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KiRa [710]
3 years ago
12

You have $59.95 in your wallet and want to buy some new CDs. If the CDs are $11.99 each, what number of CDs, x, can you buy? Wri

te and solve an inequality. Math symbols Relations Geometry Groups Trigonometry Statistics Greek Previous Next
Mathematics
1 answer:
juin [17]3 years ago
3 0

Answer: x≤5

Step-by-step explanation:

Let the one CD be given by= x

So,

11.99x≤ 59.95

or x≤ \frac{59.95}{11.99}

x≤5

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What are the solutions of the equation x^4 – 5x^2 – 36 = 0? Use factoring to solve.
hammer [34]

Answer:

Step-by-step explanation:

The equation is x^4 – 5x^2 – 36 = 0

We will break the middle term:

Firstly multiply the coefficient of x^4 by constant term of the equation:

1*36 = 36

Now find any two numbers whose product is 36 and their sum or difference is equal to 5

9*4 = 36

9-4 = 5

Now,

x^4 – 5x^2 – 36 = 0

x^4-9x^2+4x^2-36=0

Now take the common:

x^2(x^2-9)+4(x^2-9)=0

(x^2+4)(x^2-9)=0

x²+4=0,

x²= 0-4,

x²=-4,  

Take root on both sides:

√x²=+/-√-4

+/-√-4 = +/-√-1 *√4

√-1 = i

Then +/-√-1 *√4 = √4 i

We know that the root of 4 is 2

Then we can write it as +/-2i

Thus x = 2i , -2i

Now (x^2-9)= 0

x²=0+9

x²=9

Take square root on both sides:

√x²=√9

x=+/-3

x= 3, -3

Therefore the values of x are 2i, -2i, 3 , -3 ....

3 0
3 years ago
The sum of 5 consecutive even numbers is 100. What is the first number in this sequence?
gayaneshka [121]

Answer:

16

Step-by-step explanation:

Let's represent this with an equation, where x is the first number. The next number must be x+2, because it has to be even, not x+1, and the rest continue the same way:

x+(x+2)+(x+4)+(x+6)+(x+8) = 100

Solve for x.

5x+20 = 100

5x = 80

<u>x = 16</u>

4 0
3 years ago
Please help me on math homework! <br> File attached! :D
r-ruslan [8.4K]
Use pythagorena theorme

D=\sqrt{(x1-x2)^{2}+(y1-y2)^{2}}
NOTE: x1 and x2 means the first x and second x, not x^1 and x^2

points given are
(1,1)
(5,6)
x1=1
y1=1
x2=5
y2=6
D=\sqrt{(1-5)^{2}+(1-6)^{2}}
D=\sqrt{(-4)^{2}+(-5)^{2}}
D=\sqrt{16+25}
D=\sqrt{41}
6.403


answer is B
7 0
3 years ago
Read 2 more answers
If a puppet requires 3/4 yard of material, how many puppets can be made from 9 yards of material?
klasskru [66]
First find out how many times 3/4 yard goes into 9. 3/4 fits into 9 twelve times, so twelve puppets can be made.

Did I help? Thank me by clicking best answer!
5 0
3 years ago
Read 2 more answers
For a binomial distribution with p = 0.20 and n = 100, what is the probability of obtaining a score less than or equal to x = 12
notsponge [240]
The binomial distribution is given by, 
P(X=x) =  (^{n}C_{x})p^{x} q^{n-x}
q = probability of failure = 1-0.2 = 0.8
n = 100
They have asked to find the probability <span>of obtaining a score less than or equal to 12.
</span>∴ P(X≤12) = (^{100}C_{x})(0.2)^{x} (0.8)^{100-x}
                    where, x = 0,1,2,3,4,5,6,7,8,9,10,11,12                  
∴ P(X≤12) = (^{100}C_{0})(0.2)^{0} (0.8)^{100-0} + (^{100}C_{1})(0.2)^{1} (0.8)^{100-1} + (^{100}C_{2})(0.2)^{2} (0.8)^{100-2} + (^{100}C_{3})(0.2)^{3} (0.8)^{100-3} + (^{100}C_{4})(0.2)^{4} (0.8)^{100-4} + (^{100}C_{5})(0.2)^{5} (0.8)^{100-5} + (^{100}C_{6})(0.2)^{6} (0.8)^{100-6} + (^{100}C_{7})(0.2)^{7} (0.8)^{100-7} + (^{100}C_{8})(0.2)^{8} (0.8)^{100-8} + (^{100}C_{9})(0.2)^{9} (0.8)^{100-9} + (^{100}C_{10})(0.2)^{10} (0.8)^{100-10} + (^{100}C_{11})(0.2)^{11} (0.8)^{100-11} + (^{100}C_{12})(0.2)^{12} (0.8)^{100-12}


Evaluating each term and adding them you will get,
P(X≤12) = 0.02532833572
This is the required probability. 
7 0
3 years ago
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