With tables A, B and D, we have repeated input (x) values.
Table A has x = 4 repeated. So the input x = 4 leads to both outputs y = 2 and y = 7 at the same time. With any function, we must have exactly one and only one output for any given input. So this is why table A is not a function. Tables B and D are not functions for similar reasons.
Table C on the other hand has unique inputs that do not repeat. The input x = 4 only leads to y = 3, x = 6 pairs with y = 5, and x = 2 outputs to y = 7. Therefore we have a function here.
The scores on an entrance exam to a university are known to have an approximately normal distribution with mean 65% and standard
deviation 7.1%. What is the standardized score for a student who scores 60% on this test?
on 70
Answer:
-0.704 (corrected to 3 significant figures).
Step-by-step explanation:
Standardized score = (actual score - mean) / standard deviation
Standardized score = (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
Standardized score = (actual score - mean) / standard deviation
= (60% - 65%) / 7.1%
= -0.704 (corrected to 3 significant figures).
What is supposed by way of ordinary distribution?A regular distribution is an association of facts set in which maximum values cluster in the center of the range and the relaxation taper off symmetrically in the direction of either intense.
What are everyday distributions with examples?Peak, beginning weight, studying potential, activity satisfaction, or SAT scores are only some examples of such variables. due to the fact that commonly distributed variables are so not unusual, many statistical checks are designed for commonly disbursed populations.
Learn more about the normal distribution here: https://brainly.com/question/4079902
#SPJ2
Explain why f(x) = x^2-x-6/x^2-9 is not continuous at x = 3.
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Required
Why is the function not continuous at x = 3
First substitute 3 for x at the denominator
[tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex]
Factorize the numerator and the denominator
[tex]f(x) = \frac{x^2 - 3x+2x -6}{x^2 - 3^2}[/tex]
[tex]f(x) = \frac{x(x - 3)+2(x -3)}{(x - 3)(x+3)}[/tex]
[tex]f(x) = \frac{(x+2)(x - 3)}{(x - 3)(x+3)}[/tex]
Divide the numerator and denominator by (x - 3)
[tex]f(x) = \frac{x+2}{x+3}[/tex]
Substitute 3 for x
[tex]f(3) = \frac{3+2}{3+3}[/tex]
[tex]f(3) = \frac{5}{6}[/tex]
Because [tex]f(x) = \frac{x^2 - x -6}{x^2 - 9}[/tex] is defined when x = 3;
Then the function is continuous
Answer:
A: f is not defined at x = -3
Step-by-step explanation: EDGE 2020
1. In your own words please describe a Relations vs. Function
2. please describe the mathematical order of operation(photo attached)
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
1. Relations are the set of y (output) and x (input) values that are related. A function is when each input has a relation with one output.
2. The mathematical formula is the formula of Pythagoras theorem. Where the length c (hypotenuse) is equal to the square root of the sum of the legs squared.
PLEASE HELP Question 1(Multiple Choice Worth 4 points) (08.03)A system of equations is given below: y = –2x + 1 6x + 2y = 22 Which of the following steps could be used to solve by substitution? 6x + 2(−2x + 1) = 22 −2x + 1 = 6x + 2y 6(−2x + 1) + 2y = 22 6(y = −2x + 1) Question 2(Multiple Choice Worth 4 points) (08.03)Solve the system of equations and choose the correct answer from the list of options. d + e = 15 −d + e = −5 Label the ordered pair as (d, e). (0, 0) (10, −5) (5, 10) (10, 5) Question 3(Multiple Choice Worth 4 points) (08.03)A set of equations is given below: Equation H: y = −x + 2 Equation J: y = 3x − 4 Which of the following steps can be used to find the solution to the set of equations? −x = 3x − 4 −x +2 = 3x −x + 2 = 3x − 4 −x + 1 = 3x + 2 Question 4(Multiple Choice Worth 4 points) (08.03)A set of equations is given below: Equation M: y = 3x + 4 Equation P: y = 3x + 7 Which of the following options is true about the solution to the given set of equations? No solution One solution Two solutions Infinite solutions Question 5(Multiple Choice Worth 4 points) (08.03)Solve the system of equations and choose the correct answer from the list of options. x + y = −3 y = 2x + 2 five over 3 comma 4 over 3 negative 5 over 3 comma negative 4 over 3 negative 3 over 5 comma negative 3 over 4 3 over 4 comma 3 over 5
Answer:
6x + 2(−2x + 1) = 22
Step-by-step explanation:
Answer: The answer is 6x + 2(−2x + 1) = 22
A ladder is placed 8 feet away from the base of a tree. If the ladder forms a 57° angle
with the ground, how high up the tree will the ladder reaach
Answer:
3.88 feet
Step-by-step explanation:
let the length the ladder reaches be x
[tex] \tan(57) = \frac{x}{8} [/tex]
[tex]x = 8 \tan(57) [/tex]
x = 3.8775938143
i cant see the answers does anyone else have this problem
Answer:
yeah....same!
Step-by-step explanation:
I'm having the same problem I thought it was just me
M
Which angle is an adjacent interior angle to ZJKM?
LJKL
ZMKL
J
K
ZKLM
L
LMK
Answer:MLK
Step-by-step explanation:
The angle that is placed sideways with <JKM is <MKL
Interior adjacent angle of a triangleThe adjacent interior angle of a triangle are angles placed sideways with each other.
For the given diagram attached, you can see interior angles of the triangle are <LMK, <MKL and <KLM
Among the listed interior angles, the angle that placed sideways with <JKM is <MKL
Learn more on interior angles here: https://brainly.com/question/24966296
In the table, describe the shape of the cross section formed when a particular plane passes through the cylinder.
triangle is the best answer
Answer:
Step-by-step explanation:
Use multiplication to solve the proportion.
9/5 = z/20
Answer:
36
Step-by-step explanation:
9/5 = z/20
First, we have to divide what we know
9/5 = 1.8
1.8 = z/20
Next, we have to multiply both sides of the equation by 20 to cancel out the division sign
1.8•20 = z/20•20
36 = z
what is
[tex] \frac{2ax + 3}{ax + 3} = - 1[/tex]
x value
[tex]\dfrac{2ax+3}{ax+3}=-1[/tex]
Rewrite -1 as a fraction
[tex]\dfrac{2ax+3}{ax+3}=\dfrac{-1}{1}[/tex]
Cross multiply
[tex]2ax+3=-1(ax+3)[/tex]
Distribute the -1
[tex]2ax+3=-ax-3[/tex]
Add both sides by ax
[tex]3ax+3=-3[/tex]
Subtract both sides by 3
[tex]3ax=-6[/tex]
Divide both sides by 3a
[tex]x=-\dfrac{6}{3a}[/tex]
Simplify
[tex]=-\dfrac{2}{a}[/tex]
That's the value of x respect to a. Let me know if you need any clarifications, thanks!
Answer:
Step-by-step explanation:
[tex]\frac{2ax+3}{ax+3} =-1\\2ax+3=-ax-3\\2ax+ax=-3-3\\3ax=-6\\x=-\frac{2}{a}[/tex]
In AABC, which trigonometric ratio has the value a/c?
Answer:
tan A has the ratio a/c
Step-by-step explanation:
Pleased to help u...
30% of a number is 45 what is the number ?
Hey there! I'm happy to help!
When talking about percents, the word "is" usually means equals. Let's use this to solve an equation! We will call our number n. Note that 30% is equal to 0.3 in decimal form because 0.3 is 30% of one! :D
0.3n=45
To solve, we need to isolate the n. To do this, we divide both sides by 0.3 because this cancels out the 0.3 that is being multiplied by n and it shows us what n will then equal.
0.3n÷0.3=45÷0.3
n=150
Therefore, 30% of 150 is 45. Try multiplying 0.3 by 150 and you will get 45!
Have a wonderful day! :D
If a field researcher wanted to learn a political organization's pattern of recruitment over time, the researcher mightbegin by interviewing a fairly recent recruit and ask who introduced that person to the organization. Then theresearcher might interview the person named and ask who introduced that person to the political organization.This would be an example of: systematic sampling. accidental sampling. snowball sampling. quota sampling deviant cases sampling.
Answer:
C. snowball sampling
Step-by-step explanation:
Snowball sampling also known as referral sampling or chain sampling is a sampling method in research where the participants in the research are recruited to find new participants. This is a non-probability sampling method because participants choose other participants through their own insight. Just as a ball takes up more snow as it rolls by, so also this research method takes up more participants as it progresses.
So, when the field researcher who wanted to learn about a political organization's recruiting pattern begins by interviewing a participant who in turn suggests another participant, he has applied the snowball sampling method.
How
are in
3 5 dozens ?
many eggs
6
Answer: 46 eggs
Step-by-step explanation:
There are 12 eggs in a dozen. Thus, there are 3 5/6*12, or 46 eggs.
Hope it helps <3
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
w²-30w+210=0
Step-by-step explanation:
2w + 2l = 60 , w + l = 30, l = 30 - w
wl = 210
w(30-w) -210 = 0
30w - w²-210 = 0
w²-30w+210=0
help me plz its math plz help
Hi there! :)
Answer:
a = 12 units.
Step-by-step explanation:
Using the Pythagorean Theorem (c² = a² + b²), where
c = length of the Hypotenuse
a = length of the shorter leg
b = length of the longer leg
We can calculate the length of "a" by substituting in the values into the equation:
c = 15
a = "x"
b = 9
----------------
15² = x² + 9²
Simplify the squares:
225 = x² + 81
225 - 81 = x²
144 = x²
Take the square root of both sides:
√144 = x
x = 12 units.
Therefore, the length of a = 12 units.
Answer:
a= 12
Step-by-step explanation:
Pythagorean Theorem: a²+b²=c²
b= 9
c= 15
a= x = what we are looking for
For this problem, we need to set c² equal to x² and b², which would look like:
15²= x²+9²
225= x²+81
Subtract 81 from both sides
144=x²
Square root both sides
x=12
a= 12
There are 6 chemical elements represented by Li, Na, Mg, Rb, Cs, and Fr that
are written on separate pieces paper. You randomly choose 3 elements, one
at a time, without replacement.
Find the probability that the third element is Na.
Enter the correct answer in the box.
Answer:
1/6
Step-by-step explanation:
I think this is tricky.
when you randomly choose the 1st two times, it doesn't matter as long as Na was not chosen, otherwise the probability would become ZERO for the 3rd one be Na.
So, after 1st two is removed, there are only 4 left in the pool, so picking Na at the 3rd draw is 1/4 probability.
But, come to think of it, when 1st draw, you have to draw the other 5 out of 6, 2nd draw the 4 out of 5, then 3rd is 1 Na out of the 4.
So, 5/6 x 4/5 x 1/4 = 1/6
Solve by the quadratic formula: x^2= 6x-4
Answer:
3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Step-by-step explanation:
x^2 = 6x - 4
x^2 - 6x + 4 = 0
Now, we can use the quadratic formula to solve.
[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.
[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]
= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]
= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]
= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]
x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].
Hope this helps!
The hardcover version of a book sells for 15 dollars and the paperback sells for 11.50. If a store sells 70 copies of the book in one month and charges 917 dollars how many hardcover versions were sold
Answer: 32 copies of hardcover version.
Step-by-step explanation: Suppose the quantity of hardcover version copies sold is H and the paperback copies is P.
1) A store sells a total of 70 copies:
H + P = 70
2) One hardcover is sold for $15 and one paperback for $11.50. In one month was charged $917:
15H + 11.5P = 917
Solving the system of equations:
H + P = 70 (I)
15H + 11.5P = 917 (II)
Since it is asked for the hardcover version, find H.
Multiply equation (I) by -11.5:
-11.5H - 11.5P = - 805 (III)
Add (II) and (III):
-11.5H - 11.5P = - 805
15H + 11.5P = 917
3.5H = 112
H = 32
In one month, it was sold 32 hardcover version of a book.
Using the quadratic formula to solve x2 + 20 = 2x, what are the values of x??
These are the options
O 12/21
O 1 2 191
O 1+2,1191
O 12.191
[tex]x^2-2x+20=0\implies D=b^2-4ac<0\implies x_1,x_2\notin\mathbb{R}[/tex].
There are no real solutions to the quadratic equation.
Hope this helps.
A metal cube
of
side 4.4cm was melted
and the molten material used to make a Sphere
Find to 3 significant figures the radius of
the
sphere [take It - 22/7].
Answer: 2.73 cm
Step-by-step explanation:
Given that :
Side (a) of cube = 4.4cm
Volume of a cube (V) = a^3
V = 4.4^3
V = 85.184cm^3
Therefore, volume of the sphere made = 85.184cm^3
Volume of sphere = 4/3 πr^3
Where r = radius
85.184 = (4/3)*(22/7)*r^3
85.184 = (88/21)*r^3
85.184 = 4.1905 * r^3
r^3 = 85.184 / 4.1905
r^3 = 20.327884
Take the cube root of both sides
r = 2.73 cm
Lucy is going to invest in an account paying an interest rate of 7% compounded daily. How much would Lucy need to invest, to the nearest dollar, for the value of the account to reach $84,000 in 6 years?
Answer:
Lucy needs to invest $55,194.16
Step-by-step explanation:
The given information are;
The interest rate of the account = 7% compounded daily
The amount at the end of 6 years = $84,000
The time duration = 6 years
The amount Lucy
The formula for compound interest is
[tex]A(t) = P \times \left ( 1 + \dfrac{r}{n} \right )^{n \times t}[/tex]
Where;
r = The interest rate = 7% = 0.07
n = The number of times a year = 365
t = The number years = 6 years
A(t) = The amount after 6 years = $84,000
P = The initial amount invested
Therefore, we have;
[tex]\$ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}[/tex]
[tex]P = \dfrac{\$84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\$84,000}{1.522} = \$55,194.16[/tex]
Therefore, Lucy needs to invest $55,194.16.
Please explain: Find the measure of angle A. a. 32 b. 57 c. 59 d. No angle exists.
Answer:
The answer is option B.
57°Step-by-step explanation:
To find Angle A we use cosine
cos ∅ = adjacent / hypotenuse
From the question
The adjacent is 14
The hypotenuse is 26
So we have
cos A = 14/26
cos A = 7/13
A = cos-¹ 7/13
A = 57.42
A = 57° to the nearest degreeHope this helps you
Answer:
57 deg
Step-by-step explanation:
(see attached for reference)
we are given a right triangle together with the lengths of one side (= 14 units) and the hypotenuse (= 26 units)
Using the trigonometry formulas, we can find angle A
cos A = adjacent length / hypotenuse
cos A = 14 / 26
A = cos⁻¹ (14/26) (use calculator)
A = 57.42 deg
A = 57 deg (rounded to nearest whole degree)
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule. A(n)=-6+(n-1)(1/5) A)-6,-5 1/5, -4 B)5, -5 1/5,1 4/5 C)-6, -5 2/5, -4 1/5 D) 0, 3/5, 1 4/5
Step-by-step explanation:
An arithmetic sequence is given by relation as follows :
[tex]A(n)=-6+(n-1)\dfrac{1}{5}[/tex]
For the first term, put n = 1. So,
[tex]A(1)=-6+(1-1)\dfrac{1}{5}\\\\A(1)=-6[/tex]
For fourth term, put n = 4. So,
[tex]A(4)=-6+(4-1)\dfrac{1}{5}\\\\A(4)=\dfrac{-27}{5}\\\\A(4)=-5\dfrac{2}{5}[/tex]
For tenth term, put n = 10. So,
[tex]A(10)=-6+(10-1)\dfrac{1}{5}\\\\A(10)=-6+\dfrac{9}{5}\\\\A(10)=\dfrac{-21}{5}\\\\A(10)=-4\dfrac{1}{5}[/tex]
Hence, the correct option is (C).
Answer:
the answer in C)-6, -5 2/5, -4 1/5
x-15 = 8
A. x= 23
B. x = 7
C. x=-23
D. x=-7
Answer:
[tex]\boxed{ x = 23}[/tex]
Step-by-step explanation:
=> x - 15 = 8
Adding 15 to both sides
=> x - 15 + 15 = 8 + 15
=> x = 23
Answer:
A. x = 23
Step-by-step explanation:
Step 1: Write out equation
x - 15 = 8
Step 2: Add 15 to both sides (Addition Equality)
x - 15 + 15 = 8 + 15
x = 23
John should drive to his workplace and back to home. On the way to the workplace it was raining, so he drove at speed of 42mph. On the way back the rain was over so his speed was 54mph. What was John's average speed, for the whole trip?
Answer:
48 mph.
Step-by-step explanation:
You need to calculate the average. So,
42 + 54 = 96
Because there are two quantities, 42 and 54, divide 96 by 2.
The average speed is 48.
Angles α and β are angles in standard position such that: α terminates in Quadrant III and sinα = - 5/13 β terminates in Quadrant II and tanβ = - 8/15
Find cos(α - β)
-220/221
-140/221
140/221
220/221
Answer:
140/221.
Step-by-step explanation:
For the triangle containing angle α:
The adjacent side is -√(13^2-5^2) = -12.
For the triangle containing angle β:
Hypotenuse = √(-8)^2 + (15)^2) = 17.
cos(α - β) = cos α cos β + sin α sin β
= ((-12/13) * (-15/17) + (-5/13)* (8/17)
= 180/221 + - 40/221
= 140/221.
Triangle TQRS Find the value of x.
O x = 2
O x = 3
O x= 33
O x= 52
Answer:
x=3
Step-by-step explanation:
To solve for x, we will follow the steps below:
First note that exterior angle =two opposite interior angle
From the diagram below
(25x) ° + (57 + x)° = (45x)°
25x° + 57° + x° = 45x°
next step is to collect the like term
45x° - 25 x° - x° = 57°
19x° = 57°
Divide both-side of the equation by 19
19x°/ 19 = 57° /19
On the left-hand side of the equation 19 will cancel out 19 leaving us with just x° while on the right-hand side of the equation 57 will be divided by 19
x = 3
plz answer this question
Answer:
D is correct one
Step-by-step explanation:
The pattern consists of repeating 4 faces
1000 is fully divisible by 4
1000/4= 250The 1000th face ends the pattern of 4
The next, 1001th one is the very first face
Correct choice is D
Determine the possible rational zeros of this polynomial function using the rational zeros theorem: p(x) = 4x^4 + 13x^3 – 49x^2 – 73x –15
Answer:
[tex]\large \boxed{\sf \ \ \ -1, \ -5, \ -\dfrac{1}{4} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's determine the possible rational zeros of this polynomial function using the rational zeros theorem:
[tex]P(x) = 4x^4 + 13x^3-49x^2-73x-15[/tex]
First of all, what is the rational zeroes theorem?
If P(x) is a polynomial with integer coefficients
and if (p and q being integer)
[tex]\dfrac{p}{q}[/tex]
is a zero of P(x), meaning
[tex]P(\dfrac{p}{q})=0[/tex]
then p is a factor of the constant term of P(x) and
q is a factor of the leading coefficient of P(x).
How to apply it here?
The constant term of P(x) is -15
The leading coefficient of P(x) is 4
so p is a factor of -15
q is a factor of 4
15 = 1 * 5 * 3
4 = 2 * 2 * 1
q can be 1, 2, 4
-p can be 1, 3, 5, 15
so it gives the following potential solutions
-1, -3, -5, -15
[tex]\dfrac{-1}{2}, \dfrac{-3}{2}, \dfrac{-5}{2}, \dfrac{-15}{2}[/tex]
[tex]\dfrac{-1}{4}, \dfrac{-3}{4}, \dfrac{-5}{4}, \dfrac{-15}{4}[/tex]
Let's compute P(x) for x in this list of potential solutions
x P(x)
-1 0
-3 -264
-5 0
-15 148680
-0.5 7.875
-1.5 -39.375
-2.5 -185.625
-7.5 4948.125
-0.25 0
-0.75 7.96875
-1.25 -15.9375
-3.75 -324.84375
It gives -1, -5 and -0.25
Conclusion
The possible rational zeroes of P(x) are
-1
-5
[tex]\dfrac{-1}{4}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you