1) The data in the table below represents the pressure of the gas as the temperature changes. Plot a graph of the data, using the space below. Draw a trend line and calculate its slope. How are the variables related? What will he pressure of the gas be at 0C?
the graph looks like this
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
Answers
Answer:
The pressure of the gas 0°C is about 699.
Step-by-step explanation:
The given table of values is
Temperature Pressure
10 723
25 763
40 800
55 845
80 900
The general form of a trend line is
[tex]y=a+bx[/tex]
where, b is slope and a is y-intercept.
[tex]b=\frac{\sum_{i=1}^nx_iy_i-n\overline{x}\overline{y}}{\sum_{i=1}^nx_i^2-n\overline{x}^2}[/tex]
[tex]a=\overline{y}-b\overline{x}[/tex]
Using graphing calculator, we get
[tex]a=699.006826[/tex]
[tex]b=2.552218[/tex]
The equation of line of best bit is
[tex]y = 2.552218x + 699.006826[/tex]
where, y is pressure at x°C.
We need to find the pressure of the gas at 0°C.
Substitute x=0 in the above equation.
[tex]y = 2.552218(0) + 699.006826[/tex]
[tex]y =699.006826[/tex]
[tex]y \approx 699[/tex]
Therefore the pressure of the gas 0°C is about 699.
Related Questions
√19 approximated to nearest tenth
Answers
Square root of 19 ≈ 4.35889
Round to nearest tenth would be 4.4
Find the x-coordinates of all points on the graph of: f(x)=6sinx-sin^2x
at which the tangent line is horizontal.
Answers
Then find f '(x)
f '(x) = 6cosx - 2sinxcosx = 2cosx (3 - sinx) =0
=> 3 - sinx = 0, which is never
or cosx = 0, which is for x = π/2, 3π/2, 5π2, ...., -π/2 , -3π/2, -5π/2 , ...
You can represent that by x = π/2 + kπ, for k ∈ Z.
Final answer:
To find the x-coordinates where the function f(x)=6sin(x)-sin^2(x) has a horizontal tangent line, we calculate the derivative, set it equal to zero, and solve for x, using trigonometric identities and potentially numerical methods. Thus, the solutions for \( x \) in the interval [tex]\( [0, 2\pi] \) are \( x = \frac{\pi}{2} + k\pi \), where \( k \)[/tex] is an integer. These solutions represent the points where [tex]\( \cos(x) = 0 \)[/tex], causing the equation to be satisfied.
Explanation:
The question asks to find the x-coordinates of all points on the graph of the function f(x)=6sin(x)-sin2(x) at which the tangent line is horizontal. To find these coordinates, we need to look for points where the derivative of the function is equal to zero since a horizontal tangent line has a slope of zero.
We start by finding the derivative of the function:
f'(x) = d/dx[6sin(x)-sin2(x)]
f'(x) = 6cos(x)-2sin(x)cos(x)
f'(x) = 6cos(x)-sin(2x) (using the double angle identity sin(2x)=2sin(x)cos(x))
To find when the derivative is zero, we set the derivative equal to zero:
0 = 6cos(x) - sin(2x)
We then need to solve this equation for x. This involves using trigonometric identities and potentially numerical methods if the equation cannot be solved analytically. The x-coordinates will be the solutions to this equation within the domain for which we are interested, typically 0 to 2π for one full cycle of a trigonometric function.
To solve the equation [tex]\( 0 = 6\cos(x) - \sin(2x) \)[/tex], we'll first try to rewrite it in terms of a single trigonometric function using known identities.
The double angle identity for sine states that [tex]\( \sin(2x) = 2\sin(x)\cos(x) \)[/tex]. Substituting this identity into the equation, we get:
[tex]\[ 0 = 6\cos(x) - 2\sin(x)\cos(x) \]\\Now, let's factor out \( \cos(x) \):\[ 0 = \cos(x)(6 - 2\sin(x)) \][/tex]
Now, for the equation to be true, either [tex]\( \cos(x) = 0 \) or \( 6 - 2\sin(x) = 0 \)[/tex].
1. If [tex]\( \cos(x) = 0 \), then \( x = \frac{\pi}{2} + k\pi \)[/tex], where \( k \) is an integer.
2. If [tex]\( 6 - 2\sin(x) = 0 \), then \( \sin(x) = 3 \)[/tex]. However, the sine function has a range of \([-1, 1]\), so there are no solutions for \( x \) in this case.
Thus, the solutions for \( x \) in the interval [tex]\( [0, 2\pi] \) are \( x = \frac{\pi}{2} + k\pi \), where \( k \)[/tex] is an integer. These solutions represent the points where [tex]\( \cos(x) = 0 \)[/tex], causing the equation to be satisfied.
Write the expression 4 log x − 6 log (x + 2) as a single logarithm
Answers
4 log x − 6 log (x + 2)
log x⁴ - log (x + 2)⁶
now you can use log properties to combine this into a single logarithm. once you change the coefficients, you can now see that this is simply a log minus another log--and that subtraction symbol actually becomes division by the logarithm quotient property.
log (x⁴)/(x + 2)⁶ is the condensed version of this logarithm. in case the formatting isn't easy to read, it's log of x to the fourth power over x plus 2 to the sixth power.
To write the expression 4 log x − 6 log (x + 2) as a single logarithm, apply the properties of logarithms.
Explanation:To write the expression 4 log x − 6 log (x + 2) as a single logarithm, we can make use of the following logarithmic properties:
The logarithm of a product of two numbers is the sum of the logarithms of the two numbers: log(xy) = log(x) + log(y)The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number: log(x^n) = n log(x)The logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers: log(x/y) = log(x) - log(y)Using these properties, we can simplify the given expression as follows:
4 log x − 6 log (x + 2) = log(x^4) - log((x + 2)^6)
Therefore, the expression can be written as the single logarithm log(x^4) - log((x + 2)^6).
Consider the level surface given by
x2−y2+z2=2. Draw a picture for the following:
1. Slice for y=2
2. Slice for x=1
3. Slice for y=0
4. Slice for x=2 ...?
Answers
Answer:
First of all, each slice represents an intersecting plane at that level.
For example, y = 2 is a plane that passes thorugh that level and cuts the volume given by [tex]x^{2} -y^{2}+z^{2}=2[/tex]
1. Slice for y = 2.We replace this value in the given volume.
[tex]x^{2} -y^{2}+z^{2}=2\\x^{2} -(2)^{2}+z^{2}=2\\x^{2}+z^{2}=2+4\\x^{2}+z^{2}=6[/tex]
So, results in a circumference with radius [tex]\sqrt{6}[/tex], because a circumference is defind as [tex]x^{2} +y^{2} =r^{2}[/tex]. (On plane XY).
2. Slice for x = 1.We repeat the process.
[tex](1)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-1\\z^{2}-y^{2}=1[/tex]
It forms a horizontal hyperbola on plane ZY.
3. Slice for y = 0.[tex]x^{2} -0^{2}+z^{2}=2\\x^{2}+z^{2}=2[/tex]
Another circle with radius of [tex]\sqrt{2}[/tex] on plane XZ.
4. Slice for x = 2.[tex](2)^{2} -y^{2}+z^{2}=2\\z^{2}-y^{2}=2-4\\z^{2}-y^{2}=-2\\\frac{z^{2}-y^{2}}{-2} =\frac{-2}{-2} \\\frac{y^{2} }{2} -\frac{z^{2} }{2} =1[/tex]
It forms a hyporbola on plane YZ.
The figure shown is formed by the arcs joining the midpoints of the four sides of a square with a side length of 15 centimeters.
The area of the shape is __
square centimeters
Answers
Hope this is useful
What is the value of the function y = 2x + 3 when
x=−1
?
Answers
solve.
3/4x=18 please show work ...?
Answers
18 times 4/3
this will be 72/3
72 divided by 3 is 24
X = 24
3 = 18 x 4x
4x = 3/18
4x = 1/6
x = 1/24
Problem Page A car is traveling at a rate of 63 miles per hour. What is the car's rate in feet per second? How many feet will the car travel in 15 seconds? In your computations, use the fact that 1 mile is equal to 5280 feet. Do not round your answers.
Answers
[tex]v=63 miles/s=63\times5280 feet/s=332640\ \ \ \ feet/s[/tex]
It will travel,
[tex]space=v\cdot t=332640\cdot 15/3600=1386\ \ \ feet[/tex]
in 15 seconds.
which of the following r one dimensional figures?
check all that apply.
a. ray
b. angle
c. square
d. point
e. segment
f. line
Answers
Answer: Segment, line, ray
Step-by-step explanation: too answer was confusing and point was wrong.
The answers are a. ray, e. segment and f. line
In geometry, a one-dimensional figure has only length and no other dimensions such as width or height. Let's analyze each option:
Ray - A ray is one-dimensional as it starts from a point and extends infinitely in one direction.Angle - An angle is formed by two rays meeting at a point, which makes it not one-dimensional.Square - A square is a two-dimensional figure with length and width.Point - A point has no dimensions; it is zero-dimensional.Segment - A segment is one-dimensional as it consists of two endpoints and the line connecting them.Line - A line is one-dimensional as it extends infinitely in both directions.Thus, the one-dimensional figures are the ray, segment, and line.
The scientific notation 2.15 × 10-3 has what value?
Answers
So, your answer is 0.00215
Answer:
The scientific notation 2.15 × 10-3 has a value of
0.00215
Step-by-step explanation:
Step one
This problem bothers conversion from standard form otherwise known as scientific notation to decimal form
Step two
Now we are presented with the expression
2.15 × 10-³
To convert this it is equivalent to
2.15/10³= 2.15/1000
= 0.00215
On the other hand this can also be achieved without calculations by visually counting from the decimal point to the right 2 placements before inserting the first integer
This method saves alot of time expecialy when time is of essence.
Hence the scientific notation 2.15 × 10-3 has a value of
0.00215
What is the unit rate of max wrote 10 pages of his lab report in 4 hours?
Answers
so, in 1 hour it would be: 10/4 = 2.5 pages
So, your answer is 2.5 pages in an hour
Hope it helped.
Alan is putting weed killer on a field to get it ready for planting. The directions on the can say to use 4/5 of a quart for each acre of land. How much weed killer will Alan need for two fields, one that is 22 1/2 acres and one that is 38 1/4 acres?
28 1/8 quarts
47 4/5 quarts
60 3/4 quarts
48 3/5 quarts
Answers
[tex](22\frac{1}{2} + 38\frac{1}{4}) *\frac{4}{5}[/tex]. Simplified, this is 48.6, or [tex]48\frac{3}{5}[/tex]
[tex]48\frac{3}{5}[/tex]
Which shows the expression below in simplified form?
(7.4 × 10^-1) - (4.1 × 10^-4)
A. 7.3959 × 10^-1
B. 7.39959 × 10^-1
C. 7.359 × 10^-2
D. 7.3959 × 10^-2
Answers
What percent of 600 is 24?
Answers
Hope this helps :)
Which equations show that the set of whole numbers is not closed under subtraction?
Choose all answers that are correct.
A.
1 – (–2) = 3
B.
1 – 2 = –1
C.
2 – 0 = 2
D.
2 – 4 = –2
Answers
1 – 2 = –1 and D.2 – 4 = –2
To determine which ones are correct, you have to find one that has whole numbers and not a whole in the end. After that the only thing you have to do is subtraction,and you will have the needed set of whole numbers.
Do hope it will help you!
Solve for x. Type a numerical answer in the space provided. Do not use spaces in your answer. For example, if the answer is x = 15, type 15.
15x + 6 = 10x + 21
Answers
subtract 6 from both sides, then subtract 10x from both sides. You then have 5x=15; divide 5 from both sides and you get 3. Therefore, x is 3.
(x + 2)4 = x4 + 8x3 +... Use the Binomial Theorem to complete the binomial expansion. Enter only the next three terms; use the ^ key for exponents, example: 10x^2+20x+30.
Answers
Another math help ^_^
Answers
What is the answer to 86-11/11+4
Answers
86-1+4
86+3
=89..
100, 96, 104, 88, 120, 56, ? what comes next? here are the choices (184, 140, 77, 124, 128)
Answers
The function t(n)=8n represents the number of tires t(n) that are needed for n trucks. How many tires are needed for 25 trucks? A.32 tires B.150 tires C.200 tires D.250 tires
Answers
t = 200
The answer is C.
The function t(n)=8n represents the number of tires needed for each truck. By substituting n=25 into the function, we find we need 200 tires for 25 trucks.
Explanation:The function that represents the number of tires needed for each truck is t(n) = 8n. This means for each truck we need 8 tires, as n is the number of trucks and 8n signifies the total number of tires needed for those trucks.
If we want to find out the number of tires we would need for 25 trucks, we substitute n = 25 into the function, yielding t(25) = 8 * 25. When you perform this multiplication, the result is 200 tires.
So, for 25 trucks we would need 200 tires. Meaning "the correct answer is C. 200 tires".
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If there is 7018 mm, what is the metric unit for 7.018?
Answers
write an equation in slope intercept form with a slope 3/2 and y-intercept -2
Answers
what is the five non zero multiples of 5
Answers
Is this what you are looking for?
The first five non-zero multiples of 5 are 5, 10, 15, 20, and 25. These are obtained by multiplying the number 5 by the integers 1 to 5. All non-zero multiples of 5 will end with the digit 5 or 0, confirming their divisibility by 5.
Identifying Non-Zero Multiples of 5
When you're looking for non-zero multiples of 5, it's important to remember that the basic property of a multiple of 5 is that it ends in either 0 or 5. However, since we're focusing on non-zero multiples, we will exclude any multiples that end in zero. A multiple of a number is obtained by multiplying that number by an integer. For the number 5, the first five non-zero multiples are 5, 10, 15, 20, and 25. Notice that these numbers are the result of multiplying 5 by the integers 1 through 5, respectively.
Understanding that the concept of multiples relates to a number being multiplied by a sequence of whole numbers or integers gives us the ability to identify patterns within these numbers. For example, all non-zero multiples of 5 will end with the digit 5 or 0, reinforcing the idea that if a number ends in 5, it is divisible by 5 without remainder. This concept is supported by empirical observation and the understanding that patterns and numbers, such as these, can offer insight into broader mathematical ideas. Furthermore, the significance of the number 5 in various mathematical circumstances, such as the number of digits in a number or the properties of multiples, is apparent throughout different contexts.
1.For f(x)= 5x+1 : Find(-4).
a.-19 b.1 c.-21 d. 21
2. Write in Standard form an equation of the line passing through the given point with the given slope.
slope=-8 ; (-2,-2)
a.8x+y=-18 b.-8x+y=-18 c. 8x-y=-18 d.8x+y=18
Answers
f(x)= 5x+1f(-4) = 5(-4) + 1
so
f(-4) = -19 is correct
2)
y = mx+b
-2 = -8(-2)+b
-2 = 16+b
-2-16 = b
-18 = b
b = -18
-------------
y = mx+b
y = -8x-18
8x+y = -18
Answer is choice A
1.a. -19 at x = -4 for f(x) = 5x + 1.
2.a. 8x + y = -18 the standard form of the equation.
What is a line ?A line has no definite length it can extend in both the directions indefinitely.
According to the given question a functions f(x) = 5x + 1 is given and we have to find the value of this function when x = -4.
Given f(x) = 5x + 1
f(-4) = 5(-4) + 1
f(-4) = -20 + 1
f(-4) = -19.
In the second question we have to write an equation of the line passing through the point (-2,-2) with slope -8.
We know equation of a line in slope intercept form is y = mx + b.
∴ -2 = (-8)(-2) + b
-2 = 16 + b
b = - 18.
So, y = -8x -18 OR 8x + y = -18.
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a boat travels 66 miles in 2 hours. what is its rate in feet per minute?
Answers
The rate of the boat that travels 66 miles in 2 hours is approximately 2904 feet per minute.
Given:
Distance traveled = 66 miles
Time taken = 2 hours
We know that:
1 mile = 5280 feet
66 miles = 66 [tex]\times[/tex] 5280
348,480 feet
Next, we'll convert the time from hours to minutes.
1 hour = 60 minutes,
2 hours = 120 minutes
Now, we can calculate the rate in feet per minute:
Rate (feet per minute) = [tex]\dfrac{ Distance \ in\ feet}{Time\ in\ minutes}[/tex]
Rate = [tex]\dfrac{348480}{120}[/tex]
Rate ≈ 2904 feet per minute
So, the rate of the boat is approximately 2904 feet per minute.
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What is the value of the underlined digit in the number 1,711,799 with the lst 7 being underlined
Answers
In the context of the number 1,711,799, the first 7 underlined is in the hundred thousands position, which gives it a value of seven hundred thousand (700,000).
Explanation:In the given number 1,711,799, we're asked to find the value of the first underlined 7. Considering the location of the number, 7 is in the hundred thousands position. The value of a digit depends on its place in the number. Therefore, despite the fact that the digit is '7', because it is in the hundred thousands place, its value is seven hundred thousand (700,000).
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A dilation on a rectangle has a scale factor of 4. what is the effect on the perimeter of the rectangle ? ...?
Answers
I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
The dilation of a rectangle with a scale factor of 4 will result in each side of the rectangle being multiplied by 4, thus the perimeter will also be quadrupled.
Explanation:When a rectangle undergoes a dilation with a scale factor of 4, the lengths of all sides of the rectangle are multiplied by 4. Since perimeter is the sum of all the side lengths of a rectangle, the perimeter will also be affected by the scale factor. Therefore, if the original perimeter of the rectangle is P, the new perimeter after dilation will be 4 × P.
Using the property of dilations, the new dimensions of the rectangle will be proportional to the original dimensions. For example, if the original length l and width w of the rectangle are scaled by a factor of 4, the new dimensions will be 4l and 4w respectively. Subsequently, the new perimeter will be 2(4l + 4w) which is the same as saying 4 × (2l + 2w), proving the perimeter is scaled by the same factor of 4.
Which of the following equations could be used to solve for the tenth term of the following sequence?
15, 13, 11, 9, ...
A(10) = 15 + 10(-2)
A(10) = 15 + 9(-2)
A(10) = 15 + 9(2)
A(10) = 15 + 10(2)
Answers
where n is the term u want to find, which is 10.......a1 = first term = 15...d is common difference = -2.
A(10) = 15 + (10 - 1) * -2.....
A(10) = 15 + 9(-2) <===
Answer:
Option(B) is correct.
The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
Step-by-step explanation:
Given : The sequence 15, 13, 11, 9,....
We have to determine the equation that can be used to find the tenth term of the given sequence 15, 13, 11, 9,....
Consider the given sequence 15, 13, 11, 9,..
[tex]a_1= 15, a_2=13, a_3= 11[/tex]
Difference between each term is
[tex]a_2-a_1=13-15=-2\\ a_3-a_2=11-13=-2[/tex]
Since, The difference between each term is constant -2
Thus, The given sequence is an arithmetic sequence with first term 15 and common difference -2.
Thus, The general term is given by
[tex]a_n=a+(n-1)d[/tex]
where a is first term and d is common difference nd n is number of term.
Subsitute, we have,
[tex]a_{10}=15+(10-1)(-2)[/tex]
Simplify, we have,
[tex]a_{10}=15+9(-2)[/tex]
Thus, The tenth term is given by [tex]a_{10}=15+9(-2)[/tex]
you are studying for your final exam of the semester. up to this point,you recieved 3 exam scores of 83%,85%, and 84%. to recieve a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
Find the widest range of scores that you can get on the final exam in order to recieve a grade of B for the class.Use interval notation ...?
Answers
This will allow you to get a B score.
To solve find the medium by adding the values divided by 4, solve for the unknown of the final exam, with the minimum value equalling 80, this will give you 68.
Answer:
The widest range lies between [68,100]
Step-by-step explanation:
Given is - to receive a grade of B in the class you must average exam score between 80% and 89% for all 4 exams including the final.
So, the range of the addition of all 4 scores is -
[tex]80*4=320[/tex]
[tex]89*4=356[/tex]
Now given scores addition is = [tex]83+85+84=252[/tex]
Now, the widest range of scores that you can get on the final exam in order to receive a grade of B can be found as :
[tex]320-252= 68[/tex]
[tex]356-252= 104[/tex]
So, the range lies between [68,100]