Lawrence High prevailed in Saturday's track
meet with the help of 20 individual event
placers earning a combined 68 points. A
first place finish earns 5 points, a second-
place finish earns 3 points, and a third-place
finish earns 1 point. Lawrence had a strong
second-place showing, with as many second
place finishers as first and third-place
finishers combined.
Answer:
The answer is below
Step-by-step explanation:
Let x represent a first place finish, y represent a second place finish and z represent a third place finish.
Since there is a total of 20 individual events, hence:
x + y + z = 20 (1)
A first place finish is 5 point, a second place finish is 3 point and third place finish is 1 point. Therefore:
5x + 3y + z = 68 (2)
The second place finishers is as much as first and third-place finishers combined. Hence:
y = x + z (3)
Solving equation 1, 2 and 3 simultaneously gives:
x = 7, y = 10 and z = 3
This means the number of first place finishes was 7, second place finishes was 10 and third place finishes was 3
Translate the sentence into an equation. Four more than the quotient of a number and 8 is 9. Use the variable y for the unknown number.
AC but is 20 m above the surface of the ocean what is the Evevation
Sea level starts at 0m
Since we start at 0 and it is 20m above sea level, we can add.
0 + 20 = 20m
Therefore, the elevation is 20m
Best of Luck!
A vehicle factory manufactures cars. The unit cost (the cost in dollars to make each car) depends on the number of cars made. If cars are made, then the unit cost is given by the function . What is the minimum unit cost? Do not round your answer.
Answer:
The function is missing in the question. The function is [tex]$ C(x) = 0.8x^2 -544x +97410 $[/tex]
The answer is 4930
Step-by-step explanation:
Unit cost of a car is given as
[tex]$ C(x) = 0.8x^2 -544x +97410 $[/tex]
Cost will be minimum when
x = -(-544)/ 2 x 0.8
= 340
Therefore, minimum cost for unit car is
[tex]$ C(x) = 0.8x^2 -544x +97410 $[/tex]
[tex]$ = 0.8(340)^2 -544(340) +97410 $[/tex]
= 4930
the sum 4 times a number and 7 is 31
Step-by-step explanation:
I'm not sure what you're looking for exactly, but it translates to this equation
4x + 7 = 31
Add 0 and write t
8
+
0
Answer:
8t
Step-by-step explanation:
Add 0 to 8 and then add the letter variable t.
A 351- foot rope is cut into three pieces. The second piece is twice as long as the first. The third piece is 3 times as long as the second. How long is the shortest piece of rope?
Answer:
87.75
Step-by-step explanation:
(r/s)(3) = ?
please help.
Answer:
[tex]\frac{3r}{s}[/tex]
Answer:
It’s 2
Step-by-step explanation:
Fill in the missing steps and justifications used to solve the given equation.
In Left BOX
6x-7 + 7 = 12+ 7x = 19/6in Right Box
Simplification Addition property of equationWhat are the Properties of the equation?Equilibrium, reflexivity, symmetry, transitivity, and the properties of operations are all solved by equations' properties. These properties hold true in propositional language as well as in algebra and arithmetic.
Hence, Here the solution is a step toward solving the given equation by using simplification.
Learn more about the properties of the equation here:
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Which of these choices is equivalent to the expression: i85
Answer:
[tex]i^{85} = i[/tex]
Step-by-step explanation:
The options are missing; however, the question can still be solved.
Given
[tex]Number = i^{85}[/tex]
Required
Simplify
[tex]Number = i^{85}[/tex]
Rewrite 85 as 84 + 1
[tex]Number = i^{84 + 1}[/tex]
Split the expression using the law of indices
[tex]Number = i^{84} * i^1[/tex]
Rewrite 84 as 4(21)
[tex]Number = (i^{4})^{21} * i^1[/tex]
In complex numbers, [tex]i^4 = 1[/tex]
So, we have
[tex]Number = 1^{21} * i^1[/tex]
[tex]Number = 1 * i[/tex]
[tex]Number = i[/tex]
Hence;
[tex]i^{85} = i[/tex]
The sum of 2 times a number and 10 is the same as 6 times the difference of the number and 1. What is the number? -4 -1 1 4
Answer:
4
Step-by-step explanation:
let 'x' be the unknown number
let's change the statment to an equation
2x + 10 = 6 (x-1)
2x + 10 = 6x - 6
2x - 6x = -6 - 10
-4x = -16
-4x = - 16
-4. -4
x = 4
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For any question comment me
Answer:
4
Step-by-step explanation:
Solve the equation: only write the number is the box
2( 5x+2)=54
If a+b+c=9 ab +bc+ca=12 find a2+b2+c2
Step-by-step explanation:
(a + b + c)^2 = (a^2 + b^2 + c^2) + 2(ab + bc + ca).
Therefore 9^2 = (a^2 + b^2 + c^2) + 2(12).
a^2 + b^2 + c^2 = 81 - 24 = 57.
Please find attached photograph for your answer.
4. Assume that you have a part-time job at which you work 20 hours per week at the rate
of $7.50 per hour (net of all payroll deductions). You are also required by your parents to
pay all your expenses, except rent and three meals a day, from those earnings. How much
per minute would you earn?
Answer:
0.125
7.50/60=1.25
since there 60 minutes in one hour you would divide the hourly rate by 60.
(x-6)(x2+3x+4) Please show working or at type a sentence on how you got it.
Answer:
x³-3x²-14x-24
Step-by-step explanation:
(x-6)(x^2+3x+4)
first multiply x by x^2+3x+4
x×x²=x³
x×3x=3x²
x*4=4x add
x³+3x²+4x ( first part)
multiply -6 by x²+3x+4
-6x²-18x-24
x³+3x²+4x -6x²-18x-24 ( simplify)
x³-3x²-14x-24
find the answer to = d/4 < 16
Answer:
d < 64
.....................
A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.
Answer:
The confidence interval is (0.1008, 0.1792)
Step-by-step explanation:
According to the question, the data provided is as follows
p′=0.14
sampling standard deviation of σp′= 0.02
Based on the above information
The computation of the 95% confidence interval for the true or correct proportion is
Here we apply the z value of 95% confidence interval i.e. 1.96
Now the confidence interval is
[tex]= (pcap - z\times sigma, pcap + z\times sigma)\\\\= (0.14 - 1.96\times 0.02, 0.14 + 1.96\times 0.02)\\\\= (0.1008, 0.1792)[/tex]
What are the solution(s) of X2-4=0?
Answer:
-2 or 2
Step-by-step explanation:
So we have the equation:
[tex]x^2-4=0[/tex]
Add 4 to both sides:
[tex]x^2=4[/tex]
Take the square root of both sides:
[tex]x=\pm 2[/tex]
Therefore, our answers are -2 or 2.
And we're done :)
(-2)+1 can someone help me
Answer:
-1
Step-by-step explanation:
When you add a positive num to a negative number the negative number goes in the direction towards zero.
hope this helps you:)
Which of the following is most likely the next step in the series?
The most likely next step in the series is Option B.
Option B is the correct answer.
What is a series of patterns?A series of patterns is a sequence of related designs, shapes, colors, or other elements that follow a consistent and predictable order.
The patterns may repeat or vary in a systematic way, creating a sense of rhythm, symmetry, or harmony.
We have,
From the series of patterns, we see that,
The number of arrows is increasing in odd arithmetic numbers.
So,
1, 3, 5,
The next step must have 7 arrows.
And,
The color is alternated as:
Red, Blue, Red Blue.
So,
The next step in the series must be a blue color.
Thus,
The most likely next step in the series is Option B.
Learn more about a series of patterns here:
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How do you write 0.1 as a fraction?
Answer:
1/100
Step-by-step explanation:
Answer:
0.1 can be written as 1/10
Step-by-step explanation:
0.1*10/1*10
calculate the perimeter of a triangle whose dimensions are 1 m 60cm, 1m 80cm and 2m
Answer:
540 CM
Step-by-step explanation:
The perimeter means the sum of the distance around a particular shape
1M=100 CM
2M=200 CM
200+60+80+100+100=540CM
I have tried 3 times to solve this.
Step-by-step explanation:
Year 2006- y = 0.09 (6) + 0.04 = 0.58
Year 2008- y = 0.09 (8) + 0.04 = 0.76
Year 2010- y = 0.09 (10) + 0.04 = 0.94
Year 2012- y = 0.09 (12) + 0.04 = 1.12
Year 2014- y = 0.09 (14) + 0.04 = 1.3
"Let x = 6 which is corresponded to 2006", so 8 would correspond to 2008, 10 would correspond to 2010, 12 would correspond to 2012, and 14 would correspond to 14. Plug 6 for x into your equation and do them same for the others.
Hopefully this helps you! :)
3. Write an equation to represent the situation:
The total cost of three equally priced DVDs is
$45. How much does each DVD cost?
Answer:
x=45/3
Step-by-step explanation:
Since total cost for equally priced three DVDs is $45. Therefore, each should cost 45 divided by 3.
Answer:
$15
Step-by-step explanation: easy 45/3 since they are equally prized which would equal 15
Can anyone help me with this question ?
Answer:
addition
Step-by-step explanation:
18 ( d - 9 ) = 198
3
divide both side by 18
d - 9 = 198
3 18
d - 9 = 11
3
multiply both sides by 3
d - 27 = 33
add 27 to both sides
d = 33 + 27
lastly, add them together
d = 60
therefore, the last step is addition
4x + 2(x - 5) - 3(2x -4)
Answer:
2
Step-by-step explanation:
Pull out like factors :
2x - 4 = 2 • (x - 2)
(4x + (2 • (x - 5))) - 6 • (x - 2)
(4x + 2 • (x - 5)) - 6 • (x - 2)
Final Answer:
2
5/6 + 2/3 = ?
Your
answer
Answer:
1.5
Step-by-step explanation:
Answer:
Improper Fraction: [tex]\frac{10}{6}[/tex]
Proper Fraction: [tex]1\frac{4}{6}[/tex]
Simplified Proper Fraction: [tex]1\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\frac{5}{6} + \frac{2}{3}[/tex] Is our equation... first we must find a common denominator! Let's take a look...
6: 1, 6, 12
3: 1, 3, 6
We see that both numbers get to 6 so we use that as our common denominator. Now we plug that in...
[tex]\frac{5*1}{6*1} +\frac{2*2}{3*2}[/tex]
We get...
[tex]\frac{5}{6} +\frac{4}{6} = \frac{10}{6}[/tex]
Now if you want to leave it as an improper fraction your answer will be [tex]\frac{10}{6}[/tex]. However, if you want you answer to be a proper fraction your answer is [tex]1\frac{4}{6}[/tex] which can be simplified further to,[tex]1\frac{2}{3}[/tex].
Whew! What a toughie! We showed that math problem!
The square root of 39 is between which two integers?
Answer:
6 and 7 sorry if im wrong
The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects, Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let a represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.
Answer:
Statement 2, Statement 4, and Statement 5 all applies
Step-by-step explanation:
Statement 1:
The expression 50ℎ represents the total charge for Rock the House Digital Designs.
Rock the House Digital Designs:
Initial consultation charge of $500 + $50 for every additional hour of work for the house plans
500 + 50h
NOT TRUE
Statement 2:
The expression 75ℎ represents the total charge for Elegance Home Architects.
Elegance Home Architects:
$75 per hour for the house plans
75h
TRUE
Statement 3:
The cost for using Rock the House Digital Designs for an initial consultation only is $550.
The cost for using Rock the House Digital Designs for an initial consultation only is $500
NOT TRUE
Statement 4:
If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.
Rock the House Digital Designs = 500 + 50h
500 + 50(15)
= 500 + 750
= $1,250
Elegance Home Architects = 75h
= 75(15)
= $1,125
TRUE
Statement 5:
If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.
Rock the House Digital Designs = 500 + 50h
= 500 + 50(40)
= 500 + 2,000
= $2,500
Elegance Home Architects = 75h
= 75(40)
= $3,000
TRUE
4(2x-8)=3(2-3x) Pls tell Me what the answer is