Answer:
The probability that the sample mean is more than 110 is 0.0384.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the sampling distribution of the sample mean will be approximately normally distributed.
Then, the mean of the sampling distribution of sample mean is given by:
[tex]\mu_{\bar x}=\mu[/tex]
And the variance of the sampling distribution of sample mean is given by:
[tex]\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}[/tex]
The information provided is:
[tex]n=50\\\\\mu=100\\\\\sigma^{2}=1600[/tex]
Since n = 50 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the normal distribution.
The mean variance of the sampling distribution for the sample mean are:
[tex]\mu_{\bar x}=\mu=100\\\\\sigma^{2}_{\bar x}=\frac{\sigma^{2}}{n}=\frac{1600}{50}=32[/tex]
That is, [tex]\bar X\sim N(100, 32)[/tex].
Compute the probability that the sample mean is more than 110 as follows:
[tex]P(\bar X>110)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{110-100}{\sqrt{32}})[/tex]
[tex]=P(Z>1.77)\\=1-P(Z<1.77)\\=1-0.96164\\=0.03836\\\approx 0.0384[/tex]
*Use a z-table.
Thus, the probability that the sample mean is more than 110 is 0.0384.
Factorize:
625a^4 + 4b^4
(625 • (a4)) + 22b4
54a4 + 22b4
Final result :
625a4 + 4b4
Execute the following 18/3+2*8-5.
Adeyemi who is 15 years old is 3 years older than his younger brother Ojo . If Okonkwo the eldest brother is 21 years old . What is the average of the three brothers.
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18 inches and a second side that is 3 inches less than twice the third side, what are the possible lengths for the second and third sides?
Answer: One side could be 18 and the other side will be 33.
Step-by-step explanation:
Side #1 = 18Side #2 = 2x - 3Side #3 = xOne way of setting up the inequality is: Side #2 + Side #3 > Side #1
[tex]2x-3+x>18\\3x-3>18\\3x>18+3\\3x>21\\x>7[/tex]
Another way of setting up the inequality is: Side #1 + Side #3 > Side #2
[tex]18+x>2x-3\\18+3>2x-x\\x<21[/tex]
Final way of setting up the inequality is: Side #1 + Side #2 > Side #3
[tex]18+2x-3>x\\15>x-2x\\15>-x\\x>-15[/tex]
Therefore, we have the range for our value of x, which is between 7 and 21. Any possible value between works. Negative measurements are rejected. One of the sides would equal the x-value, while the other side would equal the value of 2x-3.
Aaron uses 18% of the paper in a printer paper package when she print a report for social studies class this is 90 sheets of paper how many sheets of paper are there in the printer paper in a package?
Answer:
percentage of paper used= 18%
Number of papers printed= 90
Total number of papers in the paper package= 'y'
total number of papers
= [tex]\frac{18}{100}[/tex] × y =90
transpose to the other side,
y= 90 ×[tex]\frac{100}{18}[/tex]
y=10 x100
y=1000
hence total number of papers in the package is 1000
Hope this helps
Please mark me as brainliest
Find the root of 11+2square30
[tex]\\ \sf\longmapsto \sqrt{11+2^230}[/tex]
[tex]\\ \sf\longmapsto \sqrt{11+4(30)}[/tex]
[tex]\\ \sf\longmapsto \sqrt{11+120}[/tex]
[tex]\\ \sf\longmapsto \sqrt{131}[/tex]
[tex]\\ \sf\longmapsto 11.3[/tex]
What is the product of these two binomials?
(x2 - 5)(2x - 1)
Select the correct answer.
o 2x3 - x2 + 10x - 5
O 2x3 - x2 - 10x-5
o 2x3 - x2 - 10x + 5
o 2x3 - x2 + 10x + 5
Answer:
2x³ - x² - 10x + 5
Step-by-step explanation:
Use FOIL method.
(x² - 5) (2x - 1) = x²*2x +(x²)*(-1) + (-5)*(2x) + (-5)*(-1)
= 2x³ - x² - 10x + 5
Please answer this correctly without making mistakes
Answer:
so to get a third you divide it by 3
first convert it to fraction
so it is 26/3
so do 26/3 divided by 3
so we do keep switch flip
26/3*1/3
so answer is 26/9 or 2 8/9
Step-by-step explanation:
Answer:
[tex]\large \boxed{\mathrm{2 \ 8/9 \ tablespoons \ of \ red \ chilies }}[/tex]
Step-by-step explanation:
8 2/3 tablespoons of red chilies is required for a recipe.
One-third of the original recipe would mean that the quantity of red chilies will be also one-third.
8 2/3 × 1/3
Convert to an improper fraction.
26/3 × 1/3
Multiply the fractions.
26/(3 × 3) = 26/9
Convert to a mixed fraction.
26/9 = 2 8/9
if the nth term is , then the (n+1)st is: Sorry if formatting is off, check the image to see the equation better!
Answer:
5
----------
( n+1)(n+2)
Step-by-step explanation:
5
----------
n ( n+1)
Replace n with n+1
5
----------
(n+1) ( n+1+1)
5
----------
( n+1)(n+2)
We replace every 'n' with n+1 and simplify
[tex]\frac{5}{(n+1)(n+1+1)} = \frac{5}{(n+1)(n+2)}[/tex]
What is 2 cm converted to feet?
Answer:
0.065617 ft
Step-by-step explanation:
Answer:
0.0656168 feet.
Step-by-step explanation:
Solve for x.
A. 37
B. 27
C. 30
D. 31
Answer:
B
Step-by-step explanation:
The formula for finding the relationship between a secant and a tangent is
tangent length ^2 = external segment secant/full length of secant
In this case
60^2 = 48*(x + 48) Expand
3600 = 48*(x + 48) Remove the brackets/
3600 = 48x + 48^2 Expand
3600 = 48x + 2304 Subtract 2304 from both sides
3600 - 2304 = 48x
1296 = 48x Divide both sides by 48
1296 / 48 = x
x = 27
4(c+3) =4+c+c+c+c+17
Whats the volume of this aquarium?
PLZ HELP!!
X = y + 12
How to solve for variable
Answer:
x-y=12
Step-by-step explanation:
what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?
Answer:
Approximately 3.05
Step-by-step explanation:
Using "compatible numbers" we can simply round these numbers to integer values. Let's make 76.32 => 76 and 24.98 => 25
So from here let's do 76/25 to get 3 R 1/25
1/25 as a decimal is .04
So far, we have 3.04. Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98. So we should consider an extra value in our decimal.
Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.
Thus our number will be 3.04 + .01.
Making our quotient approximately 3.05.
Cheers.
Together, Emily and Charlotte have a total of 60 strawberries. Emily sats 4 times the amount that Charlotte eats. How many strawberries does Charlotte eat?
Answer choices:
A. 6
B. 8
C. 10
D. 12
E. 14
F. 15
Answer:
12
Step-by-step explanation:
Since Emily eats four times the amount that Charlotte eats, then Emily will eat: = (4 × x) = 4x. Therefore, Charlotte eats 12 strawberries
Activity 12-4: A large monohybrid crossa corn ear with purple and yellow kernels The total number of purple and yellow kernels on 8 different corn ears were counted: Purple kernels 3593 Yellow kernels 1102 What is the ratio of purple kernels to yellow kernels
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
From the question we are told that
The number of purple kernel is [tex]n_k = 3593[/tex]
The number of yellow kernel is [tex]n_y = 1102[/tex]
Generally the ration of the purple to the yellow kernels is mathematically evaluated as
[tex]r = \frac{n_k}{n_y}[/tex]
substituting values
[tex]r = \frac{3593}{1102}[/tex]
[tex]r = 3.3[/tex]
[tex]r \approx 3[/tex]
Therefore the ratio is
[tex]1 \ Yellow : 3 \ Purple[/tex]
pls halllllllpppppppp
Answer:
85 degrees
Step-by-step explanation:
To find the range, take the high temperature and subtract the low temperature
40 - -45
40 + 45
85
The range is 85 degrees
Answer:
85
Step-by-step explanation:
The definition of range is the subtraction between the highest and lowest numbers.
In this problem, there are only two numbers so they will be subtracted.
40 - -45
40 + 45 = 85
The range is 85.
Hope this helped.
3. Simplify the following
a)[(116)3 x 114]x 1212
Answer:
48082464 is the answer
Step-by-step explanation:
=[(116)3×114] × 1212
=[348×114] × 1212
=39672 × 1212
=48082464 is the answer
hope it will help :)
Hey There!!
All you really need To do is: Divide [(116)] 3 x 114] x 1212) ( 20 + 51 + 43) ÷ 7
Hope It Helped!~ ♡
ItsNobody~ ☆
Annie tried to solve an equation step by step. Find Annie's mistake. *
Answer:
Hi, sorry, please could you resend the question again this isn't clear enough to properly answer your question .
maybe you should type in the steps before it is answered. thanks
Answer:
answer= C
Step-by-step explanation:
20 liters of mixture contain milk nad water in the ratio 5:3 of 4 liters of the mixture are replaced by 4 liters of milk find the new ratio of milk to water
Answer:
7:3
Step-by-step explanation:
5 + 3 = 8
The ratio is
5 milk : 3 water : 8 total
Milk is 5/8 of the total.
Water is 3/8 of the total.
The 20-liter mixture contains:
5/8 * 20 = 12.5 liters of milk, and
3/8 * 20 = 7.5 liters of water
4 liters of the mixture contain:
5/8 * 4 = 2.5 liters of milk, and
3/8 * 4 = 1.5 liter of water
When you remove 4 liters of the mixture from 20 liters of the mixture, you end up with
12.5 L - 2.5 L = 10 L milk, and
7.5 L - 1.5 L = 6 L water
Now you add 4 liters of milk. Now you have
10 L + 4 L = 14 L milk
6 L water
The new ratio of milk to water is 14:6 = 7:3
Answer
Step-by-step explanation:
sum of ratio=5+3=8
Does anyone know the answers to the graded activities on plato?
Answer:
Explanation
There are some activities in Courseware content that report scores and some that just report mastery and/or completion status.
Resolution
Dynamic vs. Non-dynamic mastery tests
Mastery tests give mastery status if the score is 80% or higher, but not all tests report a score. There are two types of mastery tests in Courseware content:
Non-dynamic tests: Those that do report a score, such as those in the Writing Process and Practice titles, in the Grammar and Mechanics modules, give the same number of questions each time; these are non-dynamic tests. For example, Splitting Fused Run-ons: Mastery Test presents ten questions. Even if the Learner answers the first three questions incorrectly and is, at that point, no longer able to answer eight correctly to achieve mastery, the remaining seven questions are presented.
Dynamic tests: Mastery tests from some content titles, such as Essential Reading Skills, however, are dynamic, which means they adapt to the Learner's responses. These tests do not always give the maximum number of questions; instead, they will end sooner if 80% is either achieved or no longer achievable. These tests show mastery if 80% or better was achieved, but do not show a score. For example, in Essential Reading Skills, Pronouns: Mastery Test, the maximum number of questions presented is five; mastery requires four questions are answered correctly. The test will end early if the student answers the first four correctly or two incorrectly out of the first four. Mastery is still based on achieving 80% or better, but the score is not fully determined, so no score is reported, by design.
Step-by-step explanation:
What’s the range of A and B and both
This is of Both
Range = Highest - Lowest data
Range = 45 - 10
Range = 35
Only A
Range = 45 - 10
Range = 35
Only B
Range = 40 - 15
Range = 25
Must click thanks and mark brainliest
1. What is the value of (1/2)^3?
O A. 76
O B. 119
O C.12
O D. 18
Answer:
1/2 to the power of 3= 1/8
Step-by-step explanation:
1/2*1/2=1/4
1/4*1/2=1/8
d?
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{(\dfrac{1}{2})^3}[/tex]
[tex]\mathsf{= \dfrac{1}{2}^3}[/tex]
[tex]\mathsf{= \dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2}}[/tex]
[tex]\mathsf{= \dfrac{1 \times 1 \times 1}{2 \times 2 \times 2}}[/tex]
[tex]\mathsf{\mathsf{= \dfrac{1 \times 1} {4 \times 2}}}[/tex]
[tex]\mathsf{= \dfrac{1}{8}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{Option\ D.\ \dfrac{1}{8}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
The sum of two consecutive even integers is 54. What are the two integers?
Answer:
26 and 2
Step-by-step explanation:
Given,
Sum of two even numbers = 54
let one number be x
another number be x +2
x + x +2 = 54
2x + 2 = 54
2x = 54 - 2
2x = 52
x = 52/2
x = 26
Therefore, the numbers are 26 and 26 + 2 = 28..
A football team is currently number 19 in overall offence. They have gotten 1,940 yards, while the number one
offence has received 2,728 yards. They've both played four games. How many more yards per game is the top
team receiving?
Answer:
20
that's grbrhrhbrhshsheheehebbebdbshwjwwmkwkw
Answer:
197 yards per game
Step-by-step explanation:
divide both values by 4 and subtract the value of the losing team from the value of the winning team to get your answer.
The triangle below is equilateral. Find the length of side
x in simplest radical form with a rational denominator.
===========================================================
Explanation:
Any equilateral triangle has all three angles of 60 degrees each. Splitting the triangle in half like this produces two identical copies of 30-60-90 triangles.
Any 30-60-90 triangle will have its hypotenuse twice as long compared to the short leg. The short leg here is 5 (it's opposite the smallest angle), so that doubles to 2*5 = 10 which is the value of x.
Note: the other side of this right triangle is 5*sqrt(3).
Answer:
x=10
Step-by-step explanation:
∵ Δ IS Equilateral.
∴ sides are equal.
perpendicular from vertex bisects it.
x=2×5=10
Show all work to solve 3x2 − x − 2 = 0.
Answer:
x=-2/3 and 1
Step-by-step explanation:
3x^2-x-2=0
(3x+2)(x-1)
3x=-2
x=-2/3
x=1
Complete the equation describing how
x and y are related.
5
1 2 3 4
8 13 18
-2
3
23
28
y = 5x + [?]
Enter the answer that belongs in [?].
Answer:
y=5x+3
Step-by-step explanation:
The equation of line is y=5x+3 since the y intercept is 3
Which algebraic expression means “three more than a number squared”? 2 n + 3 2 n minus 3 n squared + 3 n squared minus 3
The algebraic expression that means "three more than a number squared" is n² + 3, where n is the number.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The statement is given in the question, as follows:
“three more than a number squared”
The expression n² represents the square of the number, and the expression + 3 represents the addition of three more to the square of the number.
So, n² + 3 represents the value of the square of the number plus three.
Thus, the algebraic expression that represents "three more than a number squared" is n² + 3.
Learn more about the algebraic expression here :
brainly.com/question/21751419
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