The two values of x which are root of the given equation are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
What are the two values of x which are root of the given quadratic equation?It follows from the task content that the two values of x which are roots of the given quadratic equation be determined.
Recall that the roots of quadratic equations are given by the formula;
x = {-b ± √(b² - 4ac)} / 2a
Since the given equation is; x² + 3x - 5; it follows that; a = 1, b = 3 and c = -5.
Therefore, the roots are as follows;
x = {-3 ± √(3² - 4•1•-5)} / 2(1)
x = (-3 ± √29)/2
Therefore, the required roots are;
x = (-3 + √29)/2 and x = (-3 - √29)/2
Ultimately, the roots of the given quadratic equation x² + 3x - 5 are; x = (-3 + √29)/2 and x = (-3 - √29)/2.
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a survey of a congressional race finds 52 percent of voters supporting candidate a and 48 percent supporting candidate b, with a 5 percent margin of error. given this information, we can say that:
Answer:
When you round the number to 5
Step-by-step explanation:
the ages of five randomly chose cars in the parking lot are determined to be 7, 9, 3,4, and 6 years old. if we consider these 5 cars in groups of 3, how many groups can be formed?
The number of groups formed is 10 if we consider 5 cars in groups of 3.
Given, 5 cars in groups of 3, we can use the formula,
(5 3) = 5! / 3! × 2!
= 10
Permutation and combination are the various ways in which one can form a set that may be selected without any replacement. When the selection of a subset is where we use the permutation and when the ordering of the subset is there we use a combination.
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Please graph this equation y=4|x-1|+3
The graph of equation y=4|x-1|+3 is as shown below.
In this question, we need to graph the equation y=4|x-1|+3
We know that the parent function of given equation is z = |x|
A parent function is translated right by 1 unit then it is dilated vertically by 4 units and the resulting image is translated up by 3 units.
The graph of equation y=4|x-1|+3 is as shown below.
The vertex of equation y=4|x-1|+3 is at (1, 3)
Therefore, the graph of equation y=4|x-1|+3 is as shown below.
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IM BEGGING FOR HELP !!! find the volume of each shape and then compare do not reduce your fractions.
Answer:
64/125 > 150/512
Step-by-step explanation:
4/5 *4/5 *4/5 = 64/125 (also equals 0.512)
5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)
Therefore: 0.512 > 0.293
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry. In words, describe the graph of the proportional relationship.
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
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Answer:
Step-by-step explanation:
The required expression for the laundry service is y = 0.89x.
Given that,
The total cost for laundry service, in dollars, depends on the weight of the laundry, in pounds. This relationship is proportional, as it costs $22.25 for 25 pounds of laundry and $36.49 for 41 pounds of laundry.
What is proportionality?
proportionality is defined as between two or more sets of values, and how these values are related to each other in a sense are they directly proportional or inversely proportional to each other.
here
Let the pound of laundry be x and the charge corresponding to the pound of the laundry be y.
According to the question,
y ∝ x
y = kx
Put x = 25 and y = 22.25
22.25 = k 25
k = 0.89
Put back k in the proportional equation,
y = 0.89x
Thus, the required expression for the laundry service is y = 0.89x.
a scout group has a raffle to rasie money for charity there is 1 prize to be won in the raffle
laura buys 12 raffle tickets a total of 350 raffle tickets are sold
find the probability that laura does not win the prize
The probability that Laura does not win the prize is 119 / 175.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of raffle rickets to be sold is 350.
The number of tickets bought by Laura is 12.
Since, the probability of an event is defined as the ratio of favorable outcome to the total outcomes, the probability of winning the prize is,
P = 12 / 350
Thus, the probability of not winning the prize is,
1 - 12 / 350
= 338 / 350
= 119 / 175
Hence, the probability of not winning a prize is 119 / 175.
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Translation rule:
(x, y) (x + 2, y – 4)
Either draw in the translated image or write down the new coordinates for the translated image
Step-by-step explanation:
it is really simple :
every x is increased by 2, every y is decreased by 4.
C = (-4, 2) -> C' = (-2, -2)
R = (-5, -1) -> R' = (-3, -5)
T = (-1, 1) -> T' = (1, -3)
help me pleaseeeeeeeeeeeeeeeeee !!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
the flight path of a rocket or a thrown object is a parabola as described by the function.
h(t) = -16t² + 40t + 7
the negative sign of the prime coefficient (-16) tells us that the parabola opens downwards, and that the vertex as the extreme point of the parabola is a maximum.
we get the extreme point of a curve by finding the zero solution of the first derivative of the function.
and the extreme value itself by using that value in the original equation and calculate the result.
h'(t) = -32t + 40
0 = -32t + 40
32t = 40
t = 40/32 = 5/4 = 1.25 seconds
h(5/4) = -16×(5/4)² + 40×5/4 + 7 =
= -16×25/16 + 10×5 + 7 =
= -25 + 50 + 7 = 32 ft
the rocket will reach its maximum height of 32 ft after 1.25 seconds.
please answer this question (answer is needed as a fraction)
Answer:
4/6 means 2/3 it is most likely 0, 67 or 0, 66.
Step-by-step explanation:
a fence is to be built to enclose a rectangular area of 310 square feet. the fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 14 dollars per foot. find the dimensions of the enclosure that is most economical to construct.
The dimension for the enclosure that is most economical to construct will be length=11.13 feet and width=27.85 feet.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a shape or planar lamina.
A=l*b
=310
b=310/l
total cost=(8b+4l+16l)
=8b+20l
=8*310/l+20l
t=2480/l+20l
t'=20-2480/l²
t'=0
20l²=2480
l²=124
l=11.13 feet
b=310/11.13
b=27.85 feet
The enclosure's length and width, which add up to 11.13 feet and 27.85 feet respectively, will be the most cost-effective dimensions to build.
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The pages of a book are numbered consecutively from 1 to 100. What is the sum of all the digits used in numbering the pages of the entire book?
5050
Step-by-step explanation:
1+2+3+.....+100 add all the numbers and u get that
What is the constant of variation, k of the direct variation, y=kx,through (5,8)
Constant of variation, k of the direct variation is 8/5.
Equation -> y = kx
Point (x,y) = (5,8)
Putting the value in the equation,
8 = 5k
k = 8/5
Hence, k = 8/5.
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javieretta earned $9.50 each hour she works at camp clap happy during summer vacation. she earned $304 one week in june and $247 during a week in july. how many hours did she work that week in june? please help
Javieratta worked for a total of 32 hours in the week of June to earn an amount of 304 dollar.
Javieretta earns $9.50 each hours she works at camp clap happy.
She earned $304 in week of june and $247 during a week in july.
Let us assume that she works X hours.
So, using unitary method, we can write,
X times the amount she earns in one hour = Earning in the week of june.
X(9.50) = 304
X = 304/9.50
X = 32 hours.
So, she worked for a total of 32 hours in the camp clap happy summer vacation.
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Charlotte’s weekly paycheck is based on the number of hours worked during the week and on the weekend. If she works 13 hours during the week and 14 hours on the weekend, she earns $250.90. If she works 15 hours during the week and 8 hours on the weekend, she earns $204.70. How much more does Charlotte earn per hour on the weekends than she earns during the week? Round to the nearest cent.
$0.40
$1.90
$2.30
$8.10
The amount that Charlotte earn per hour on the weekends than she earns during the week is: C. $2.30.
How to find the earning per hour?Number of dollars earn per hour during the week = x
Number of dollars earn per hour on the weekend =y
Formulate an equation
13x + 14y = 250.90 Equation 1
15x + 8y = 204.70 Equation 2
Solving for x and y by multiply equation 1 by -8 and equation 2 by 14 -104x - 112y = -2007.20
210x +112y = 2865.80
106x = 858.60
Divide both sides by 106x
x = 858.60/106
x = $8.10
Substitute x into eq 1 so as to solve for y
13(8.10) + 14y = 250.90
105.30 + 14y = 250.90
Subtract 105.30 from both sides
14y = 145.60
Divide both side by 14y
y = 145.60 /14
y = 10.40
Hence,
Additional earning per hour = y-x
Additional earning per hour = $10.40 - $8.10
Additional earning per hour=$2.30 per hours
Therefore the correct option is C.
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6. Find the number of each category of voters based on the
information given below.
Total number of votes = 300000 votes
Percentage of
Votes, Others,
4%, 4%
Percentage
of Votes,
Females,
47%,
Percentage
of Votes
Males, 49%
Number of Male voters =
Number of female voters =
Number of voters to "Others" category=
The number of Male voters =14700, The number of female voters =14100 and the number of voters to "Others" category=1200
How do you calculate a percentage?
A % is a quantity or ratio that, in mathematics, represents a portion of one hundred. It's frequently represented by the sign "%" or just "percent" or "pct." For instance, the decimal 0.35, or the fraction, represents 35%.
Given : Total votes = 300000
males = 49%
females = 47%
Others = 4%
Number of votes for males = [tex]\frac{49}{100} *300000[/tex] = 14700
Number of votes for females = [tex]\frac{47}{100} *300000[/tex] = 14100
Number of votes for others = [tex]\frac{4}{100} *300000\\[/tex] = 1200
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An element with a ma and of 200 gram decay by 12. 6% per minute. To the nearet minute, how long will it be until there are 30 gram of the element remaining
The time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.
An element with an initial mass of 200 gram, decays by 12.6% per minute. We need to find out, to the nearest minute, how long it took for the element to decay until only 30 grams were left.
In exponential decay, a quantity diminishes slowly at first and then rapidly. The exponential decay formula is used to calculate population decay (depreciation), and it may also be used to calculate half-life (the amount of time for the population to become half its size).
Let the initial mass, remaining mass, decay rate, and time taken be represented by the variables M, m, d, and t, respectively. We can form the equation given below.
m = M(1 - d)^t
30 = 200(1 - 0.126)^t
3/20 = (0.874)^t
Take the logarithm on both sides of the equation.
log(3/20) = t × log(0.874)
t = log(3/20)/log(0.874)
t = 14.087
t ≈ 14
Hence, the time taken, to the nearest minute, by the element to decay until only 30 grams of it are left is 14 minutes.
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3y minus 27 i have no idea
3(y-9)
Step by step explanation:3y-27
Factorizing
3(y-9)
what finding the range of possible values for the length of missing side of a triangle means
Answer:
range
Step-by-step explanation:
Given g(x)=x-4 and h(x)=2x-8use the graph shown to evaluate the composition (f•g)(0)
Answer:
(f ￮ g)(0) = 3
Step-by-step explanation:
evaluate g(0) then substitute the value obtained into f(x)
g(0) means what is the value of g(x) when x = 0
from the graph g(0) = 2 , then
f(2) , that is what is the value of f(x) when x = 2
from the graph f(2) = 3
then
(f ￮ g)(0) = 3
in this exercise you are asked to approximate the growth of the world population using the logistic differential equation:
From the logistic population differential equation for approximate the growth of the world population , which is given here as [tex]P = L/1+ e^{-k(x-x_{0} )[/tex]
The general form of the logistic population equation is given as [tex]dP/dt = kP(1- P/L)[/tex]. While k is the relative growth rate, L is the carrying capacity.An ordinary differential equation with a logistic function as the solution is known as a logistic differential equation. Standard exponential functions do not account for the limitations that prevent infinite growth, but logistic functions correct this oversight. This is how bounded growth is represented by logistic functions. These contexts include machine learning, chess ratings, medical therapy (e.g., modelling tumour growth), economics, and even language adoption research.
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Brian loves to bake blueberry muffins for his friends and family.
there is a proportional relationship between the volume of flour brian uses (in cups), x, and
the number of muffins he bakes, y.
10
9
8
7
9
s
s
3
2
2
s
9
00
9
10
For a proportional relationship between the volume of flour used (in cups), x, and the number of baked muffins, y, the constant of proportionality is 4.
Constant of proportionality, also known as constant ratio or constant rate, refers to is the ratio that relates two given values in a data set that is represented as a proportional relationship. When two parameters are proportional, either directly or indirectly, the relationship is expressed as a = kb or a = k/b, where k indicates the relationship between the two variables and is known as the proportionality constant. In the given data, the proportionality constant is:
k =b/a = 8/2 =12/3 = 16/4 = 20/4 = 4
Hence, the proportionality constant for the given data is 4.
Notes: The question is incomplete. The complete question is: Brian loves to bake blueberry muffins for his friends and family. There is a proportional relationship between the volume of flour brian uses (in cups), x, and the number of muffins he bakes, y. What is the constant of proportionality. (Refer to the table).
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what is 315.00 divided by 30.
Answer:
Step-by-step explanation:
Answer 10.5
solve the inequality write the solution in interval notation
-x/3 < 5
The inequality expression given as -x/3 < 5 has a solution of x > -15
How to solve the inequality?From the question, the inequality is given as
-x/3 < 5
The above inequality can be re-written as follows
-x/3 < 5
There is no constant to add or subtract in the expression
So, we start by multiplying both sides of the expression by a constant
Multiply both sides by 3
expression
-x < 15
Divide both sides by -1
So, we have the following representation
x > -15
Hence, the solution to the expression is x > -15
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if f(x) = 2x - 4 find f(k+1)
Answer: [tex]f(k+1)=2k-2[/tex]
Step-by-step explanation:
Substituting [tex]k+1[/tex] for [tex]x[/tex],
[tex]f(k+1)=2(k+1)-4\\\\f(k+1)=2k+2-4\\\\f(k+1)=2k-2[/tex]
a researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.
Define prospective study.Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.
Given,
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
Prospective study
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Find an equation for the perpendicular bisector of the line segment whose endpoints are (4,−1) and (8,7).
Answer: [tex]y=-\frac{1}{2}x+6[/tex]
Step-by-step explanation:
The slope of the line segment is [tex]\frac{-1-7}{4-8}=2[/tex].
So, the slope of the perpendicular bisector is -1/2.The midpoint of the line segment is [tex]\left(\frac{4+8}{2}, \frac{-1+7}{2} \right)=(6, 3)[/tex].
Thus, the equation is:
[tex]y-3=-\frac{1}{2}(x-6)\\\\y-3=-\frac{1}{2}x+3\\\\y=-\frac{1}{2}x+6[/tex]
a bank auditor claims that credit card balances are normally distributed, with a mean of $2870 and a standard deviation of $900. a) what is the probability that a randomly selected credit card holder has a credit card balance less than $2500? b) you randomly select 25 credit card holders. what is the probability that their mean credit card balance is less than $2500? c) compare the probabilities from a) and b).
(a) -0.255 is the probability that a randomly selected credit card holder has a credit card balance less than $2500. (b) You randomly select 25 credit card holders. 0.0228 is the probability that their mean credit card balance is less than $2500.
Let us pull out the critical elements
Population: Normally distributed with mean of 2870
population standard deviation = 900 standard deviation of the sample mean (standard error) is 900 / √25. or 180
As population sigma is known, we do not have apply any corrections
P(xbar < $2500) = ?
Since μ and σ are known (population mean and standard deviation) we can use a simple Z test.
Ztest = (2500-2870 )/ 180 or -370/180 = -2.055
As this is very close to -2 one can use the rule of thumb for probability within ± 2 sigma being 95.44% to get a close estimate. If the area between -2 and 2 sigma = .9544 then the area outside = .0456. Half of this (the amount under the curve LESS THAN -2) would be .0228
Using a calculator or computer for an exact answer we find (using a TI-83/86):
nmcdf(-9E6,2500,2870,180) = .0199
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You are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first? Explain
Answer:
Find the slope between the points (1,2) and (9,12).
Step-by-step explanation:
If I was going to draw the line of best fit without a calculator, I would draw it including these two points. Once I had these two points, I would find the slope using these points.
ben sat outside his school in cambridge and made a note of the colour of the first 100 cars that passed .
27 of them were red.
in britain there were around 35 million cars on the road.
use bens findings to give pout an estimate of how many cars on the road are red
The estimate for the number of cars that are red will be 9450000.
What is the estimate of the number of cars?From the information, when Ben sat outside his school in Cambridge and made a note of the colour of the first 100 cars that passed, he found out that 27 of them were red.
Based on the above, the ratio of red cars to total cars is 27:100.
Therefore, if thee are 35 million cars, the red cars will be:
= Ratio of red cars × Total cars
= 27/100 × 3500000
= 9450000
The number of red cards is 9450000.
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a pizzeria makes pizzas that are shaped as perfect circles, and measures pizza size by the diameter of a pizza. by surface area, approximately what percent larger is a 16-inch pizza than a 12-inch pizza?
Using the concept of percentage we get 16-inch pizza is 43.75% larger than a 12-inch pizza.
What is the percentage?Percentage means out of hundred. A number that is expressed as a fraction of a hundred is called a percentage. Percentage change = Change in the value / Initial value.
Area of circle = π R²,
Where R is the radius of circle.
Given that size of a pizza is measured by its diameter and surface area.
Diameter of the first pizza = 16 inch
So its radius = 8 inch
Hence area = π×8²
= 64π
And the diameter of the other pizza = 12 inch
So, its radius = 6 inch
Hence its area = π×6²
= 36π
Now the difference in areas of Both the pizza = 64π - 36π
= 28π
Now percentage difference in areas of both pizzas = 28π×100)/64π%
= 2800/64
=43.75%
Hence, 16-inch pizza is 43.75% larger than a 12-inch pizza.
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