Answer:
Step-by-step explanation:
Sample One, Parts and % Sample Two, Parts and %
Fe 90 (90%) 45 (90%)
C 3 (3%) 1.5 (3%)
Other 7 (7%) 3.5 (7%)
100 parts 50 parts
Parts Fe/Parts Carbon = 90/3 or 30/1 in both cases [45/1.5 = 30/1]
Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1hr 50 min. Amanda comes in second with a time of 2hr 42 min. Bryce finishes last with a time of 3hr 16 min. Find the distance (in mi) for each part of the race.
The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.
Each racer travels the same distance and the sum of the distances travelled ([tex]x[/tex]), in miles. By definition of average speed ([tex]v[/tex]), in miles per hour, we get the following system of equations:
Amanda
[tex]t_{A} = \frac{x_{R}}{v_{A, R}}+\frac{x_{S}}{v_{A,S}}+\frac{x_{C}}{v_{A,C}}[/tex] (1)
Where:
[tex]x_{R}[/tex] - Running distance, in miles.[tex]x_{S}[/tex] - Swimming distance, in miles.[tex]x_{C}[/tex] - Cycling distance, in miles. [tex]v_{A,R}[/tex] - Speed of Amanda in the running distance, in miles per hour.[tex]v_{A,S}[/tex] - Speed of Amanda in the swimming distance, in miles per hour.[tex]v_{A,C}[/tex] - Speed of Amanda in the cycling distance, in miles per hour.[tex]t_{A}[/tex] - Total time of Amanda, in hours.Bryce
[tex]t_{B} = \frac{x_{R}}{v_{B, R}}+\frac{x_{S}}{v_{B,S}}+\frac{x_{C}}{v_{B,C}}[/tex] (2)
Where:
[tex]v_{B,R}[/tex] - Speed of Bryce in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Bryce in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Bryce in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Bryce, in hours.Corey
[tex]t_{C} = \frac{x_{R}}{v_{C, R}}+\frac{x_{S}}{v_{C,S}}+\frac{x_{C}}{v_{C,C}}[/tex] (3)
Where:
[tex]v_{B,R}[/tex] - Speed of Corey in the running distance, in miles per hour.[tex]v_{B,S}[/tex] - Speed of Corey in the swimming distance, in miles per hour.[tex]v_{B,C}[/tex] - Speed of Corey in the cycling distance, in miles per hour.[tex]t_{B}[/tex] - Total time of Corey, in hours.If we know that [tex]t_{A} = 2.7\,h[/tex], [tex]v_{A,R} = 10\,\frac{mi}{h}[/tex], [tex]v_{A,S} = 4\,\frac{mi}{h}[/tex], [tex]v_{A, C} = 20\,\frac{mi}{h}[/tex], [tex]t_{B} = 3.27\,h[/tex], [tex]v_{B,R} = 7.5\,\frac{mi}{h}[/tex], [tex]v_{B,S} = 6\,\frac{mi}{h}[/tex], [tex]v_{B,C} = 15\,\frac{mi}{h}[/tex], [tex]t_{C} = 1.833\,h[/tex], [tex]v_{C,R} = 15\,\frac{mi}{h}[/tex], [tex]v_{C,S} = 3\,\frac{mi}{h}[/tex] and [tex]v_{C,C} = 40\,\frac{mi}{h}[/tex], then the solution of the linear system of equations is:
[tex]\frac{x_{R}}{10} + \frac{x_{S}}{4} + \frac{x_{C}}{20} = 2.7[/tex] (4)
[tex]\frac{x_{B}}{7.5}+\frac{x_{S}}{6} +\frac{x_{C}}{15} = 3.27[/tex] (5)
[tex]\frac{x_{R}}{15}+\frac{x_{S}}{3} +\frac{x_{C}}{40} = 1.833[/tex] (6)
[tex]x_{R} = 4.23\,mi[/tex], [tex]x_{S} = 1.98\,mi[/tex], [tex]x_{C} = 35.64\,mi[/tex]
The running distance is 4.23 miles, the swimming distance is 1.98 miles and the cycling distance is 35.64 miles.
We kindly invite to check this question on systems of linear equations: https://brainly.com/question/20379472
x/-4 - 4 = -13 How do you solve for x? I am really struggling on this someone please help
Answer:
x/-4=-13+4
x/-4=9
x=(9)(-4)
x=-36
Find the measure of angles A and B in the diagrams below.
Answer:
A = 147°
B = 33°
1 inch = 2feet . what would be the real life measurement of an object that measures 3 inches on a scale drawing
Given,
1 inch = 2 feet
3 inches = ? feet
3 inches = (2 × 3) feet
3 inches = 6 feet
=》3 inches in the scale drawing is 2 feet in real life.
_______
Hope it helps ⚜
what is the slope of the line // take my points !!!!
Answer:
Im not sure
Step-by-step explanation:
Im not sure what the exact slope is, but instead of being useless, and a waste of your time, here is how to find the slope.To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
Multiplication:
(a) 7/3×2/9 (b) 3/7×5/11 (c) 15/8×6/25 (d) 21/20×15/14
Division:
(a) 3/4÷5/7 (b) 9/5÷6/11 (c) 15/8 ÷6 (d) 8/7÷12
Culcul constant des fractions:
(a) 3/7+15/7×3/2 (b) 9/5×(1/4-5/12) (c) (3/8+7/5)÷(9/4-5/3)
Multiplication:-
a. 7/3 × 2/9 = 7x2/3x9 = 14/27.
b. 3/7 × 5/11 = 3×5/7×11 = 15/77.
c. 15/8 × 6/25 = 3×3/4×5 = 9/20.
d. 21/20 × 15/14 = 3×3/4×2 = 9/8.
Division:
a. 3/4 ÷ 5/7 = 3/4 x 7/5 = 21/12 = (3 x 7) / (3 x 4) = 7/4
b. 9/5 ÷ 6/11 = 9/5 x 11/6 = 99/30 = (3 x 33) / (3 x 10) = 33/10
c. 15/8 ÷ 6 = 15/8 x 1/6 = 15/48 = (3 x 15) / (3 x 16) = 15/16
d. 8/7 ÷ 12 = 8/7 x 1/12 = 8/84 = (4 x 2) / (4 x 21) = 2/21.
Culcul constant des fractions:
a. 3/7 + 15/7 x 3/2
= 3/7 + 45/14
= (3 x 2) / (7 x 2) + 45/14
= 6/14 + 45/14
= 51/14
b. 9/5 x (1/4 - 5/12)
= 9/5 x [(1 x 3) / (4 x 3) - 5/12]
= 9/5 x (3/12 - 5/12)
= 9/5 - 2/12
= (9 x 12) / (5 x 12) - (2 x 5) / (12 x 5)
= 108/60 - 10/60
= 98/60
= (2x 49) / (2 x 30)
= 49/30.
c. (3/8 + 7/5) ÷ (9/4 - 5/3)
= [(3 x 5) / (8 x 5) + (7 x 8) / (5 x 8)] ÷ [(9 x 3) / (4 x 3) - (5 x 4) / (3 x 4)]
= (15/40 + 56/40) ÷ (24/12 - 20/12)
= 71/40 ÷ 4/12
= 71/40 x 12/4
= 852/160
= (4 x 213) / (4 x 40)
= 213/40.
Hope this helps..
15.
(05.04 MC)
Estimate and solve 4,298 ÷ 56 = ________. (1 point)
76 r 42
76 r 8
78 r 42
82 r 8 pls help asap!
Answer:
82 r 8
Step-by-step explanation:
i took the flvs test and its right!
How would you write 262 × 3 in addition form?
600 + 18 + 6
600 + 180 + 6
618 + 6
600 + 180 + 6 × 3
Answer:
262x3=768 so you need to find which answer equals 786 in addition form.
option a is equal to 624
option b is equal to 786
option c is equal to 624
option d is equal to 2358
your answer would be option b.
Step-by-step explanation:
hope this helps
At the sewing store, Brittany bought a bag of mixed buttons. The bag included 30 buttons, of
which 10% were large. How many large buttons did Brittany get?
Answer:
3 large buttons
Step-by-step explanation:
Multiply 30 by .10 to get 3 large buttons
which type of image format is constructed using proportional formulas rather than pixels?
Answer:
vector.
Step-by-step explanation:
4. Answer a through c
Answer:
Hello is this math i can help you with your answer
what is the improper fraction 2 7/8what is the improper fraction 8 2/3
Answer:
1. 23/8
2.26/3
Step-by-step explanation:
Evaluate the formula χ2=
(n−1)s2
σ2 when σ=3.32, n=38, and s=3.36.
Answer:
Step-by-step explanation:
volume of a cube with 7,5 cm
Answer:
421.88
Step-by-step explanation:
7.5^3=421.88
11.
A circle with a radius of 6 cm is enlarged to be a circle with a radius of 15 cm. What scale
factor was used to dilate the small circle into becoming the larger circle?
a) 0.4
b) 4.5
C) 2.5
d) 9.0
5. What percent of 36 is 24?
A. 50%
B. 66.7%
C. 75%
D. 80%
Answer: B. 66.7%
Step-by-step explanation:
Divide 24 by 36:
24/36 = 2/3
B. 66.7%
Answer:
answer is B I just had the test
Step-by-step explanation:
The area of a circle is 88.42cm2. Find the length of the radius rounded to 2 DP.
Answer:
r=5.31
Step-by-step explanation:
A=π r²
88.42cm²=3.14r².................π =3.14
88.42cm²÷3.14=r²
r²=28.16cm²
r=5.31
convert into precent...
convert 0.(6) as a precent the parenthesis mean something
Answer:
60%
Step-by-step explanation:
0.(6) is just not proper mathematical format.
I will assume you meant 0.6.
Then the equivalent percentage would be 0.6(100%), or 60%
[tex]log_{4} (x+3)(x-3) = 2[/tex]
solve for x
Answer:
x = √11
Step-by-step explanation:
(x + 3)(x - 3) = 2
=> x² - 3x + 3x - 9 = 2
=> x² - 9 = 2
=> x² = 11
=> x = √11
Hoped this helped.
PLZ HELP ME with this hw
Find the measures of the interior angles.
what is angle C
Calculate the values of a, b and c. Give reasons for your answers.
Quickly plsss
50 points
a = 70°
b = 55°
c = 40°
7+(4x8)-9
i need help this is weird
Answer:
30
Step-by-step explanation:
7+(4*8)-9
Multiply first inside the parentheses
7+(32)-9
Then add and subtract from left to right
39 - 9
30
Answer:
If x is a variable then the answer is 4x⁸ - 2
If x is a multiplication representation then the answer is 30
Step-by-step explanation:
If x is a variable:
1) Eliminate redundant parentheses
[tex]7+(4x^{8} )-9\\7+4x^{8} -9[/tex]
2) Subtract the numbers
[tex]7+4x^{8} -9\\-2+4x^{8}[/tex]
3) Rearrange Terms
[tex]-2+4x^{8} \\4x^{8} -2[/tex]
8. Write an equation for the line in slope- intercept form.
Answer:
y equals 3x plus 4 is the answer
Step-by-step explanation:
hope it helps
What are the terms in the following expression? Choose all that apply.
c + 4a + 2b + 7
Answer:
C, 4a, 2b and 7
Step-by-step explanation:
what is the value of x + y?
Answer:
55°
Step-by-step explanation:
180°-70°=110° (sum of angles on a straight line gives 180°
The size of each of the four remaining angles=110°/4 = 27.5°
<X + <Y = 27.5° + 27.5°=55°
Peter was thinking of a number. Peter adds 8 to the number, then doubles the result to get an answer of 57.4. Form an equation with
x
from the information.
Answer:
x+8*2=57.4
x=41.4
Step-by-step explanation:
Peter is thinking about a number. So, let's represent that number by x. So, he adds 8 to that number. x+8 so far. Then he doubles the result. x+8*2 to get an answer of 57.4. x+8*2=57.4. Ok, now in order to solve for x we would take 8*2 and get 16. 57.4-16=41.4. Now we know that x is 41.4. Substitute x into the equation. 41.4+8*2=57.4. 57.4=57.4. Have a great day! :)))))
How to write in simplified slope intercept form
Answer:
y = 4x - 3
Step-by-step explanation:
1. Pick tow points that is on the line; (1, 1) and (2, 5).
2. Find the Slope: Slope = (change in the y-values)/(change in the x-values)
Slope = (5 - 1)/(2 - 1) = 4/1 = 4
3. Use the slope and one point on the graph and substitute into y = mx + b
and solve for "b"
y = mx + b Slope = 4 point (1, 1)
1 = 4(1) + b
1 = 4 + b
1 - 4 = b
-3 = b
4. Write the equation of the line: m = 4 and b = -3
y = 4x - 3
What is p squared in math?
A line passes through the points (-4,5) and (1,-5). Write the equation of the line in slope-
intercept form.
A. y = - 2x - 3
B.y = - 2x +3
C. y=2x-3
D. y = 2x + 3
Answer:
y = -2x - 3
Step-by-step explanation:
Slope: (5 - - 5)/(-4 -1) = 10/-5 = -2
y-intercept: 5 - (-2)(-4) = -3