Answer:
0.1056
Step-by-step explanation:
Mean(μ) = 12 ounce
Standard deviation (σ) = 0.2 ounce
P(x<11.75) = ???
Let x be the random variable for the amount of soda a machine will dispense.
Using normal distribution
Z = (x - μ) / σ
Z = (11.75 - 12) / 0.2
Z = (-0.25)/0.2
Z = -1.25
From the normal distribution table
1.28 is 0.3944
Φ(z) is the tabular value of z
Φ(z) = 0.3944
Recall that when Z is negative
P(x<a) = 0.5 - Φ(z)
P(x < 11.75) = 0.5 - 0.3944
= 0.1056
Answer:
(2,2)
Step-by-step explanation:
(5+-1/2,8+-4/2)
(-2,2)
Answer: 12 blue marbles
Step-by-step explanation: Set up a proportion.
4/5 = x/15
Solve for x, the number of blue marbles. Cross multiply. You will get 60 = 5x
Divide by 5 on each side.
x = 12
There are 12 blue marbles.
difference of squares means that both the terms are square terms. (also there must be a - symbol)
for example
y^2 - 4
square root of y^2 is y
square root of 4 is +2 as well as -2
so you would factorise it like this:
(y+2)(y-2)
1. y^4 has a square root of y^2 as y^2 × y^2 is y^4.
<em>h</em><em>o</em><em>w</em><em>e</em><em>v</em><em>e</em><em>r</em><em>,</em><em> </em>-2 doesnt have a whole number square root so it is not a difference of squares.
2. 25 has a square root of 5. m^2 has a square root of m. n^4 has a square root of n^2. so this 25m^2n^4 is a square term.
1 has a square root of +1 and -1.
therefore, this one is a difference of squares. <u>(</u><u>5</u><u>m</u><u>n</u><u>^</u><u>2</u><u> </u><u>+</u><u>1</u><u>)</u><u> </u><u>(</u><u>5</u><u>mn^2</u><u> </u><u>-</u><u>1</u><u>)</u>
3. p^8 has a square root of p^4. q^4 has a square root of +q^2 and -q^2)
so it is a difference of squares. <u>(</u><u>p</u><u>^</u><u>4</u><u>+</u><u>q</u><u>^</u><u>2</u><u>)</u><u>(</u><u>p</u><u>^</u><u>4</u><u> </u><u>-</u><u>q</u><u>^</u><u>2</u><u>)</u>
4. 16x^2 is a square term as irs square root is 4x.
<em>h</em><em>o</em><em>w</em><em>e</em><em>v</em><em>e</em><em>r</em><em>,</em><em> </em>24 is not a square term.
therefore, it is not a difference of squares.
<span>Each ticket costs $10. He bought "x" tickets. Ticket cost = 10*x
Each bag of popcorn costs $5.
He bought "y" bags of popcorn.
Popcorn cost = 5*y
Service fee: $3
Total cost = 10x + 5y + 3 <= $75 is the inequality.
10x + 5y <= 72
If x = 4,
then 40 + 5y <= 72
5y <= 32
y <= 6.4
So y = 6 bags of popcorn.</span>