Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
What is area?A region's size on a planar or curved surface can be expressed mathematically as its area. The term "surface area" refers to the area of a surface or the border of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.
Here,
Here, take note that the shape is still a rectangle and the fencing is still 84 feet long.
As a result, the area is equal to xy and the sum of the sides NOT along the river is 84.
Thus, 2x + y = 84 and A = xy are the two equations.
We must find A as a function of x or y to determine the area with the largest value. My recommendation is to solve the first equation for y and substitute that value into the second equation.
A(x) = x and y = 84 - 2x (84-2x)
Currently, we must maximize A(x) = 84x - 2.
Recall that if we determine the vertex's x value by substituting, x = -b/(2a), we may find the vertex's y value.
Therefore, x = -84/(-4) = 21 ft because a = -2 and b = 84. If x = 21, y = 84 - 2(21) = 42
Thus, the dimensions are 21 by 42, and the maximum size is 21 by 42, or 882 square feet.
Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
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• Practice Questions: Write an equation for a rational function wita. Hole at x = 1 1and vertical asymptote at x = - 3b. Vertical asymptote at x = - 2 and horizontal asymptote at y = 3c. An oblique asymptote y = x+1 but no vertical asymptoted. Vertical asymptote at x = 3 and f(x) > 0
The ratio of two polynomial functions with a non-zero denominator is known as a rational function. R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions, is the typical way to describe it. We studied the idea of the rational number in previous grades. It is the ratio or product of two integers with a non-zero denominator. As a result, the word ratio is where the name rational comes from.
a. A rational function with a hole at x = 1 and a vertical asymptote at x = -3 can be written as:
(x-1)/(x+3)
b. A rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 3 can be written as:
(x+2)/(x+2) = 3
c. A rational function with an oblique asymptote y = x+1 but no vertical asymptote can be written as:
(x-1)/(x-1) = x+1
d. A rational function with a vertical asymptote at x = 3 and f(x) > 0 can be written as:
(x-3)/(x-3) > 0
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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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In triangle XYZ, m∠Y = 71.02° and m∠Z = 29.6°. Determine the measure of the exterior angle to ∠X.
18.98°
60.4°
100.62°
79.38°
The measure of exterior angle to ∠X is 79.38°. So, option 4 is correct.
What is meant by triangle?Triangles are polygons because they have three vertices and three edges. This is one of the basic shapes in geometry.
In Euclidean geometry, any three non-collinear points determine a distinct triangle and a distinct plane (i.e. a two-dimensional Euclidean space). To put it another way, every triangle has a plane that it is contained in, and there is only one plane that contains every triangle. If and only if all geometry is the Euclidean plane, all triangles are contained in a single plane; however, this is no longer true in higher-dimensional Euclidean spaces. The topic of this article, unless otherwise stated, is triangles in Euclidean geometry, specifically the Euclidean plane.
Given,
In ΔXYZ, m∠Y=71.02° and m∠Z=29.6°
We know that,
The angles sum in a triangle is 180°.
m∠X+m∠Y+m∠Z=180°
m∠X+71.02°+29.6°=180°
m∠X=180°-100.62°
m∠X=79.38°
Therefore, the measure of exterior angle to ∠X is 79.38°.
So, option 4 is correct.
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In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen to study the relationship between gender and participation in the last election. The results were:
Men Women
Voted 2366
3611
Didn't Vote 1499
2524
If we are testing for a relationship between gender and participation in the last election, what is the p-value and decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)]
a) [p-value = 0.019, RH0]
b) [p-value = 0.140, RH0]
c) [p-value = 0.019, FRH0]
d) [p-value = 0.010, RH0]
e) [p-value = 0.140, FRH0]
An invalid speculation is a sort of measurable theory that suggests that no factual importance exists in a bunch of offered viewpoints.
Speculation testing is utilized to evaluate the validity of a speculation by utilizing test information. It is represented as H0, and it is sometimes referred to as the "null."
Give the null hypotheses a name.
Negative hypothesis:
H. There is no correlation between gender and election participation.
Other possibilities:
H: Gender and participation in the most recent election are linked.
Rule of rejection:
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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%, $ 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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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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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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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:
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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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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 triangle XYZ has vertices X(0,2), Y(4,4), and Z (3,-1). Triangle XYZ is rotated 180° counter clockwise about Z. in which quadrant is the image of point X 
Answer 34
...................................................................................
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
HALPPP, 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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A spherical balloon is being inflated at a rate of 8 cm³s-1. Find the rate of change of the surface area when the radius is 10 cm.
Answer:
1.6
Step-by-step explanation:
Firstly, we know the rate of change of volume [tex]v'=8[/tex].
The equation for surface area is: [tex]A = 4\pi r^2[/tex].
The derivative (rate of change) is then: [tex]A'=8\pi r*r'[/tex]
The equation of the volume of a sphere is: [tex]V=\frac{4}{3}\pi r^3[/tex].
The derivative (rate of change) is then: [tex]V' = 4\pi r^2 * r'[/tex].
This means that [tex]r'=\frac{V'}{4\pi r^2}[/tex].
We can then plug that into our equation for [tex]A'[/tex] and get:
[tex]A'=8\pi r*\frac{V'}{4\pi r^2}=2*\frac{V'}{r}[/tex]
After that, we can just plug in:
[tex]2*\frac{8}{10}=1.6[/tex]
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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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
(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 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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Which set of fractions is ordered from greatest to least? 3/10,1/4,2/5
Answer: 1/4,2/5,3/10
Step-by-step explanation:
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
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
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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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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Mrs. Smith has 40 students in her class. The ratio of students who stay after school for extra help to students who stay after school for soccer practice is 3:5. How many students stay after school for soccer practice?
Answer:
25
Step-by-step explanation:
1: Add up the ratio then divide by the number of students.
3+5=8
40/8=5
2: Each count is equal to 5 students.
3: Multiply the ratio of students who stay after soccer practice by Each count
5*5=25
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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-1/4 x [ x 12 -32 ] = [ 5 -3 y ]
The x and y values for the given equation are x= -20 and y=8
What is meant by scalar multiplication?One of the fundamental operations defining a vector space in linear algebra in mathematics is scalar multiplication (or more generally, a module in abstract algebra). When a real Euclidean vector is multiplied scalarly by a positive real number, the direction of the vector remains unchanged, but the magnitude of the vector increases. A scalar is anything that scales vectors, which is how the word "scalar" itself came to be. It is important to distinguish between the inner product of two vectors and scalar multiplication, which is the multiplication of a vector by a scalar with a vector as the product.
Given,
-1/4[ x 12 -32 ] = [ 5 -3 y ]
[(-1/4)x (-12/4) (-32/-4)]=[5 -3 y]
-x/4=5
-x=20
x= -20
-32/-4=y
y=8
Therefore, the x and y values for the given equation are x= -20 and y=8
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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 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:
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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