Which formula can be used to find the math term of a geometric sequence where the first term is 8 and the common ratio is -3?

Lynna [10]

Answer:

$\boxed{\sf d. \ \frac{a}{b} = \frac{10}{7}}$

Step-by-step explanation:

$\sf \implies \dfrac{a - b}{b} = \dfrac{3}{7} \\ \\ \sf \implies \frac{a}{b} - \frac{b}{b} = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 = \frac{3}{7} \\ \\ \sf \implies \frac{a}{b} - 1 + 1 = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + 1 \\ \\ \sf \implies \frac{a}{b} = \frac{3}{7} + \frac{7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{3 + 7}{7} \\ \\ \sf \implies \frac{a}{b} = \frac{10}{7}$

6 0

3 years ago

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Luigi uses 39 cups of flour for every 6 pizzas he makes.Complete the table using equivalent ratios. Pizzas

zlopas [31]

Answer:

Part 1) The number of cups of flour needed to make 4 pizzas is 26

Part 2) The number of pizzas Luigi can make with 13 cups of flour is 2

Step-by-step explanation:

we know that

Luigi uses 39 cups of flour for every 6 pizzas he makes

Let

y ----> the number of cups of flour used

x ---> the number of pizzas he makes

In this problem

The relationship between the variables x, and y, represent a proportional variation

we have the ordered pair (6,39)

so

$\frac{y}{x}=\frac{39}{6}$

Part 1) Find out the number of cups of flour needed to make 4 pizzas

using a proportion

$\frac{y}{4}\ \frac{cups\ of\ flour}{pizzas}=\frac{39}{6}\ \frac{cups\ of\ flour}{pizzas}$

Solve for y

$y=\frac{39}{6}(4)$

$y=26\ cups\ of\ flour$

Part 2) Find out the number of pizzas Luigi can make with 13 cups of flour

using a proportion

$\frac{13}{x}\ \frac{cups\ of\ flour}{pizzas}=\frac{39}{6}\ \frac{cups\ of\ flour}{pizzas}$

Solve for x

$x=13(6)/39$

$x=2\ pizzas$

6 0

2 years ago

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Shelby earns $190 per week at her part time job and she spends $15.20 each week eating at the local fast food restaurant. What p

Hoochie [10]

I think the correct answer would be 8%...I'm not for sure.

5 0

3 years ago

Please, help me out!

nasty-shy [4]

A = lw + πr²
A = (125)(56) + (3.14)(28)²
A = 7000 + 3.14(784)
A = 7000 + 2461.76
A = 9461.76 yd²

8 0

3 years ago

16. From past experience, a company has found that in cartons of transistors, 92% contain no defective transistors, 3% contain o

Lynna [10]

Answer:

E(x)=0.15

V(x)=0.3075

S(x)=0.5545

Step-by-step explanation:

The mean of a discrete variable is calculated as:

$E(x)=x_1*p(x_1)+x_2*p(x_2)+...+x_n*p(n)$

where $x_1,x_2,...,x_n$ are the values that the variable can take and $p(x_1),p(x_2),...,p(x_n)$ are their respective probabilities.

So, if we call x the number of defective transistors in cartons, we can calculate the mean E(x) as:

$E(x)=(0*0.92)+(1*0.03)+(2*0.03)+(3*0.02)=0.15$

Because there are 0 defective transistor with a probability of 0.92, 1 defective transistor with a probability of 0.03, 2 defective transistors with a probability of 0.03 and 3 defective transistors with a probability of 0.01.

At the same way, the variance V(x) is calculated as:

$V(x)=E(x^2)-(E(x))^2$

Where $E(x^2)=x_1^2*p(x_1)+x_2^2*p(x_2)+...+x_n^2*p(n)$

So, the variance V(x) is equal to:

$E(x^2)=(0^2*0.92)+(1^2*0.03)+(2^2*0.03)+(3^2*0.02)=0.33\\V(x)=0.33-(0.15)^2\\V(x)=0.3075$

Finally, the standard deviation is calculated as:

$S(x)=\sqrt{V(x)} \\S(x)=\sqrt{0.3075} \\S(x)=0.5545$

8 0

3 years ago

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