as a cube or a regular tetrahedron.

The formula is based on the fact that every face of a polyhedron is bounded by a closed loop of edges, and each vertex is where three or more edges meet. The total number of edges is the sum of the number of edges around each face, which is equal to twice the number of faces since each edge is shared by two faces, and the number of edges meeting at each vertex, which is equal to the degree of the vertex (the number of edges meeting at the vertex).

Therefore, by knowing the number of faces, vertices, and edges of a three-dimensional object, we can determine if it is a convex polyhedron and use Euler's formula to check if the numbers are consistent with a solid shape.

Answer:

#1 isnt porportional and #2is porportional and is 3

Answer:

Step-by-step explanation:

\(\sf a^{m}*a^{n} =a^{m +n}\\\\a^{\frac{1}{n}}=\sqrt[n]{a}\)

\(\sf a^{-n}=\dfrac{1}{a^{n}}\\\\\dfrac{a^{n}}{a^{m}}=a^{n-m}\\\\\\a^{0}=1\)

\(\sf (a^{n})^{m} = a^{n*m}\\\\(a^{n}*b^{m})^{p}=a^{np}b^{mp}\\\\(ab)^{n}=a^{n}b^{n}\)

Answer:

Gym: A=100 P=41

Cafeteria: A=144 P=48

Locker room: A=75 P= 37

Answer: 6.8622 ; 8.1778

Step-by-step explanation:

Given the data:

2 6 7 8 9 9 9 10 10 10 10 9 4 5 6 6 8 7 9 10 9

6 5 7 6 8 4 2 10 9 9 10 10 9 8 7 5 9 9 3 6 2 9

7 10 7 9 9 9 9

Assume a confidence interval of 95%

Using calculator :

The mean of the distribution (m) = 7.52

Standard deviation (s) = 2.314

Sample size),

Obtaining the t score ;

Degree of freedom (df) = (n-1) = 50 - 1 = 49

t(1-α/2), 49 = t(0.025, 49) = 2.01 ( t distribution table)

Margin of Error :

2.01 * s/√n = 2.01 * 2.314/7.0710678

Margin of Error (E) = 0.6578

Confidence interval:

(Mean - E) ≤μ≤ (mean + E)

(7.52 - 0.6578) ≤μ≤ (7.52 + 0.6578)

6.8622 ≤μ≤ 8.1778