Last year, a baseball team paid $20 per bat and $12 per glove, spending a total of $552. They bought 34 pieces of equipment. What are a system of equations and an augmented matrix that can represent this situation
Answers
Answer:
- 20b +12g = 552
- b + g = 34
Step-by-step explanation:
Two equations can be written: one for the total expense, and one for the number of pieces of equipment. The unknowns in this scenario are the numbers of bats and gloves, which we can represent using the variables b and g. Then the system of equations is ...
20b +12g = 552 . . . . . . equation for total expense
b + g = 34 . . . . . . . . . . . equation for pieces of equipment
The augmented matrix is the matrix of the coefficients in these equations:
_____
The solution to these equations is ...
(b, g) = (18, 16)
Final answer:
The system of equations representing this situation is 20b + 12g = 552 and b + g = 34. In augmented matrix form, this is [[20,12,552],[1,1,34]].
Explanation:
In this situation, we can represent the number of bats and gloves a baseball team bought as variables, let's say 'b' and 'g' respectively. From the query, we have two pieces of information which provide two equations:
- 20b + 12g = 552 (This represent the total cost of the bats and gloves)
- b + g = 34 (This represents the total number of items bought)
In matrix form, we can put this system of equations in an augmented matrix as:
[[20,12,552],
[1,1,34]].
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A television is 36 inches by 18 inches. What is the area?
Answers
Answer:
Probability of getting sum less than
10 = \frac{30}{36}= \frac{5}{6}
Probability of getting a multiple of 3= \frac{20}{36}= \frac{5}{9}
(A) P(B|A)= \frac{P(B∩A)}{P(A)} = \frac{15/36}{30/36}= \frac{15}{30}=0.5
(B)P(A|B)= \frac{P(A∩B)}{P(B)}= \frac{15/36}{5/9}=0.75
(C) {A∩B} = {3, 6, 9, 12, 15, 18}
(D) {A} = {1, 2, 3, 4, 5 ,6, 7, 8, 9}
-Hope this helps-
Answers
Answer:
The contestant should not play.
Step-by-step explanation:
As per the given question, their current winning is $1 million.
The probability of the guessing to be true is 50% = .
There is also a possibility of 50% to be wrong, which can reduced the winning amount to $500,000 that is the half of the current amount.
Hence, the contestant should not play.
True or False? Please explain.
Thanks!
Answers
a regular polygon has all equal angles, interior and exterior, as well as all equal sides.
Check the picture below.
the one on the left is a regular octagon, as well as a convex one.
the one on the right is also an octagon, but is concave, the issue is that, though all sides remain equal, the angles do not, and so is not a regular octagon.
Answers
The value of the car in 2020 is $5532.53
What is exponential decay?
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.
The exponential decay is given by =
A = final amount
P = principal amount
r = rate of decrease.
t = 10
Therefore,
A = 25000(1-0.14)¹⁰
A = 25000×0.86¹⁰
A = 5532.53
Hence, the value of the car in 2020 is $5532.53
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Answer:
42,690
Step-by-step explanation:
it is the rule of LONG numbers
x/3-x-1/2≥1 a. x≤-3 b. x≥-3 c. x≤3 d. x≥3
Answers
Answer:
x ≤-9/4
Step-by-step explanation:
x/3-x-1/2≥1
Multiply each side by 6 to get rid of the fractions
6(x/3-x-1/2)≥1*6
2x -6x -3≥6
Combine like terms
-4x-3≥6
Add 3 to each side
-4x-3+3≥6+3
-4x ≥9
Divide each side by -4, remembering to flip the inequality
-4x/-4 ≤9/-4
x ≤-9/4
Logx-log(x+13)=1
Step by step explanation please
Answers
Answer:
Step-by-step explanation:
Applying logarithm rule
Log A - Log B= Log(A/B). Division rule
Now, Logx-log(x+13)=1
Log(x/(x+13))=1
Assume that the log is a natural log whose base is 10.
Then apply logarithm law
Log10 base 10=1
Comparing this to Log(x/(x+13))=1
This implies that
x/(x+13)=10
x=10(x+13)
x=10x+130
x-10x=130
-9x=130
x=130/-9
x=-14.444