Chris's time 3.058 sec faster than Michael's.
What is meaning of faster?
Fast and fast refer to moving quickly. Fast can be used as an adverb or an adjective. Quick is an adjective, while rapidly is its adverbial counterpart.
Given that,
Chris completed a 100-meter breaststroke swimming race in 92.542 seconds.
Michael completed the 100-meter breaststroke swimming race in 95.6 seconds.
The difference of time between Chris and Michael to complete 100-meter breaststroke swimming is = (95.6 - 92.542) = 3.058 sec.
Since both are completed 100 meter breaststroke, thus the difference of time denotes the faster time.
Thus Michael's timing was 3.058 seconds slower than Chris'.
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Please show your work
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
Answer:
$530--------------------------------
If the amount of sales for current week is x, Jamie's earning is:
150 + 0.15x = 229.50Solve it for x:
150 + 0.15x = 229.500.15x = 229.50 - 1500.15x = 79.50x = 79.50/0.15x = 530HALPPP, for pre calc
The interval containing the rational zero of f(x) = 3x³ - 5x² + 5x + 7 is given as follows:
-1 < x < 0.
How to obtain the zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 7.The factors are given as follows:
Factors of 3: {1,3}.Factors of 7: {1,7}.Hence the possible zeros are given as follows:
±1/3, ±1, ±7/3, ±7.
The numeric values for the function are these points are of:
f(-7) = 3(-7)³ - 5(-7)² + 5(-7) + 7 = -1302. f(-7/3) = 3(-7/3)³ - 5(-7/3)² + 5(-7/3) + 7 = -70. f(-1/3) = 3(-1/3)³ - 5(-1/3)² + 5(-1/3) + 7 = 4.6.This means that there is a zero between -7/3 and -1/3, as the function changes from negative to positive, hence the interval is given as follows:
-1 < x < 0.
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the best measure of central tendency for these data?
X f
5+ 2
4 3
3 2
2 1
1 1
0 1
Answer:
the mean (i.e. the average)
Step-by-step explanation:
There's no clear outlier or inconsistency therefore the mean should be used.
Research shows that the radioactive isotope Americium-241 has a half-life of 432.2 years Use the following to construct a function that will model the amount of Americium-241 remaining after t years, from an initial amount of 10 kg. Q(t) = Pe^rtPent Where Q(t) describes the amount of Americium-241 remaining after t years from an initial quantity of P kg, 1.Q(t) =2. How long in years) will it take for the amount of Americium-241 remaining to reach 6 kg
It will take approximately 7.66 years for the amount of Americium-241 remaining to reach 6 kg, assuming that the initial amount was 10 kg. We can use formula Q(t) = Pe^(rt) to calculate half-life of Americium-241.
To construct a function that will model the amount of Americium-241 remaining after t years from an initial amount of 10 kg, we can use the formula:
Q(t) = Pe^(rt)
where Q(t) is the amount of Americium-241 remaining after t years, P is the initial quantity (10 kg in this case), r is the decay rate (the negative of the half-life of Americium-241, which is -432.2 years), and e is the mathematical constant approximately equal to 2.71828.
Plugging in the values, we get:
Q(t) = 10 * e^(-432.2t)
This is the function that will model the amount of Americium-241 remaining after t years from an initial quantity of 10 kg.
To find out how long it will take for the amount of Americium-241 remaining to reach 6 kg, we can solve the equation Q(t) = 6 for t.
[tex]Q(t) = 6\\6 = 10 * e^(-432.2t)\\0.6 = e^(-432.2t)\\ln(0.6) = -432.2t\\t = ln(0.6) / -432.2\\[/tex]
t = approximately 7.66 years
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mai rode on a train at a rate of speed of 70 miles per hour for 3 hours than she rode in a ar at a rate of speed of 50 miles per hour for 2 hours what is the difference between the number of miles ai rode on the train and the number of miles she rode in the car
The difference between the number of miles travelled on train and car is 110 miles
How to determine the difference between the number of milesFrom the question, we have the following parameters that can be used in our computation:
Distance 1 (train): 70 miles per hour for 3 hoursDistance 2 (car): 50 miles per hour for 2 hoursThe difference between the distance covered can be calculated as
Distance difference = The difference of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance difference = 70 * 3 - 50 * 2
Evaluate the products
This gives
Distance difference = 210 - 100
Evaluate the
Distance difference = 110 miles
Hence, the distance difference is 110 miles
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An investor deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.3% and 2.4%. The
total amount invested was $25,000, and the total annual interest earned was $568. How much was invested at each
rate?
At the rate 1.7%, $blank was invested.
Based on Simple Interest, 8125 was invested at the rate 1.7%.
What is the Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Although some mortgages employ this calculation approach, this kind of interest typically relates to auto loans or short-term loans.
> The daily interest rate, the principle, and the number of days between payments are multiplied to determine simple interest.
> Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest.
> Simple interest loans are frequently used for auto loans and short-term personal loans.
Calculation:Let the amount at 1.7% be x. Then:
[tex]0.017x+0.023(\frac{(25000-x)}{2}) +0.024(\frac{(25000-x)}{2})=535[/tex]
[tex]0.023+0.024 = 0.047 \\\frac{0.047}{2} = 0.0235[/tex]
Now we got rid of the two divisions. Rewrite the equation:
[tex]0.017x+0.0235(25000-x) = 535[/tex]
[tex]0.017x+587.5-0.0235x = 535[/tex]
[tex]-0.006x = -52.5[/tex] Divide both sides by -0.006 and remember -/- = +
x = 8750
This is how much was invested at 1.7% The rest, the problem says, was invested in equal amounts:
[tex]25000-8750 = 16250[/tex]; [tex]\frac{16250}{2}=8125[/tex] So, 8125 was invested each at 2.3% and 2.4%
Based on Simple Interest, 8125 was invested at the rate 1.7%.
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Which of the following shows a correct method to calculate the surface area of the cylinder?
cylinder with diameter labeled 2.8 feet and height labeled 4.2 feet
SA = 2π(2.8)2 + 2.8π(4.2) square feet
SA = 2π(1.4)2 + 2.8π(4.2) square feet
SA = 2π(2.8)2 + 1.4π(4.2) square feet
SA = 2π(1.4)2 + 1.4π(4.2) square feet
You can quickly calculate the radius of a cylinder using an online calculator.
How to Find Radius of a Cylinder?The term "cylinder" refers to a three-dimensional solid shape made up of two circular bases joined by two parallel lines. We may calculate the radius of the cylinder using the formula for cylinder volume.A cylinder's capacity or the quantity of space it takes up are both determined by the cylinder's volume. V = πr²h, a formula, is used to compute it.Cylinder radii (r) √(V / π × h), where V denotes a cylinder's volume, h denotes its height, and (Pi) denotes a mathematical constant having a roughly 3.14 value.Solved Examples on the Radius of a Cylinder Calculator ExampleWhat is the radius of a cylinder with a capacity of 100 cubic units and a height of 5 units?
Solution:
The radius of a cylinder (r) is equal to (V / h).
= √(100 / π × 5)
= 2.523 units
As a result, a cylinder's radius is 2.523 units.
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Answer:
Step-by-step explanation:
its a
a coin is flipped, and a number cube is rolled. what is the probability of getting heads on the coin and a number less than 3 on the number cube
The probability of getting heads on the a coin and a number less than 3 on cube is given as 1/6.
How to find the probability for an event?In order to find the probability take the ratio of the favorable outcome to the total possible outcome.
The set of total possible outcomes is known as sample space.
The number of elements in the sample space is given as,
Possible outcomes for coin × Possible outcomes for cube
= 2 × 6 = 12
The given two events flipping of coin and rolling of cube are mutually independent.
Which implies it is not the case of conditional probability.
The favorable number of outcomes are as below,
Number of head × Number of numbers less than 3
= 1 × 2 = 2
Now, the probability is given as,
P(getting head on coin and less than 3 on cube) = 2/12 = 1/6
Hence, the probability of getting the required outcome is given as 1/6.
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Construct the fourth proportional between a, b, and c.
The fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).
What are proportional parameters? What is a mathematical function, equation and expression? proportional parameters : A proportional relationship is one in which two quantities vary directly with each other.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 are three length parameters as [a], [b] and [c].
For the fourth proportional {x}, the relationship can be written as -
a/x = b/c = k {constant}
x = (ac/b) = k {constant}
Therefore, the fourth proportional {x} between a, b, and c can be written as {x} = (ac/b).
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Arun runs a farm stand that sells raspberries and grapes. Each pound of raspberries sells for $1.50 and each pound of grapes sells for $2.75. Arun made $130.25 from selling a total of 66 pounds of raspberries and grapes. Determine the number of pounds of raspberries sold and the number of pounds of grapes sold.
Arun sold 41 pound of raspberries and 25 pound of grapes.
What is a linear equation?
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables. Each of the two variables in these equations has the largest exponent order of 1. A two-variable linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).
Given that the cost of 1 pound of raspberries is $1.50 and 1 pound of grapes is $2.75.
Arun sells 66 pounds with cost $130.25.
Assume that Arun sells x pound of raspberries and y pound of grapes.
Therefore,
x + y = 66 ......(i)
The cost of x pound of raspberries and y pound of grapes is 1.50x + 2.75y.
1.50x + 2.75y = 130.25 .....(ii)
Solving equation (i) and (ii) by using elimination method.
Multiply equation (i) by 1.5
1.50x + 1.50y = 99 ....(iii)
Subtract equation (iii) from (ii)
1.50x + 2.75y = 130.25
1.50x + 1.50y = 99
(-) (-) (-)
________________
1.25 y = 31.25
y = 25
Putting y = 25 in equation (i)
x + 25 = 66
x = 41
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PLEASE HELP ASAP
Three key features of a linear function are described as shown.
• The graph of the function has a y-intercept of (0, 3) .
• The function is increasing over its entire domain.
• The x-intercept of the function is (-4, 0).
Step-by-step explanation:
the slope-intercept form is
y = ax + b
a being the slope, b being the y-intercept (the y-value when x = 0), which we get from (0, 3) : 3.
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
we got 2 points, so, let's use them :
(-4, 0) and (0, 3)
x changes by +4 (from -4 to 0).
y charges by +3 (from 0 to +3).
so, the slope is +3/+4 = 3/4.
therefore, our equation is
y = f(x) = (3/4)x + 3
Select all of the following equation(s) that are quadratic in form. x4 – 6x2 – 27 = 0 3x4 = 2x 2(x + 5)4 + 2x2 + 5 = 0 6(2x + 4)2 = (2x + 4) + 2 6x4 = -x2 + 5 8x4 + 2x2 – 4x = 0
um consider it serious or don't :)
The quadratic equations, or the equations that are quadratic in form, for this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.What is a quadratic equation?The degree of a function is given by the highest exponent that appears in the definition of the function.
A quadratic function is a function that has a degree of 2.
The standard format of a quadratic function is given as follows:
y = ax² + bx + c.
(in which the coefficient a must assume a value different of zero).
The quadratic function in this problem is given as follows:
6(2x + 4)² = 2x + 4 + 2.
As (2x + 4)² = 4x² + 16x + 16, meaning that the highest exponent would be of 2.
However, equations of the fourth degree can also be quadratic in form, as long as the exponents go as follows: 4, 2 and 0.
Hence these following equations are also quadratic in form:
x^4 - 6x² - 27 = 0.6x^4 = -x² + 5.They are classified as quadratic in form because a transformation such as y = x² can make them quadratic.
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give an example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is your point of discontinuity removable or essential
An example of a function that is discontinuous at one and only one point in its domain but is continuous at every other point is the function
f(x) = x^2.This function is continuous at every point in its domain, which is the set of all real numbers (-infinity < x < infinity). However, at the point x = 0, the function is discontinuous.
At x = 0, the function f(x) = x^2 is equal to 0, but if we approach the point x = 0 from the left (x = -0.1, -0.01, etc.), the function is equal to a negative value (-0.01, -0.0001, etc.), and if we approach the point x = 0 from the right (x = 0.1, 0.01, etc.), the function is equal to a positive value (0.01, 0.0001, etc.). This means that the function is not continuous at the point x = 0, and is therefore discontinuous at this point.
The point of discontinuity in this example is an essential discontinuity, which means that it cannot be removed by redefining the function at that point. This is because the function f(x) = x^2 is defined differently for x < 0 and x > 0, and there is no way to redefine the function at x = 0 to make it continuous.
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what is the number x such that G.C.F(x,54)=6 and L.C.M(x,54)=432.
By the Application of Prime factorization method the value of x is 48
what is Prime factorization method?
Writing all numbers as the product of primes is a procedure known as prime factorization. Consider the case of the number 20, for instance. We can divide that into two elements. Well, that's four times five, we can say. Furthermore, 5 is a prime number.
Solution:
HCF = ( X, 54 ) = 6
LCM = ( X, 54 ) = 432
a = x b = 54
using property
a * b = LCM * HCF
54a = 6 * 432
a = (6 * 432) / 54
a = 48
Hence the value of x is 48.
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Can don help me on this please?
Step-by-step explanation:
always remember that 100% is the whole.
so, 15% means 15/100 of the whole.
1/5 = 0.2 = 20/100 of the whole.
so, Target is taking 15/100 off the price.
Walmart is taking 20/100 off the price.
20/100 is bigger than 15/100, so Walmart deducts more off the price, and has therefore the lower and therefore better sale price.
Target sale price :
100/100 - 15/100 = 85/100 × 80 = $68
in short
80 × (1 - 0.15) = 80 × 0.85 = $68
Walmart sale price :
100/100 - 20/100 = 80/100 × 80 = $64
in short
80 × (1 - 0.20) = 80 × 0.80 = $64
How do I solve a whole number and a fraction?
Answer:
To solve a problem involving a whole number and a fraction, you can first convert the whole number to a fraction by writing it as a fraction with a denominator of 1. For example, if the whole number is 4, you can write it as the fraction 4/1.
Then, you can add or subtract the fractions as you would normally, making sure to find a common denominator if necessary. For example, suppose you want to add the whole number 4 and the fraction 3/5. You can first write 4 as the fraction 4/1, giving you:
4/1 + 3/5
To add these fractions, you need to find a common denominator. A common denominator for 1 and 5 is 5, so you can rewrite the fractions with denominators of 5:
4/1 = 20/5
3/5 = 3/5
Now you can add the fractions:
20/5 + 3/5 = 23/5
So the solution to the problem is 23/5.
If you need to multiply or divide the whole number and fraction, you can treat the whole number as a fraction with a denominator of 1 and then perform the multiplication or division as you would normally with fractions.
Step-by-step explanation:
An experiment was conducted in which planks of wood painted red and green were shown to pigeons to investigate a pigeon's ability to select a certain color. Pigeons could accurately select the color of the plank of wood 20 percent of the time. A simulation was conducted in which a trial consisted of a pigeon being shown eight planks of wood and its number of successes being recorded. This process was repeated many times, and the results are shown in the histogram.
Based on the results of the simulation, which of the following is closest to the probability that there were at most three successes in a trial?
The probability that there were at most three successes in a trial is approximately 0.9.
It looks like the histogram shows the probability mass function (PMF) for the number of successes in a trial. The PMF for a random variable gives the probability of each possible value of the random variable.
To find the probability that there were at most three successes in a trial, we need to add up the probabilities of 0, 1, 2, and 3 successes. From the histogram, it looks like the probabilities of these values are approximately 0.2, 0.4, 0.2, and 0.1, respectively. Adding these up, we get an approximate probability of 0.2 + 0.4 + 0.2 + 0.1 = 0.9.
Therefore, the probability that there were at most three successes in a trial is approximate $\boxed{0.9}$.
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the scatter plot shows the total number of rebounds caught and the total number of points scored for the five starting players of the cleveland cavaliers and of the golden state warriors in game 7 of the 2016 nba finals.
The cleveland cavaliers and of the golden state warriors in game 7 of the 2016 nba finals the player are 8.
A scatter plot is a hard and fast of factors plotted on a horizontal and vertical axes. Scatter plots are essential in facts due to the fact they could display the quantity of correlation, if any, among the values of determined portions or phenomena (referred to as variables).
Scatter plots are used to plan facts factors on a horizontal and a vertical axis withinside the strive to expose how a great deal one variable is laid low with another. Each row withinside the facts desk is represented through a marker whose role relies upon on its values withinside the columns set at the X and Y axes.
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The double number line shows that Bira has ridden 28m on a carousel, which is 80% of a full rotation on the carousel
The distances that represent the percentages are given as follows:
Distance of 28 m -> 80% of a rotation.Distance of 7 m -> 20% of a rotation.Distance of 35 m -> 100% of a rotation.What is a proportion?A proportion is a fraction of a total amount, used along with the unit measures and basic arithmetic operations to obtain the desired measures in the context of a problem.
28m is 80% of the distance, hence 100% of the distance is obtained applying the proportion as follows:
0.8x = 28
x = 28/0.8
x = 35.
Then the distance that represents 20% of a rotation is calculated as follows:
0.2 x 35 = 7 meters.
Missing InformationThe complete problem is given by the image shown at the end of the answer.
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A book shelf is 3 1/2 feet long. Each book on the shelf is 5/8 inches wide. How many books will fit on the shelf?
67 books will fit on the shell.
How many inches are in a feet?One foot has 12 inches (in) (ft). In the US customary and imperial measurement systems, both feet and inches are units of length. The foot has had many different definitions throughout history, but since 1959, it has been defined as exactly 0.3048 meters, and the inch as 2.52 centimeters. The meter is the International System of Units' base unit of length (SI).
12 inches are one foot.In the given question,
36 inches make 3 feet.42 inches equals 3 1/2 feet.Then the number of books
= 42 / (5/8)
= 42 (8/5)
= 336/5
= 67 1/5
Finally, we round 67.2 to the nearest LESSER integer number and obtain
67.
Hence, 67 books will fit on the shell.
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Calculate the area
Of this square
The area of the shape as shown in the diagram is 11.25 cm².
What is area?Area is the region occuppied by a plane shape.
To calculate the area of the shape, we use the formula below.
Formula:
A = LW+l²................ Equation 1Where:
A = Area of the shapeFrom the diagram,
Given:
L = 4.5 cmW = 2 cml = 1.5 cmSubstitute these question into equation 1
A = (4.5×2)+(1.5²)A = 9+2.25A = 11.25 cm²Hence, the area of the shape is 11.25 cm².
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Cans of paint weigh 6 pounds each. Let x represent the number of cans of paint and y represent the total weight of the cans. Write the equation to this situation as slope intercept form (y=mx+b). Then create a table of possible values
The equation for the relationship between the number of cans of paint, x, and the total weight of the cans, y, in slope-intercept form is y = 6x + 0. This equation can be derived from the formula for the slope-intercept form of a line, y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, since the weight of each can of paint is 6 pounds and there is no y-intercept (the line passes through the origin), the slope of the line is 6 and the y-intercept is 0.
A table of possible values for the number of cans of paint, x, and the total weight of the cans, y, based on this equation is shown below:
x (number of cans of paint) y (total weight of cans)
1 6
2 12
3 18
4 24
5 30
As the table shows, for each additional can of paint, the total weight of the cans increases by 6 pounds. This is because each can of paint weighs 6 pounds, and the weight of the cans is equal to the number of cans multiplied by the weight of each can.
Answer: y = 6x
Step-by-step explanation:
For each can of paint (x) 6 pounds is added. This is represented as;
y = 6x
For the table of possible values, we will plug a value in for x, and then evaluate the function for y. See attached.
y = 6(1) = 6
y = 6(2) = 12
y = 6(3) = 18
An investor deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.3% and 2.4%. The
total amount invested was $25,000, and the total annual interest earned was $568. How much was invested at each
rate?
At the rate 1.7%, $ was invested.
deposited some money at 1.7% annual interest, and two equal but larger amounts at 2.2% and 24%. The total amount invested was $26,000 and the total annual interest earned was $574. How much was invested at each rate?
What is an investor?
An investor is an individual or an organization that gives money to A person or entity that invests in another with the hopes of making a profit in the future is known as an investor. According to the rules, anyone can invest: You are an investor if you put money into something.
Answer provided by our tutors
Let
x = the money invested at 1.7%
y = the money invested at 2.2%
y = the money invested at 24%
Since the total money invested was $26,000 we have:
x + 2y = 26000
The total annual interest was $574 means:
0.017x + 0.022y + 0.24y = 574
0.017x + 0.262y = 574
We have the following system of equations:
x + 2y = 26000
0.017x + 0.262y = 574
click here to see the system of equations solved for x and y
x = $24,842
y = $578
$24,842 was invested at 1.7%
$578 was invested at 2.2% and another $578 was invested at 24%.
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(Factoring Algebraic Expressions MC)
Factor −7x2 + 35x.
−7x(x + 5)
7x(−x + 5)
7(−x2 + 35x)
x(7x + 35)
Answer:
7x ( - x + 5 )
Step-by-step explanation:
- 7x² = 7x × - x
35x = 7x × 5
- 7x² + 35x = 7x ( - x + 5 )
What is the surface area of the box shown? Will give Brainliest!!
Answer:
304
Step-by-step explanation:
To find the surface area of a rectangular prism with length 4, width 10, and height 8, you can use the formula 2 * (length * width + width * height + height * length).
Plugging in the given values, the surface area is equal to 2 * (4 * 10 + 10 * 8 + 8 * 4) = 2 * (40 + 80 + 32) = 2 * 152 = 304.
Answer: 304
Step-by-step explanation:
Please give me detailed information
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Calculation:Given that ΔHPS≅ΔCNF.
We can see that angle H in triangle HPS is obtuse whereas angle N in triangle CNF is obtuse so comparing this we get,
6x - 29 = 115
6x = 144
x = 24
Comparing angle C and angle P we get
4z - 32 = 36
4z = 68
z = 17
Now the remaining angle in trinagle CNF is angle F which is 3y - 1 as we know that sum of angles in a triangle is 180 and the angle C and N are 36 and 115 we can say that F is 29
Now to find y we equalise it to 29
3y - 1 = 29
3y = 30
y = 10.
The values of x, y and z are 24, 10 and 17 using the similar triangles properties and triangles sum properties.
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A particular truck in a transportation fleet was
driven 109,970 miles last year. In comparison,
it was driven 40% less this year. How much
was the truck driven this year?
bro this is middle school work not college
Fwam is a high school basketball player. In a particular game, he made some free throws (worth one point each) and some three point shots. Fwam made a total of 10 shots altogether and scored a total of 18 points. Graphically solve a system of equations in order to determine the number of free throws made, x, and the number of three point shots made, y.
Answer:
x = 6 ans y=4
Step-by-step explanation:
The number of free throws made = x
The number of three points shots made = y
We can make an equation
x+y= total shots made
x+y= 10
So if we want "x",
x=10-y (First equation)
x is one point
y is three point
We can make another equation on how much points gained
(1)x + 3(y) = total points gained
x + 3y =18
If we want "x" ,
x =18-3y (second equation).
Now that we got two equation solve the question with simultaneous equations
x=10-y
x=18-3y
Substitute "x=18-3y" into equation 1
18-3y=10-y
10-y=18-3y
3y-y=18-10
2y=8
y=4 (Three points shots)
x=10-y
x=10-4
x=6 (Free throws made)
Therefore , x=6 and y=4
An airplane had a total of 387 seats. The number of coach class seats is 2 more than 4 times the number of first class seats. How many of each type of seat are there on the plane?
Answer:
coach seats is 310 and first class seats are 77
Step-by-step explanation:
x+4x+2=387
5x+2=387
5x=385
x=77
4x+2
4(77)+2=310
Answer:
There are 77 first-class seats. We can use this information to now define the number of seats in coach. And there are 310 seats in coach.
Step-by-step explanation:
Farm Grown, Inc., produces cases of perishable food products. Each case contains an assortment of vegetables and other farm products. Each case costs $5 and sells for $15. If there are any cases not sold by the end of the day, they are sold to a large food processing company for $3 a case. The probability that daily demand will be 100 cases is 0.3, the probability that the demand will be 200 cases is 0.4, and the probability that daily demand will be 300 cases is 0.3.
Farm Grown has a policy of always satisfying customer demands. If its own supply of cases is less than the demand, it buys the necessary vegetables from a competitor. The estimated cost of doing this is $16 per case.
Probabilty 0.3 .04 .03 Demand/#of cases 100 200 300 EMV
100 $1000 $900 $800 $900
200 $800 $2000 $1900 $1610
300 $600 $1800 $3000 $1800
Required:
You have reason to believe the probabilities many not be reliable due to changing conditions. If these probabilities are ignored, what decision would be made using: (a) the optimistic criterion? b) the pessimistic criterion?
Therefore, In Optimistic Criterion decision of cases : 300 and in Pessimistic Criterion decision of cases : 200
What does probability mean as a process?Probabilities can be written as percentages with a 0%–100% range or proportions with a 0–1 range. An event's probability is measured from 0 to 1, with 0 being the most unlikely scenario and 1 being the most likely. When an event's probability is 0.45 (45%), there are 45 percent (100) odds that it will happen.
Here,
a) Optimistic Criterion
Demand/#of No. of cases
cases
100 $1,000 $900 $800
200 $800 $2,000 $1,900
300 $600 $1,800 $3,000
Maximum of
Column $1,000 $2,000 $3,000
Maximum
Decision: 300 cases
b) Pessimistic Criterion
Demand/#of No. of cases
cases
100 $1,000 $900 $800
200 $800 $2,000 $1,900
300 $600 $1,800 $3,000
Minimum Of
Column $600 $900 $800
Maximin
Decision: 200 cases
Therefore in Optimistic Criterion decision of cases : 300 and in Pessimistic Criterion decision of cases : 200
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