There will be 350 different haiku that can be made with the given words.
How to calculate the valueIn this case, there are 5 syllables in the first line, 7 syllables in the second line, and 5 syllables in the last line, so the number of different haiku is given by the number of combinations of 3 elements taken from the set containing 5 elements (for the first and last lines) and 7 elements (for the second line), respectively.
This can be calculated as:
C(5,3) * C(7,3) = 10 * 35
= 350
So, there are 350 different haiku that can be made with the given words.
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lights of america claims that the life length of one of its light bulbs, the twister 7 years bulb2, is normally distributed with a mean of 10,000 hours and a standard deviation of 1000 hours. lang selects one of these light bulbs at random and places it on accelerated life test. (i) what is the probability that the bulb that lang selects will last exactly 9950 hours? (ii) what is the probability that the bulb that lang selects will last at most 9950 hours? (iii) what is the probability that the bulb that lang selects will last at least 9950 hours? (iv) what is the probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours? (v) what is the probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively? (vi) what lifelength represents the 95th percentile?
(i) The probability that the bulb that lang selects will last exactly 9950 hours is 0.3085.
(ii) The probability that the bulb that lang selects will last at most 9950 hours is 0.5
(iii) The probability that the bulb that lang selects will last at least 9950 hours is 0.6915.
(iv) The probability that the bulb that lang selects will last less than 9000 hours or more than 11,500 hours is 0.0668
(v) The probability that the bulb that lang selected will last between 9000 hours and 11,000 hours, inclusively is 0.6826.
(vi) The life length represents the 95th percentile is 11,645
The lifespan of the Lights of America light bulb is normally distributed, with a mean of 10,000 hours and a standard deviation of 1000 hours. This means that the majority of bulbs will last around 10,000 hours, but there will be some that last longer or shorter than this.
(i) To find the probability that the bulb selected by Lang will last exactly 9950 hours, we need to use the normal distribution formula. We know that the mean is 10,000 hours and the standard deviation is 1000 hours. Using these values, we can calculate the z-score (standardized value) for 9950 hours.
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. Therefore, the probability that the bulb will last exactly 9950 hours is 0.3085.
(ii) To find the probability that the bulb will last at most 9950 hours, we need to find the area under the normal curve to the left of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at most 9950 hours, we need to add the area under the normal curve to the left of -0.5, which is 0.3085 + 0.1915 = 0.5. Therefore, the probability that the bulb will last at most 9950 hours is 0.5.
(iii) To find the probability that the bulb will last at least 9950 hours, we need to find the area under the normal curve to the right of 9950 hours. We can use the z-score formula to calculate the z-score for 9950 hours as we did in part (i).
z = (9950 - 10000) / 1000 = -0.5
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -0.5, which is 0.3085. However, since we want the probability of the bulb lasting at least 9950 hours, we need to add the area under the normal curve to the right of -0.5, which is 1 - 0.3085 = 0.6915. Therefore, the probability that the bulb will last at least 9950 hours is 0.6915.
(iv) To find the probability that the bulb will last less than 9000 hours or more than 11,500 hours, we need to find the areas under the normal curve to the left of 9000 hours and to the right of 11,500 hours, and add them together. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,500 hours.
For 11,500 hours: z = (11,500 - 10,000) / 1000 = 1.5
Then the corresponding probability from Z table is written as,
=> 0.0668
(v) To find the probability that the bulb will last between 9000 hours and 11,000 hours, inclusively, we need to find the area under the normal curve between the z-scores for 9000 hours and 11,000 hours. We can use the z-score formula to calculate the z-scores for 9000 hours and 11,000 hours.
For 9000 hours: z = (9000 - 10,000) / 1000 = -1
For 11,000 hours: z = (11,000 - 10,000) / 1000 = 1
Using a standard normal distribution table or calculator, we can find the probability of a z-score of -1 (for 9000 hours), which is 0.1587, and the probability of a z-score of 1 (for 11,000 hours), which is 0.8413. Subtracting the area under the normal curve to the left of -1 from the area under the normal curve to the left of 1, we get the probability of the bulb lasting between 9000 hours and 11,000 hours inclusively, which is 0.8413 - 0.1587 = 0.6826.
(vi) To find the lifelength that represents the 95th percentile, we need to find the z-score that corresponds to the 95th percentile of the normal distribution. We can use a standard normal distribution table or calculator to find this value, which is approximately 1.645.
Using the z-score formula, we can solve for the life length that corresponds to a z-score of 1.645:
1.645 = (x - 10,000) / 1000
Multiplying both sides by 1000 and adding 10,000, we get:
x = 11,645
Therefore, the life length that represents the 95th percentile is 11,645 hours, which means that only 5% of bulbs will last longer than this value.
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the general rule of thumb is that it takes a driver 3/4 of a second to percieve the need to stop her car. it then takes another 3/4 of a second to react and move her foot from the accelerator to the brake and begin streeing out of the way. how far will a car traveling at 60 miles per hour travel (in feet) before the driver reacts to an obstacle?
A car traveling at 60 miles per hour will travel distance of 66 feet before the driver reacts to an obstacle.
To convert miles per hour to feet per second, we need to multiply by the conversion factor of 1.4667 (since 1 mile = 5280 feet and 1 hour = 3600 seconds, 5280/3600 = 1.4667).
Therefore, a car traveling at 60 miles per hour is traveling at 88 feet per second.
Using the given reaction time of 3/4 of a second, the distance traveled before the driver reacts is:
distance = rate x time = 88 feet/second x 3/4 second = 66 feet
Hence,
A car traveling at 60 miles per hour will travel a distance of 66 feet before the driver reacts to an obstacle.
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how to graph y=-2x+2 and y=-2x+1(will give branliest)
A graph of the system of linear equations y = -2x + 2 and y = -2x + 1 is shown in the image attached below.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.
Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.
Based on the graph (see attachment), we can logically deduce that the given system of equations has no solution because both lines have the same slope and are parallel.
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B) Mr. S Ralph spends $165. 31 on oranges INCLUSIVE of a 15% sales tax. Her total is $165. 31 with tax. (115% = original price is 100% plus tax of 15%). Calculate the ORIGINAL PRICE of the oranges, which means the cost of the oranges
without the tax
The total cost of the item would be [tex]$115[/tex].The original price of oranges purchased by Mr. S Ralph can be calculated by subtracting the sales tax from the total cost.
Sales tax is calculated as a percentage of the original price. In this case, the sales tax is 15%, meaning that the original price can be found by dividing the total cost (which includes the sales tax) by 1.15.To calculate the original price of the oranges, divide the total cost of $165.31 by 1.15. This gives us a total of $143.87. Thus, the original price of the oranges purchased by Mr. S Ralph is $143.87 without the sales tax included.Sales tax is a form of taxation imposed by governments on goods and services. Generally, for the majority of goods and services, the sales tax is calculated as a percentage of the original price. This means that the total cost of the goods or services can be calculated by adding the percentage of sales tax to the original price.For example, if an item costs $100, and the sales tax rate is 15%, the total cost of the item would be calculated by multiplying the original price by 1.15 (100% + 15% = 115%). The total cost of the item would be [tex]$115[/tex].
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what answer below best addresses the following statistical problem? a new advertisement for ben and jerry's ice cream introduced in late may of last year resulted in a 30% increase in ice cream sales for the following three months. does this mean that the advertisement was effective? a. yes, because an increase in sales means the advertisement worked. b. no, because the increase in sales was all caused by another variable (specifically a change in weather) c. uncertain, because there are other variables at play and correlation does not equal causation d. uncertain, because it's impossible to measure the effectiveness of advertising.
The correct answer to this statistical problem is (c) uncertain, because there are other variables at play and correlation does not equal causation.
In this scenario, we're looking at the sales of Ben and Jerry's ice cream before and after the advertisement was introduced. The sales increased by 30% for the following three months after the advertisement. So, does this mean that the advertisement was effective? The answer is not as straightforward as a simple "yes" or "no."
Option (c) acknowledges that there are other variables at play and that correlation does not equal causation.
This is the most accurate answer because it recognizes that while the increase in sales may be related to the advertisement, it's impossible to say for sure whether the advertisement was the cause of the increase in sales.
There could be other factors, such as the weather or a change in consumer preferences, that also contributed to the increase in sales.
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One fine day your dog buys 3 rawhide bones, 4 balls, and a squeaky toy at Woofville Mall. The next day he buys another ball and 2 more rawhide bones. Create an expression that represents the total cost.
A space dome theatre is composed of a cylindrical base and a hemispherical roof. The space dome theatre has a base radius of 20m and a cylindrical height of 20m. what is the total volume of the space dome theatre?
The total volume of the space dome theatre is 41867 m³.
What is a sphere?In geometry, a sphere is a three-dimensional solid figure, which is round in shape.
The surface area is 4πr².
The volume is (4/3)πr³.
The diameter is 2×radius of the sphere.
What is a cylindrical shape?A cylinder is a three-dimensional solid object having two similarly circular bases that are joined by a curving surface that is positioned a certain distance from the center.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
Given, The space dome theatre has a base radius of 20m.
Therefore, The volume of the hemispherical dome is,
= (2/3)π(20)³.
= (2/3)π×8000.
= (16000/3)π m³.
And, As the dome base has a radius of 20 m the cylindrical shape will also have the same.
Therefore, The volume of the cylindrical shape is,
= π(20)²×20.
= 8000π m³.
And, The total volume is the sum of the volumes of two shapes,
= 8000π + (16000/3)π m³.
= [(24000 + 16000)/3]π m³.
= (40000/3)π m³.
= 41867 m³.
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You’ve saved $45, which is 70% of the amount you want to save. What is the total amount you want to save? (round to nearest cent) * *
Rounding this to the nearest cent, the total amount that was wanted to be saved is $64.29.
To solve this problem, we can set up a proportion using the given information. Let x be the total amount that was wanted to be saved.
We know that the amount saved ($45) is 70% of the total amount that was wanted to be saved. Therefore, we can write:
45 = 0.7x
To solve for x, we can divide both sides by 0.7:
x = 45 ÷ 0.7
x = 64.28571429
The answer to the problem is $64.29, rounded to the nearest cent. This means that the total amount that was wanted to be saved was $64.29, and 70% of this amount is equal to the amount that was actually saved ($45). To check our work, we can multiply 64.29 by 0.7 to see if it equals 45. When we do this, we get:
64.29 x 0.7 = 45.003, which rounds to $45, so our answer is correct.
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Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 • Customers – 28.83.
Use the drop-down menus to complete the statements below about what this linear model tells you about Ivan's daily profit.
Ivan would expect to make $43.67 in profit if he had 50 customers.
How much profit would Ivan expect to makeFrom the question, we have the following parameters that can be used in our computation:
Expected Profit = 1.45 • Customers – 28.83.
If Ivan had 50 customers, using the least squares regression equation, the expected profit would be:
Expected Profit = 1.45 * 50 - 28.83
So, we have
Expected Profit = 72.5 - 28.83
Evaluate the difference
Expected Profit = 43.67
Hence, the expected profit is $43.67
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Complete question
Ivan has a lemonade stand. He keeps records of his daily profits and how many customers he had that day. The scatter plot shows his profits versus the number of customers for 25 days.
The least squares regression equation is:
Expected Profit = 1.45 * Customers - 28.83.
How much profit would Ivan expect to make if he had 50 customers?
Please help me
the town's population has increased for 80000 to 9000 in the past 10 years . what was the present % increase
The percent increase of the population in the past 10 years is 12.5%.
What is the percent increase of the population?Percent increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.
It is expressed as;
C = ((x₂ - x₁) / x₁)100%
Where x₁ is initial value and x₂ is new value
Given that;
Initial population x₁ = 8000New population x₂ = 9000Percentage increase C = ?Plug in the given values into the above equation and simplify.
C = ((x₂ - x₁) / x₁) × 100%
C = (( 9000 - 8000 ) / 8000) × 100%
C = ( 1000 / 8000) × 100%
C = 0.125 × 100%
C = 12.5%
Therefore, the percent increase is 12.5.
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The picture has the question
The exponential function for the given table will be y=0.01(2)ˣ where x=positive integer.
What exactly are exponential functions?
An exponential function is a mathematical function with the formula f (x) = aˣ, where "x" is a variable and "a" is a constant that is termed the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most often used exponential function basis.
Growth that is exponential
The amount expands extremely slowly at first, then rapidly in Exponential Growth. The rate of change accelerates with time. As time passes, the pace of growth accelerates. The quick expansion is designed to represent a "exponential rise".
The exponential growth formula is: y = a (1+ r)ˣ, where r is the growth percentage.
Now,
as given in the table initial value = 0.01
and it is increasing into multiples of 2ˣ where x=positive integer
Then for the value of y for any value of x will be
y=0.01(2)ˣ where x=positive integer
Hence,
The exponential function for the given table will be y=0.01(2)ˣ.
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A colored spinner with eight equal sections is given.
spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow
Using the fair spinner, determine P(less than 4) when the spinner is spun once.
0.125
0.25
0.375
0.5
The probability using the fair spinner to get P less than 4 is 3/8.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The total sections = 8.
The probability of less than 4 is:
P(less than 4) = Number of outcomes less than 4/ Total sections
P(less than 4) = 3/8
Hence, the probability using the fair spinner to get P less than 4 is 3/8.
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Answer: ITS 0.25!
Step-by-step explanation: i took the test
please help me i dont understand this
Answer: 57
Step-by-step explanation: I recommend learning angle properties, pictures on the internet might help ya out
convert the following measurements into centimeters
A. 15m
B. 1.6km
C. 467mm
Answers:
A. 150 cmB. 160,000 cmC. 46.7 cm===========================================
Work Shown:
[tex]15 \text{ m} = (15 \text{ m})*\frac{100 \text{ cm}}{1 \text{ m}} = 1500 \text{ cm}\\\\\\1.6 \text{ km} = (1.6 \text{ km})*\frac{1000 \text{ m}}{1 \text{ km}}*\frac{100 \text{ cm}}{1 \text{ m}} = 160,000 \text{ cm}\\\\\\467 \text{ mm} = (467 \text{ mm})*\frac{1 \text{ cm}}{10 \text{ mm}} = 46.7 \text{ cm}[/tex]
Each conversion fraction is set up to cancel out any unit that isn't "centimeters".
Side notes:
1 m = 100 cm1 km = 1000 m1 cm = 10 mmHeight: 15 ft area: 285 ft 2
What's the missing dimension
Answer: 19
Step-by-step explanation: 15 x 19 = 285ft^2
which statement justifies step three? Which statement justifies step four?
Given: AB=AD;BC=DC
Prove:
The two statements that justifies step three and four in the congruency proof are;
Reason 3: SSS Congruency Postulate
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
How to Identify the Congruency Proof?The two column proof is as follows;
Statement 1: AB ≅ AD, BC ≅ DC
Reason 1: Given
Statement 2: AC ≅ AC
Reason 2: Reflexive Property of Congruence
Statement 3: ΔABC ≅ ΔADC
Reason 3: SSS Congruency Postulate
Statement 4: ∠ABC ≅ ∠ADC
Reason 4: CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
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question 5
pls help me as soon as possible
i'm being timed i only have a hour
Answer:
CD = 36°
Step-by-step explanation:
the measure of secant angle BFE is half the difference of the measures of the intercepted arcs , that is
[tex]\frac{1}{2}[/tex] (BE - CD) = ∠ BFE
[tex]\frac{1}{2}[/tex] (128 - x) = 46 ( multiply both sides by 2 to clear the fraction )
128 - x = 92 ( subtract 128 from both sides )
- x = - 36 ( multiply both sides by - 1 )
x = CD = 36°
Please help me by finding the missing side length using trig!
On solving the provided question, we cans ay that in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
here, in this triangle by Pythagorean theorem
[tex]A^2 = B^2 + C^2[/tex]
AC = [tex]\sqrt{14^2 - 9^2}[/tex]
AC = [tex]\sqrt{196 - 81}[/tex]
AC = [tex]\sqrt{115}[/tex]
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If the diameter of the pie is ten inchefls, what is the approximate arc length of one slice of pie?
A. 1.67 inches
B. 13.08 inches
C. (c) 3.14 inches
D. D 5.24 inches
The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.
Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.
Diameter (D)=10.
So the radius will be D/2.
Radius (R)=10/2=5.
The pie's circumference is given by:
C=2πR
C=2π*5
C= 10π (in)
Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,
Length of Arc (L)= 10π/6
L = 5π/3
L= 5(3.14)/3
L=5.234=5.24
Therefore the approximate arc length of one slice of pie is 5.24 inches.
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The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $95.40, how many minutes did the executive use the phone?
Answer: 151 minutes
Step-by-step explanation:
95.40 - 35 =
60.40
60.40/.40 = 151
Assume you owe $16,783 to a credit card company and interest is at 19% compounded monthly, at the end of the month, how much do you owe in interest?
This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
The interest rate in this situation is 19% compounded monthly. This means that each month, the interest rate is applied to the total balance. The formula to calculate the amount of interest owed is:Interest Owed = Balance x (Interest Rate/12) .In this case, the formula would be:Interest Owed = 16,783 x (0.19/12).This equals a total of $281.55 in interest owed at the end of the month. This means that the total balance owed to the credit card company would be 16,783 + 281.55 = 17,064.55.
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Help please it´s urgent
Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
Answer: E
Step-by-step explanation:
The solution means the intersection point, so in this case, it's (3, 2). The intersection point represents a value that is true for both equations, which is why it's considered the solution.
Find out pls this is algebra 1 and I need to know the answer ;)
Answer:|x-1|-2
Step-by-step explanation: see picture below!
Ideas Math FL B.E.S.T. - Geometry > Checkpoint: Similarity transformations G6J
The side lengths of AGHI are 8, 12, and 16 units. Two of the side lengths of ALMN are 10 and
15 units. If AGHI and ALMN are similar, what is the length of the third side of ALMN?
units
The length of the third side of ALMN is 20 units.
What is the length of the third side of ALMN?
If AGHI and ALMN are similar, then their corresponding sides are proportional.
Let's call the length of the third side of ALMN "x". We can set up the proportion using the two sides of AGHI and ALMN that we know:
10/8 = 15/12 = x/16
To find x, we can cross-multiply and simplify:
15 × 16 = 12x
240 = 12x
x = 240/12
x = 20
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Write an inequality.
You need to buy several pencils and an eraser. You can spend no more than $7. The eraser costs $.75 and
pencils cost $.25.
Answer: .75 + .25x ≤ 7
Step-by-step explanation: The x equals the amount that you can buy for each item.
The coefficient of x² in the expansion of (2-x)(3 + bx)³ is 45. Find possible values of the
constant b.
Answer:
The possible values of the constant b are:
[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]
Step-by-step explanation:
The coefficient of x² in the expansion of (2 - x)(3 + bx)³ can be found by expanding the brackets.
Expand the cubed part by using the (a + b)³ formula:
(a + b)³ = a³ + 3a²b + 3ab² + b³
Therefore:
[tex]\begin{aligned}(3 + bx)^3 &= (3)^3 + 3(3)^2(bx) + 3(3)(bx)^2 + (bx)^3\\&= 27 + 27bx + 9b^2x^2 + b^3x^3\end{aligned}[/tex]
So:
[tex](2-x)(3 + bx)^3 = (2-x)(27 + 27bx + 9b^2x^2 + b^3x^3)[/tex]
To find the coefficient of the term in x², multiply the constant in the first parentheses by the coefficient of the term in x² in the second parentheses and add this to the product of the coefficient of the term in x in the first parentheses and the coefficient of the term in x in the second parentheses:
[tex](\bold{2}-x)(27 + 27bx + \bold{9b^2}x^2 + b^3x^3)\\\phantom{.}\underbrace{\uparrow \qquad \qquad\qquad\qquad\;\uparrow}\\ \phantom{wlwww}\text{multiply}[/tex]
[tex](2-x)(27 + \bold{27b}x + 9b^2x^2 + b^3x^3)\\\phantom{bbb..}\underbrace{\uparrow \qquad \quad\;\uparrow}\\ \phantom{ww.w}\text{multiply}[/tex]
Therefore, the expression for the coefficient of x² is:
[tex]2 \cdot 9b^2 + (-1) \cdot 27b[/tex]
Since the coefficient of x² in the expansion is 45, set the expression to 45 and solve for b:
[tex]\begin{aligned}2 \cdot 9b^2+(-1) \cdot 27b&=45\\18b^2-27b&=45\\18b^2-27b-45&=0\\9(2b^2-3b-5)&=0\\2b^2-3b-5&=0\\2b^2-5b+2b-5&=0\\b(2b-5)+1(2b-5)&=0\\(b+1)(2b-5)&=0\\\\ \implies b+1&=0 \implies b=-1\\ \implies 2b-5&=0 \implies b=\dfrac{5}{2}\end{aligned}[/tex]
Therefore the possible values of the constant b are:
[tex]b = -1, \quad b = \dfrac{5}{2}[/tex]
Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (x, y) = (2, 87). y=
The equation is [tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
What is meant by zeroes of polynomials?
All the x-values that bring a polynomial, p(x), to zero are referred to as its zeros. They are intriguing to us for a variety of reasons, one of which is that they provide information on the graph's x-intercepts for the polynomial.
It is given that degree of the equation is 5. so the highest power is 5 and there will be 5 zeroes.
It is given that 2 zeroes at x=1 and 3 zeroes at x= 3.
So, the equation is [tex]y=a(x-1)^{2} (x-3)^{3}[/tex].
We will substitute x=2 and y= 87 in the above equation.
[tex]87=a(2-3)^{3} \\a=-87[/tex]
Therefore now the equation will be:
[tex]y=-87(x-1)^{2} (x-3)^{3}[/tex].
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Lina is older than her cousin Sarika. This year the sun or their ages is 31, and the difference between their ages is 5. Which system of equations correctly represents the situations where L represents Linas age and S represents sarikas age
The system of equations that correctly represents the situation of Lina and Sarika's ages are:
L + S = 31L - S = 5.What is a system of equations?A system of equations is two or more equations solved concurrently or at the same time.
A system of equations is called simultaneous equations.
The sum of Lina and Sarika's ages = 31
Lina's age > Sarika's by 5 years
Let Lina's age = L
Let Sarika's age = S
L + S = 31... Equation 1
L - S = 5... Equation 2
2L = 36
L = 18.
Substituting L = 18 into either Equation 1 or 2:
18 + S = 31
S = 31 - 18
S = 13
Learn more about simultaneous equations at https://brainly.com/question/148035.
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solve graphically: 3x + y=15 ; 3x-4y=0
Answer:
To solve the system of equations graphically, you can plot the two lines on a coordinate plane and find the point where they intersect, which represents the solution to the system.
First, let's start by rewriting the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
For the first equation:
3x + y = 15
y = -3x + 15
For the second equation:
3x - 4y = 0
y = (3/4)x
Next, we can plot these two lines on a coordinate plane by using any two points on each line and connecting them with a straight line.
Once the lines are plotted, we can find the point where they intersect, which represents the solution to the system. In this case, the solution is (2, 9), meaning that at x = 2 and y = 9, both equations are satisfied.
So, the solution to the system of equations is (2, 9), which means that the two lines intersect at the point (2, 9).
Solve the equation -5(y +0.2) = 25.
y =
Answer:
y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal
Step-by-step explanation:
-5(y + 0.2) = 25 Distribute the -5
-5(y) + -5(0.2) = 25 Adding a negative is the same as subtracting a positive
-5y - 1 = 25 add 1 to both sides
-5y - 1 + 1 = 25 + 1
-5y = 26 Divide both sides by -5
[tex]\frac{-5y}{-5}[/tex] = [tex]\frac{26}{-5}[/tex]
y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal
Answer: To solve the equation -5(y + 0.2) = 25, we need to isolate y by performing the following steps:
Distribute the -5 to the expression inside the parenthesis:
-5 * y - 5 * 0.2 = 25
-5y - 1 = 25
Add 1 to both sides of the equation to isolate -5y on one side:
-5y - 1 + 1 = 25 + 1
-5y = 26
Divide both sides of the equation by -5 to find y:
(-5y) / -5 = 26 / -5
y = -5.2
So, the solution to the equation -5(y + 0.2) = 25 is y = -5.2.
Step-by-step explanation:
