Joe paid $10 for 8 batteries. Which graph represents the cost of the batteries he bought?

1 – 4k – 5 = -5 +4- 7K + 6 K = 3 K= -5 K=0 K = -7

sveta [45]

Answer:

K=3

Step-by-step explanation:

1 - 4K = 4 - 7K + 6

1 - 4K = 10 - 7K

-4K + 7K = 10 - 1

3K = 9

3K/3 = 9/3

K = 3

4 0

3 years ago

Alma charges $97 for a job that takes 2 hours and $187 for a job that takes 4 hours. Write an equation in slope-intercept form t

lara [203]

Answer:

y = 45x + 7

Step-by-step explanation:

From the given data, we have ordered pairs (2, 97) and (4, 187). We can use them to find the slope, as such:

$m=\frac{187-97}{4-2}=\frac{90}{2}=45$

We can then use the slope and one of the ordered pairs to find the y-intercept, as such:

$y=mx+b\\97=45(2)+b\\97=90+b\\7=b$

Therefore, m = 45 and b = 7. We get the equation:

y = mx + b

y = 45x + 7

7 0

3 years ago

7(16-6)+3^3= 7 (16 minus 6) + 3 equivalent to 3 equals

BARSIC [14]

Answer:

7(16-6)+3^3=7(16minus6) +3equivalent to 3equals

5 0

3 years ago

Based upon a long period of record keeping the following represents the probability distribution of the number of times the John

Nesterboy [21]

Given a table representing the probability distribution of the number of times the John Jay wifi network is slow during a week. We call the random variable x.

$\begin{tabular}
{|c|c|c|c|c|c|c|c|}
x&0&1&2&3&4&5&6\\[1ex]
p(x)&.08&.17& .21& k& .21& k& .13
\end{tabular}$

Part A:

The total value of p(x) = 1.

Thus, 

.08 + .17 + .21 + k + .21 + k + .13 = 1

0.8 + 2k = 1

2k = 1 - 0.8 = 0.2

k = 0.2 / 2 = 0.1

Therefore, the value of k is 0.1

Part B:

The expected value of x is given by

$E(x)=\Sigma
 xp(x) \\ \\ =0(0.08)+1(0.17)+2(0.21)+3(0.1)+4(0.21)+5(0.1)+6(0.13) \\ 
 \\ =0+0.17+0.42+0.3+0.84+0.5+0.78=3.01$

Therefore, the expected value of x is 3.01

Part C:

The expected value of $x^2$ is given by

$E(x^2)=\Sigma x^2p(x) 
\\ \\ =0^2(0.08)+1^2(0.17)+2^2(0.21)+3^2(0.1)+4^2(0.21)+5^2(0.1)+6^2(0.13) \\ \\ 
=0(0.08)+1(0.17)+4(0.21)+9(0.1)+16(0.21)+25(0.1)+36(0.13) \\ \\ =0+0.17+0.84+0.9+3.36+2.5+4.68=12.45$

Therefore, the expected value of $\bold{x^2}$ is 12.45


Part D:

The variance of x is given by

$Var(x)=E(x^2)-(E(x))^2 \\ \\ =12.45 - (3.01)^2=12.45-9.06 \\ \\ =3.39$

Therefore, the variance of x is 3.39.

Part E

The standard deviation of x is given by

$\sqrt{Var(x)} = \sqrt{3.39} =1.84$

Therefore, the standard deviation of x is 1.84.

Part F:

The variance of ax, where a is a constant is given by

$Var(aX)=a^2Var(X)$

Thus, the variance of 3x is given by

$Var(3X)=3^2Var(X)=9(3.39)=30.51$

Therefore, the variance of 3x is 30.51.

Part G:

The probability that the network has no more that 4 slow times in one week is given by

$P(x\leq4)=P(0)+P(1)+P(2)+P(3)+P(4) \\ \\ =0.08+0.17+0.21+0.1+0.21=0.77$

Since, the network slowness is independent from week to week, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is given by

$(0.77)^5=0.27$

Therefore, the probability that if we look at 5 separate weeks, the network has no more than 4 slow times in any of those weeks is 0.27

Part H:

The variance of x^2 is given by

$Var(x^2)=E((x^2)^2)-(E(x^2))^2=E(x^4)-(E(x^2))^2$

$E(x^4)=\Sigma
 x^4p(x) \\ \\ 
=0^4(0.08)+1^4(0.17)+2^4(0.21)+3^4(0.1)+4^4(0.21)+5^4(0.1) \\ +6^4(0.13)
 \\ \\ 
=0(0.08)+1(0.17)+16(0.21)+81(0.1)+256(0.21)+625(0.1)\\+1,296(0.13) \\ \\
 =0+0.17+3.36+8.1+53.76+62.5+168.48=296.37$

Thus,

$Var(x^2)=296.37-(12.45)^2=296.37-155.00=141.37$

Therefore, the variance of the random variable $\bold{x^2}$ is 141.37

5 0

3 years ago

two friends are knitting scarves. Each scarf has 3 rectangles and 2/3 of the rectangles have stripes, If the friends are making

Natasha_Volkova [10]

Answer:

They need 30 rectangles and 20 of those rectangles will have stripes.

Step-by-step explanation:

3 x 10 = 30, (2/3) x 30 = 20

5 0

3 years ago