The factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3)
What is grouping?In algebra, "grouping" refers to a method of factoring polynomials that involves grouping together pairs of terms within the polynomial, in order to factor out a common factor.
What is polynomial?In mathematics, a polynomial is a mathematical expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
In the given question,
To factor the four-term polynomial by grouping, we can follow these steps:
Step 1: Group the first two terms and the last two terms together.
x³ + 9x² + 3x + 27
= (x³ + 9x²) + (3x + 27)
Step 2: Factor out the common factor from each group.
= x²(x + 9) + 3(x + 9)
Step 3: Notice that the expression (x + 9) is a common factor of both terms, and factor it out.
= (x + 9)(x² + 3)
Therefore, the factorization of the polynomial x³ + 9x² + 3x + 27 by grouping is:
x³ + 9x² + 3x + 27 = (x + 9)(x² + 3).
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You applied for k40 000.00 for a bank loan and you where given a flat rate interest of 9% for 2½ years. What is the amount he will pay the bank?
Answer:
The formula to calculate the amount of loan with flat rate interest is:
Amount = Principal + (Principal x Rate x Time)
Where,
Principal = the amount of loan
Rate = the interest rate per year
Time = the time period in years
Given,
Principal = K40,000.00
Rate = 9% per year
Time = 2.5 years
Substituting the values in the formula, we get:
Amount = K40,000.00 + (K40,000.00 x 0.09 x 2.5)
Amount = K40,000.00 + K9,000.00
Amount = K49,000.00
Therefore, the amount he will pay the bank is K49,000.00.
22 and 28 are two numbers Express the smallest number as a percentage of the sum of the two numbers
Answer: 44%
Step-by-step explanation:
22 is the smallest of the two numbers, and you want that number as a percentage of the sum of the two numbers. So basically it is asking you to put 22/(22+28) as a percentage. The step by step is as follows:
1. Simplify denominator
22+28 = 50
2. Rewrite the fraction so that the numerator is out of 100
22/50 = 44/100
3. Convert this new fraction to percentage
44/100= 44%
Hope this helps!!
Bokomo produced 300 Granola megapacks for the Mogoditshane market. Bokomo’s marginal cost equation is as follows: MC=2x-100. Find the cost of producing an additional 200 items due to increased demand.
The cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.
What is marginal cost?Marginal cost is the additional cost incurred by producing one additional unit of a good or service. In other words, it is the cost of producing one more unit of output.
According to question:The marginal cost (MC) equation given is MC = 2x - 100, where x is the number of units produced.
To find the cost of producing an additional 200 items due to increased demand, we need to calculate the marginal cost of producing these 200 items and then multiply that by 200.
The marginal cost of producing 200 additional items is given by:
MC(200) = 2(300 + 200) - 100
MC(200) = 2(500) - 100
MC(200) = 900
So the marginal cost of producing 200 additional items is 900. To find the total cost of producing these 200 items, we can simply multiply the marginal cost by the number of units produced, which in this case is 200:
Total cost = MC(200) × 200
Total cost = 900 × 200
Total cost = 180,000
Therefore, the cost of producing an additional 200 items due to increased demand is 180,000 Botswana Pula.
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James placed an online order for an item that costs US$75 via the Internet. Shipping and handling costs were charged at US$39. Given the exchange rate of US$1.00 to S$1.65, how much, in Singapore dollars, would James have to pay altogether?
James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
What is prοbability?Prοbability is a measure οf the likelihοοd οf an event οccurring. It is a numerical value between 0 and 1, where 0 means the event is impοssible and 1 means the event is certain tο οccur. Fοr example, the prοbability οf flipping a fair cοin and getting heads is 1/2 οr 0.5.
Tο calculate the tοtal cοst in Singapοre dοllars, we need tο cοnvert the US dοllars tο Singapοre dοllars using the given exchange rate, and then add the twο cοsts tοgether.
The cοst οf the item in Singapοre dοllars is:
75 USD * 1.65 SGD/USD = 123.75 SGD
The shipping and handling cοst in Singapοre dοllars is:
39 USD * 1.65 SGD/USD = 64.35 SGD
The tοtal cοst in Singapοre dοllars is the sum οf these twο cοsts:
Tοtal cοst = 123.75 SGD + 64.35 SGD = 188.10 SGD
Therefοre, James wοuld have tο pay a tοtal οf 188.10 Singapοre dοllars fοr the item and shipping and handling cοsts.
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Rewrite without absolute value for the given condition: |(square root 2) +3 -5|
Answer: We can simplify the expression inside the absolute value first:
|(sqrt(2) + 3 - 5)|
= |(sqrt(2) - 2)|
Since sqrt(2) > 2, we know that sqrt(2) - 2 is negative. Therefore, we can rewrite the absolute value as a negative:
|sqrt(2) - 2| = -(sqrt(2) - 2)
So the expression without absolute value is:
-(sqrt(2) - 2)
Step-by-step explanation:
A shop is having a 40% sale. A jumper originally costs £50. How much will it be in sale?
Answer:
30 pounds
Step-by-step explanation:
Since the jumper costs 50 pounds, the decimal for the number will be:
50.
To find ten percent of the number, you move the decimal one time to the LEFT.
Therefore, 10% of 50 pounds will be 5 pounds. To find 40%, we simply will multiply the 10% amount by 4.
40% of 50 will be:
20
Therefore, the jumper will have 20 pounds off.
Since the original cost is 50 pounds, we simply will just subtract 50 - 20:
50 - 20 = 30
The jumper will cost 30 pounds with the sale deal.
For the graph, find the average rate of change on the intervals given
See attached picture
The average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] are 2, -1.5, 1, and -1.5, respectively.
What is the average rate in math?It expresses how much the function changed per unit on average during that time period. It is computed by taking the slope of the straight line connecting the interval's endpoints on the function's graph.
To calculate the average rate of change for the intervals shown in the graph, we must first determine the slope of the line connecting the endpoints of each interval.
0-3 interval:
Because the interval's endpoints are (0, 1) and (3, 7), the slope of the line connecting them is:
slope = (y change) / (x change) = (7 - 1) / (3 - 0) = 2
pauses [3, 5]:
Because the interval's endpoints are (3, 7) and (5, 4), the slope of the line connecting them is:
slope = (y change) / (x change) = (4 - 7) / (5 - 3) = -1.5
[5–7] Interval:
Because the interval's endpoints are (5, 4) and (7, 6), the slope of the line connecting them is:
slope = (y change) / (x change) = (6 - 4) / (7 - 5) = 1
Interval 7 and 9:
Because the interval's endpoints are (7, 6) and (9, 3), the slope of the line connecting them is:
slope = (y change) / (x change) = (3 - 6) / (9 - 7) = -1.5
As a result, the average rate of change on the intervals [0, 3], [3, 5], [5, 7], and [7, 9] is 2, -1.5, 1, and -1.5.
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In a certain region of space the electric potential is given by V=+Ax2y−Bxy2, where A = 5.00 V/m3 and B = 8.00 V/m3.1) Calculate the magnitude of the electric field at the point in the region that has cordinates x = 1.10 m, y = 0.400 m, and z = 0.2)Calculate the direction angle of the electric field at the point in the region that has cordinates x = 1.10 m, y = 0.400 m, and z = 0.( measured counterclockwise from the positive x axis in the xy plane)
The direction angle of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is approximately 74.5 degrees clockwise from the positive x-axis in the xy plane.
To calculate the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0), we need to take the negative gradient of the electric potential V:
E = -∇V
where ∇ is the del operator, which is given by:
∇ = i(∂/∂x) + j(∂/∂y) + k(∂/∂z)
and i, j, k are the unit vectors in the x, y, and z directions, respectively.
To calculate the magnitude of the electric field at the point, we first need to find the partial derivatives of V with respect to x and y:
∂V/∂x = 2Axy - By^2
∂V/∂y = Ax^2 - 2Bxy
Substituting the values of A, B, x, and y, we get:
∂V/∂x = 2(5.00 V/m^3)(1.10 m)(0.400 m) - (8.00 V/m^3)(0.400 m)^2 = 0.44 V/m
∂V/∂y = (5.00 V/m^3)(1.10 m)^2 - 2(8.00 V/m^3)(1.10 m)(0.400 m) = -1.64 V/m
Next, we can calculate the magnitude of the electric field:
E = -∇V = -i(∂V/∂x) - j(∂V/∂y) - k(∂V/∂z)
= -i(0.44 V/m) + j(1.64 V/m) + 0k
= (0.44 i - 1.64 j) V/m
The magnitude of the electric field is given by:
|E| = sqrt((0.44 V/m)^2 + (-1.64 V/m)^2) = 1.70 V/m
Therefore, the magnitude of the electric field at the point (x = 1.10 m, y = 0.400 m, z = 0) is 1.70 V/m.
To calculate the direction angle of the electric field, we need to find the angle that the electric field vector makes with the positive x-axis in the xy plane.
The angle can be found using the arctan function:
θ = arctan(Ey/Ex)
Substituting the values of Ex and Ey, we get:
θ = arctan(-1.64 V/m / 0.44 V/m) = -1.30 radians
The negative sign indicates that the direction angle is measured counter clockwise from the negative x-axis, which is equivalent to measuring clockwise from the positive x-axis.
Converting to degrees, we get:
θ = -1.30 radians * (180 degrees / pi radians) = -74.5 degrees
Therefore, the direction angle is approximately 74.5 degrees clockwise in the xy plane.
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A pond in the shape of a right-angled triangle is shown below. Calculate the perimeter of the pond. Give your answer in metres to 1 d.p. 1.46 m 100 73°
The perimeter of the pond is 2.92 meters.
What s a right-angle triangle:
A right-angled triangle is a triangle in which one of the angles measures exactly 90 degrees, also known as a right angle.
The side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.
The perimeter of a right-angled triangle is the sum of the lengths of its three sides.
Here we have
The Hypotenuse of the triangle is 1.46 m
The angle between hypotenuse and perpendicular height = 73°
From triagonometric ratios,
=> cos A = Perpendicular height/ Hypotenuse.
=> cos (73) = Perpendicular height/1.46
=> Perpendicular height = 1.46 × 0.29 = 0.42 m
As we know from Pythagoras' theorem,
Hypotenuse² = side² + side²
Side = √Hypotenuse² - side²
= √[(1.46)²- (0.42)²] = 1.04
Therefore, the sides of the pond are 1.46 m, 0.42 m, and 1.04
Hence, perimeter of the pond = 1.46 + 0.42 + 1.04 = 2.92 meters
Therefore,
The perimeter of the pond is 2.92 meters.
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The complete Question is given below
mr Li wishes to give each of his five relatives in China 500 renminbi (RMB) Find the amount he would need in Singapore dollars, if the exchange rate is S$100 to RMB510.20
Exchange rate calculation.
To find out the amount in Singapore dollars that Mr Li would need to give each of his five relatives 500 RMB each, we can follow these steps:
Calculate the total amount in RMB that Mr Li needs to give:
500 RMB/relative x 5 relatives = 2500 RMB
Convert the total amount in RMB to Singapore dollars using the given exchange rate:
2500 RMB x (S$100/RMB510.20) = S$490.64 (rounded to the nearest cent)
Therefore, Mr Li would need S$490.64 to give each of his five relatives 500 RMB each, given the exchange rate of S$100 to RMB510.20.
ChatGPT
Zoe was comparing the variability of three of her stocks. Over the last month ACE stock had a mean price of $37.03 per share with a standard deviation of $1.5, while FHJ stock had a mean price of $60.55 per share with a standard deviation of $2.62, and LMP stock had a mean price of $124.9 per share with a standard deviation of $3.06. Out of these three stocks, what was the greatest coefficient of variation?
Round your answer to a hundredth of a percent. Input just the number. Do not input the percent sign. Do not use a comma. Example 4.35
In respοnse tο the questiοn, we may say that As a result, FHJ stοck has equatiοn highest cοefficient οf variatiοn, with a value οf arοund 4.33%.
What exactly is an equation?In mathematics, an equatiοn is a statement that expresses the equality οf twο expressiοns. Equatiοn is made up οf twο sides that are jοined by the algebraic symbοl (=). Fοr example, in this argument, it is asserted that "2x + 3 = 9" denοtes that "2x plus 3" equals the number "9".
Equatiοn sοlving is the prοcess οf determining the value(s) οf the variable(s) required fοr the equatiοn tο be true. There are many different kinds οf equatiοns, such as regular and nοnlinear οnes with οne οr mοre elements. This fοrmula raises the variable x tο the secοnd pοwer: "x² + 2x - 3 = 0." Lines are used in the study οf mathematics in the fields οf algebra, calculus, and geοmetry.
The cοefficient οf variatiοn (CV) represents the standard deviatiοn as a percentage οf the mean and is a relative measure οf variability. It is cοmputed as fοllοws:
CV = (standard deviatiοn / mean) multiplied by 100%
Tο determine which οf the three stοcks has the highest cοefficient οf variatiοn, we must cοmpute the CV fοr each and cοmpare the results.
Fοr ACE inventοry:
CV = (1.5 / 37.03) x 100% ≈ 4.05%
In the case οf FHJ stοck:
CV = (2.62 / 60.55) x 100% ≈ 4.33%
In the case οf LMP stοck:
CV = (3.06 / 124.9) x 100% ≈ 2.45%
As a result, FHJ stοck has the highest cοefficient οf variatiοn, with a value οf arοund 4.33%.
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7. Jada walks up to a tank of water that can hold up to 10 gallons. When it is active, a
drain empties water from the tank at a constant rate. When Jada first sees the tank, it
contains 7 gallons of water. Three minutes later, the tank contains 5 gallons of water.
a. At what rate is the amount of water in the tank changing? Use a signed number, and
include the unit of measurement in your answer.
b. How many more minutes will it take for the tank to drain completely? Explain or
show your reasoning.
c. How many minutes before Jada arrived was the water tank completely full? Explain
or show your reasoning.
In the word problem,
a)Gallons per minute change is -2/3 gallons per minute
b) 7.5 minutes to drain the other 5 gallons
c)The tank was full 4 1/2 minutes before Jada arrived.
What is word problem?
Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.
a) Gallons per minute change is -2/3 gallons per minute since it decreases by 2 gallons in 3 minutes.
b) we have 5 gallons and lose 2/3 gallons per minute
=> (2/3 gal/minute)(x minutes) = 5 gallons
=> x = 5(3/2) = 15/2 = 7.5 minutes to drain the other 5 gallons
c) There was 10 gallons when the tank is full . That is 3 gallons more than the 7 gals there when Jada arrived.
=> (2/3)(x) = 3
=> x = 3(3/2) = 9/2 = 4 1/2 minutes
The tank was full 4 1/2 minutes before Jada arrived.
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can’t seem to get this any help
A. 27.4
B. 37.3
C. 40.0
D. 42.0
Answer:
Step-by-step explanation:
In the boys triangle:
[tex]tanx=\frac{56}{48}[/tex]
[tex]x=tan^{-1}(\frac{56}{48} )=49.4\textdegree[/tex]
Because triangles are similar:
[tex]tan 49.8=\frac{h}{32}[/tex]
[tex]h=32tan49.8 = 37.3[/tex]
find the two numbers whose ratio is 3:7 and their difference is 20
Answer:
the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.
Step-by-step explanation:
A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish.
In order to see the school of fish, the scuba diver descended to a depth of 14 feet below sea level.
What dοes "depth" mean?Hοw far sοmething stretches is described by the cοncept οf depth. The pοοl has a six-fοοt depth. Unknοwn is the well's depth. We can use the fοllοwing equatiοn tο determine the scuba diver's initial depth:
Initial depth = Final depth + Depth Change The scuba diver's change in depth is positive because he rose f feet (positive because he went up) and ended up 16 feet below the surface. Therefοre:
initial depth = 16 + f - 30 initial depth.
Simplifying the phrase:
Original depth = -14 + f
The scuba diver reached his initial depth there after descended another 14 feet below sea level to observe the school of fish.
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Questions-
A scuba diver was 30 feet below sea level when he ascended f feet to a depth of 16 feet below sea level to see a school of fish. what is her new elevation now?
How this app works? Why I can’t find any answers? I need pay for points when I ask questions? I subscribe this app and when I’m lucky to the answers almost the answers are wrong
Jonathan says that the function represented by the graph is always decreasing. Is he correct? fI not, where is the function decreasing?
Explain your reasoning.
If the slope of the graph is increasing from positive x-axis to negative x-axis, then the function is not that decreasing. Therefore, Jonathan's statement is incorrect.
What is the graph function about?The function is decreasing on intervals where the slope is negative. In this case, since the slope is increasing from positive x-axis to negative x-axis, the function is decreasing on the interval where x is negative.
To determine this interval more precisely, we would need to find the x-value(s) where the slope changes sign from positive to negative. These x-values correspond to critical points, such as local maximums or minimums. The function is decreasing before a local maximum and after a local minimum.
Therefore, Jonathan's statement is not correct, and the function represented by the graph is decreasing on the interval where x is negative.
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Which of the following random variables can be approximated to discrete distribution and continuous distribution? a. b. C. d. The wages of academician and non-academician workers in UPSI. The time taken to submit online quiz answer's document. The prices of SAMSUM mobile phones displayed at a phone shop The number of pumps at Shell petrol stations in Perak. [2 marks] 10% chance of contamination by a particular
10% chance of contamination by a particular: It's not clear what random variable is being referred to here, but if it's the probability of contamination.
What is Distribution?In general terms, a distribution refers to the way something is divided or spread out. In the context of statistics and probability theory, a distribution is a mathematical function that describes the likelihood of different possible outcomes or values that a variable can take.
There are various types of distributions, but some of the most commonly used ones include:
Normal distribution: also known as the Gaussian distribution, it is a continuous probability distribution that is symmetrical around the mean, with most of the data falling within one standard deviation of the mean.
Binomial distribution: this is a discrete probability distribution that describes the likelihood of a certain number of successes in a fixed number of trials.
Poisson distribution: another discrete probability distribution that describes the likelihood of a certain number of events occurring in a fixed interval of time or space.
Exponential distribution: a continuous probability distribution that describes the time between events occurring at a constant rate.
Distributions are essential in statistical analysis as they can help to understand and analyze data, make predictions, and draw conclusions about a population based on a sample of data.
Given by the question.
a. The wages of academician and non-academician workers in UPSI: This random variable can be approximated to a continuous distribution as wages can take on any numerical value within a range. However, it's worth noting that in practice, there may be discrete intervals or categories of wages, in which case a discrete distribution may be more appropriate.
b. The time taken to submit online quiz answer's document: This random variable can also be approximated to a continuous distribution as it can take on any numerical value within a range.
c. The prices of SAMSUNG mobile phones displayed at a phone shop: This random variable can be approximated to a continuous distribution as prices can take on any numerical value within a range.
d. The number of pumps at Shell petrol stations in Perak: This random variable can be approximated to a discrete distribution since the number of pumps can only take on integer values.
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If A = [ 1 2 4 0 5 6 ] and B= [ 7 3 2 5 1 9] find C= A+B and D=A-B
Step 1: Arrange the arrays so that A and B are in the same order: A = [ 1 2 4 0 5 6 ], B = [ 7 3 2 5 1 9]
Step 2: To find C = A+B, add each element of A and B together.
C = [1+7, 2+3, 4+2, 0+5, 5+1, 6+9]
C = [8, 5, 6, 5, 6, 15]
Step 3: To find D = A-B, subtract each element of B from A.
D = [1-7, 2-3, 4-2, 0-5, 5-1, 6-9]
D = [-6, -1, 2, -5, 4, -3]
Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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Some friends went out for a meal. The restaurant added a 10% service charge to the cost of the meal. The total bill was £126.50 including the service charge. What was the cost of the meal? Give your answer in pounds (£). Receipt Cost of the meal: £ Service charge: +10% Total: £126.50
Answer:
Let's start by setting up an equation to represent the problem. Let x be the cost of the meal:
x + 0.1x = 126.50
Simplifying the left side of the equation:
1.1x = 126.50
Dividing both sides by 1.1:
x = 115
Therefore, the cost of the meal was £115.
Find x, if √x +2y^2 = 15 and √4x - 4y^2=6
pls help very soon
Answer:
We have two equations:
√x +2y^2 = 15 ----(1)
√4x - 4y^2=6 ----(2)
Let's solve for x:
From (1), we have:
√x = 15 - 2y^2
Squaring both sides, we get:
x = (15 - 2y^2)^2
Expanding, we get:
x = 225 - 60y^2 + 4y^4
From (2), we have:
√4x = 6 + 4y^2
Squaring both sides, we get:
4x = (6 + 4y^2)^2
Expanding, we get:
4x = 36 + 48y^2 + 16y^4
Substituting the expression for x from equation (1), we get:
4(225 - 60y^2 + 4y^4) = 36 + 48y^2 + 16y^4
Simplifying, we get:
900 - 240y^2 + 16y^4 = 9 + 12y^2 + 4y^4
Rearranging, we get:
12y^2 - 12y^4 = 891
Dividing both sides by 12y^2, we get:
1 - y^2 = 74.25/(y^2)
Multiplying both sides by y^2, we get:
y^2 - y^4 = 74.25
Let z = y^2. Substituting, we get:
z - z^2 = 74.25
Rearranging, we get:
z^2 - z + 74.25 = 0
Using the quadratic formula, we get:
z = (1 ± √(1 - 4(1)(74.25))) / 2
z = (1 ± √(-295)) / 2
Since the square root of a negative number is not real, there are no real solutions for z, which means there are no real solutions for y and x.
Therefore, the answer is "no solution".
If a ll b, find the value of x.
Answer:
x = 18
Step-by-step explanation:
Alternate exterior angles are congruent. Set the equations equal to each other and solve for x.
7x + 11 = 10x - 43 Subtract 7 x from both sides
7x - 7x + 11 = 10x - 7x - 43
11 = 3x - 43 Add 3 to both sides
11 + 43 = 3x -43 + 43
54 = 3x Divide both sides by 3
[tex]\frac{54}{3}[/tex] = [tex]\frac{3x}{3}[/tex]
18 = x
Helping in the name of Jesus.
(b) a dy integral that represents the surface area of the solid formed when c is rotated about the (x or y)-axis
The surface area of the surface generated by rotating the curve y = x² about the y-axis, and we found that the surface area is approximately 54.33 square units.
In this case, the curve we want to rotate is y = x², and we want to rotate it about the y-axis. To use the formula above, we need to express the equation of the curve in terms of x. Therefore, we need to rewrite y = x² as x = √y.
Next, we need to find the derivative of x = √y with respect to y, which is:
dx/dy = 1/2√y
Substituting this into the formula for the surface area, we get:
Surface Area = 2π ∫[0,4] √y √(1+(1/2√y)²) dy
Simplifying the expression inside the square root, we get:
Surface Area = 2π ∫[0,4] √(y+(1/4)) dy
We can evaluate this integral using the power rule of integration, which gives:
Surface Area = 2π [2/3(y+(1/4))^(3/2)]₀⁴
Simplifying further, we get:
Surface Area = 2π [2/3(17/4)^(3/2)]
Surface Area ≈ 54.33 square units
Therefore, the surface area of the surface generated by rotating the curve y = x² about the y-axis is approximately 54.33 square units.
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Complete Question:
How do you find the area of the surface generated by rotating the curve about the y-axis y = x^2 , 0 ≤ x ≤ 2 ?
What is the probability that a 58% free-throw shooter will miss her next free throw?
6x+16=8x-18 i need x
Answer:
x = 17
Step-by-step explanation:
Subtract 6x from both sides:
2x - 18 = 16
Add 18 on both sides to isolate the variable:
2x = 18 + 16
2x = 34
Divide by 2: x = 17
in a batch of 10,000 clock radios 500 are defective. A sample of 10 clock radios is randomly selected without replacement from the 10,000 and tested. The entire batch will be rejected if at least one of those tested is defective. what is the probability that the entire batch will be rejected?
Answer:
Step-by-step explanation:
This is an example of a hypergeometric distribution problem, where we have a population of 10,000 clock radios with 500 defective ones, and we want to calculate the probability of getting at least one defective radio in a random sample of 10 without replacement.
The probability of getting no defective radios in the sample is:
(9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
This is because, for the first radio, there are 9500 good radios out of 10,000, and for the second radio, there are 9499 good radios out of 9,999, and so on.
The probability of getting at least one defective radio in the sample is then:
1 - (9500/10000) * (9499/9999) * (9498/9998) * ... * (9491/9992)
which is approximately equal to 0.401.
Therefore, the probability that the entire batch will be rejected is 0.401.
The Ford F-150 is the best selling truck in the United States.
The average gas tank for this vehicle is 23 gallons. On a long
highway trip, gas is used at a rate of about 3.2 gallons per hour.
The gallons of gas g in the vehicle's tank can be modeled by the
equation g(t)=23 -3.2t where t is the time (in hours).
a) Identify the domain and range of the function. Then graph
the function.
b) At the end of the trip there are 6.4 gallons left. How long
was the trip?
a) The domain and the range of the function are given as follows:
Domain: [0, 7.1875].Range: [0,23].The graph of the function is given by the image presented at the end of the answer.
b) The trip was 5.1875 hours long.
What are the domain and the range of a function?The function for this problem is defined as follows:
g(t) = 23 - 3.2t.
The domain is the set of input values that can be assumed by the function. The time cannot have negative measures, hence the lower bound of the domain is of zero, while the gas cannot be negative, hence the upper bound of the volume is given as follows:
23 - 3.2t = 0
3.2t = 23
t = 23/3.2
t = 7.1875 hours.
The range is given by the set of all output values assumed the function, which are the values of the gas, hence it is [0,23].
The graph is a linear function between points (0, 23) and (7.1875, 0).
At the end of the trip there were 6.4 gallons left, hence the length of the trip is given as follows:
23 - 3.2t = 6.4
t = (23 - 6.4)/3.2
t = 5.1875 hours.
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Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
What is function in mathematics?Function in mathematics is a relation between two sets, where one set is the input and the other set is the output. Functions are an important tool in mathematics and can be used to describe and model real-world phenomena. Functions take inputs, manipulate them and produce outputs. They can be used to represent relationships between two or more variables, or to represent a complex process. Functions allow us to break down complex problems into smaller, more manageable pieces and to study how changes in one variable affect other variables.
The function represented by the table is linear. It can be determined by the fact that the y-values change by the same amount every time the x-values increase by one unit. In this case, the y-values decrease by 2 each time the x-values increase by one unit. This is an example of a linear function.
Linear functions have the shape of a straight line and are characterized by having a constant rate of change. The constant rate of change is represented by the slope of the line, which in this case is -2. This means that for every one unit increase in the x-values, the y-values decrease by two.
A quadratic function is the opposite of a linear function, as it has a rate of change that is not constant. Quadratic functions are characterized by their parabolic shape and their rate of change increases as x-values increase. Exponential functions are characterized by their curved shape and increase exponentially as x-values increase.
In conclusion, the function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
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3. Each sample of water from a river has a 10% chance of contamination by a particular heavy metal. Find the probability that in 18 independent samples taken from the same river, only two samples were contaminated. [3 marks]
The probability that, out of 18 independent samples received from one river, just two were contaminated is 0.8438.
Explain about the independent samples?Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that sampling are independent underlies many statistical analysis.When each trial possesses the same probability of achieving a given value, the number of trials or observations is represented using the binomial distribution.In the following 18 samples to be evaluated,
Let X = the number of samples that now the pollutant is present in.
Thus, with p = 0.10 and n = 18, X is a binomial random variable.
Using the binomial theorem:
[tex](^{n} _{r} ) p^{x} q^{n-x}[/tex]
p = 0.10
q = 1 - 0.10 = 0.9
n = 18
The likelihood that only two samples out of 18 obtained in different ways from the same river were polluted
P(x = 2) = [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{18-2}[/tex]
= [tex](^{18} _{2} ) (0.1)^{2} (0.9)^{16}[/tex]
= 153 x 0.01 x 0.1853
= 0.8438
Thus, the probability that, out of 18 separate samples received from one river, just two were contaminated is 0.8438.
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