Find the slope of the line 6x – 2y = 6 (hint: find 2 points; then use the slope formula)

If the probability of an event is what is the probability of the event not happening?20/69Write your answer as a simplified frac

Vilka [71]

If an event has a probability P of happening, then there is a probability of (1-P) of the event not happening.

In this case the probability of the event is p=20/69.

Then, the probability of the event not happening is:

$P(\text{not happening})=1-p=1-\frac{20}{69}=\frac{69-20}{69}=\frac{49}{69}$

Answer: the probability of the event not happening is 49/69.

6 0

5 months ago

A circle passes through (3,-1),(-2, 4), and (6,8)

Vaselesa [24]

Answer:

D = -6, E = -8 , F = 0

Step-by-step explanation:

standard form = $x^{2} + y^{2} + Dx + Ey + F = 0$

now, when circle passes through (3,-1);

⇒ $3^{2} + (-1)^{2} + D(3) + E(-1) + F = 0$

⇒ $3D - E + F + 10 = 0$ ...............( equation 1)

when circle passes through (-2,4);

⇒ $(-2)^{2} + 4^{2} + D(-2) + E(4)+ F = 0$

⇒ $-2D + 4E + F + 20 = 0$ ...............( equation 2)

when circle passes through (6,8);

⇒ $6^{2} + 8^{2} + D(6) + E(8) + F = 0$

⇒ $6D + 8E + F + 100= 0$ ................( equation 3)

by solving these 3 equations , we get;

D = -6, E = -8, F = 0

hence,

standard form = $x^{2} + y^{2} + Dx + Ey + F = 0$

= $x^{2} + y^{2} - 6x - 8y = 0$

5 0

2 years ago

Help needed for assignment

bearhunter [10]

The answer is C........

3 0

2 years ago

PLEASE HELP ME!

algol13

Step-by-step explanation:

$1.\sum_{i=1}^{5}3i$

The simplest method is "brute force". Calculate each term and add them up.

∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)

∑ = 3 + 6 + 9 + 12 + 15

∑ = 45

$2.\sum_{k=1}^{4}(2k)^{2}$

∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²

∑ = 4 + 16 + 36 + 64

∑ = 120

$3.\sum_{k=3}^{6}(2k-10)$

∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)

∑ = -4 + -2 + 0 + 2

∑ = -4

4. 1 + 1/4 + 1/16 + 1/64 + 1/256

This is a geometric sequence where the first term is 1 and the common ratio is 1/4. The nth term is:

a = 1 (1/4)ⁿ⁻¹

So the series is:

$\sum_{j=1}^{7}(\frac{1}{4})^{j-1}$

5. -5 + -1 + 3 + 7 + 11

This is an arithmetic sequence where the first term is -5 and the common difference is 4. The nth term is:

a = -5 + 4(n−1)

a = -5 + 4n − 4

a = 4n − 9

So the series is:

$\sum_{j=1}^{5}(4j-9)$

5 0

2 years ago

A man invests his savings in two accounts, one paying 6% and the other paying 10% simple interest per year. He puts twice as muc

Masteriza [31]

Let x represent amount invested in the higher-yielding account.

We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be $2x$ .

We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.

$I=Prt$ , where,

I = Amount of interest,

P = Principal amount,

r = Annual interest rate in decimal form,

t = Time in years.

We are told that interest rates are 6% and 10%.

$6\%=\frac{6}{100}=0.06$

$10\%=\frac{10}{100}=0.10$

Amount of interest earned from lower-yielding account: $2x(0.06)=0.12x$ .

Amount of interest earned from higher-yielding account: $x(0.10)=0.10x$ .

$0.12x+0.10x=6600$

Let us solve for x.

$0.22x=6600$

$\frac{0.22x}{0.22}=\frac{6600}{0.22}$

$x=30,000$

Therefore, the man invested $30,000 at 10%.

Amount invested in the lower-yielding account would be $2x\Rightarrow 2(30,000)=60,000$ .

Therefore, the man invested $60,000 at 6%.

8 0

2 years ago