The probability that the sample mean cholesterol level is greater than 205 is 0.62%.
To find the probability that the sample mean cholesterol level is greater than 205, we need to use the standard normal distribution and the formula for a normal distribution.
The sample mean cholesterol level, μ, is the population mean cholesterol level, 196, and the standard deviation of the sample mean, σ, is the standard deviation of the population divided by the square root of the sample size:
μ = 196
σ = 36 / √104 = 3.17
We want to find the probability that the sample mean cholesterol level is greater than 205, so we need to find the area under the curve of the standard normal distribution to the right of z = (205 - 196) / 3.17 = 2.5.
We can use the TI-84 calculator to find this probability by using the normal cdf function. In the function, we enter 2.5 as the lower bound and infinity as the upper bound to find the area under the curve to the right of z = 2.5.
The probability that the sample mean cholesterol level is greater than 205 is about 0.0062, or 0.62%.
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These marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two yellow marbles if the first one is placed back before the second draw. Write your answer as a ratio. Reduce to simplest terms
The probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
Explain the term probability with replacement?For queries where the results are repeated in the sample space, probability with replacement is utilized. This indicates that the item is replaced with in sample space after being picked, keeping the sample space's total number of items constant.The formula for the probability;
probability = favourable outcome/total outcome
The bag contains the marbles as;
yellow marbles: 2pink marble: 3blue marble: 5Total marble: 10Thus, probability of drawing 1st yellow marble.
probability(1st yellow) = 2/10 = 1/5
As the ball is placed again in the bag.
probability(2nd yellow) = 2/10 = 1/5
So, probability of drawing two yellow marble = 1/5 x 1/5 = 1/25.
Thus, the probability of drawing two yellow marbles if the first one is placed back before the second draw is 1/25.
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1. Find the measure of y.
110°
z
yº
100°
87°
Answer:
97.8263768112
Step-by-step explanation:
Geometric Mean is denoted as 'x'
x = √(110×87)
x = √9570
∴ x = 97.8263768112
Define Geometric MeanThe Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers. In essence, we multiply the numbers together and calculate their nth root, where n is the total number of data values. For instance, the geometric mean for a given pair of numbers, say 3 and 1, is equivalent to (3 + 1) = 3 = 1.732.In other terms, the geometric mean is the product of n numbers divided by the nth root. The geometric mean differs from the arithmetic mean, as is noted. As a result of the fact that in arithmetic mean, the data values are added before being divided by the total number of values. However, when calculating the geometric mean, we multiply the provided data values before taking the root of the entire number of data values using the radical index. Take the square root, for instance, if there are two data points, the cube root if there are three, the fourth root if there are four, and so on.To learn more about Geometric Mean refer https://brainly.com/question/28347817
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1-36) what is the sum of 2 + (1/5 + 1/5² + 1/5³ +...,.. +... 1/(5 to power n) ..)
help how
Answer:
[tex]\displaystyle \frac{9}{4}[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} )[/tex]
The second term of this sum is an Infinite Geometric Progression
To find the sum of an Infinite Geometric Progression,
- Find the first term ( 1/5 ) of the progression and call it a
- Find the common ratio, (divide any term by it's predecessor. i.e [tex]\displaystyle \frac{\frac{1}{5^2} }{\frac{1}{5} } = \frac{5}{5^2} = \frac{1}{5}[/tex]) and call it r
Finding the sum of given Geometric Progression:
Sum of Infinite GP: [tex]\displaystyle \frac{a}{1-r}[/tex]
Plugging our values in this equation, we get:
Sum of Geometric Progression = [tex]\displaystyle \frac{\frac{1}{5} }{1 - \frac{1}{5} } = \frac{\frac{1}{5} }{\frac{5 - 1}{5} } = \frac{1}{4}[/tex]
Adding to find the actual answer:
[tex]\displaystyle (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = 2 + \frac{1}{4}[/tex]
[tex]\displaystyle 2 + (\frac{1}{5^1} + \frac{1}{5^2} + \frac{1}{5^3} + ... + \frac{1}{5^n} ) = \frac{9}{4}[/tex]
The triangle below is equilateral. Find the length of side x to the nearest
tenth.
Answer:
1.7
to the nearest tenth
Step-by-step explanation:
Since the triangle is equilateral, all three sides are the same which is x
The vertical line of length [tex]\sqrt{7}[/tex] bisects the base so each of the two right triangles that is formed has lengths x, x/2 and [tex]\sqrt{7}[/tex]
Using the Pythagorean theorem,
c² = a² + b²
where c is the hypotenuse which has a length x and a and b are the two shorter sides which are x/2 and √7 in this case
Substituting for c, a and b we get
x²= (√7)² + (x/2)²
==> x² = 7 + x²/4
==> x² - x²/4 = 7
==> 3x²/4 = 7
==> x² = 7 x 4/3 = 28/3
x = √(28/3) = 1.732 or 1.7 to the nearest tenth
Solve for e.
2e + 3 + 7 = 2
e = [?]
What is the value of 5/9 ÷ 5/6? Responses
Answer:
2/3 or 0.667
Step-by-step explanation:
5/9 ÷ 5/6
5/9 * 6/5
1/3 * 2/1 (after cancelling off)
= 2/3
ayden deposits $2000 into a savings account with an annual interest rate of 3%. If he makes no further deposits or withdrawals, which graph shows the growth of his account balance?
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
How to resolve our equation?Ayden deposits $2000 into a savings account with an annual interest rate of 3%.
To calculate simple interest, multiply the daily interest rate by the principle and the number of days between payments. Consumers that make on-time or early monthly loan payments benefit from simple interest.
A = $2,060.00
I = A - P = $60.00
A is equal to P(1 + rt).
First, convert R percent to r a decimal; for example, R/100 is 3%/100, or 0.03 per year.
A = 2000(1 + (0.03 × 1)) = 2060 \sA = $2,060.00
$2,060.00 is the entire amount accrued from simple interest on a principal of $2,000.00 at a rate of 3% per year for 1 years, including principal and interest.
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the amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 110 minutes and a standard deviation of 11 minutes. what is the probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes?
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes is 0.0474 or 0.033.
Given,
In a normal random variable
Mean , [tex]\mu[/tex] = 110 minutes
Standard deviation , [tex]\sigma[/tex] = 11 minutes
then
The probability that a randomly selected product will be assembled in less than 91.630 minutes or more than 130.35 minutes will be
a)
To find the Probability that a randomly selected product will be assembled in less than 91.630 minutes, first calculate the z-score at 91.360 minutes
[tex]z-score = \frac{x-\mu}{\sigma}\\\\z-score=\frac{91.63-110}{11}\\\\z-score=\frac{-18.37}{11}=-1.67\\[/tex]
from z-score table , [tex]p(x < -1.67)=0.04746[/tex]
b)
To find the Probability that a randomly selected product will be assembled in more than 130.35 minutes, first calculate the z-score at 130.35 minutes.
[tex]z-score = \frac{130.35-110}{11}\\\\z-score=\frac{20.35}{11}=1.85[/tex]
From z-score table,
[tex]p(x > 1.85)\\\\=1-p(x < 1.85)\\\\=1-0.967\\\\=0.033[/tex]
Thus, the probability for product assembled in more than 130.35 minutes is 0.033
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What is the sum of x + y for the system of equations
below?
y=-3x-1
y = -2/3x + 6
O-24
-3
O-11
O5
The sum of x and y is 5.
What is an equation?An equation is a statement of two expressions connected by equal sign.
Given that, the system of equations, y=-3x-1 and y = -2/3x + 6
Simplifying the equations,
-3x-1 = -2x/3+6
Multiplying the both sides by -3
9x +3 = 2x-18
7x = -21
x = -3
Put x = -3 in any one of the equations,
y = -3(-3)-1
y = 9-1
y = 8
Hence, the sum is 5
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the function f(x) goes through the point (-2,6). which of the following translation of f(x) will go through the point (3,5)?
option 1; f(x-5)+1
option 2; f(x+5)-1
option 3; f(x-5)-1
option 4; f(x+5)+1
Answer:
Option 3: the function that goes through the point (3, 5) is f(x-5)-1
Step-by-step explanation:
To find which function goes through the point (3, 5), we can substitute 3 for x and solve for the value of f(x).
For option 1, f(x-5)+1, we have:
f(3-5)+1 = f(-2)+1 = 6+1 = 7
For option 2, f(x+5)-1, we have:
f(3+5)-1 = f(8)-1 = ?
For option 3, f(x-5)-1, we have:
f(3-5)-1 = f(-2)-1 = 6-1 = 5
For option 4, f(x+5)+1, we have:
f(3+5)+1 = f(8)+1 = ?
Please help me thanks :)
After doing the equation the area of ΔABC is 15√7.
The Heron area formula is what?
Heron of Alexandria (c. 62 ce) is credited with developing the Heron's formula, which determines the area of a triangle in terms of the lengths of its sides. If the side lengths are represented by the symbols a, b, and c: Area is equal to the square root of (a + b + c)/2, where s is half the perimeter.
Given that:
Let AB = 6x , BC = 5x , AC = 4x
then 6x+5x+4x = 30
15x = 30
x = 2
so AB = 12
BC = 10
AC = 8
Area = √s(s - a)(s - b)(s - c)
s = a+b+c/2
s = 12+10+8/2
s = 30/2
s = 15
Area = √15(15- 12)(15 - 10)(15 - 8)
Area = √15(3)(5)(7)
Area = √1575 = 15√7
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luka is making lemonade to sell at a school fundraiser. his recipe requires 4 times as much water as sugar and twice as much sugar as lemon juice. he uses 3 cups of lemon juice. how many cups of water does he need?
Luka will require 24 cups of water to make lemonades as calculated from the data given.
The quantity of sugar which he use is twice the amount of lemon which he us ,
= 2 x 3 = 6
and ,
as we know the amount of water is 4 times as much as lemon juice
Therefore, amount of water
= 4 * 6
= 24
A quantity in a Maths equation is a number or variable plus any algebraic combination of additional quantities. In an equation like x + 6 = 15, four values are represented.
A quantity can be described as the amount of something or how much of it there is. Quantity can also be used to refer to the size of something (its magnitude), whether in terms of numbers, units of measurement, or just relative size.
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I need some with this I would really appreciate if you could be able to help me with this.
I don't see the picture. Can you send it in the message.
Naomi's car used \frac{2}{5} 5 2 of a gallon to travel 15\tfrac{1}{2}15 2 1 miles. how many miles can the car go on one gallon of gas?
Answer:
To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 miles. We are told that the car used \frac{2}{5} 5 2 of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 to get the total number of gallons used:
\frac{2}{5} \cdot 15\tfrac{1}{2} = 9
Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:
15\tfrac{1}{2} \div 9 = \frac{31}{18}
This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:
\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}
Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:
\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}
Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.
What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
(Question 15)
Answer:
D
Step-by-step explanation:
when we have the zeroes, we can build the polynomial by multiplying factors that will turn the functional value to 0 at exactly these points.
f(x) = (x - 3)(x + 6)(x - 1)
we don't need to do the full multiplications to see that the constant term of the polynomial is the result of the multiplication of all 3 constant terms of the factors :
-3 × +6 × -1 = +18
and therefore, D is the correct answer (as it is the only answer option with +18 as constant term).
what are the three strategy of cube roots
i need explanation pls
Answer:
look at the explanation below
Step-by-step explanation:
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing the same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number not a perfect cube and we cannot find the cube root of that number
i hope this helps
solve the system if x = 2y + 3 and 4x - 5y = 9
The solution of the system of equations:
x = 2y+ 3
4x - 5y = 9
Is x = 1, y = -1.
How to solve the system of equations?Here we have the following system of equations:
x = 2y+ 3
4x - 5y = 9
To solve it, we can notice that the variable x is already isolated on the first equation, then we can take it and replace it on the other equation, then we will get:
4*(2y + 3) - 5y = 9
Now we can solve that equation for y:
4*(2y + 3) - 5y = 9
8y + 12 - 5y = 9
8y - 5y = 9 - 12
3y = -3
y = -3/3
y = -1
And the value of x is:
x = 2y + 3
x = 2*(-1) + 3
x = -2 + 3 = 1
So the solution is x = 1 and y = -1.
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Find the volume of the pyramid.
Answer:
180 ft^3
Step-by-step explanation:
volume of the pyramid = (1/3)(area of base) (height)
v= 1/3×(10×12÷2)×(9)
= 180 ft^3
Answer:
answer on the picture.....
There are 2 1/4 cups of orange juice in a container. The container holds 3 servings for a toddler, what is the serving size of vitamin C for a toddler
Hello,
I hope you and your family are doing well!
To find the serving size of vitamin C for a toddler, we need to know how much vitamin C is in each serving of orange juice. If we assume that each serving of orange juice contains a certain amount of vitamin C, then we can use the following equation to find the serving size:
serving size = (total amount of vitamin C in container) / (number of servings)
Since there are 2 1/4 cups of orange juice in the container, and the container holds 3 servings, the serving size is:
serving size = (2 1/4 cups) / (3 servings) = 3/4 cup per serving
So the serving size of vitamin C for a toddler is 3/4 cup.
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Happy Holidays!
The average height of the five players on the basketball team was 77 inches. One of the players was 71 inches tall. Another was 74 inches tall, and two were each 78 inches tall. How tall was the tallest player on the team?
How to solve this question
Answer:
The tallest player on the team was 78 inches tall
Step-by-step explanation:
9x + 2 = 10x +7
solve for x
Answer:
The value of x is (-5)
Step-by-step explanation:
9x + 2 = 10x + 7
9x - 9x + 2 - 7 = 10x - 9x + 7 - 7
(-5) = x
x = (-5)
Thus, The value of x is (-5)
Here is part of a recipe for different-size cakes, showing the ratio of eggs to flour.
Make a table that represents the same situation.
eggs : 0 2 4 6
flour (cups) : 0 1.5 3 4.5
question, we have to calculate the ratio by dividing a by b we will get the ratio as [tex]\frac{4}{3}[/tex].
What is a ratio formula?Using the ratio formula, ratios can be represented as a fraction. The ratio formula for any two quantities says a and b, is a:b = a/b. Because a and b are individual amounts for two portions, the total quantity is given as (a + b).
How do you calculate the ratios of a recipe?Known Total Amount
Determine the total quantity to be produced.
Determine the total number of parts in the ratio.
Divide the total quantity made by the total number of parts to get the amount per part.
Calculate the amount of each ingredient by multiplying each component by the amount per part.
Given:
Here is the ratio of eggs to flour
Eggs(a) 0 2 4 6
Flour(b) 0 1.5 3 4.5
For the table look at the image.
as per the question, we have to calculate the ratio by dividing a by b we will get the ratios as [tex]\frac{4}{3}[/tex].
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Find two consecutive positive integers such that the square of the first decreased by 21 equals 6 times the second
The given two consecutive positive integers are 9 and 10.
What is an integer?It is a whole number that can be positive, negative, or zero.
Let consider x and x+1 as two consecutive positive integers.
Given that,
[tex]x^{2} -21=6(x+1)[/tex]
[tex]x^{2} -6x-27=0[/tex]
It can be written in fractional form like,
(x-9)(x+3)=0
so the values of x are 9 and -3.
Here, only positive integers are considered.
Hence 9 and 10 are the two consecutive positive integers.
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please please please help i’m desperate!!!!
Answer:
parallel
Step-by-step explanation:
You want to know the parallel/perpendicular status of the lines described by the equations ...
2x -5y = 25y = 2/5x +3Parallel linesParallel lines have the same slope. The slope is the coefficient of x when the equation is written in the form ...
y = mx +b
as is the second equation.
The first equation can be put in that form by solving for y.
2x -5y = 25 . . . . . . given equation
2x -25 = 5y . . . . . . add 5y -25
2/5x -5 = y . . . . . . divide by 5
The coefficient of x (slope) is 2/5, same as the second equation.
The lines are parallel.
__
Additional comment
Your graphing calculator can help you figure this out, too. The graphed lines are parallel.
The sum of the digits of a certain two digit number is 13. Twice the tens digit exceeds the unit digit by 2. What is the number?
Answer:
Step-by-step explanation:
6.5
2. Divide. Write the answer in simplest
form.
6 2/3 divided by 4 1/5
Answer:
100/63
Step-by-step explanation:
6 2/3 ÷4 1/5
20/3÷21/5
20/3×5/21
1 37/63 or 100/63 or 1.587301587
so the answer is one (whole number) thirty seven over sixty three
FINALS PLEAZ HEL One year after you start a savings account you have $480 in the account. You were adding $120 each year write a linear function in the form y=mx+b that models your savings account a each year t after you start the account
Answer:
y = 120t + 480
Step-by-step explanation:
cross-tabulation can only be used for two variables; each variable must have well-defined labels. true false
The statement "cross-tabulation can only be used for two variables; each variable must have well-defined labels " is false
The cross tabulation is defined as the tool that is used in statistics to categorical data. We can also says that that present the results of the entire group of respondents
The given statement is "cross-tabulation can only be used for two variables; each variable must have well-defined labels "
The cross tabulation method can be used to represent two or more variables. The cross tabulation table has x axis as one variable and y axis as another variables
The cross tabulation can be used for two or more variables
Therefore, the the given statement is false
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ow many ways can you get exactly six heads and exactly six tails if after six tosses you have had three tails and three heads?
The number of possible combinations available as calculated from the given data is 259200.
Coin just has a head and a tail.
The potential configuration is (6! * 6!)/2.
Divide by two because each coin has two faces.
The potential configuration is (6! * 6!)/2.
The potential configuration is (( 720 x 720)/2
The potential configuration is 259200.
259200 different combinations are available.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to represent a group of objects. It outlines the numerous configurations for a particular set of data.
Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations can be counted in simpler situations. Combination is the taking together of n items, k at a time, without repetition.
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Which expression is equivalent to (m−2n−3)−4?
m−6n−7
m8n12
m−8n−12
1 over the quantity m raised to the sixth power times n raised to the seventh power end quantity
Answer:
B
Step-by-step explanation:
(m^-2 n^-3)^-4
-2 x -4 = 8
-3 x -4 = 12
m^8n^12
The given expression (m − 2n − 3) − 4 is equivalent to →
(m - 2n - 7).
What is a mathematical function, equation and expression?function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.
Given is the expression -
(m − 2n − 3) − 4
The given expression is -
(m − 2n − 3) − 4
m - 2n - 3 - 4
m - 2n - 7
Therefore, the given expression (m − 2n − 3) − 4 is equivalent to →
(m - 2n - 7).
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