Answer:
0.1587 = 15.87% probability that the factory will run out of lubricant before the next replenishment arrives
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Addition of normal variables.
When we add two normal variables, the mean is the sum of the separate means, and the standard deviation is the square root of the sum of the variances. So
The first machine has a mean usage of 50.6 gallons and standard deviation of 12 gallons. The second machine has a mean usage of 64.4 gallons and standard deviation of 16 gallons.
Total consumption is of both machines, combined. So
[tex]\mu = 50.6 + 64.4 = 115[/tex]
[tex]\sigma = \sqrt{12^2 + 16^2} = 20[/tex]
What is the probability that the factory will run out of lubricant before the next replenishment arrives?
Probability of consuming more than 135 gallons, which is 1 subtracted by the pvalue of Z when X = 135. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 115}{20}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that the factory will run out of lubricant before the next replenishment arrives
The area of a rectangle is 48 m^2 the length is (x+2) and width is (x). What is the value of x?
Answer:
Please find attached pdf
Step-by-step explanation:
Evaluate the equation. 193b = 212.3
Answer:
b= 1.1
Step-by-step explanation:
193b= 212.3
divide both sides by 193 to isolate b
212.3÷193=1.1
Answer:
b=1 .1
Step-by-step explanation:
Nimer was driving to a hotel he looked at his sat nav at 13:30 and saw the following, distance to destination =65 miles miner arrived at the hotel at 14:48
Step-by-step explanation:
The total is 37000.
Hope it helps for your education
Simplify answer
ms . Morgan plans to serve cookies at a class party each package of cookies cost $2.49 and contains 6 cookies. Ms. Morgan has $17.00 to spend. Will ms. Morgan have enough money to provide each of her 19 students with 2 cookies each ?
Answer:
No
Step-by-step explanation:
A package has 6 cookies for $2.49
Ms. Morgan has 19 students. She wants to give each student 2 cookies, which means each package is enough for 3 students.
19 students × 2 cookies = 38 cookies is what you need
7 packages times $2.49 = $17.43
7 packages × 6 cookies = 42 cookies
42 cookies ÷ 19 students = 2.21 cookies for each student
A pack of 5 of board games costs $75.
If there is a direct proportion between the price (y) and number of board games (x), which equation represents the
situation?
Answer:
x:y
1:15
2:30
3:45
4:60
5:75
Step-by-step explanation:
A store is instructed by corporate headquarters to put a markup of 25% on all items. An item costing $16 is displayed by the store manager at a selling price of $4. As an employee, you notice that this selling price is incorrect. Find the correct selling price. What was the manager's likely error?
Answer:
$20
Step-by-step explanation:
the manager's error could likely be putting the percentage mark up rather than the markup price added to the original price
25%×16
= $4
mark up price= (16+4)$
= $20
It says to find the value of X, one point is 110 and there’s two X’s
Tesla Battery Recharge Time.The electric vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle’s battery (Tesla company website). Assume that the actual recharging time required is uniformly distributed between 90 and 120 minutes.
a. Give a mathematical expression for the probability density function of battery recharging time for this scenario.
b. What is the probability that the recharge time will be less than 110 minutes?
c. What is the probability that the recharge time required is at least 100 minutes?
d. What is the probability that the recharge time required is between 95 and 110 minutes?
Answer:
a.) f(x) = [tex]\frac{1}{30}[/tex] where 90 < x < 120
b.) [tex]\frac{2}{3}[/tex]
c.) [tex]\frac{2}{3}[/tex]
d.) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Let
X be a uniform random variable that denotes the actual charging time of battery.
Given that, the actual recharging time required is uniformly distributed between 90 and 120 minutes.
⇒X ≈ ∪ ( 90, 120 )
a.)
Probability density function , f (x) = [tex]\frac{1}{120 - 90} = \frac{1}{30}[/tex] where 90 < x < 120
b.)
P(x < 110) = [tex]\int\limits^{110}_{90} {\frac{1}{30} } \, dx[/tex]
= [tex]\frac{1}{30}[x]\limits^{110}_{90} = \frac{1}{30} [ 110 - 90 ] = \frac{1}{30} [ 20] = \frac{2}{3}[/tex]
c.)
P(x > 100 ) = [tex]\int\limits^{120}_{100} {\frac{1}{30} } \, dx[/tex]
= [tex]\frac{1}{30}[x]\limits^{120}_{100} = \frac{1}{30} [ 120 - 100 ] = \frac{1}{30} [ 20] = \frac{2}{3}[/tex]
d.)
P(95 < x< 110) = [tex]\int\limits^{110}_{95} {\frac{1}{30} } \, dx[/tex]
= [tex]\frac{1}{30}[x]\limits^{110}_{95} = \frac{1}{30} [ 110 - 95 ] = \frac{1}{30} [ 15] = \frac{1}{2}[/tex]
Round to the nearest tenth
Answer:
17.7
Step-by-step explanation:
[tex]a^{2} =29^{2} -23^{2} \\a=\sqrt{312} \\=17.6635[/tex]
What is 0.91 in percentages?
Answer: 91%
Step-by-step explanation:
A club raised 80% of its goal for a charity. The club raised $1076. What was the goal?
Answer:
860.8
Step-by-step explanation:
A small book publisher knows that 20 books weigh 37 lbs. How much do 34 books weigh
Answer:
62.9 lbs
Step-by-step explanation:
20 34
37 x
20x = 1258
x = 62.9
Answer:
[tex]\boxed {\boxed {\sf 62.9 \ pounds}}[/tex]
Step-by-step explanation:
Let's create a proportion using this setup:
[tex]\frac{books}{weight}=\frac{books}{weight}[/tex]
We know that 20 books weight 37 pounds. We don't what 34 books weigh, so the weight is x pounds.
[tex]\frac{20 \ books}{37 \ pounds}=\frac{34 \ books}{x \ pounds}[/tex]
[tex]\frac{20}{37}=\frac{34}{x}[/tex]
Cross multiply. Multiply the first numerator by the second denominator. Then, the first denominator and second numerator.
[tex]20*x=37*34\\20x=1258[/tex]
Since we are solving for x, we have to isolate the variable. It is being multiplied and the inverse of multiplication is division. Divide both sides by 20.
[tex]20x/20=1258/20 \\x= 1258/20 \\x=62.9[/tex]
34 books weigh 62.9 pounds.
Sally has 10 months to read all 60 books on the sixth grade reading list. What is the minimum rate Sally can read in order to
finish all the books in time?
OA 10 books per month
ОВ.
6 books per month
OC. 7 books per month
OD
5 books per month
Answer:
6 books per month
Step-by-step explanation:
because 6x10 equals 60
If Dan had 20 packs of gum and he didn't have any this week and next week he had 10 packs left. What happened to the other 10 packs of gum?
Answer:
He ate it or he may have ate some in some packs then refilled the other packs.
Step-by-step explanation:
Answer:
Someone else ate them!
A certain cell phone advertises a mean battery life of 32 hours. Suppose the battery life of these phones follows a Normal distribution with standard deviation 2.5 hours. If 5 of these phones are randomly selected from the factory, then there is about a 95% probability that the sample mean will fall in which interval?
Find the z-table here.
7.5–56.5 hours
21.0–43.0 hours
27.1–36.9 hours
29.8–34.2 hours
31.0–33.0 hours
Answer:
29.8–34.2 hours
Step-by-step explanation:
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Population:
Mean of 32, standard deviation of 2.5.
Sample:
Sample of 5, so [tex]n = 5, s = \frac{2.5}{\sqrt{5}} = 1.1[/tex]
There is about a 95% probability that the sample mean will fall in which interval?
Within 2 standard deviations of the mean. So
32 - 2*1.1 = 32 - 2.2 = 29.8
32 + 2*1.1 = 32 + 2.2 = 34.2 hours
Find the values of x and y
Rose wants to buy a toy that costs $14. If she gives the cashier $20, which equation will tell you how much change Rose gets back?
Answer:
B) x + 14 = 20
Step-by-step explanation:
The "X" is the change. And the change has to equal 20. So it would be 6 + 14, since thats the only number that equals 20.
Therefore, it is B) x + 14 = 20.
125% of what number is 20
Answer:
16
Step-by-step explanation:
We can rewrite this as 125/100 · x = 20
This works because a percentage is out of 100, which means 125% is 125/100. "Of" usually means multiplied, and "what number" is the variable.
Now we can simplify this
125/100 · x = 20
5/4 · x = 20
x = 16
HELPPP!!! WILL MARK BRAINLIEST OF RIGHT!!!
y=
Answer:
y = (x + 3)² - 1
Step-by-step explanation:
Rob Is saving to buy a new MP3 player. For every $15 he earns babysitting, he saves $5. On Saturday, Rob
earned $60 babysitting. How much money did he save?
he eamed $60, he saved $
Answer:
20 dollars
Step-by-step explanation:
Martha earns $15 per hour for babysitting. The parents always giver her a $5 tip.
How many hours did Martha babysit if she made $65?
Enter the correct answer in the box.
? Hours
Answer:
4 hrs
Step-by-step explanation:
65-5=60
60/15=4
4 hrs
Help pleasee need asap ill give you brainly things
The Williams are buying a house that costs $349,863 and need to 25% of the price for a down payment. How much money do they need for their down payment?
Step-by-step explanation:
In most cases, you'll need a down payment of 20% – 25% to qualify. If you have a credit score that's higher than 720, you may qualify for an investment property loan with 15% down. FHA loan: You cannot use an FHA loan to buy an investment property.
solve each equation for the unknown
1. 5 + y = 7.
2. 3.8 = a + 2.5
5. + p = 9 1/3
Answer:
1. 5 + y = 7
⇒ y = 7 - 5
⇒y = 5
2. 3.8 = a + 2.5
⇒ a = 2.5 - 3.8
⇒ a = -1.3
3. 5 + p = 9 1/3
⇒ p = 9 1/3 - 5
⇒ p = 28/3 - 5
⇒ p = 28/3 - 15/3
⇒ p = 13/3
⇒ p = 4 1/3
List the following numbers in order from least to greatest.
2, -3, 9 what is this
Answer:
-3, 2, 9Step-by-step explanation:
Plz, I need help! Give out 5 stars and thank!
4 in the 42,672.
4 in the 37,426 isn't greater since 4 on 42. is 10 thousands than 37,426
A cylinder has volume 78 cm ^3. What is the volume of a cone with the same radius and height?
Group of answer choices
26 cm ^3
39 cm ^3
156 cm ^3
234 cm: ^3
Answer:Option A -
Step-by-step explanation:
What is 5 x 5 is it 25 or 35
Answer:
25 7 x 5 is 35
Step-by-step explanation:
hope this helps have a good rest of your afternoon :) ❤
Answer:
5 times 5 is 25.
Step-by-step explanation:
Hope this helps you dude
s h r e k (in a maid outfit)
IN FACTORED FORM PLZ!!
DUE TONIGHT HELP!!! WILL MARK THE BRAINLIEST!!
Answer:
Step-by-step explanation:
y=(2x+3)^2(x-5)
30% of what number is 33?
Mariana owed her grandmother $2.75 but was recently able to pay her back $1.25. How much does Mariana currently owe her grandmother?