Answer:
The standard deviation of the age is 6.16
Step-by-step explanation:
* Lets talk about the variance and the standard deviation
- The variance is the measure of how much values in a set of data are
likely to differ from the mean value of the same data
- The steps to find the variance are:
1- Find the mean of the data
2- Subtract the mean from each value and square the answer
3- Add all of these squared answer and divide the sum by the number
of the values
- The answer of the step 3 is The variance (σ²)
- The standard deviation (σ) is the square root of the variance
* Now lets solve the problem
∵ The variance of the ages of the people who attended a rock
concert is 38
∴ σ² = 38
∵ The standard deviation is the square root of the variance
∴ σ = √38 = 6.16
* The standard deviation of the age is 6.16
Answer:
[tex]\sigma=6.16[/tex]
Step-by-step explanation:
By definition, the variance V of a population is defined as:
[tex]V = \sigma^2[/tex]
Where [tex]\sigma[/tex] is the standard deviation
We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]
[tex]38 = \sigma^2[/tex]
[tex]\sigma^2=38[/tex]
[tex]\sigma=\sqrt{38}[/tex]
[tex]\sigma=6.16[/tex]
Finally the standard deviation is: [tex]\sigma=6.16[/tex]
What is 25% more than 80?
Answer:
100
Step-by-step explanation:
When being asked what is x% more than y (y is something), you can use the formula 25% * y + y. However, you must convert the percent into a decimal for it to be used mathematically.
25% = 0.25
Now we can plug all of the numbers in.
0.25 * 80 + 80
20 + 80
100
An 'A' is considered 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0. If you received the following grades in your first semester, what would your grade point average be?
To calculate the GPA, convert each grade to its numerical equivalent, add these up, and then divide by the total number of grades given. For example, the GPA for grades 'A', 'A', 'B', 'C', and 'D' would be 2.8.
Explanation:To find the grade point average (GPA), you add up all the grade points and then divide by the total number of grades. Let's imagine you received the following grades: 'A', 'A', 'B', 'C', and 'D'.
First convert each grade to its grade point: A=4.0, B=3.0, C=2.0, D=1.0Next, add these up: 4.0 + 4.0 + 3.0 + 2.0 + 1.0 = 14.0Then, count the number of grades which is 5 in this case.Finally, divide the total grade points by the number of grades: 14.0 / 5 = 2.8
So your GPA would be 2.8.
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Final answer:
To calculate your grade point average (GPA), assign numerical values to each letter grade and average them. In this case, the GPA would be 2.5 for the given grades.
Explanation:
To calculate your grade point average (GPA), you need to assign the respective numerical value to each letter grade and then average them. In the given scenario, an 'A' is equal to 4.0, a 'B' is 3.0, a 'C' is 2.0, a 'D' is 1.0, and an 'F' is 0.0. Let's assume the grades for your first semester are A, B, C, and D. To calculate your GPA, add up the numerical values of the grades and divide by the number of grades you have.
So, the calculation would be: (4.0 + 3.0 + 2.0 + 1.0) / 4 = 2.5.
Therefore, your grade point average for the first semester would be 2.5.
What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?
Answer:
[tex]\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}[/tex]
Step-by-step explanation:
The explicit formula for a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
[tex]a_n[/tex] - n-th term
[tex]a_1[/tex] - first term
[tex]r[/tex] - common ratio
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}[/tex]
We have
[tex]a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...[/tex]
The common ratio:
[tex]r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}[/tex]
It's not a geometric sequence.If [tex]a_3=-\dfrac{1}{16}[/tex] then the common ratio is [tex]r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}[/tex]
Put to the explicit formula:
[tex]a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}[/tex]
Put [tex]a_n=\dfrac{1}{1024}[/tex] and solve for n :
[tex]-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1[/tex]
[tex]\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6[/tex]
Evaluate ƒ(x) when x = 10
Answer:
f(x) = 10² + 3 = 100 + 3 = 103
Final answer:
Without a specific definition of ƒ(x), we can't provide a precise evaluation at x = 10. However, if ƒ(x) is a constant function such as ƒ(x) = 20 for the range of 0 to 20, then ƒ(10) would be 20.
Explanation:
To evaluate the function ƒ(x) when x = 10, we need to know the specific form of the function. However, based on the information provided, which seems fragmented and from different contexts, I can assume that ƒ(x) is defined for certain ranges. There’s reference to a horizontal line graph representation of a function, which suggests that ƒ(x) could potentially be a constant function within a certain range. If the function ƒ(x) is indeed a constant function, such as ƒ(x) = 20 for 0 ≤ x ≤ 20, then evaluating it at x = 10 would simply give the constant value, which is 20.
From the other contexts provided, it's implied that there could be scenarios where ƒ(x) represents different mathematical or physics concepts, such as force, probability distribution, or equations of motion. Without a direct specification of ƒ(x) for the x value in question, the remaining information cannot be used to definitively evaluate ƒ(x) at x = 10.
15 POINTSPLEASE HELP WITH MY MATH PROBLEM
Answer:
Another point is (3,1) and the vertex is (0,0)
Step-by-step explanation:
The vertex is still (0,0) since the parabola has only been stretched some way and not shifted from the parent function f(x)=x^2.
Enter in any x you like like 3 (I chose 3 because I see I'm going to multiply by 1/3). Anyways
g(3)=(1/3*3)^2=(1)^2=1 so another point on the parabola is (3,1)... Now just use the fact that all parabolas are symmetrical to graph it.
Write the equation of the line that passes through the given points (2,3) (2,5)
Answer:
x = 2
Step-by-step explanation:
Note that the coordinates (2, 3) and (2, 5) both have the same x- coordinate.
This indicates that the points lie on a vertical line parallel to the y- axis.
The equation of a vertical line is
x = c
where c is the value of the x- coordinates the line passes through.
In this case the x- coordinate is 2, hence the equation of the line is
x = 2
The tables represent two linear functions in a system,
What is the solution to this system?
(1,0)
(1,6)
(8, 26)
(8, -22)
Answer:
(8, -22)Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
First table:
(-4, 26), (0, 10) → b = 10
[tex]m=\dfrac{10-26}{0-(-4)}=\dfrac{-16}{4}=-4[/tex]
[tex]\boxed{y=-4x+10}[/tex]
Second table:
(-4, 14), (0, 2) → b = 2
[tex]m=\dfrac{2-14}{0-(-4)}=\dfrac{-12}{4}=-3[/tex]
[tex]\boxed{y=-3x+2}[/tex]
We have the system of equations:
[tex]\left\{\begin{array}{ccc}y=-4x+10&(1)\\y=-3x+2&(2)\end{array}\right\\\\\text{Put (1) to (2):}\\\\-4x+10=-3x+2\qquad\text{subtract 10 from both sides}\\-4x=-3x-8\qquad\text{add 3x to both sides}\\-x=-8\qquad\text{change the signs}\\x=8\\\\\text{Put the value of x to (2):}\\\\y=-3(8)+2\\y=-24+2\\y=-22[/tex]
The solution to the given system of equations is (8, -22). Therefore, option C is the correct answer.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
From the table 1.
Slope (m) = (18-26)/(-2-(-4))
= -8/2
m=-4
Substitute m=-4 and (x, y)=(-2, 18) in y=mx+c, we get
18=-4(-2)+c
18=8+c
c=10
So, the equation is y=-4x+10 -----(i)
From table 2:
Slope (m)=(8-14)(-2-(-4))
m=-3
Substitute m=-3 and (x, y)=(-2, 8) in y=mx+c, we get
8=-3(-2)+c
c=2
So, the equation is y=-3x+2 --------(ii)
From equation (i) and (ii), we get
-4x+10 =-3x+2
x=8
Substitute x=8 in equation (i), we get
y=-4(8)+10
y=-22
So, the solution is (8, -22)
Therefore, option C is the correct answer.
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If two dice are rolled one time find the probability
A 3 on one die or both dice
[tex]|\Omega|=6^2=36\\|A|=1\cdot5\cdot2+1=11\\\\P(A)=\dfrac{11}{36}\approx30.6\%[/tex]
Answer:
[tex]P=\frac{13}{36}=0.361[/tex]
Step-by-step explanation:
There are six possible outcomes when rolling a die. Therefore the probability of obtaining a 3 is a given is
[tex]P = \frac{1}{6}[/tex].
When throwing the two dice together, the probability of obtaining a 3 is the same:
[tex]P_1 = \frac{1}{6} * \frac{5}{6} + \frac{5}{6} * \frac{1}{6}=\frac{5}{18}[/tex]
Since the events are independent then the probability of obtaining a three in both dice is:
[tex]P_2 = \frac{1}{6} * \frac{1}{6} = \frac{1}{12}[/tex].
Finally the probability of obtaining a 3 on a given or both is equal to the sum of the probabilities [tex]P_1[/tex] and [tex]P_2[/tex]
[tex]P=\frac{1}{12}+\frac{5}{18}=\frac{13}{36}=0.361[/tex]
Complete the missing parts of the table for the following function
Answer:
At x=-2, y=16
At x=0, y=1
At x=3, y=1/64
Step-by-step explanation:
As we know that the function is given by:
[tex]y=(\frac{1}{4})^{x}[/tex]
The table represents the output values on given inputs.
So, when the input is -2:
[tex]y=(\frac{1}{4} )^{-2}\\y= \frac{(1)^{-2}}{(4)^{-2}}[/tex]
To convert the power in positive:
[tex]y=\frac{(4)^{2}}{(1)^{2} }\\y=16[/tex]
So the output for x=-2 is 16.
For x=0
[tex]y=(\frac{1}{4})^{0}[/tex]
Anything whose exponent is zero equals to 1, so y=1
For x=3, output is incomplete.
To complete,
[tex]y=(\frac{1}{4})^{3}\\y=\frac{(1)^{2} }{(4)^{2} }\\y=\frac{1}{64}[/tex] ..
Which system of equations can be used to find the roots of the equation 4x5 - 12x4 + 6x = 5x? - 2x?
ANSWER
Last option
EXPLANATION
The given equation is
[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]
We can form a system of equations by equating each side of the equation to y.
Equating the left hand side to y, we get
[tex]y = 4 {x}^{5} - 12 {x}^{4} + 6x...(1)[/tex]
Equating the right hand side to y gives
[tex]y= 5 {x}^{3} - 2x...(2)[/tex]To find the solution to
[tex]4 {x}^{5} - 12 {x}^{4} + 6x = 5 {x}^{3} - 2x[/tex]
We graph the two equations and locate the x-values of their points of intersection.
The last option is the correct answer
Answer:
D
Step-by-step explanation:
What is the answer to this question
Answer:
Number of Black grapes = 32
Step-by-step explanation:
This is a problem related to ratio and proportion. We are given the number of Green Grapes and the ration of Green Grapes to the Black Grapes
The ratio is 3:4
This means
[tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]
Now assume that the number of Black Grapes = x
Given that [tex]G_g[/tex]=24
Substituting these values in [tex]\frac{G_g}{G_b} = \frac{3}{4}[/tex]
[tex]\frac{24}{x} = \frac{3}{4}[/tex]
[tex]24*4 = 3*x\\x=\frac{24*4}{3}\\x=\frac{8*4}{1}\\x=32[/tex]
Hence the number of Black Grapes are 32
Answer:
32
Step-by-step explanation:
If 3:4 then 24:x (x represent the unknown)
So you have to divide 24 by 3 and the answer you get, which is 8, you multiply with four to get 32.
So we can say that both types of grapes are 8 times the amount that they originally were.
The value of x is ___ ?
Answer:
159
Step-by-step explanation:
Please see attachment
An airplane takes off at an angle of 75° from its starting point. When the plane has traveled a total distance of 600 feet, its vertical height above the runway to the nearest foot is 580 feet.
true or false
Witch of these has a slope of -3/4 and a y intercept of 3/2
Answer:
See explanation. (Also you can write an equation several different ways so without the choices I cannot tell you which)
Step-by-step explanation:
Slope-intercept form is y=mx+b
So one way to write the equation is y=-3/4 x +3/2
There are more ways to write it.
Every line about to write is a way to write it.
Multiply both sides by 4: 4y=-3x+6
Add 3x on both sides: 3x+4y=6
Subtract 6 on both sides: 3x+4y-6=0
There are a lot of ways to write an equation like this.
To better assist you I would need to see options.
Select the factors of x2 − 10x + 25.
Answer:
(x-5)2
Step-by-step explanation:
you must solve the expression (x-5)2 as the form (a-b)2 = a2 -2ab + b2
So it becomes x2-10x+25
Answer: (x-5)(x-5) or (x-5)²
Step-by-step explanation:
(a-b)(a-b)= a² - 2ab + b²
→ x² - 10x - 25
→ √25 = 5
so a= x, b= 5
this gives us (x-5)(x-5)
Quadrilateral PERK has vertices at P(4,4), E(12,4), R(10,−2), and K(2,−2). Find the vertices of the quadrilateral after a dilation with scale factor 32.
These are the options. 1,2,3, and 4.
1. P'(8/3, 8/3), E'(8, 8/3), R'(20/3, −4/3), and K'(4/3, −4/3)
2. P'(−6, −6), E'(−18, −6), R'(−15, 3), and K'(−3, 3)
3. P'(6, 6), E'(18, 6), R'(15, −3), and K'(3, −3)
4. P'(−8/3, −8/3), E'(−8, −8/3), R'(−20/3, 4/3), and K'(−4/3, 4/3)
Answer:
option 3
Step-by-step explanation:
Dilation by a scale factor of 3/2 multiplies each of the coordinate values by 3/2. For example, P' = (3/2)P = (3/2)(4, 4) = (6, 6).
The only choice with coordinates matching these is option 3.
Please help with ratios of the area of triangles.....thank you
Answer:
Part 1) The ratio of the areas of triangle TOS to triangle TQR is [tex]\frac{4}{25}[/tex]
Part 2) The ratio of the areas of triangle TOS to triangle QOP is [tex]\frac{4}{9}[/tex]
Step-by-step explanation:
Part 1) Find the ratio of the areas of triangle TOS to triangle TQR
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/TR
substitute the values
6/(6+9)
6/15=2/5
step 2
Find the ratio of the areas of triangle TOS to triangle TQR
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{5})^{2}=\frac{4}{25}[/tex]
Part 2) Find the ratio of the areas of triangle TOS to triangle QOP
step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor
The scale factor is equal to
TS/QP
substitute the values
6/9
6/9=2/3
step 2
Find the ratio of the areas of triangle TOS to triangle QOP
we know that
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
so
[tex](\frac{2}{3})^{2}=\frac{4}{9}[/tex]
What is the equation of a line that is parallel to the line 2x+5y=10 and passes through the point (-5,1)? Check all that apply.
Answer:
y=-2/5 x -1 (It says check all that apply... I hope this equation hasn't been written in a different form in your choices-let me know)
Step-by-step explanation:
Rearrange 2x+5y=10 into slope-intercept form.
First step: Subtract 2x on both sides: 5y=-2x+10
Second step: Divide both sides by 5 giving: y=-2/5 x+2
The slope is -2/5.
Parallel lines have the same slope.
So we know the equation of our new line is in the form y=-2/5 x+b.
We need to find the y-intercept of our line... let's just use the point they have our line going through to find it. Plug in and solve for b.
1=-2/5 (-5)+b
1=2+b
-1=b
So the equation is y=-2/5 x -1
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 2x + 5y = 10 into this form
Subtract 2x from both sides
5y = - 2x + 10 ( divide all terms by 5 )
y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form
with slope m = - [tex]\frac{2}{5}[/tex]
• Parallel lines have equal slopes, so
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (- 5, 1) into the partial equation
1 = 2 + c ⇒ c = 1 - 2 = - 1
y = - [tex]\frac{2}{5}[/tex] x - 1 ← in slope- intercept form
Multiply through by 5
5y = - 2x - 5 ( add 2x to both sides )
2x + 5y = - 5 ← in standard form
What is the least common multiple of 16 and 3?
Answer:
48
Step-by-step explanation:
Multiply 16 and 3 together! This isn't usually the case but for this question it is. Hope this helps and have a nice day!
Answer:
48
explanation:
prime factorisation of 16 and 3.
[tex]16 = 2 \times 2 \times 2 \times 2 = {2}^{4} [/tex]
[tex]3 = 1 \times 3[/tex]
taking the greatest power from both the equation for multiplication
[tex]2 \times 2 \times 2 \times 2 \times 3 = 48[/tex]
hence the L.C.M of 16 and 3 is "48"
i know it’s not a ser choice a but im still not sure
Step-by-step explanation:
[tex]f(x)=\dfrac{2}{x}\ and\ g(x)=\dfrac{2}{x}\\\\(f\circ g)(x)=f(g(x))\to\text{substitute}\ 2-3x\ \text{instead}\ x\ \text{in}\ f(x):\\\\(f\circ g)(x)=\dfrac{2}{\frac{2}{x}}=2\cdot\dfrac{x}{2}=x[/tex]
What is the equation of the line perpendicular to y=2/3x+1 that passes through the point (12, –6)?
A. 3x + 2y = 24
B. 3x + 2y = 6
C. 2x – 3y = 42
D. 2x – 3y = –48
Answer:
Step-by-step explanation:
Start with y=(2/3)x+1 . The slope of any line perpendicular to this is the negative reciprocal of 2/3: -3/2.
Then we have y = mx + b, which, using the given data (12, -6), becomes
-6 = (-3/2)(12) + b, or
-6 = -18 + b, so b = 12 and y = (3/2)x + 12.
We must put this into standard form. Mult. all three terms by 2:
2y = 3x + 24
Melinda Randolph bought 1,500 shares of Huge Corporation stock for $155,250. She sold the stock for $101 per share and paid a sales commission of $39. What is the profit or loss from the sale? (Enter the dollar amount followed by a space and the word loss or profit.)
Can someone help me?
Answer:
3789.00 loss
Step-by-step explanation: Well She sold the stock but for every stock she sold she had to pay commission which was 39 Dollars for every stock sold. She only Made 2.5% of the Stocks sold, Which is an L, So the answer would be 3789.00, Loss.
When x = 5, the value of the expression 20/-25+ –2(x – 10) is a.–21 b. –9 c. 9 d. 19
Answer:
I get 9.2 but if the answer is rounded then 9 should be correct
Step-by-step explanation:
Plug in the 5 and solve.
Hope this helps a bit,
Flips
Write parametric equations of the line -4x+y=-2.
Answer:
x(t)=-t/4
y(t)=-t-2
(answer can vary)
Step-by-step explanation:
Many different ways to do... you are just introducing a different variable, t, to rewrite x and y. We are rewriting x and y as functions of t.
So if we let -4x=t then x=t/-4 or x=-t/4
So if -4x=t then t+y=-2 so y=-t-2
So you could write the following:
x(t)=-t/4
y(t)=-t-2
Answer: the answer is a)x=t,y=4t-2
Step-by-step explanation: I guessed and got it right so sorry i do not know how to explain anything but hopefully it helps someone in the future at least
Emma gets paid $5,000 per month.
1,250 a month for rent. What percent of her monthly pay goes to rent?
Answer:
25 percent.
Step-by-step explanation:
1,000 would be 20% of 5,000
250 is 5% of 5,000
20+5=25
25% of Emma's monthly income goes towards rent.
To calculate the percentage of Emma's monthly pay that goes towards rent, we need to divide the amount spent on rent by the total monthly income, and then multiply that result by 100 to convert it to a percentage.
Emma spends $1,250 a month on rent and earns $5,000 per month. The calculation is as follows:
Divide the monthly rent by the monthly income: $1,250 / $5,000 = 0.25.
Convert the decimal to a percentage: 0.25 * 100 = 25%.
Therefore, 25% of Emma's monthly income goes towards rent.
Which is the graph of the function f(x)=x3+x2+4?
this is what the graph look like
ANSWER
See attachment.
EXPLANATION
The given function is
[tex]f(x) = {x}^{3} + {x}^{2} + 4[/tex]
The degree of this function is odd and the leading coefficient is positive.
The graph of this function rises on the left and keeps rising on the right.
The y-intercept of this graph is 4.
The graph intersects the y-axis at 4.
The graph of this function is the one shown in the attachment.
What is the common ratio of the sequence?
-2,6,-18,54
ANSWER
The common ratio is -3.
EXPLANATION
In general, the common ratio of a Geometric Sequence is given by:
[tex] r = \frac{a_{n+1}}{a_{n}} [/tex]
We can find the common ratio using any two consecutive terms of the geometric sequence by dividing the subsequent term by the previous term.
The given sequence is -2,6,-18,54
Using the first two terms the common ratio is
[tex]r = \frac{6}{ - 2} = - 3[/tex]
We could also used the second and third terms to get
[tex]r = \frac{ - 18}{6} = - 3[/tex]
and so on and so forth.
Therefore the common ratio is -3.
Compare and contrast interpolations and extrapolations based on a scatterplot
Answer:
An interpolation has a result which lies within the scatterplot’s cluster of data points. An extrapolation lies outside the cluster. An interpolation is more reliable than an extrapolation.
Step-by-step explanation:
Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.
Explanation:Interpolations and extrapolations are both methods used to estimate values based on a scatterplot, but they differ in their approach.
Interpolations involve estimating values within the range of the given data points, while extrapolations involve estimating values beyond the range of the given data points.
For example, if we have a scatterplot of temperature measurements at different times throughout a day, interpolation would involve estimating the temperature at a specific time between the given measurements, while extrapolation would involve estimating the temperature at a time outside of the given measurements, such as predicting the temperature at midnight.
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Find the slope of a line perpendicular to 3x + y =15.
5
-3
1/3
-1/3
[tex]\bf 3x+y=15\implies y=-3x+15\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-3\implies -\cfrac{3}{1}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{1}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{1}{3}}}[/tex]
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
In the given equation 3x + y =15, the slope of the line will be,
3x + y = 15
y = 15 - 3x
y = -3x + 15
Thus, the slope of the equation is -3.
Now, the product of the slope of two perpendicular lines is always equal to -1. Therefore, the product can be written as,
-3 × m = -1
m = -1/-3
m = 1/3
Hence, the slope of a line perpendicular to 3x + y =15 is 1/3. Thus, the correct option is C.
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At which root does the graph of f (x) = (x - 5)3 (x + 2)2 touch the xaxis
ANSWER
x=-2
EXPLANATION
The given polynomial function is:
[tex]f(x) = {(x - 5)}^{3} {(x + 2)}^{2} [/tex]
The polynomial has two factors, one with an odd multiplicity which is
[tex] {(x - 5)}^{3} [/tex]
and the other with an even multiplicity which is
[tex] {(x + 2)}^{2} [/tex]
The graph does not cross the x-axis at where the multiplicity is even.
Therefore the graph touches the x-axis at
[tex]x = - 2[/tex]
We got this by solving
[tex]{(x + 2)}^{2} = 0[/tex]