The expression provided models the monthly long distance telephone charges, with a fixed fee of $4.95 plus $0.07 per minute of call time. To determine the monthly charge, multiply the number of minutes by $0.07 and add the result to the base charge of $4.95.
The given expression 4.95 + 0.07x represents a model for calculating a household's monthly long distance telephone charges, where x is the number of minutes of long-distance calls. To find the monthly charges for any number of minutes (x), we simply plug in the value of x and calculate the total cost.
If a household uses 0 minutes, the cost would be $4.95 (since 4.95 + 0.07(0) = 4.95).For 100 minutes of use, the cost would be $4.95 + (0.07 x 100) = $4.95 + $7.00 = $11.95.The formula incorporates a fixed fee of $4.95, which we can see as the base charge regardless of usage, plus a variable component that depends on the number of minutes used (0.07 times the number of minutes).
Identify any vertical asymptotes and horizontal asymptotes? (Enter your answers as comma-separated lists of equations. If an answer does not exist, enter DNE.) f(x) = −3(x + 3)(x − 2) / (x − 4)(x − 2)
The vertical asymptotes are x = 4 and x = 2, and the horizontal asymptote is y = -3.
Explanation:The given function is f(x) = −3(x + 3)(x − 2) / (x − 4)(x − 2).
To find the vertical asymptotes, we need to determine the values of x for which the function approaches positive or negative infinity. The denominator of the rational expression cannot be equal to zero, so we set it equal to zero and solve for x: (x − 4)(x − 2) = 0. This gives us two vertical asymptotes at x = 4 and x = 2.
To find the horizontal asymptote, we need to examine the highest power of x in the numerator and denominator. In this case, both the numerator and denominator have the same highest power, which is x^1 or simply x. Therefore, to find the horizontal asymptote, we compare the coefficients of the highest power of x. The coefficient of x in both the numerator and denominator is -3. So the horizontal asymptote is y = -3.
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The vertical asymptotes of this rational function are x = 4 and x = 2.
The horizontal asymptote is y = -3.
What is a rational function?In Mathematics and Geometry, a rational function refers to a type of function which is expressed as a fraction.
By critically observing the rational function [tex]f(x)=\frac{-3(x + 3)(x - 2)}{(x -4)(x - 2)}[/tex] shown above, we can logically deduce that its vertical asymptote can be determined by solving the denominator as follows;
(x - 2)(x - 4) = 0
x = 2 and x = 4.
Since the degree of the numerator is the same as the degree of the denominator, we can reasonably infer and logically deduce that this rational function's horizontal asymptote can be calculated by dividing the leading coefficient of the numerator by the leading coefficient of the denominator as follows;
y = -3/1
y = -3.
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An elementary school collected 1,705 bottles for a recycling program.a high school also collected some bottles.both schools collected 3,627 bottles combined. Now many bottles did the high school collected
what is -0.38,-3/8,-0.04 in order from least to greatest
Sketch the region bounded by the curves y=9x3,y=9 and x=0 then find the volume of the solid generated by revolving this region about the x-axis.
The volume of the solid generated is 218.01 cubic units
The curves are given as:
[tex]y = 9x^3[/tex], y = 9
[tex]x = 0[/tex]
Start by calculating x at [tex]y = 9x^3[/tex]
Substitute 9 for y
[tex]9x^3 = 9[/tex]
Divide both sides by 9
[tex]x^3 = 1[/tex]
Take the cube roots of both sides
[tex]x = 1[/tex]
So, the equation of the volume is then represented as:
[tex]V = \pi \int\limits^a_b {9^2 - (9x^3)^2} \, dx[/tex]
[tex]V = \pi\int\limits^a_b {81 - 81x^6} \, dx[/tex]
Where [a,b] = [1,0]
So, we have:
[tex]V = \pi\int\limits^1_0 {81 - 81x^6} \, dx[/tex]
Factor out 81
[tex]V = 81\pi\int\limits^1_0 {1 - x^6} \, dx[/tex]
Integrate
[tex]V = 81\pi [x - \frac 17x^7]|\limits^1_0[/tex]
Expand
[tex]V = 81\pi ([1 - \frac 17(1)^7] - [0 - \frac 17(0)^7] )[/tex]
[tex]V = 81\pi ([1 - \frac 17] )[/tex]
[tex]V = 81\pi * \frac 67[/tex]
So, we have:
[tex]V = 81 * 3.14 * \frac 67[/tex]
[tex]V = 218.01[/tex]
Hence, the volume of the solid generated is 218.01 cubic units
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The highest point in Texas ,Guadalupe peak is 8749 feet high the highest point in California Mount Whitney is 14497 feet high. How much higher is Whitney then Guadalupe?
a wire 30 cm long is cut into two pieces. the longer piece is 6 cm longer than the shorter piece. find the length of the shorter piece of wire
The length of the shorter piece of wire is 12 cm, which is found by setting up the equation x + (x + 6) = 30, where x is the length of the shorter piece.
The student has asked to find the length of the shorter piece of wire when a 30 cm long wire is cut into two pieces, with the longer piece being 6 cm longer than the shorter piece. To solve this, we need to set up a simple equation based on the information given.
Let's represent the length of the shorter piece as x cm. Since the longer piece is 6 cm longer than the shorter piece, we can represent the longer piece as (x + 6) cm
We are told that the total length of the wire before it was cut was 30 cm. Therefore, the sum of the lengths of both pieces must equal 30 cm. This gives us the equation:
x + (x + 6) = 30
Simplifying the equation, we get:
2x + 6 = 30
Subtracting 6 from both sides of the equation gives us:
2x = 24
Dividing both sides by 2 to solve for x gives us:
x = 12
smamantha deposits ＄300 in a bank account thats earns an annual rate of 2.5%.after 9months,she computes the simple interest what is the correct amount of simple interest after 9 months
What is the distance around a triangle that has sides measuring 2 1/8 ft 3 1/2 ft and 2 and 1/2 ft
Which equation represents a line that passes through (–2, 4) and has a slope of 2/5 ?
Answer:
Y-4 =2/5(x-(-2)) is answer on edge
Step-by-step explanation:
Use point slope equaction y-y1=m(x-x1)
y1= 4 x1= -2 and m= 2/5 just plug in numbers
Which equation can be solved to find one of the missing side lengths in the triangle?
Solve for y in a=9y+3yx
Answer:
[tex]y=\frac{a}{(9+3x)}[/tex]
Step-by-step explanation:
we have
[tex]a=9y+3yx[/tex]
Solve for y
That means -----> isolate the variable y
Step 1
Factor the variable y in the right side
[tex]a=y(9+3x)[/tex]
Step 2
Divide by [tex](9+3x)[/tex] both sides
[tex]a/(9+3x)=y(9+3x)/(9+3x)[/tex]
Step 3
Simplify
[tex]y=\frac{a}{(9+3x)}[/tex]
A sporting goods manufacturer designs a golf ball having a volume of 2.48 cubic inches.
What is the radius of the golf ball?
If the ball's volume can vary between 2.45 cubic inches and 2.51 cubic inches, how can the radius vary?
identify epsilon and limit
Please solve for x
(X+4)/x=45
On a bike across the United States rodney notes that he covers about 190 miles every 4 days if he continues
at this rate use a ratio table to determine how many miles he could buy in 6 days
Which of the following symbols correctly replaces the question mark (?) in the number comparison below?
0.700 ? 0.7
>
≠
=
<
Answer:
=
Step-by-step explanation:
When solving this, we just have to remember that the zero´s to the right after the decimal point are meaningless, so basically 0.700 is the same as 0.7 so in this case both number are the same, 0.700 and 0.7 are the same number expressed in different ways.
Find the amount of money in an account after 10 years if a principal of $2500 is invested at 3.5% interest compounded quarterly
in 2010 there were 98 thousand us troops in iraq. This is 23 thousand more than half the number of us trrops in iraq in 2003 find the number of us trrops in iraq in 2003
What is the best answer to report for (679 × 0.0025) 24.17?
To solve (679 × 0.0025) + 24.17, multiply 679 by 0.0025 to obtain 1.6975, then add this to 24.17 to get the final result, which rounded to the nearest thousandth is 25.868.
To find the best answer to report for the calculation (679 × 0.0025) + 24.17, we first perform the multiplication of 679 by 0.0025. This step is crucial to solve the problem accurately. After carrying out the multiplication, we add the result to 24.17 to find the final answer.
Calculating 679 × 0.0025 gives us 1.6975. The next step is to add this product to 24.17:
1.6975 + 24.17 = 25.8675
Thus, the best answer to report, rounded to the nearest thousandth as is common in many mathematical contexts, would be 25.868.
Complete Question:
What is the best answer to report for: (679 × 0.0025) + 24.17?
A certain plant grows 1 1/6 inches every week. How long will it take the plant to grow 6 1/6 inches
If it is springtime, you will plant flowers in the garden.
If you plant flowers in the garden, your yard will smell good.A.
If your yard smells good, then it is springtime.
law of syllogism
B.
If your yard smells good, then it is springtime.
law of detachment
C.
If it is springtime, then your yard will smell good.
law of syllogism
D.
If it is springtime, then your yard will smell good.
law of detachment
Option C correctly applies the Law of Syllogism. By combining the hypothesis from the first statement, 'If it is springtime, you will plant flowers in the garden' with the conclusion of the second, 'If you plant flowers in the garden, your yard will smell good' we form 'If it is springtime, then your yard will smell good'.
Explanation:The question deals with logical reasoning, specifically the laws of syllogism and detachment. The Law of Syllogism takes two conditional statements and forms a conclusion by combining the hypothesis of one statement with the conclusion of another. The Law of Detachment, also known as Modus Ponens, applies when a single conditional statement and the affirmation of its hypothesis lead to the affirmation of its conclusion.
Looking at the options:
A. The statement does not apply the law of syllogism.
B. The statement does not apply the law of detachment.
C. This statement correctly applies the Law of Syllogism. We have two statements: 'If it is springtime, you will plant flowers in the garden' and 'If you plant flowers in the garden, your yard will smell good'. Combining the hypothesis of the first with the conclusion of the second gives us 'If it is springtime, then your yard will smell good'.
D. This accurately applies the law, but the law it uses is not mentioned.
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As mercury revolves around the sun, it travels at a speed of approximately 30 miles per second. Convert this speed to kilometers per second. At this speed how many kilometers will Mercury travel in 2 seconds ? In your computations, assume that 1 mile is equal to 1.6 kilometers.
The speed of Mercury around the Sun in kilometers/second is 48 kilometers/second.
In 2 seconds, Mercury will travel 96 kilometers.
What is the speed of an object?The speed of an object is the ratio of the distance travelled by the object to the time taken by the object to travel that distance.
Given, the speed of Mercury around the Sun is 30 miles/second.
Therefore, the speed of Mercury around the Sun in kilometers/second
= (30 × 1.6) kilometers/second
= 48 kilometers/second
Now, in 2 seconds, Mercury will travel
= 48 × 2 kilometers
= 96 kilometers
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divide 300 g^2 0.0005 g and express using scientific notation
Answer:
[tex]\Rightarrow 6\times 10^5\ g[/tex]
Step-by-step explanation:
Given : Divide two number and write as scientific notation.
Scientific notation:
[tex]\Rightarrow k\times 10^n[/tex]
Number 1: 300 g²
Number 2: 0.0005 g
Divide [tex]=\dfrac{300\ g^2}{0.0005\ g}[/tex]
[tex]\Rightarrow \dfrac{30\times 10}{5\times 10^{-4}\ g{2-1}[/tex]
[tex]\Rightarrow 6\times 10^{1+4}\ g[/tex]
[tex]\Rightarrow 6\times 10^5\ g[/tex]
Scientific notation:
[tex]\Rightarrow k\times 10^n[/tex]
Hence, The result of division is [tex]\Rightarrow 6\times 10^5\ g[/tex]
A silo composed of a cylinder topped by a half-sphere. The height of the cylinder is 6.2 meters and the radius of both the cylinder and the half-sphere is 1.6 meters. Use 3.14 for pi. Find the volumes of the half-sphere, the cylinder, and the entire silo to the nearest tenth. Explain how you found the volume of the silo.
Answer:
55.88
Step-by-step explanation:
The weight of outlet boxes is proportional to the volume of boxes involved. if 400 boxes weigh 120 pounds, how much would 500 boxes weigh?
Answer:
150 lbs
Step-by-step explanation:
set up proportion
400/120 = 500/x
cross multiply
120x500 = 400x
then simplify
60000 = 400x
solve for x
60000/400 = x
x = 150
Using graph paper, determine the line described by the given point and slope. Click to show the correct graph below. (2, -4) and - 3/2
The answer should look something like this:
Another common multiple of 30 and 42 besides 210
Evaluate the exponential function ƒ(x) = 8x + 1.
the answer, by putting 1/3 in the place of x the answer comes out to 3.
What is 40 1/2 divided by 13 1/2?
Jenny ball bounced 8 times farther than clarks ball. The two balls bounced a total distance of 36 inches. How far did Jenny's ball bounce?
The correct answer is that Jenny's ball bounced 32 inches.
To solve the problem, let's denote the distance that Clark's ball bounced as [tex]\( d \)[/tex] inches. According to the problem, Jenny's ball bounced 8 times farther than Clark's ball, so the distance Jenny's ball bounced is [tex]\( 8d \)[/tex] inches.
The total distance bounced by both balls is the sum of the distances each ball bounced, which is given as 36 inches. Therefore, we can set up the following equation:
[tex]\[ d + 8d = 36 \][/tex]
Combining like terms, we get:
[tex]\[ 9d = 36 \][/tex]
To find the value of [tex]\( d \)[/tex], we divide both sides of the equation by 9:
[tex]\[ d = \frac{36}{9} \][/tex]
[tex]\[ d = 4 \][/tex]
Now that we have the distance Clark's ball bounced, which is 4 inches, we can find the distance Jenny's ball bounced by multiplying [tex]\( d \)[/tex] by 8:
[tex]\[ 8d = 8 \times 4 \][/tex]
[tex]\[ 8d = 32 \][/tex]
So, Jenny's ball bounced 32 inches.
Consider the type of clothes dryer (gas or electric) purchased by each of five customers at a certain store. A. If the probability that at most one of these purchases an electric dryer is 0.428 what is the probability that at least two purchase an electric dryer?