Probability for the sample mean to have been 18.2 ounces or larger = 0.0003
Sample size, n = 30 boxes
Sample mean, [tex]\bar x[/tex] = 18.2 ounces
Population mean, μ = 18 ounces
Standard deviation of the population, σ = 0.32 ounces
We assume that this follows normal distribution.
Then the z-score, z = [tex]\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}} }[/tex]
= [tex]\frac{18.2-18}{\frac{0.32}{\sqrt{30}} }[/tex]
= 3.42
This z-score follows Standard Normal Distribution with mean = 0 and standard deviation = 1
Probability for the sample mean to have been 18.2 ounces or larger =
P(z ≥ 3.42) = 0.5 - P(0 < z < 3.423)
= 0.5 - 0.4997
= 0.0003
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A trivia contest asks both multiple choice and free response questions. Contestants receive 333 points for each correct multiple choice question and 555 points for each correct free response question, and they must score more than 606060 points to advance to the next round. If Eva advanced to the next round of the contest, which of the following inequalities describes xxx, the number of multiple choice questions, and yyy, the number of free response questions, that she answered correctly?
When Eva advanced to the next round of the contest, the inequality that describes the number of questions will be 3x + 5y > 60
What is an inequality?It should be noted that an inequality will simply used to illustrate the expressions that aren't equal. This is illustrated with the use of greater than, less, than, etc.
In this case, the contestants receive 3 points for each correct multiple choice question and 5 points for each correct free response question, and they must score more than 60 points to advance to the next round.
Therefore, the inequality that describes the number of questions will be:
= 3(x) + 5(y) > 60
= 3x + 5y > 60
where x = number of multiple choice questions,
y = number of free response questions,
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find the point that is 2/4 the way from A to B where A(-2, 5) and B(4, 9)
Pls help
The coordinates of the point that is 2/4 the way from A to B are (1, 7).
What is the Segment Ratio Formula?The coordinates of the point that divides a segment into a fractional component, n (n+m), or an arbitrary ratio, n:m, are given by:
x = [n ⁄ (n+m)] (x₂ - x₁) + x₁ and y = [n ⁄ (n+m)] (y₂ - y₁) + y₁
Given:
For this problem, n = 2 and m = 2 since (2 ⁄ (2+2) = 2 ⁄ 4, ( x,₁ y₁) =(-2, 5) and ( x₂, y₂) = (4, 9)
Where n and m are both positive integers, [n (n+m)] is the required distance ratio from the beginning position, (x₁, y₁) are the coordinates of one endpoint, and (x₂, y₂) are the coordinates of the other endpoint.
x = [n ⁄ (n+m)] (x2 - x1) + x1
= (2/4 ) (4 - (-2)) + (-2)
= (2/4 ) (4 + 2) + (-2)
= (2/4 ) × 6 + (-2)
= 3 - 2 = 1
y = [n ⁄ (n+m)] (y2 - y1) + y1
= (2/4 ) (9 - 5) + 5
= (2/4 ) (4) + 5
= 2 + 5 = 7
Therefore, the coordinates of the point are (1, 7).
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rearrange the distance Formula d=rd to solve for time
Answer:
[tex]t=d/r[/tex]
Step-by-step explanation:
Assuming you meant [tex]d=rt[/tex], dividing both sides by [tex]r[/tex] yields [tex]t=d/r[/tex].
improperly handled or undercooked poultry and eggs are the most frequent cause of salmonella food poisoning. salmonellosis can be deadly, although most individuals recover on their own. cases must be reported to the cdc, where they are closely monitored. the average number of salmonellosis cases per month in illinois is 2.56. if x is the monthly count of salmonellosis cases in illinois, what distribution does x follow, approximately?
The distribution that x follow approximately is a Poisson distribution
Given that the the average number of Salmonellosis cases per month in Illinois is 2.56
We now find the approximate distribution of X :
If outcomes the random variable are occurring on a certain time period or in a certain space, then random variable is called Poisson random variable.
In our case, X is the monthly count of Salmonellosis food poisoning cases , so outcomes are occurring on time period of month and are discrete.
Hence distribution of X : the monthly count of Salmonellosis cases follows a Poisson distribution.
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Which of the following values is less than −|62|?
71
53
−53
−71
Answer:
-71
Step-by-step explanation:
−|62| is equal to -62, and -71 is less than -62.
14. There are 3 teaspoons in a tablespoon. Show how to convert 15 teaspoons to tablespoons using a
ratio table and using a conversion factor.
There are 3 teaspoons in a tablespoon, 15 teaspoons to tablespoons using a ratio table and using a conversion factor will be total as 5 tablespoons.
What is a ratio table?The consistent relationship between two values is shown in a ratio table. A rate is a unique ratio that is used to compare two quantities with different units of measurement. There are various ways to examine a ratio table.
What is displayed in a ratio table?Equivalent ratios between two quantities are displayed in ratio tables. In order to find an equal ratio, you can make a ratio table by multiplying (or dividing) the quantities in the ratio by the same number.
You can use a ratio table to determine equal ratios and solve difficulties.
What is an example of a conversion factor?A conversion factor is a kind of number that is used to multiply or divide one set of units into another.
If any kind of a conversion is required, it must be done using the proper and correct conversion factor to get an identical value. For instance, 12 inches equals a total of one foot when converting between inches and feet.
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Eli used the place value strategy to add the numbers 4.69 and 7.7.
What is the very first step he should do to add these numbers correctly?
The addition according the place value is 12.39
What is place value?The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its location in the number, which might result in a number having two comparable digits with distinct values.
Place value refers to how much a digit is worth in relation to where it is in a number, such as the ones, tens, hundreds, and so on. For instance, 5 in 3458 has a place value of 5 tens, or 50. However, 5 thousands, or 5,000, is used to represent the place value of 5 in 5781. Understanding that a digit can have the same value regardless of where it appears in the number is crucial.
Given:
Eli used the place value strategy to add the numbers 4.69 and 7.7.
So, to add using place value strategy we use place value to break the addends into tens and ones.
Now, we add the tens and ones individually to find the whole sum.
So, breaking 4.69
at ones = 4
at tenth = 6
at hundredth = 9
In 7.7
at ones= 7
at tenth = 7
at hundredth = 0
Now, adding according to the place value
=(0 + 9 ) x 1/100 + (7 + 6) x 1/10 + (4 +7) x1
=9/100 + 13/10 + 11
=0.09 + 1.3 + 11
=12.39
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while on vacation Francisco sent postcards and letters to his friends. he spent $3.18 on postage. a stamp for a letter costs 39 cents. How many postcards and letters did he send.
Answer: 8
Step-by-step explanation: 3.18 divided by 0.39 is 8 (without the decimals)
You earn $100 per month and want to save 10% in a savings account. Use the savings
calculator to find out how much your total savings would be in 5 years if your account
has an annual interest rate of 1%. (Do not include the $ sign in your reponse) PLEASE HELPP
With the annual interest of 1%, the total saving after 5 years is $6060.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
You earn $100 per month and want to save 10% in a savings account.
Here we have to use the savings calculator to find out how much your total savings would be in 5 years if your account has an annual interest rate of 1%.
Through the given details we have identified that,
Monthly earning = $100
Saving per month = 10%
So, in amount it can be
=> 100 x 10/100 = $10
So, for one year the saving without interest is
=> 10 x 12 = 1200
So, When we add the interest of 1% for the year,
Then the interest amount for one year will be,
=> 1200 x 1/100 = 12
So, the total amount including interest for one year,
=> 1200 + 12 = 1212
So, the savings after 5 years will be,
=> 5 x 1212
=> 6060.
Therefore, the total saving amount after 5 years is $6060.
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Which answer choice shows seventy and twenty-three thousandths written in standard form? A 70.023 B 70.230 C 7.023 D 70.0023
Answer:
A
Step-by-step explanation:
seventy and twenty-three thousandths = 70.023
Answer:
A
Step-by-step explanation:
thank
you
:D
Please help I’m struggling so bad right now
HELP ASAP NEEDS TO BE DONE BY TONIGHT
The linear function that contains the point (-4, -3) and is perpendicular to the line 4x + 5y = 15 is given by:
y = 5/4x + 2.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which:
The coefficient m is the slope of the function, which is the constant rate of change.The coefficient b is the y-intercept of the function, which is the initial value of the function.When two lines are perpendicular, the multiplication of their slopes is of -1, hence, considering the line is perpendicular to 4x + 5y = 15, we have that:
5y = 15 - 4x
y = 3 - 4/5x
Then:
-4/5m = -1
m = 5/4
Hence the rule is:
y = 5/4x + b
When x = -4, y = -3, hence the intercept b is found replacing these points into the equation as follows:
-3 = 5/4(-4) + b
-3 = -5 + b
b = 2.
Hence the equation is:
y = 5/4x + 2.
Both perpendicular equations are graphed at the end of the answer.
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6. Write two equivalent rates for each comparison. a) 5 goals in 10 games b) 10 km jogged in 60 min c) 6 pizzas eaten in 30 min d) 10 penalties in 25 games
The equivalent rates for each of the given options are;
A) 1 goal in 2 games
10 goals in 20 games
B) 1 km jogged in 6 min
5 km jogged in 12 min
C) 1 pizza eaten in 5 minutes
2 pizzas eaten in 10 minutes
D) 2 penalties in 5 games
20 penalties in 50 games.
What are the equivalent rates?We want to write two equivalent rates for the given rates.
It should be noted that different rates that have the same value are equivalent rates. You can find an equivalent rate the same way you find equivalent ratios which is to divide or multiply the numerator and the denominator by the same number.
A) 5 goals in 10 games can also be written as;
5/10 = 1/2 = 10/20
These equivalent rates are;
1 goal in 2 games
10 goals in 20 games
B) 10 km jogged in 60 min;
10/60 = 1/6 = 5/12
These equivalent rates are;
1 km jogged in 6 min
5 km jogged in 12 min
C) 6 pizzas eaten in 30 min;
6/30 = 1/5 = 2/10
These equivalent rates are;
1 pizza eaten in 5 minutes
2 pizzas eaten in 10 minutes
D) 10 penalties in 25 games;
10/25 = 2/5 = 20/50
These equivalent rates are;
2 penalties in 5 games
20 penalties in 50 games.
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The midpoint M of UV has coordinates (5, 6). Point U has coordinates (10, 5). Find the
coordinates of point V.
Write the coordinates as decimals or integers.
The coordinates of point V is ( 15/2, and 11/2).
What is the Midpoint of a Line Segment?A line segment's midpoint is a point that divides the line segment across two equal sections. The midpoint of a line segment with coordinates at both ends X₁, Y₁ and X₂, Y₂ is calculated using the:
According to the given information:
Point M has Coordinates (5, 6).
point U has coordinates (10, 5).
We know that to find the Midpoint of a Line Segment:
( X₁+X₂)/2 , (Y₁ + Y₂ )/2
Now Putting the value in the formula;
MU = ( X₁+X₂)/2 , (Y₁ + Y₂ )/2
= (5 + 10)/2 , (6 + 5)/2
= 15/ , 11/2
Therefore, The coordinates of point V ( 15/2, 11/2).
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for the month of april in a certain city, 48% of the days are cloudy. also in the month of april in the same city, 26% of the days are cloudy and snowy. what is the probability that a randomly selected day in april will be snowy if it is cloudy?
53/300 is the probability that a randomly selected day in April will be snowy if it is cloudy.
What do we mean by probability?Probability is a branch of mathematics that deals with numerical representations of the probability that an event will happen or that a statement is true.The probability of an event is a number between 0 and 1, with 0 roughly denoting impossibility and 1 denoting certainty.A typical definition of probability is the ratio of favorable outcomes to all other outcomes in the sample space.The formula for the probability of an event is P(E) = (Number of favorable outcomes) (Sample space).So,
The probability that the day is cloudy: 48/100The probability that the day is snowy and cloudy: 26/48The probability that day will be snowy and cloudy at random selection:
48/100 × 26/481248/480053/300Therefore, 53/300 is the probability that a randomly selected day in April will be snowy if it is cloudy.
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Find the equation of the line that passes through the points (-1,7) and (-3,8) in the form of: a) y=mx+b. b) ax+by+c=0?
Answer:
-0.25 or -1/4
Step-by-step explanation:
y2-y1/x2-x1
8-7/-3-1
1/-4
-0.25
Draw triangle PQR with vertices P(1,2),Q(3, 3),R(2,6).find PQ.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 1~~)^2 + (~~3 - 2~~)^2} \implies PQ=\sqrt{( 2 )^2 + ( 1 )^2} \\\\\\ \implies PQ=\sqrt{ 4 + 1 } \implies PQ=\sqrt{ 5 }\implies PQ\approx 2.24[/tex]
What is the scientific notation of 500,000,000,000
Answer:
The scientific notation for 500000000000 is 5 × 1011
Step-by-step explanation:
The 11 is going to be a superscripts(meaning its going to be placed at the top right corner of the 10)
please help meeeeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!!!!
Answer:
3 x 3 x 3 or 3 to the 3rd power :)
Step-by-step explanation:
Lets solve! :)
3 x 3 x 3
9 x 3
27
The volume of the tank would be 27s :)
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Natalie has a piece of red ribbon that is 79.39 inches long and a piece of brown ribbon that is 2.05 inches long. How much longer is the red ribbon?
Red ribbon is 77.34 much longer than brown ribbon.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference.
The difference is the name given to the solution to a subtraction issue.
Given Data
Natalie has a piece of red ribbon that is 79.39 inches long
a piece of brown ribbon that is 2.05 inches long
Difference of red ribbon from brown ribbon:
= 79.39 - 2.05
= 77.34
Red ribbon is 77.34 much longer than brown ribbon.
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I need help in this maths problem
By considering the areas of the two rectangles, we have shown that 2x² - 5x - 18 = 0
The value of length AB is 4.5 cm
Calculating Area and lengthFrom the question, we are to show that 2x² - 5x - 18 = 0
From the given information,
The total area of the compound shape ABCDEF is 36 cm²
That is,
Total area = 36 cm² = Area of small rectangle + Area of big rectangle
From the given diagram, we can write that
Area of small rectangle = x(x -4)
Area of small rectangle = x² - 4x
and
Area of big rectangle = (2x + x)(x -2)
Area of big rectangle = 3x(x - 2)
Area of big rectangle = 3x² - 6x
∴ 36 = x² - 4x + 3x² - 6x
36 = 4x² -10x
4x² -10x - 36 = 0
Divide through by 2
2x² - 5x - 18 = 0
Thus, we have shown that 2x² - 5x - 18 = 0
Now, we are to determine the value of length AB
The value of length AB is x cm.
Therefore, we will solve for x
From,
2x² - 5x - 18 = 0
2x² + 4x - 9x - 18 = 0
2x(x + 2) -9(x + 2) = 0
(2x - 9)(x + 2) = 0
2x - 9 = 0 OR x + 2= 0
2x = 9 OR x = -2
x = 9/2 OR x = -2
x = 4.5 OR x = -2
Since x cannot be negative, the value of x is 4.5
Thus,
AB is 4.5 cm
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Solve.
7. Maria walks at a speed of 2 1/2 miles per hour. How long will it take her to walk a
10-mile trail?
Answer:
4 hours :)
Step-by-step explanation:
Lets multiply to solve :)
1 hr: 2 1/2
2 hrs: 5
3 hrs: 7 1/2
4 hrs: 10 hrs
it will take 4 hours to walk 10 miles :)
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The height of a building is proportional to the number of floors. The figure shows the height of a building with 7 floors. Complete parts a and b. H equals 98 ft a. Write the ratio of height of the building to the number of floors. Then, find the unit rate, and explain what it means in this situation.
If H equals 98 ft and the number of floors of the building is 7 then the unit rate will be 14 feet.
Define ratio:
Ratios are defined as the comparison between two or more quantities or things.
In this question, we will compare the height of the building with the number of floors it has.
We are given;
the height of building 'h' = 98 ft
Number of floors = 7 floors
Ao we can compare their ratios as follow
ratio = 98 feet / 7 floors
Now, in order to get the unit ratio. we will divide the numerator by the denominator.
Unit rate = 14 feet/floor
Thus, each floor of the building has a height of 14 feet.
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(d) solve this differential equation explicitly, either by using partial fractions or with a computer algebra system. use the initial populations 350 and 450.
Temperature Suppose there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky If the temperature on the ground is 616, what
will be the temperature when the plane reaches an altitude of 4,000 ?
The temperature will be (Type an integer or a decimal)
The temperature when the plane reaches an altitude of 4,000 will be 560°F.
What is temperature?It should be noted that temperature simply means the degree of hotness and coldness of a body.
In this case, there is a 14°F drop in temperature for every thousand feet that an alplane climbs into the sky.
Since the the temperature on the ground is 616, the temperature when the plane reaches an altitude of 4,000 will be:
= 616 - 14(4000/1000)
= 616 - 14(4)
= 616 - 56
= 560°F
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The coordinates of the point H are (−2,2) and the coordinates of point I are (6,2). What is the distance, in units, between the point H and point I?
the distance between the point H (- 2, 2) and point I (6, 2) is 8 units.
We are given the coordinates of the point as:
H = (- 2, 2)
I = (6, 2)
We need to find the distance between the two points.
We get that:
x₁ = - 2
y₁ = 2
x₂ = 6
y₂ = 2
Distance formula is given as:
Distance = √(y₂ - y₁)² + (x₂ - x₁)²
Substituting the values in the formula, we get that:
D = √(2 - 2)² + (6 + 2)²
D = √ 0² + 8²
D = √8²
D = 8 units.
Therefore, the distance between the point H (- 2, 2) and point I (6, 2) is 8 units.
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40 squared is between which two positive consecutive integers
first find 40 squared
[tex] {40}^{2} \\ = 1600[/tex]
1598,1599, 1600, 1601,1602
You can see that 1600 is between 1599 and 1601
Order four and seven tenths repeating, negative four and eight ninths, 490%, and −4.9 from least to greatest.
Answer:
-4.9, negative four and eight ninths, four and seven tenths, 490%
Step-by-step explanation:
4 7/10 =approx. 4.7
-4 8/9 = -4.888889
490% = 4.9
-4.9
write an expression using exponents that represents the volume of a cube with egde length 4/7 yard. what is the volume of the cube?
Answer:
[tex]\sf \dfrac{64}{343} \ cubic \ yard[/tex]
Step-by-step explanation:
Volume of cube:[tex]\sf \boxed{\bf Volume \ of \ cube =a^3}[/tex]
Here, a is the edge of the cube.
[tex]\sf a =\dfrac{4}{7} \ yard[/tex]
[tex]\sf Volume \ of \ cube = \dfrac{4}{7}*\dfrac{4}{7}*\dfrac{4}{7}[/tex]
[tex]\sf =\dfrac{64}{343} \ cubic \ yard[/tex]
Use an integer or a fraction to describe a slope of this line please!
Answer:
Step-by-step explanation: