Final answer:
To solve the word problem, we define three variables representing the number of first-, second-, and third-place finishers, respectively. We set up three linear equations based on the information provided, and by solving the system, we determined that 10 swimmers finished in first place, 8 in second, and 6 in third.
Explanation:
Setting Up the Equations
Let's denote the number of first-place finishers as x, second-place finishers as y, and third-place finishers as z. According to the information provided:
Total number of individuals placed: x + y + z = 24
Total points earned: 3x + 2y + z = 53
The number of first-place finishers equals the number of second and third-place finishers combined: x = y + z
This is our system of three equations.
Solving the System of Equations
To solve for the number of swimmers in each place, use the substitution or elimination method:
Since x = y + z, substitute x in the first two equations.
You'll get two equations with two variables (y and z).
Solve these equations to find the values of y and z.
Finally, substitute the found y and z back into x = y + z to get the value of x.
By solving this system, we find that 10 swimmers finished in first place, 8 swimmers finished in second, and 6 swimmers finished in third.
What unit of measurement would Guatemalans typically use to measure the weight of flour?
in the decimal number .98703, the 0 holds what place value
Answer:
it is in the 10 thousansth place.
Step-by-step explanation:
.98703
9=10nth place
8=100th place
7=thousandth place
0=ten thousandth place
3=hundred thousandth place
I hope this helps.
Help please =]
Solve system of equations using any method 2x-6y=8 and 2x-6y=3
My math homwork is asking me for the word form and the expanded form for 3.4 and 2.51,and i don't understand this. we just started it today and she my teacher gave us 3 pages of the math.
in DEF DE=17 m angle =32 Find DF nearest tenth
Answer:
(A) 32.1
Step-by-step explanation:
It is given that in ΔDEF, DE=17 and m∠F=32, thus
Using the trigonometry, we have
[tex]sinx=\frac{Perpendicular}{Hypotenuse}=\frac{DE}{DF}[/tex]
⇒[tex]sin32^{\circ}=\frac{17}{DF}[/tex]
⇒[tex]DF=\frac{17}{sin32^{\circ}}[/tex]
⇒[tex]DF=\frac{17}{0.529}[/tex]
⇒[tex]DF=32.1[/tex]
Therefore, the value of DF is 32.1.
Hence option A is correct.
What is the common ratio for the geometric sequence?
54, 36, 24, 16...
Answer:
Here is the answer and proof :)
Step-by-step explanation:
a rectangeler field is twice as long as it is wide a golf cart travrling at 12 miles per hour takes 7.5 minutes to travel the perimeter of the field what is the length (in miles) of the field
Determine the indicated side length of the golden rectangle. round your answer to the nearest hundreth....
(Picture below)....
....a. 4.85 ... b. 4.94 ... c. 5.26 ... d. 3.09
Answer:
a. 4.85
Step-by-step explanation:
im right
? = a+b
a = 3
(3+b)/3=3/b
b= -4.85 or 1.85
it cant be negive.
so ? = 3+1.85 = 4.85
A regression model in which more than one independent variable is used to predict the dependent variable is called
? a simple linear regression model
? a multiple regression model
? an independent model
? none of the above
Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?
a. v +4 = 8 – v
b. v +4 = 8
c. 4 + v = 8 – v
d. 2v + 4 = 8
Answer:
The resulting equation after the first step is 2v+4=8
d is the correct option
Step-by-step explanation:
We have been given the equation v + 4 + v = 8. In order to solve it for v, we'' perform the below mentioned steps.
Add the like terms in the left hand sideSubtract 4 to both sides of the equationFinally divide both sides by 2Hence, in the first step, we can group the like terms and combine. In the left hand side v and v are like terms and hence, we can add them
On adding v and v we get 2v
Thus, we have
[tex]v+v+4=8\\2v+4=8[/tex]
Thus, the resulting equation after the first step is 2v+4=8
How are rigid transformations used to justify the SAS congruence theorem?
The method in which rigid transformations used to justify the SAS congruence theorem is given.
What is rigid transformation?A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).
We are given that;
Theorem is SAS
Now,
The SAS congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent. To prove this theorem using rigid transformations, we can start with two distinct triangles that have a pair of corresponding congruent sides and a corresponding congruent included angle23. Then we can use a translation to move one triangle so that its congruent side matches the other triangle’s congruent side. Next, we can use a rotation to align the congruent angles of both triangles. Finally, we can use another translation to move the second congruent side of one triangle to match the second congruent side of the other triangle. By doing these rigid transformations, we have shown that one triangle can be mapped onto the other triangle exactly, which means they are congruent
Therefore, by the transformations the answer will be given above.
Learn more about rigid transformations;
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If i drove 34 times over a 7 mile bridge. how many miles in all did i drive?
f(x)=2x*e^2x. find lim of f(x) as x--> - infinity and +infinity ...?
39x10^3 in standard form
What is the product? enter your answer as a fraction, in simplified form, in the box. −1/4⋅(−6/11)?
yeah it would be 3/11 i just did the test
true or false. If f is a function, the f(s+t) = f(s)+f(t). ...?
The statement is true for linear functions, but not in general for all functions.
Explanation:The statement is true if f(x) is a linear function.
However, it is not true in general for all functions, so the statement is false.
An example of a linear function where the statement is true would be f(x) = 2x.
If we substitute s + t into the function, we get f(s + t) = 2(s + t) = 2s + 2t.
On the other hand, if we substitute f(s) + f(t) into the function, we get f(s) + f(t) = 2s + 2t.
Therefore, the equality holds and the statement is true for linear functions.
The complement of an acute angle is always
Rewrite 30/6 as a whole number
The fraction 30/6 can be rewritten as the whole number 5 after performing the division operation 30 ÷ 6.
Explanation:The problem asks to rewrite 30/6 as a whole number. In mathematics, this implies using the operation of division. Division is one of the four basic operations in math, along with addition, subtraction, and multiplication.
To solve this problem, you need to divide 30 by 6. Perform the division operation as follows: 30 ÷ 6. The result of this operation is 5.
Therefore, the fraction 30/6 can be rewritten as the whole number 5.
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sin^2(75)-cos^2(75)=?
In the triangle below, determine the value of a.
The tax rate on Harriet walker $80,000 vacation home is 2 mills. The property is assessed at full value. How much will Harriet Walker pay in taxes this year?
Answer:
Step-by-step explanation:
1600
125, 0.12, 0.1 listed to least to greatest
For spring break this year your family decided to visit Michigan, but it snows the first weekend you are there. You decide to make a snowman. If the bottom ball is 3 feet across, the middle ball is 2 feet across, and the top is 1 foot across, how much snow is needed to build the whole snowman? Round your answer to the nearest cubic foot.
A)
19 cubic feet of snow
B)
31 cubic feet of snow
C)
511 cubic feet of snow
D)
1022 cubic feet of snow ...?
Answer:
A
Step-by-step explanation:
Final answer:
To find the amount of snow needed to build the snowman, we need to calculate the volume of each ball and then add them together. The total volume is 18.84 cubic feet, rounded to 19 cubic feet.So,Option A.19 cubic feet of snow is correct.
Explanation:
To find how much snow is needed to build the whole snowman, we need to calculate the volume of each ball and then add them together. The volume of a sphere can be found using the formula V = (4/3) * pi * r³, where r is the radius of the sphere.
The bottom ball has a diameter of 3 feet, so the radius is 3/2 = 1.5 feet. The volume of the bottom ball is (4/3) * 3.14 * (1.5³) = 14.13 cubic feet.
The middle ball has a diameter of 2 feet, so the radius is 2/2 = 1 foot. The volume of the middle ball is (4/3) * 3.14 * (1³) = 4.19 cubic feet.
The top ball has a diameter of 1 foot, so the radius is 1/2 = 0.5 feet. The volume of the top ball is (4/3) * 3.14 * (0.5³) = 0.52 cubic feet.
The total volume of the snowman is 14.13 + 4.19 + 0.52 = 18.84 cubic feet. Therefore, the answer is 19 cubic feet of snow.
Write the equation of a line in slope-intercept form from the graph below.
Write the equation of a line in slope-intercept form from the graph below.
Answer: Y=x or y=1x
Step-by-step explanation:
Slope of 1 y-intercept of (0,0)
heeeelp!
Line segments with the same length are said to be __________.
Find the discriminant of the following equation.
4x2 + 16x + 16 = 0 ...?
Discriminant = b^2 - 4ac
a = 4
b = 16
c = 16
16^2 - 4(4 x 16)
256 - (4x64)
256 - 256 = 0
Therefore it only has one root
How is the graph of Y=√X) -5 translated from the graph of √X ?
shifted 5 units right
shifted 5 units down
shifted 5 units left
shifted 5 units up
how do i solve z+18=y
A heart beats 8 times in 3 seconds.About how many times will a cats heart beat in 2 minutes
What Is The Slope Of The Line In The Graph Shown Below?
-2
-1
1
2