7
A scientist is investigating the weight of 50 tigers.
Here is some information about these tigers.
Number of tigers
Mean weight of tigers (kg)
Siberian
22
260
Type of tiger
The mean weight of all 50 tigers is 218 kg
Work out the mean weight of the Bengal tigers.
Bengal
28
Answers
Consequently, there is a 0.89736 percent chance or probability that he weighs fewer than 258 kilograms.
What is probability?Probability fundamentals. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Here,
we use the z-score algorithm to answer this query.
Score Z = x - μ/σ
x = the raw score
population mean= μ
Population standard deviation is σ
Hence,
x = 258, μ = 220, σ = 30
Z = 258 - 220/30
=1.26667
Probability based on the Z-Table:
P(x<258) = 0.89736
Consequently, there is a 0.89736 percent chance that he weighs fewer than 258 kilograms.
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Related Questions
Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
Answers
Answer: 29 ft
Step-by-step explanation:
Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.
[tex]20^2+21^2=c^2[/tex] [exponent]
[tex]400+441=c^2[/tex] [add]
[tex]841=c^2[/tex] [square root both sides]
[tex]c=29[/tex]
Therefore, the distance from the girl to the bike is 29 ft.
How many 1/3 cubes does it take to fill a box with a width of 2 2/3 inches length 3 1/3 inches and height 2 1/3
Answers
It takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
In Math's or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.
It is also said to be a regular hexahedron.
We will convert the dimensions of the given box into simple fractions for easy calculations.
The dimensions of the given box:
Length = 3 + 1/3 inches = 10/3 inches
Breadth = 2 + 2/3 inches = 8/3 inches
Height = 2 + 1/3 inches = 7/3 inches
The side of each cube = 1/3 inches
Therefore,
The no. of cubes required to fill the box is,
= (volume of the box) / (volume of each 1/3 inch cube)
= ( 10/3 * 8/3 * 7/3 ) / (1/3)^2
= 10 * 8 * 7
= 560
Thus, it takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.
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In the figure, JKLM-EFGH. Complete the following table,
type your answer
Value of x
Value of y
Scale factor of JKLM to EFGH
type your answer.
type your answer
Value of z
type your answer.
Answers
The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH
What is Quadrilateral ?
Quadrilateral can be defined as the type of the polygon in which it contains four sides.
Given ,
JKLM ~ EFGH
Since , JKLM ~ EFGH
3/30 = 11/z
z = 30*11/3
z =110
3 / 30 = 8/ x
3 * x = 8 * 30
x = 80
3 / 30 = y/ 20
y = 20 * 3 / 30
y = 2
Hence the values of x , y and z are 80,2,110 respectively.
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What do the stage directions in this example most clearly show about the
character Darius?
DARIUS. [Hunched over, his gaze darting around the room, and
shouting into his phone] You better give me my money back or else.
[Indistinct sounds from the phone]
DARIUS. [Trembling and wiping sweat from his forehead That's right.
I'm your worst nightmare.
[Indistinct sounds from the phone]
A. Darius fakes being tough but is actually nervous.
B. Darius is somebody who demands what he wants.
C. Darius can't understand the person he's talking to.
D. Darius has plans but is too lazy to achieve them.
Answers
In addition to describing a character's appearance and movement on stage, stage directions also describe the sound and visual effects of the surroundings.
What is the meaning of stage direction?Stage directions may include phrases like "Katy enters the room" and "The man deals a deck of cards." They describe what the characters in the scene are doing.
Stage direction is also evident in statements about the setting, like "the early sunlight floods the space." The stage directions specify how a character will look, where they will move on the stage, and how the surroundings will sound and seem.
The links between things, characters, and locations in a book are made clear to the reader by stage directions, which also provide important details about the action. Stage directions are given by actors on the stage. "Stage right" is the area to the audience's left.
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Stage directions include things like "The man deals a deck of cards" and "Katy enters the room."
What is stage direction?Examples of stage instructions include "The man deals a deck of cards" or "Katy enters the room." In the scene, they describe how the characters move. Stage direction can also be demonstrated by describing the environment, such as "the early sunlight floods the space."
What a character looks like, where they go in the stage, and how the setting sounds and appears are all revealed in the stage instructions. The relationships between persons, things, and places in a text are described in great detail in stage directions.
To this day, the connotation remains unchanged. The three zones Upstage (in the back of the stage), Centerstage (in the middle), and Downstage are present in every theatre (front of the stage).
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Please provide step by step and answer what x and y is.
Answers
Answer:
Step-by-step explanation:
x=11
y=14
Expectation 2 Suppose that X is log-normal. For example log(x) follows a normal distribution with mean m and standard deviation k. What is the expectation of X? Pick ONE option exp(m - k2/2) exp(m + k²/2) exp(m) m
Answers
The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).
Therefore the answer is exp(m + k²/2).
The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.
The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.
The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.
For log-normal distribution, the expectation of X is calculated as follows:
E(X) = exp(m + k²/2)
where m is the mean of log(X) and k is the standard deviation of log(X).
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A corporation earned a profit of $2.5 x 104 for 1 x 10³ days in a row. What was the corporation's total profi
during this time period?
Answers
Total profit earned = 25000000 dollars
What is profit?Profit is a financial achievement which is the difference between the amount of money or resources people earned and the amount is spent in various purpose. In case of a business organization, the difference between production and cost is termed as profit. Let, someone invested money for operating business, he needs to spend money for workers, for the welfare of business and after all these he has amount that comes from business that is called profit.
What is the total profit during this time period?Given, profit earned = $ 2.5 × 10⁴ in the 1×10³ days in a row
total profit earned during this time = $(2.5 × 10⁴ × 10³)
$2.5 × 10⁷
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Find the derivative of the function. y = arctan √[(1 − x) /(1 + x)]
y' = ?
Answers
The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by
y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].
To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is
1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is
-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.
1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]
=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].
When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.
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Write and solve an inequality to find the values of x for which the perimeter of the rectangle is less than 112.
x+4
Answers
The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
what is inequality ?An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.
given
perimeter of a rectangle = length + length + width + width
length + length + width + width = perimeter of a rectangle
(x +4) + (x+4) + x + x < 112
x + 4 + x + 4 + x + x < 112
4x + 8 < 112
4x < 104
x < 26
So ,The inequality to discover the values of x for which the rectangle's perimeter is under 112 is x< 26.
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1 Which of the following trinomials can be factored?
A x² + 3x + 3
B x² + 3x - 3
C x² + 3x + 2
D x²-3x - 2
Answers
X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0, If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0
What are the trinomial rules?The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.
If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).
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Annie bought a brand new car for $32,000. The car is now worth $21,000.
(This is percent over change!!)
Answers
Using percentages we know that the value of a car decreases by 34% on average.
What is the percentage?A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.
A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.
The symbol "%" is frequently written after the number to indicate percentages.
So, we know that:
Annie brought a car at: $32000
Current price of the car: $21000
The decline in car percentage:
21000/32000 * 100
65.625%
⇒ 100 - 65.625 = 34.375%
Rounding off: 34%
Therefore, using percentages we know that the value of a car decreases by 34% on average.
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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.
By what percentage does the car's worth decrease?
A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days. When the researcher finished his study, the height of the flower was about 11.04 inches. What is a reasonable domain to plot the growth function
Answers
After solving, the possible domain in interval notation is (0, 7).
In the given question, a researcher is following the growth of a particular type of flower.
The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
According to the given information,
The height of the plant is modeled by the function= f(n)
The height of the plant is approximately 11.04cm when the number of days = 7
The days are started from n > 0 and n<=7
Hence the possible domain in interval notation = (0, 7)
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The complete question is:
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?
Part B: What does the y-intercept of the graph of the function () represent?
Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?
Angle of depression: A person standing on the top of the Petronas Tower I looks out
across the city and pinpoints her residence. If the angle of depression from the person's
eyes to her home is 5°, how far away (in feet and in miles) is the residence?
Answers
how many 1/3 inch cubes does it take to fill a box with width 1 1/3 inches, length 1 1/3 inches, and height 1 2/3 inches?
Answers
The number of 1/3 inch cubes that will fill the box is 26.
Volume of an object.The volume of an object is the amount or quantity of substance that it would conveniently contain. Different objects has their method of determining their volume depending on their shapes.
Given a cube of length 1/3 inch. The volume of the cube can be determined as;
volume of a cube = length x width x height
The volume of the cube = 1/3 * 1/4 * 1/3
= 1/9 cube inches
The volume of the box can be determined as;
Volume of the box = length x width x height
= 1 1/3 * 1 1/3 * 1 2/3
= 2.963 cubic inches
Volume of the box = 2.963 cubic inches
The number of 1/3 inch cubes that will fill the box = 2.963/ (1/9)
= 26.667
The number of 1/3 inch cubes that will fill the box is 26.
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Determine which branch of statistics was used to make the following statement. In an online survey of 500 Virginia Tech students between spring 2010 and spring 2011, 3190 said that they had missed class because of alcohol consumption. A) differential statistics C) inferential statistics B) time series statistics D) descriptive statistics
Answers
The branch of statistics used to make the given statement is Option(D) Descriptive Statistics.
Which are the different branches of statistics?
The area of mathematics that deals with data is statistics. Data collection, descriptive statistics, and inferential statistics are the three main subfields of statistics.
The process of gathering data is what data collection is all about.The area of statistics known as descriptive statistics deals with how we present the data we have. Basically, this can be done in one of two ways: either visually (using graphs, charts, etc.) or quantitatively (via averages and so on).The part of statistics that deals with drawing inferences from the data is called inferential statistics.For the given question, we are presented with data quantitatively. The data shows out of 500 students, 31% missed class due to alcohol consumption.
Therefore the branch of statistics that was used to make the above statement is descriptive statistics.
Hence Option(d) is correct.
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3. (a) How many 0.32kg portions of minced beef can be made from 15.36kg of beef? (b) If beef is sold at $25.16 per kilogram, what is the cost of six and a quarter 0.32kg portions?
Answers
Answer:
a) 48 portions
b) $157.25
Step-by-step explanation:
1) 15.36/.32 to get 48 portions
2) Since it's asking for 6.25 0.32kg portions, multiply 6.25 by $25.16 to get $157.25
5. Katie has 15/20 of a dollar in her pocket. Lisa has the same amount of money in
her pocket. What fraction of a dollar does Lisa have in her pocket?
A. 5/10 B. 3/4
C. 4/5 D. 2/10
Answers
Answer:
Step-by-step explanation:
it B.
just put in the calculator and it gives you the reduced fraction
Answer:
B. 3/4
Step-by-step explanation:
Find the GCD (or HCF) of the numerator and denominator
GCD of 15 and 20 is 5
Next, divide both the numerator and denominator by the GCD
15 ÷ 5 = 3
20 ÷ 5 = 4
Finally, put them back into a fraction
[tex]\frac{3}{4}[/tex]
Therefore, 15/20 simplified to the lowest terms is 3/4.
Jane is making lunch for 12 people. she is serving hotdogs and plans on each person get eating two hotdogs. hotdog buns are sold in packages of eight. which expression can be used to find the number of packages she needs to buy?
Answers
He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.
What are hot dog buns known as?The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.
What does the slang term "hot dogs" mean?As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.
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(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m). Electromagnetic Wave A C D Wavelength 3.0 x 10²m 4.0 x 10-6 1.2 x 10-¹2 m 2.0 x 10 m de According to the table, which electromagnetic wave has the least amount of energy?
Answers
According to the table the wavelength that has the least amount of electromagnetic energy is B having a wavelength of 4.0 x 10⁻⁶ m
What is electromagnetic energy?Radiant energy that moves in waves at the speed of light is called electromagnetic energy. It can also be referred to as radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation.
Wavelength is the separation between identical points (adjacent crests) in successive cycles of a waveform signal traveling through space or over a wire.
This length is often stated in meters when using wireless technology (m),
The relationship between a electromagnetic energy and wavelength is in inverse relation. This means that the least wavelength will result to greatest electromagnetic energy
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complete question
(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m).
Electromagnetic Wave Wavelength
A 3.0 x 10² m
B 4.0 x 10^-6 m
C 1.2 x 10-¹2 m
D 2.0 x 10 m
According to the table, which electromagnetic wave has the least amount of energy?
What is seed calculator?
Answers
Answer: The Seed Calculator app is used to calculate the amount of seed required in order to produce a desired crop yield.
Step-by-step explanation:
In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the computer? Explain your answer
Answers
If Shapera mowed 7 lawns and worked for 36 hours at pet store and delivered newspapers 7 days , then she earned $497 which is not enough to buy the computer .
the amount that she earns in mowing each lawn is = $15 ;
So , the amount earned for mowing 7 lawns is = [tex]15\times 7[/tex] = $105 ;
the amount that she earns per hour working at pet store is = $7 ;
So , amount earned for working 36 hours is = [tex]36\times 7[/tex] = $252 ;
the amount that she earns by delivering newspapers per day is = $20 ;
So , amount earned by delivering newspapers for 7 days =[tex]20\times7[/tex] = $140 ;
The total amount earned by Shapera is = [tex]\$ 105 + \$252+\$140[/tex]
On adding all the amount earned ,
we get ;
= $497 ;
The amount earned by Shapera is $497 .
Therefore , Shapera will not be able to buy the $499 computer as she is $2 less than the price .
The given question is incomplete , the complete question is
Shapera has three sources of income. She earns $15 for each lawn she mows. She earns $7 per hour working part-time at a pet store She earns $20 each day she delivers newspapers.
In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the $499 computer ?
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27/3 TO A WHOLE
NUMBER
Answers
Answer:
9, after being converted to a mixed number
Step-by-step explanation:
Just divide 27 by 3, it’ll equal 9
yw :)
hope i helped, reach out if it’s wrong (it’s not lol)
Have a great day :3
Answer: 9
Step-by-step explanation:
since fraction means we divide the numerator by denominator, we divide 27 by 3
⇒27/3
⇒27 ÷ 3
⇒9 answer
hope that helps ...
a builder wishes to fence in 60,000m of land in a rectangular shape. for security reasons, the fence along the front part of the land will cost 20 per meter, while the fence for the other three sides will cost 10 per meter. how much of each type of fence should the builder buy to minimize the cost of the fence
Answers
The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.
To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.
To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length) + 2(width)
Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:
2x + 2y = 60,000
To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:
60,000 - x = 3x + 2y
The total length of the three sides that are not the front is 3x + 2y.
Now we can calculate how much the builder will pay for each type of fence:
Cost of front fence = $20/m * x = $20xCost of other three sides = $10/m * (3x + 2y) = $30x + $20yTotal cost of the fence = $20x + $30x + $20y = $50x + $20y
To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.
However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:
x meters of $20/m fence for the front side3x + 2y meters of $10/m fence for the other three sides.This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.
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Can you solve this problem for me please
Answers
The required scale factor that Amir will use to go from Polygon F to G is 1/9.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
Area of polygon F = 36 square units
Area of polygon G = 4 square units
Now,
The scale factor to go from polygon F to polygon G is given as,
SF = Area of polygon G / Area of polygon F
SF= 4/36
SF = 1/9
Thus, the required scale factor that Amir will use to go from F to G is 1/9.
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How many solutions do the pair of linear equations 3x 2y 5 and 2x 3y 7 have?
Answers
The pair of linear equations 3x + 2y = 5 and 2x + 3y = 7 has no solution.
To solve these equations, we will use the method of elimination.
We start by multiplying the first equation by 2:
6x + 4y = 10
Now we add both equations together:
6x + 4y + 2x + 3y = 10 + 7
Combining like terms, we have:
8x + 7y = 17
We can now solve for x by dividing both sides by 8:
x = 17/8
Now we can substitute this value of x into either of the original equations to solve for y:
3(17/8) + 2y = 5
51/8 + 2y = 5
2y = 5 - 51/8
2y = -41/8
y = -41/16
However, this value for y is not a real number, so there is no solution for the pair of linear equations.
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HELP LIMITED TIME PLEASE HELP ASAP!!! THE PROBLEM I PUT IN PICTURES!
Answers
Step by step
Y1 is y = 4x -9
Y2 is y = 2x - 5
Our coordinates are (2,-1)
To find if the solution is true for each table, plug the solution in for y1 and y2
Table 1
Y1 is -13 = 4(-1) -9 = -13 ✅
Y2 is -13 = 2(-1) -5 = -7 ❌ stop no solution
Table 2
Y1 is -13 = 4(-1) -9 = -13 ✅
Y2 is -7 = 2(-1) - 5 = -7 ✅
Y1 is -9 = 4(0) -9 = -9 ✅
Y2 is -5 = 2(0) - 5 = -5 ✅
Y1 is -5 = 4(1) -9 = -5 ✅
Y2 is -3 = 2(1) - 5 = -3 ✅
Y1 is 3 = 4(2) - 9 = ❌
Y2 is 1 = 2(2) - 5 = ❌ stop no solution
Table 3
Y1 is -13 = 4(-1) -9 = -13 ✅
Y2 is -7 = 2(-1) - 5 = -7 ✅
Y1 is -9 = 4(0) -9 = -9 ✅
Y2 is -5 = 2(0) - 5 = -5 ✅
Y1 is -5 = 4(1) -9 = -5 ✅
Y2 is -3 = 2(1) - 5 = -3 ✅
Y1 is 1 = 4(2) -9 = -1 ❌
Y2 is 1 = 2(2) - 5 = -1 ❌ stop no solution
Table 4
Y1 is -13 = 4(-1) -9 = -13 ✅
Y2 is -7 = 2(-1) - 5 = -7 ✅
Y1 is -9 = 4(0) -9 = -9 ✅
Y2 is -5 = 2(0) - 5 = -5 ✅
Y1 is -5 = 4(1) -9 = -5 ✅
Y2 is -3 = 2(1) - 5 = -3 ✅
Y1 is -1 = 4(2) -9 = -1 ✅
Y2 is -1 = 2(2) - 5 = -1 ✅
Y1 is 3 = 4(3) -9 = 3 ✅
Y2 is 1 = 2(3) - 5 = 1 ✅
This table #4 has all solutions correct
Let f(x)=5x and g(x)=sinx and h(x)=g(f(x))=sin(5x) What is h’(x)?
Answers
Answer:
Step-by-step explanation:
Derivation of composite functions concept.
h'(x)=g'(f(x))·f'(x)=(sin(5x))'×(5x)'=cos(5x)×5=5cos(5x)
Eric added up on a number line to find 4 over 5 minus 5 over 10
Answers
Answer: 4/5 minus 5/10 can be simplified as:
(4/5) - (5/10)
It can also be re-written as
(4/5) - (1/2)
To subtract these fractions, we need a common denominator, which is 10 in this case.
So it becomes
(4/5)(2/2) - (1/2)(5/5) = 8/10 - 5/10 = 3/10
So the result of 4/5 minus 5/10 is 3/10 on a number line.
Step-by-step explanation:
LCM of 2, 6 and 11 must show work
Answers
The Least Common Multiple (LCM) of 2, 6, and 11 is 66.
What is the LCM of 6 and 11?We shall divide the numbers (6, 11) by their prime factors in order to determine the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is determined by the product of these divisors.
Step 1:Find the smallest prime number that at least one of the numbers, 6, or 11, can be factored into. As indicated by the ladder arrangement, place this prime number (2) to the left of the supplied numbers (6 and 11).
Step 2: Divide any of the supplied integers (6, 11) by 2 and write the quotient below it if it is a multiple of 2. Any number that is not divisible by the prime number should be brought down.
Step 3: Continue the procedure until there are only 1s left in the
The LCM of 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66
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(d) At a football match, there are 29 800 people, correct to the nearest 100. (i) At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people. Calculate the lower bound for the number of minutes it takes for all the people to leave.
Answers
The lower bound for the number of minutes that it takes for all people to leave is of:
70 minutes.
How to obtain the lower bound for the number of minutes that it takes for each person to leave?At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:
29,750.
(as 29749 would be rounded to 29,700).
At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:
424 people per minute.
(as 425 people would be rounded to 450).
Hence the time it would take is obtained applying the proportion as follows:
29750/424 = 70 minutes.
(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).
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