If you can buy one pineapple for $4, then<br> how many can you buy with $12?

tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. equation

stiks02 [169]

( x -3 )² = y - 4
y = ( x - 3 )² + 4
One solution is located at the vertex: ( 3, 4 ).
y = - x + b
4 = - 3 + b
b = 7
( x - 3 )² = - x + 7 - 4
x² - 6 x + 9 = - x + 3
x² - 5 x + 6 = 0
x² - 2 x - 3 x + 6 = 0
x ( x - 2 ) - 3 ( x - 2 ) = 0
( x - 2 ) ( x - 3 ) = 0
x 1 = 2, x 2 = 3
y 1 = 5, y 2 = 4.
In order for this solution to be reasonable, the 2nd equation must be:
y = - x + 7

8 0

3 years ago

Corey flying a kite with 105 meters of string.His string makes an angle of 42 degrees with the level ground. How high is the kit

mafiozo [28]

<u>Given</u>:

Given that Corey is flying a kite with 105 meters of string.

The string makes an angle of 42° with the ground level.

We need to determine the height of the kite.

<u>Height of the kite: </u>

The height of the kite can be determined using the trigonometric ratio.

Thus, we have;

$sin \ \theta=\frac{opp}{hyp}$

From the given data, the values are $\theta=42^{\circ}$ , opp = h (height of the kite) and hyp = 105 meters.

Substituting the values, we get;

$sin \ 42=\frac{h}{105}$

Multiplying both sides of the equation by 105, we get;

$sin \ 42 \times 105=h$

$0.669 \times 105=h$

$70.245=h$

Rounding off to the nearest meter, we get;

$h=70$

Thus, the height of the kite is 70 meters.

8 0

3 years ago

How to factor 8x^3-216

Alex777 [14]

$8x^3-216\to\boxed{8(x^3-27)}$

8 0

3 years ago

Read 2 more answers

The chances of a tax return being audited are about 21 in 1 comma 000 if an income is less than $100,000 and 29 in 1 comma 000

vladimir2022 [97]

Answer:

a) p=0.021

b) p=0.029

c) Exactly one audit: P=0.0965

More than one audit: P=0.0042

Step-by-step explanation:

a) If the income is less than $100,000, there is a probability of 21 in 1,000 of being audited. This is:

$p_1=\dfrac{21}{1,000}=0.021$

If the income is equal or more than $100,000, there is a probability of 29 in 1,000 of being audited. This is:

$p_2=\dfrac{29}{1,000}=0.029$

b) If we have 5 taxpayers with incomes under $100,000, and we want to know the probability that exactly one will be audited, we can model this a binomial randome variable, with p=0.021 and n=5:

$P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\$

There is a probability of 0.0965 that exactly one out of a sample of five taxpayers with incomes under $100,000 will be audited.

To calculate the probability that more than one will be audited, we use the same distribution:

$P(x>1)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0) = \dbinom{5}{0} p^{0}q^{5}=1*1*0.8993=0.8993\\\\\\P(x=1) = \dbinom{5}{1} p^{1}q^{4}=5*0.021*0.9186=0.0965\\\\\\P(x>1)=1-[P(x=0)+P(x=1)]\\\\P(x>1)=1-(0.8993+0.0965)\\\\P(x>1)=1-0.9958\\\\P(x>1)=0.0042$