Answer:
a) $1520
b) [tex]S_7 =[/tex] $209195
Step-by-step explanation:
The range of salaries forms an arithmetic sequence with the first term as 25325 and its 7th term as 34445:
a) The raise the person can get each year is the common difference of the progression, d.
The nth term of an arithmetic progression is given generally as:
[tex]a_n = a + (n - 1)d[/tex]
where a = first term = 25325
d = common difference
Therefore, the 7th term (34445) will be:
34445 = 25325 + (7 - 1)d
34445 = 25325 + 6d
=> 6d = 34445 - 25325 = 9120
d = 9120 / 6 = $1520
Therefore, the raise the person gets each year (common difference) is $1520.
b) The total amount the person will earn after 7 years is the sum of the salaries of all 7 yeas.
The sum of an arithmetic progression up to the nth term is given as:
[tex]S_n = \frac{n}{2}(2a + (n - 1)d)\\ \\[/tex]
Therefore, the sum of the person's salary for the 7 years is:
[tex]S_7 = \frac{7}{2}(2 * 25325 + (7 - 1)1520)\\ \\S_7 = 3.5 (50650 + 6(1520))\\\\S_7 = 3.5 (50650 + 9120)\\\\S_7 = 3.5 * 59770\\[/tex]
[tex]S_7 =[/tex] $209195
That is the total amount of salary after 7 years
I can’t figure it out
Answer:
5inch
Step-by-step explanation:
15_10=5
because full length is 15 cm given on another side and length of some part of another side is. given.so we have to subtract it
Answer:
5 inches
Step-by-step explanation:
You can notice that the 15 in side is parallel to the 10 in side and the missing side
let x be the missing side
10+x = 15 substract 10 from both sides 10-10+x = 15-10 x = 5so x is 5 inches
PLEASE HELP ME GUYS Consider adjacent angles that measure (2x + 45)° and (3x + 55)°. The sum of the measures of these two angles is 135°. Write and solve and equation to find the value of x and the measure of the two angles.
Answer:
x=7
2x+45=59
3x+55=76
Step-by-step explanation:
Answer:
7°, 59°, 76°
Step-by-step explanation:
The equation for the sum of the angles:
(2x + 45)° + (3x + 55)° = 135°Solving for x:
(5x + 100)°= 1355x= 35x= 35°/5x= 7°The angles:
(2x + 45)°= 2*7°+45° = 59°(3x+55)°= 3*7° + 55° = 76°Please answer this in two minutes
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
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
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.
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
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
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
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.
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
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
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.
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.
Solve for X and determine the measure of each angle.
X
(x - 35)
X
(2x - 75°)
it's a quadrilateral
interior angles add up to 360
x + 2x - 75 + x + x - 35 = 360
5x - 110 = 360
5x = 360 + 110
x = 470 ÷ 5
x = 95
and x - 35 = 60
2x - 75
= 190 -75
= 115
Answer:
see explanation
Step-by-step explanation:
The sum of the interior angles of a quadrilateral = 360°
Sum the given angles and equate to 360
x + x + x - 35 + 2x - 75 = 360, that is
5x - 110 = 360 ( add 110 to both sides )
5x = 470 ( divide both sides by 5 )
x = 94 , then
x - 35 = 94 - 35 = 59
2x - 75 = 2(94) - 75 = 188 - 75 = 113
Thus
The 4 angles are 59°, 94°, 94°, 113°
Omar has a new credit card.He earns 300 reward points for every 100 dollars he spends. If Omar earned 1800 reward points, how much money did he spend?Easy question for easy points
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
Answer:
$600
Step-by-step explanation:
1800/300 = 6
6 x 100 = $600
There are 5 orange bumper cars and 3 green bumper cars that are being tested
for safety for a ride at an amusement park. Two bumper cars are tested at
random, one at a time, without retesting the same car.
Find the probability that both cars are orange.
Enter the correct answer in the box.
Answer:
5/14
Step-by-step explanation:
I assume after testing the 1st car, it is not placed back into the pool.
So, 1st test orange is 5/8
2nd test orange is 4/7.
Both had to be true, so 5/8 x 4/7 = 5/14
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
Anyone want to help me out?
Answer:
SAS Postulate (third option)
Step-by-step explanation:
A trick that I use is that s stands for side and a for angle
the picture shows that two sides are the same which means the SS
and one angle is the same, hence the one A
Hope this helps!
Simplify.
B2 x b6=??
Answer:
b^8
Step-by-step explanation:
When multiplying exponents with the same base, we can add the exponents
b^2 * b^6
b^ (2+6)
b^8
Answer:b8 x
Step-by-step explanation:
Changes made to your input should not affect the solution:
(1): "b6" was replaced by "b^6". 1 more similar replacement(s).
STEP
1
:
Multiplying exponential expressions
1.1 b2 multiplied by b6 = b(2 + 6) = b8
Final result :
b8x
Based on the table, which best predicts the end
behavior of the graph of f(x)?
As x, f(x) —, and as x->-0, f(x) →..
As x 700, f(x) →, and as x -→-00, f(x) →--.
As x, f(x) →-00, and as x———00, f(x)
As x -+-0, f(x) →-00, and as x->-00, f(x) -
->
-→-00
Answer:
The correct option is;
As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞
Step-by-step explanation:
The values given are;
x, f(x)
-4, 18
-3, 9
-2, 6
-1, 3
0, 0
1, -3
2, -6
3, -9
4, -18
Based on the table, as the magnitude of x increases in the positive direction, the magnitude of f(x) increases in the negative direction
Therefore, the correct option that best predicts the end behavior of the graph of f(x) is As x → ∞ f(x) → -∞, and as x → -∞ f(x) →∞.
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
Determine if the function below is continuous.
Answer:
No
Step-by-step explanation:
I believe at the point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous.
Continuous means that there is no abrupt changes (google) and im sure you know this already (im just saying no offence to anyone's intelligence)
The given function is not continuous. The correct option is D.
What is a continuous function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
A continuous function in mathematics is one that causes the value of the function to continuously vary as the input changes over time. This indicates that there aren't any discontinuities or sudden changes in value.
The point of (1,1) there is a distinct sort of point where it looks like an edge or corner which means that it is not continuous. Continuous means that there are no abrupt changes.
It is shown in the graph that the function is reducing continuously at the point ( 1,-1) and after that, there is a sudden change in the function after that it becomes constant or parallel to the x-axis.
Because there is a sudden change in the function it will be termed a discontinuous function.
Hence, the function is not continuous, and the correct option is D.
To know more about continuous function follow
https://brainly.com/question/18102431
#SPJ5
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
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...
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
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.
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
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]