Answer:
0.9545
Step-by-step explanation:
To calculate the probability, we need to get the standard score or z-score of each of the scores.
Mathematically;
z-score = (x-mean)/SD
mean = 89 and SD(standard deviation) = 3
for 83, the z-score = (83-89)/3 = -6/3 = -2
for 95, the z-score = (95-89)/3 = 6/3 = 2
The probability we are to calculate has the following range;
P(-2<z<2)
we use the standard score table to estimate this;
= P(z<2) - P(z<-2)
P(z<2) = 0.97725
P(z<-2) = 0.02275
Plugging these values into the equation, we have ;
P(-2<z<2) = 0.97725 - 0.02275 = 0.9545
Answer:
There will be 916 ants alive after 4 months.
Step-by-step explanation:
Step 1
Let's change the percentage to a decimal by dividing by a 100.
6.5% / 100 = .065
Step 2
So, for the first month we will multiply the initial amount of ants by .065 and this will give us the number of ants that die.
1200 * .065 = 78
This means that after the first month, 1200 - 78 = 1122 ants will be alive.
Step 3
Now for the second month: 1122 * .065 = 72.93 (rounded to 73)
1122 - 73 = 1049 ants will be alive
Step 4
For the third month 1049 * .065 = 68.185 (rounded to 68)
1049 - 68 = 981 ants will be alive
Step 5
For the fourth month 981 * .065 = 63.765 (rounded to 64)
981 - 64 = 916 ants will be alive
Hope this helps!
Answer:
9x^8
Step-by-step explanation:
f(x) is a binomial. Multiplying a binomial by itself results in a trinomial. In this problem we need ONLY to specify what the leading coefficient (coefficient of this trinomial product) is.
Here this is obtained by squaring the coefficient −3x^4. We get"
(-3)^2*(x^4)^2 = 9x^8
6 centimeters
x will represent the side length of the smaller square, so 2x is the side length of the bigger square.
x*x + 2x*2x = 45
x^2 + 4x^2 = 45
5x^2 = 45
x^2 = 9 (Divide by 5)
sqrt(x^2) = sqrt(9)
x = 3
2x = 6 (Multiply by 2)
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There are 8 pints in one gallon. So, Avery would need 8 times 2 pints because she needs 2 gallons and there are 8 pints in every gallon.
8 x 2 = 16
Now subtract what she already has from the total she needs.
16 - 7 = 9
So, Avery needs 9 more pints of milk.
