9514 1404 393
Answer:
4² = 16
Step-by-step explanation:
The applicable rule of exponents is ...
1/a^-b = a^b
So, ...
[tex]\dfrac{1}{4^{-2}}=\boxed{4^2 = 16}[/tex]
_____
Additional comment
If you were to evaluate this using the Order of Operations, you would evaluate the exponent first:
1/4^-2 = 1/(1/16)
Then, you would do the division.
1/(1/16) = 16
__
We sometimes find it convenient to manipulate exponential terms to the form with the smallest positive exponents before we begin the evaluation.
A pizza company runs a marketing campaign based on their delivery time for pizzas. They claim that they will deliver a pizza within 30 minutes of ordering or it is free. In practice the time it takes to prepare a pizza and it being delivered is normally distributed with mean 25 minutes and standard deviation 3 minutes. What is the probability a pizza is delivered for free?On a particular Sunday, 40 pizzas were ordered. What is the probability that more than 2 were delivered for free?If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
Answer:
0.0475 = 4.75% probability a pizza is delivered for free.
0.2955 = 29.55% probability that more than 2 were delivered for free.
The delivery time should be advertised as 32 minutes.
Step-by-step explanation:
To solve this question, we need to understand the binomial distribution and the normal distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with mean 25 minutes and standard deviation 3 minutes.
This means that [tex]\mu = 25, \sigma = 3[/tex]
What is the probability a pizza is delivered for free?
More than 30 minutes, which is 1 subtracted by the p-value of Z when X = 30.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 25}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525
1 - 0.9525 = 0.0475
0.0475 = 4.75% probability a pizza is delivered for free
What is the probability that more than 2 were delivered for free?
Multiple pizzas, so the binomial probability distribution is used.
0.0475 probability a pizza is delivered for free, which means that [tex]p = 0.0475[/tex]
40 pizzas, which means that [tex]n = 40[/tex]
This probability is:
[tex]P(X > 2) = 1 - P(X \leq 2)[/tex]
In which
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{40,0}.(0.0475)^{0}.(0.9525)^{40} = 0.1428[/tex]
[tex]P(X = 1) = C_{40,1}.(0.0475)^{1}.(0.9525)^{39} = 0.2848[/tex]
[tex]P(X = 2) = C_{40,2}.(0.0475)^{2}.(0.9525)^{38} = 0.2769[/tex]
Then
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1428 + 0.2848 + 0.2769 = 0.7045[/tex]
[tex]P(X > 2) = 1 - P(X \leq 2) = 1 - 0.7045 = 0.2955[/tex]
0.2955 = 29.55% probability that more than 2 were delivered for free.
If the company wants to reduce the proportion of pizzas that are delivered free to 1%, what should the delivery time be advertised as?
The 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.327 = \frac{X - 25}{3}[/tex]
[tex]X - 25 = 2.327*3[/tex]
[tex]X = 32[/tex]
The delivery time should be advertised as 32 minutes.
Which statement correctly compares the centers of the distributions?
A. The median penguin height is greater at Park Zoo than at Cityview Zoo.
B. The median penguin heights are the same.
C. The median penguin height is greater at Cityview Zoo than at Park
Zoo.
D. The range of penguin heights is greater at Cityview Zoo than at
Park Zoo.
The median penguin height is greater at Cityview Zoo than at Park
Zoo, Option C is correct.
Mode is the most occuring number.
The range is the difference of the highest value and the lowest value.
The median is the middle value in a set of data
After finding the range and medians of the given data.
The median penguin at Cityview Zoo is 42 cm tall,
The median penguin at Park Zoo is barely 41 cm tall.
Cityview Zoo's median penguin height is higher than that of Park Zoo.
Hence, the median penguin height is greater at Cityview Zoo than at Park Zoo.
To learn more on Statistics click:
https://brainly.com/question/30218856
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course
Look at the following number line:
- 10
-5
0
5
10
What are two ways to write the inequality graphed?
x>-1 and -1
XS-1 and -12X
x < -1 and -1 > X
x2-1 and -1 5x
first and last one i think
What are the coordinates of the point that is 1/6 of the way from A to B? 6 A(-2, 3) 4+ B (10.3) ---- 4 4 O A. (6,0) O B. (3,0) O c. (0,6) O D. (0,3) O
Answer:
ITS C. (0, 3)
Step-by-step explanation:
I JUST ASKED THE TEACHER ;)
Factor this polynomial.
.-2x2 - 7x-3
Answer:
Its B
Step-by-step explanation:
Mark as Brainllest!!
Evaluate: 11c+5a-8 for a=4 and c=-6
Answer:
- 54
Step-by-step explanation:
11 c + 5 a - 8
11 × -6 + 5 × 4 - 8 (given :- a = 4 and b = -6)
- 66 + 20 - 8
- 54
please help with this question
Answer:
The answer to your question is given below.
Step-by-step explanation:
From the question given above, the following data were obtained:
x + 2 ≥ 2
x + 4 ≤ 3
The solutions to the equation can be obtained as follow:
x + 2 ≥ 2
Collect like terms
x ≥ 2 – 2
x ≥ 0
0 ≤ x
x + 4 ≤ 3
Collect like terms
x ≤ 3 – 4
x ≤ –1
Combining both answers, we have
0 ≤ x ≤ –1
Expressing the solution in internal notation, we have:
0 ≤ x ≤ –1
[0, –1]
by how much is 2690 less than 3780
Step-by-step explanation:
Subtract 2690 from 3780
3780
-2690
=1090
Please help will mark BRAINLIEST! This is pt.1
Answer:
See below.
Step-by-step explanation:
Problem 1.
1. QU
2. QW
3. UW
Given
4. QUW
Problem 2.
1. CB
2. <1, <2
Given
3. BD, BE
Given
4. ABD, CBE
SAS
which of the following statements is true
Answer: B ACE is similar to DCB
Step-by-step explanation:
According to the National Beer Wholesalers Association, U.S. consumers 21 years and older consumed 26.9 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H, :μ< 26.9
Ha : μ> 26.9
a. Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?b. What is the Type I error in this situation? What are the consequences of making this error?c. What is the Type II error in this situation? What are the consequences of making this error?
Answer:
Kindly check explanation
Step-by-step explanation:
If the null is rejected, then we conclude that the average Consumption of beer and cider by customers who are 21 years and above is greater than 26.1
A type 1 error is committed if the null hypothesis is incorrectly rejected ; this means we will be concluding that customers who are 21 years and older have higher average Consumption when they actually do not. This may lead to a restriction on beer consumption in the city when there actually isn't a need for it.
For type 2 error, a false null is incorrectly accepted, in this scenario, we are saying that the consumption of beer and cider is not beyond the mean value when in actual sense it is.
if 4 gallons of milk cost $11, how much would 7 gallons cost?
Answer:
$19.25
Step-by-step explanation:
11 ÷ 4 = $2.75 this is the cost per gallon of milk
2.75 * 7 = $19.25 this is the cost for 7 gallons of milk
Hope this helps
Answer:
$ 19.25
Step-by-step explanation:
Milk(gallons) Cost
4 11
7 x
[tex]\frac{4}{7} = \frac{11}{x}\\\\4 \times x = 11 \times 7\\\\4x = 77\\\\x = \frac{77}{4} = \$ 19.25[/tex]
PLEASE HELPPPPpdododp
Answer:
f(x) - g(x) = x^3 - 3x^2 - 4x - 4
Step-by-step explanation:
f(x) - g(x)
x^3 - 2x^2 - 3x - 5 - ( x^2 + x - 1 )
x^3 - 2x^2 - 3x - 5 - x^2 - x + 1
x^3 - 3x^2 - 4x - 4
There are 3600 second in 1 hour how many second are there in 24 hour
Step-by-step explanation:
hear is your answer please
Please help! What is the domain of the function shown in the graph?
Answer:
nnmb cgchmfxmgfmv vb , mnio qrstuvwxyz
abcdefghijklmnoprstuvxxyz
Step-by-step explanation:
now i know my abcs next time wont you sing with me
When the variable is on both sides of the inequality it must be isolated on one side and it doesn’t matter which side
Answer:
True
Step-by-step explanation:
Answer:
Isolate the variable and then use substitution to solve the system of equations.
Step-by-step explanation:
.
if for a dog 1 year is 7 ears for them, how many hours in 24 hours is one day for dogs?
Answer:
168hrs in division terms of every 1 year x 7 etc...
It will always be 24hrs nothing changes set of units to same units.
However because the equivalent to a same length of life as human is 1/7 we can do the reciprocal = 7 and do 24 x 7 = 168 hrs, but as many younger and healthy dogs eat and sleep the same as humans then equivalent would be not a good way to compare a dogs life.
Longer life breeds like Labrador or mixed breed dogs if walked at least 4 times a day and away from other dogs and all day young kids can live older than 20 and have actually be more compared to 4-5 years and so the comparison would be like 96 hrs or 120 hrs, but hours stay 24 a day for all animals as units don't change same units. Day represents a day and a year represents sun rise to sun fall to sun rise again x 365.
What is the conversion for m/s to km/h ?
Answer:
3.6km/hr
Step-by-step explanation:
What is the conversion for m/s to km/h ?
According to the conversion
1m = 0.001km
1s = 1/3600 hr
m/s to km/hr = 0.001/(1/3600)
= 0.001×3600
= 3.6
Hence the conversion is 3.6km/hr
Write Ratio 2:12 in the form 1:n
1:6
Hope this helps! :)
______________
Answer:
n value is 6
2:12=1:6
n is 6
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15. Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
Answer:
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
If [tex]|Z| > 2[/tex], the value of X is considered to be unusual.
Central Limit Theorem
The Central Limit Theorem establishes 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.
Assume that a population is normally distributed with a mean of 100 and a standard deviation of 15.
This means that [tex]\mu = 100, \sigma = 15[/tex]
Sample of 3
This means that [tex]n = 3, s = \frac{15}{\sqrt{3}}[/tex]
Would it be unusual for the mean of a sample of 3 to be 115 or more? Why or why not?
We have to find the z-score.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{115 - 100}{\frac{15}{\sqrt{3}}}[/tex]
[tex]Z = 1.73[/tex]
|Z| < 2, which means that it would not be unusual for the mean of a sample of 3 to be 115 or more.
What is the probability of rolling a number greater then two in a 6 sided number cube?
A.) 1/3
B.) 1/2
C.) 2/3
D.) 4/5
Answer:
c
Step-by-step explanation:
4/6 is reduced to two thirds
convert 3684 to standard form
To write a linear expression in standard form, rearrange the terms in alphabetical order.
3684
Anton needs to buy 3.5 meters of cloth for their project in TLE. If 1 meter of cloth costs P35.00, how much will he spend for 3.5 meters of cloth? a. What is asked in the problem? b. What are the given facts? c. What operation will be used? d. What is the nunber sentence? e. What is the answer?
Answer:
The correct answer is -
a. Amount Anton will spend for 3.5 m of cloth
b. 3.5 meters of cloth, 35.00 costs per meter.
c. Multiplication
d. 35.00 × 3.5/1 = N
e. P122.50 amount he will spend for 3.5 meters of cloth
Step-by-step explanation:
Solution:
A. in this question it is asked that how much it will cost Anton to buy the required cloth that is 3.5 meters cloth.
B. Given:
required cloth - 3.5 meters
price or cost of cloth per meter - 35 per meter
C. In this question multiplication will be used to get the answer so the operation would be - multiplication.
D. The number sentence is an equation to express inequality by using numbers and mathematical symbols, here the number sentence would be -
35.00 × 3.5/1 = N
E. The correct answer would be -
N = 35.00 × 3.5/1
= 122.5
Thus, the correct answer would be P 122.5.
what is the width of a triangle that has a 15 cm height and hypotenuse of 19 cm
Answer:
Pythagorean Theorem
Question Answer
Find the width of a triangle that has a 15cm height and a hypotenuse of 19cm. 11.7cm
A helicopter rises straight up 300m then flies west 400m. How far is it from the beginning (if it travels in a straight line back)?
please solve asap thanks
Find the Diameter of the circle, whose radius is 17 cm.
Answer:
34 cm
Step-by-step explanation:
The radius is half of the diameter, so 17 cm is half of 34 cm.
Diameter = 34 cm
help whats the answer??
Answer:
2 7/12
Step-by-step explanation:
You have to get all the fractions to a common denominator. Smallest common denominator would be 12.
5 and 3/4 turns to 5 and 9/12
2/3 turns to 8/12
2 and 1/2 turns to 2 and 6/12
8/12 + 2 6/12 = 3 2/12
5 9/12 - 3 2/12 = 2 7/12
2 7/12 being the remaining amount
what is the square root of 15
Step-by-step explanation:
[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]
I need help I’ll give u brainlest
Answer:
[tex]150[/tex] cubic centimeters
Step-by-step explanation:
Volume for triangular prism is [tex]V=\frac{1}{2} bhl[/tex]
[tex]V=\frac{1}{2}(6)(5)(10)[/tex]
[tex]V=\frac{1}{2} (300)[/tex]
[tex]V=150[/tex]
Hope this helps
Answer:
150 cubic centimeters
Step-by-step explanation:
The formula for the volume of a Triangular prism:
A=1/2*b*h*l
plug everything in
1/2*6*5*10=150 Cubic centimeters
When we expand (2x + 1/2)^6, what is the coefficient on the x^4 term?
Answer: The coefficient before x^4 is 60
Step-by-step explanation:
Hey! So I am not an expert at this, but you have to use the binomial theorem
I have attached of the Pascals Triangle (one shows the row numbering as well)
Basically in a pascal triangle, you add the two numbers above it to get the next number below
As you can see, the rows start from 0 instead of 1
The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms
NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)
Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)
It would be 15 × 2^4 × (1/2)^2 = 60
The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power
Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)
