Answer: The 60th term of the arithmetic sequence -29, -49, -69, … is -1209.
Step-by-step explanation:
The given arithmetic sequence is -29, -49, -69, …
To find the 60th term of this sequence, we need to use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n - 1)d
where a_n is the nth term of the sequence, a_1 is the first term of the sequence, n is the number of terms in the sequence, and d is the common difference between consecutive terms.
In this case, a_1 = -29 and d = -20 (since each term is 20 less than the previous term). We want to find a_60, so we substitute n = 60 into the formula:
a_60 = -29 + (60 - 1)(-20) = -29 + 59(-20) = -29 - 1180 = -1209
Therefore, the 60th term of the arithmetic sequence -29, -49, -69, … is -1209.
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Complete question is;
An ordinary deck of playing cards has 52 cards. There are four suits
-spades, hearts, diamonds, and clubs
-with 13 cards in each suit.
Spades and clubs are black; hearts and diamonds are red. One of these cards is selected at random. Let A denote the event that a red card is chosen.
Find the probability that a red card is chosen, and express your answer in probability notation.
Answer:
P(A) = 0.5
Step-by-step explanation:
We are told that the ordinary deck of playing cards has 52 cards.
Now, there are four suits
-spades, hearts, diamonds, and clubs
-with 13 cards in each suit.
Now, in a standard set of playing cards, there are 13 black spades and 13 black clubs as well as 13 red hearts and 13 red diamonds
Thus;
Number of red cards = 13 + 13
Thus;
Number of red cards = 26
Since, A denotes the event that red card is chosen.
This means that probability of choosing a red card is;
P(A) = number of red cards/total number in a deck of cards
P(A) = 26/52
P(A) = 0.5
Answer
To solve this system of linear equations, we can use the method of substitution.
First, let's solve the first equation for x:
x = 34 - y - z
Now, we substitute this value of x into the second equation:
1(34 - y - z) + 10y + 5z = 100
34 - y - z + 10y + 5z = 100
34 + 9y + 4z = 100
Next, we simplify the second equation:
9y + 4z = 100 - 34
9y + 4z = 66
We can rewrite this equation as:
9y = 66 - 4z
y = (66 - 4z) / 9
Now, we substitute this value of y back into the first equation:
x + (66 - 4z) / 9 + z = 34
Multiplying through by 9 to eliminate the fraction:
9x + 66 - 4z + 9z = 306
9x + 5z = 240
Now we have a system of two equations in two variables:
9x + 5z = 240
9y + 4z = 66
We can solve this using the method of substitution or elimination. Let's use the method of elimination:
Multiplying the first equation by 4 and the second equation by 5, we get:
36x + 20z = 960
45y + 20z = 330
Subtracting the second equation from the first, we eliminate z:
36x - 45y = 630
We can simplify this equation by dividing through by 9:
4x - 5y = 70
Now, let's solve the new system of equations:
4x - 5y = 70
9y + 4z = 66
We can multiply the first equation by 9 and the second equation by 4 to eliminate x:
36x - 45y = 630
36y + 16z = 264
Now, subtracting the first equation from the second, we eliminate y:
36y + 16z - 36x + 45y = 264 - 630
81y + 16z = -366
Dividing through by 3, we get:
27y + 16z = -122
Now, we have a system of two equations in two variables:
4x - 5y = 70
27y + 16z = -122
We can solve this system using the method of substitution or elimination.
The state sales tax in Colorado is 2.9%.
We know that because we divide 2.32/80. We have to find out what percent the tax is of the amount paid. The answer comes to 0.029. Multiply it by 100, and you get 2.9%
Answer: he had $61
Step-by-step explanation: 52+9=61