9514 1404 393
Answer:
$24,164,000
Step-by-step explanation:
The yearly salaries form an arithmetic sequence with a first term of 1700000 and a common difference of 4000.
The sum of n terms of an arithmetic sequence with first term a1 and common difference d is ...
Sn = (2a1 +d(n -1))(n/2)
For the given numbers, the sum of 14 years' salaries will be ...
S14 = (2·1,700,000 +4,000(14 -1))(14/2) = 24,164,000
The officer will earn $24,164,000 in a 14-year period.
Clearly, we can see that salary of the officer is in form of Arithmetic progession, where :
First term, a = $ 1,700,000Common difference = $ 4000Number of terms, n = 14And we have to find total salary i.e. [tex] \tt s_{n} = ?[/tex]
Now, we know that :
[tex] \large \underline{\boxed{\bf{S_n = \dfrac{n}{2} \Bigg(2a + (n-1) d\Bigg)}}}[/tex]
By substituting values :
[tex] \tt : \implies S_n = \dfrac{14}{2} \Bigg(2(1700000) + (14-1) (4000)\Bigg)[/tex]
[tex] \tt : \implies S_n = \cancel{\dfrac{14}{2}} \Bigg(2\times 1700000 + 13 \times 4000\Bigg)[/tex]
[tex] \tt : \implies S_n = 7 \Bigg(3400000 + 52000\Bigg)[/tex]
[tex] \tt : \implies S_n = 7 \Bigg(3452000\Bigg)[/tex]
[tex] \tt : \implies S_n = 7 \times 3452000[/tex]
[tex] \tt : \implies S_n = 24164000[/tex]
[tex] \large \underline{\boxed{\bf{S_n = \$ 24,164,000}}}[/tex]
Hence, the total amount of money the officer will earn in 14 years is $ 24,164,000.
Judith's family went on a cross-country trip. They drove exactly 232 miles a day for 12 days. How many miles did they drive?
696 miles
2,824
2,884
2,784 miles
Answer:
2,784 miles
Step-by-step explanation:
232*12=2,784
what equation does this model show?
Answer:
14x-12=9x-25
Step-by-step explanation:
Since the balance is equaled, the equation would read to be 14x-12=9x-25.
It takes 2 hours to drive 100 miles, at this rate how long does it take to drive 50 miles?
Answer:
1 hour
Step-by-step explanation:
John commutes each day to work either by train or by bus. The bus pass costs 10$ plus 2$ per trip. The train costs 15$ plus 1.50$ per trip what is the most number John can make before the bus costs more than the train?
A) 9 trips
B) 15 trips
C) 11 trips
D) 13 trips
Answer:
a
Step-by-step explanation:
i plugged in each of the numbers to the equation
at 9 trips the bus costs 28 and train cost 25.5
Screen-printing a batch of shirts requires 3 minutes per shirt in addition to 19.87 minutes of initial set-up time. How long does it take to screen-print a batch of 143 shirts? Write and solve an equation to find the answer.
Answer:
So the equation and solution will be:
Total time taken = 3 × number of shirts + 19.87 min (setup time)
= 3 × 143 + 19.87
[tex]=429+19.87[/tex]
[tex]=448.87[/tex]
Step-by-step explanation:
From the question statement, it is clear that
screen-printing a batch of shirts requires 3 minutes per shirt in addition to 19.87 minutes of initial set-up time.we have to determine how long does it take to screen-print a batch of 143 shirts.
so the equation and solution will be:
Total time taken = 3 × number of shirts + 19.87 min (setup time)
= 3 × 143 + 19.87
[tex]=429+19.87[/tex]
[tex]=448.87[/tex] min
could somebody help me please im dumbbb
Answer:
its parentheses, exponents, multiplication and division and addition and subtraction
plz help to find a
u will get 20 points
I'll mark you the brainiest if you get this right
thx x
Find the first three terms of the sequence below.
Tn = n2 + 5n + 2
Step-by-step explanation:
T1 = 1^2 + 5(1) + 2 = 8
T2 = 2^2 + 5(2) + 2 = 16
T3 = 3^2 + 5(3) + 2 = 26
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Answer:
First three terms : 8 , 16 , 26
Step-by-step explanation:
[tex]T_{n}=n^{2}+5n + 2[/tex]
n = 1 , [tex]T_{1}=1^{2}+5*1+2=1+5+2 = 8[/tex]
n = 2 , [tex]T_{2}=2^{2}+5*2+2 = 4+10+2 = 16[/tex]
n= 3, [tex]T_{3} = 3^{2}+5*3+2=9+15+2 = 26[/tex]
A chef needs to increase the temperature of a food dish. She thinks she can do this by stacking another dish on top of it. She has three dishes to choose from for the top dish: A, B, and C.
Which one of these dishes would make the food dish the warmest when placed on top of it? As part of your answer, explain how the energy and temperature of both the top dish and the food dish will change when the food dish warms up, and why.
Answer:
This question is incomplete
Step-by-step explanation:
Answer:
I may not know the answer but from what I. seeing we taking the same test TwT
Brian bought two shirts for $14.50 each and a pair for shoes for $29.99.the sales tax was 6%.how much did Brian spend?
Answer:
Brian spent 62.5294 $.
Step-by-step explanation:
The cost of two shirts = [tex]2\times \:14.5=29[/tex] $
The cost of 1 pair of shoes = [tex]1\times 29.99\:[/tex] = [tex]29.99[/tex] $
Adding the calculated costs = [tex]29+29.99=58.99[/tex] $Tax calculation:
[tex]\frac{6}{100}\times \:58.99=3.5394[/tex] $Now, adding calculated costs and tax calculation:
58.99$ + 3.5394$ = 62.5294 $
Therefore, Brian spent 62.5294 $.
Determine if the two triangles are congruent if they are state which congruence theorem is used
Answer:
yes through ASA association
(9 + 33 – 6 ) ÷ 6 – 3 to the power of 2
Answer:
Step-by-step explanation:
9+33-6)/6-3
42-6)/6-3
36/6-3
6-3
3 to the second power is 9
because three times three is 9
Answer:
9
Step-by-step explanation:
Do the numbers inside of the parenthesis first because of PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction). Then, you will get 36. Divide this by 6, the next step using PEMDAS. You will get 6. Now finally, subtract 3. Now you have 3. Now, what is 3 to the power of 2? Well simply multiply 3 by itself. You have the answer of 9 at this point.
Hope this helps! Please mark this as the brainliest!
The supply curve for a local business can be modeled by q(x) = x2 – 4x + 4, where x is the price of the item in dollars and q(x) is the number of items produced at that price. Use the graph to complete the statements.
There are
items produced at a price of $2, because the
is at (2, 0).
The number of items produced decreases when the price increases from
dollars.
Answer:
1: A: 0
2: B: x-intercept
3: A: 0 to 2
Step-by-step explanation:
I just did the assignment on EDGEN and it's 200% correct!
Also, heart and rate if you found this answer helpful! :) (P.S it makes me feel good to know I helped someone today:) )
The answers that complete the statements are a) zero, b) x - intercept, c) 0 to 2 are the correct statements.
What is graph of a function?A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).
For the given situation,
A local business can be modeled as function q(x) = [tex]x^2 - 4x + 4[/tex]
x is the price of the item in dollars and
q(x) is the number of items produced at that price.
The graph below shows the function q(x).
From the graph, there are zero items produced at a price of $2, because the x-intercept is at (2, 0).
The number of items produced decreases when the price increases from 0 to 2 dollars.
Hence we can conclude that the answers that complete the statements are a) zero, b) x - intercept, c) 0 to 2 are the correct statements.
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A number is decreased by seven. Then, the new number is multiplied by 3 to get an answer of -9.
What is the original number?
A: -30
B: -4
C: 4
D: 30
(No shown work is needed)
Answer:
C: 4
Step-by-step explanation:
when a positive and negative number are multiplied you will get a negative number.
So,
4-7= -3
-3x3= -9
Therefore, your answer is C: 4. Hope this helps! :)
Imothy evaluated the expression using x = 3 and y = –4. xy-2 3x2y−4 1. (1 3 )x−1y2 2. (1 3 )3−1(−4)2 3. (1 3 )(1 31 )(−4)2 4. (1 3 )(1 3 )(−16) 5. −16 9 Analyze Timothy's steps. Is he correct? If not, why not? Yes, he is correct. No, he needed to add the exponents when he simplified the powers of the same base. No, he needed to multiply 3 and –1 instead of creating a positive exponent in a fraction. No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.
Answer:
No, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.
Step-by-step explanation:
The expression is not well written. The expression is written as;
(xy^-2)/(3x²y^-4)
According to indices;
a^m ÷ a^n = a^{m-n}
Applying this to solve the question
1/3(x^{1-2})/(y^-2÷y^-4)
= 1/3(x^{-1})(y^{-2+4})
= 1/3(1/x)y²
= 1/(3x) × y²
Substituting x = 3 and y = -4
= 1/3(1/3)×(-4)²
= 1/9(16)
= 16/9
Imothy solution is incorrect.
According to Imothy solution, his value of (negative 4) squared should be positive because an even exponent indicates a positive value.
Answer:
Step-by-step explanation:
Which inequality is a true statement?
Select each correct answer.
−5≤−7
−5>−7
−5<−7
−5=−7
−5≥−7
PLZZ HELP
Answer It's A, B, C, and F. Or 1, 2, 3, 5
Step-by-step explanation:
To have a true Inequality there has to be a relation between the 2 sides, meaning there is a greater than or less that sign.
20+m=8m What does m equal?
Answer:
First, subtract m from both sides
20=7m
divide 7 from both sides
20/7=m
Step-by-step explanation:
Answer: = 20/7
Step-by-step explanation:
The temperature of a cooling cup of coffee can be modelled by the equation
T = 90(0.94)", where T represents the temperature of the coffee and n is the
number of hours since it was poured. Explian what 90 and 0.94 represent in
this equation.
Answer:
See below
Step-by-step explanation:
I assume the " is n.
90 is your initial/starting temperature, in other words when n = 0 hours, the temperature will be 90.
The 0.94 part shows the rate of exponential decay.
If the spinner lands on green 10 times out of 60 spins, which statement is true?
The spinner lands on green 5 more times than expected.
The spinner lands on green 5 less times than expected.
The spinner lands on green 2 more times than expected
The spinner lands on green 2 less times than expected.
Answer: The spinner lands on green 5 less times than expected.
Step-by-step explanation:
Assuming the spinner has 4 colors, the chance of it landing on green will be 25%.
If there are 60 spins, the expected number of times it should land on green is;
= 60 * 25%
= 15 times
It only landed on green 10 times which is 5 less times than expected.
Is the statement true? Explain.
Answer:
Yes it's true
Step-by-step explanation:
Which expression is equivalent to 3(4y)
I WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
Well 12y is the most obvious answer.
Anything that makes 12 is good enough.
4(3y) is another answer
12(y)
1(12y)
6(2y)
2(6y
a) 120 =(120:60)* = 2*
b) 240 (240:60)* = 4
4480 = (480: 60* = 8
d) 600 (600:601 - 10
Answer:
60
Step-by-step explanation:
what am i supposed to answer frl
Can someone help me out ? ASAP
Answer:
Reflection
Step-by-step explanation:
Answer:
Reflection
Step-by-step explanation:
the triangle reflected across x axis
Is the point (-2,5) a solution for the equation y = 10 + 4x. Explain why and ensure that math
evidence is in your response.
Answer:
No, the point (-2, 5) is not a solution.
Step-by-step explanation:
To see if the point is a solution, plug the given values for x and y into the equation:
y = 10 + 4x
5 = 10 + 4(-2)
5 = 10 - 8
5 [tex]\neq[/tex] 2
Because the two sides aren't equal to each, the point (-2, 5) can't be a solution.
Julietta and Jackson are playing miniature golf. Julietta's ball rolls into a long. straight upward incline with a speed of 2.95 m/s and accelerates at -0.876 m/s/s for 1.54 seconds until it reaches the top of the incline and then continues along an elevated section. Determine the length of the incline.
Answer:
3.504 m
Step-by-step explanation:
Given that:
The speed (u)= 2.95 m/s
The acceleration = -0.876 m/s²
TIme t = 1.54 s
The length of the incline can be estimated by determining the distance traveled which can be achieved by using the second equation of motion.
[tex]S = ut + \dfrac{1}{2}at^2[/tex]
[tex]S = 2.95 (1.54) + \dfrac{1}{2}(-0.876) (1.54)^2[/tex]
S = 4.543 - 1.039
S = 3.504 m
Thus, the length of the incline = 3.504 m
simplest form
7/15 - 1/5
Answer:
4/15
Step-by-step explanation:
7/15 - 3/15 = 4/15
Answer:
4/15
Step-by-step explanation: i did the math
It cost Mr. Stu $315 for himself and 6 friends to have dinner. How much did it cost per person?
$52.50 per person
$45 per person
$23 per person
$63 per person
Answer:45
Step-by-step explanation:
Enter in standard form (10 points)
Answer: sorry i just need points TWT
A train covers 165 km in 1.5 hours. Find the constant variation.
Answer:
Step-by-step explanation:
110
The required value of constant variation would be 110.
What is the distance?Distance is defined as the product of speed and time.
Direct variation equation can be written as:
y = kx where "k" is a constant variation.
Here y represents the distance covered by the train, and x represents the time duration.
As per the given question,
Since the train covers 165 km in 1.5 hours.
Substitute the values of y = 165 and x = 1.5 in the direct variation equation and solve for k:
⇒ 165 = 1.5k
⇒ k = 165/1.5
Apply the division operation, and we get
⇒ k = 110
Therefore, the required value of constant variation would be 110.
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