What is the explicit formula for the geometric sequence with this recursive

15x+12(10-x)=141<br>make sure to use steps to solve!

goldfiish [28.3K]

Answer: x=7

Step-by-step explanation: First you distribute the 12 to (10-x). That then gives you 15x+120-12x=141. Now you combine like terms. So you do 15x-12x=3x. Your new equation now is 3x+120=141. Subtract 120 from 141 and mark it out. That leaves you with 3x=21. Divide both sides by 3. Your final answer is x=7.

5 0

3 years ago

The amounts a soft drink machine is designed to dispense for each drink are normally distributed, with a mean of 12.1 fluid ounc

Ludmilka [50]

Answer:

$\mu = 12.1\\\sigma = 0.3$

a) Find the probability that the drink is less than 11.9 fluid ounces

We are supposed to find P(x<11.9)

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

Refer the z table

So, P(z<-0.67) = 0.2514

Hence the probability that the drink is less than 11.9 fluid ounces is 0.2514

b)Find the probability that the drink is between 11.6 and 11.9 fluid ounces

x= 11.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.6-12.1}{0.3}$

$z=-1.67$

x= 11.9

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{11.9-12.1}{0.3}$

$z=-0.67$

We are supposed to find P(11.6<x<11.9)

So, P(11.6<x<11.9)= P(x<11.9)-P(x<11.6)

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

Refer the z table

P(-1.67<z<-0.67)= P(z<-0.67)-P(z<-1.67)

P(-1.67<z<-0.67)= 0.2514-0.0475

P(-1.67<z<-0.67)= 0.2039

So, the probability that the drink is between 11.6 and 11.9 fluid ounces is 0.2039.

c)Find the probability that the drink is more than 12.6 fluid ounces

We are supposed to find P(x>12.6)

x= 12.6

We will use z score formula :

$z=\frac{x-\mu}{\sigma}$

$z=\frac{12.6-12.1}{0.3}$

$z=1.67$

Refer the z table

P(x>12.6)=1-P(x<12.6)

P(z>1.67)=1-P(z<1.67)

P(z>1.67)=1-0.9525

P(z>1.67)=0.0475

Hence the probability that the drink is more than 12.6 fluid ounces is 0.0475

d) Is the drink containing more than 12.6 fluid ounces an unusual event?

Since p value is less than alpha (0.05)

Answer = No, because the probability that a drink containing more than 12.6 fluid ounces is less than 0.05, this event is not unusual.

3 0

3 years ago

Find the slope in the equation: -2x +y = 1*

Alexxandr [17]

Answer:-2

Step-by-step explanation:

whatever the number attachted to x is, is the slope

6 0

3 years ago

Read 2 more answers

Find the slope of the line passing through the pair of points or state that the slope is undefined. Then indicate whether the li

SVEN [57.7K]

M= y2 - y1/ x2 - x1
m= 9-9/-2-2
m= 0/-4
m= 0

The slope is 0

8 0

3 years ago

Read 2 more answers

A certain pickup truck gets 20mpg in the city and 28 mpg on the highway. If the driver drives 270 mi on 11 gal of gas, determine

Snezhnost [94]

Answer:

95 city and 175 highway miles.

Step-by-step explanation:

The driver gets 20 mpg in city, and 28 mpg on the highway.

An equation that could be written is

20x+28y=270

This equation accounts for the distance traveled.

x+y=11

This equotion accounts for how many gallons were driven.

Multiply the bottom equation by 20, so you can solve the set of equations.

20x+28y=270

20x+20y=220

subtract them

8y=50

y=6.25

now plug this back into x+y=11

x+6.25=11

x=4.75

Now 4.75×20=95 city miles and 6.25×28=175 highway miles.

8 0

4 years ago