Answer:
94.1224489796
this is the answer
What are the solutions to the equation 3k² + k-3=0?
Approximate the value of both solutions. Round each answer to two decimal places. Enter your answers as
a list of numbers, separated with commas. Example: 3.25,4.16
k=
Answer:
Step-by-step explanation:
Solution
Solve with the quadratic formula
3k2+k−3=0 : k=(−1+√376)/6 , k=(−1−√376 )/6 (Decimal: k=0.84712…, k=−1.18046…)- Answer
Steps
3k2+k−3=0
Solve with the quadratic formula
For a quadratic equation of the form ax^2+bx+c=0,
the solutions are x1, 2=(−b±√b^2−4ac)/2a where a=3, b=1, c=−3
Substituting we have
k1, 2= [(−1±√1^2−4· 3(−3)]/2· 3
Apply rule 1^a=1 , therefore 1^2=1
=√1+4· 3· 3=√1+36
√1^2−4· 3(−3)=√37
Therefore,
k1, 2=(−1±√37)/2· 3
k1, 2=(−1±√37)/6
Separate the solutions
k1=(−1+√37)/6
k2=(−1−√37)/6
The solutions to the quadratic equation are:
k=(−1+√37)/6 , k=(−1−√37)/6
k1=0.84712 k2=−1.18046
Write an equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5)
An equation of the parabola is y =
Equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
Given points:
(-4, 7), (-3, 9), and (4,-5).
Let parabola equation be y = a[tex]x^{2} +bx+c[/tex].
substitute (-4,7)
7 = a(16)+b(-4)+c
16a-4b+c-7 = 0.
substitute (-3,9)
9 = a(9)+b(-3)+c
9a-3b+c-9 = 0
substitute (4,-5)
-5 = 16a+4b+c
16a+4b+c+5=0.
solving three equations we get,
a = -1/2 , b = -3/2 and c = 9
substitute a,b and c values we get,
y = (-1/2)[tex]x^{2}[/tex] + (-3/2)x + 9
y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
Therefore the equation of the parabola that passes through the points (-4, 7), (-3, 9), and (4,-5) is y = -1/2[tex]x^{2}[/tex] - 3/2 x + 9.
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Type the area of the rectangle into the box.
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
A = 15 x 2 = 30
1. A factory is testing a new machine on its production line that is intended to improve efficiency. Management randomly
selects 12 employees and measures the number of products they complete in one hour when using the new machine. Below
are the results.
Employee 1 2 3 4 5 6 7 8 9 10 11 12
# units 72 68 74 78 75 79 71 69 82 71 73 80
(a) Estimate at the 95% confidence level the average number of units an employee can produce in one hour using the
new machine.
(b) The manufacturer of the machine claims the typical efficiency for a factory worker should be 78 units per hour. What
does the interval suggest about the manufacturer’s claim
(c) An investigation at a similar factory estimates the standard deviation to be 3.91 units. Using this information, what
size sample should we select to estimate the mean number of units produced each hour to within 1.04 units at the
95% confidence level?
a) The confidence interval is given as follows: (71.43, 77.17).
b) The manufacturer's claim is not correct, as 78 is not a part of the interval.
c) A sample of 55 employees is needed to achieve the desired margin of error.
What is a t-distribution confidence interval?The bounds of the t-distribution confidence interval, used when only the standard deviation for the sample is known, are given by the equation presented as follows:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, considering the 95% confidence level and 12 - 1 = 11 df, is of:
t = 2.201.
The remaining parameters, namely sample mean, sample standard deviation and sample size are given as follows:
[tex]\overline{x} = 74.3, s = 4.52, n = 12[/tex]
(obtained using a calculator from the sample given in this problem).
The bounds of the interval are given as follows:
Lower bound: 74.3 - 2.201 x 4.52/sqrt(12) = 71.43.Upper bound: 74.3 + 2.201 x 4.52/sqrt(12) = 77.17.The interval does not contain the number 78, hence it is not a good estimate for the mean amount.
For item c, the z-distribution is used, as the population standard deviation is used, hence the minimum sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1.04 = 1.96\frac{3.91}{\sqrt{n}}[/tex]
[tex]1.04\sqrt{n} = 1.96 \times 3.91[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 3.91}{1.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 3.91}{1.04}\right)^2[/tex]
n = 55. (rounded up, as a sample size of 54 would mean that the margin of error would be slightly above 1.04).
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On December 12, Lowell Corporation accepted a $160,000, 120-day, non-interest-bearing note from Able.com. What is the maturity value of the note?
If On December 12, Lowell Corporation accepted a $160,000, 120-day, non-interest-bearing note from Able.com. the maturity value of the note is: $213,333.
How to find the maturity value of the note?Using this formula to find the maturity value of the note
Maturity value of the note = Principal + interest
Let plug in the formula
Maturity value of the note = $160,000 + ($160,000 × 120 /360)
Maturity value of the note = $160,000 + $53,333
Maturity value of the note = $213,333
Therefore the maturity value of the note is $213,333.
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help please need this rn
The equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.
Given function:
g(x) = 6/x-1
vertical asymptote for any function is denominator is equal to zero.
x - 1 = 0
x = 1.
Therefore the equation of the vertical asymptote for the graph of the rational number g(x) = 6/x-1 is x - 1 = 0 or x = 1.
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A CFL football player has an annual salary of $305 000. The player donates 1/8 of his salary to charity . What amount is this ?
Answer: $38,125
Step-by-step explanation:
1/8*305000
Write each number as a product using gcf as a factor sipping distributive property the numbers are 28 49 77 and 3 gcf
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
Define GCF.The biggest number that both numbers can be divided by to get the two numbers' largest common factor. The smallest number that is a multiple of both numbers is the least common multiple of the two numbers. The largest number that may divide evenly into two or more other numbers is known as the greatest common factor (GCF). This is also sometimes referred to as the highest common factor (HCF) or the greatest common divisor (GCD).
Given,
Factor sipping distributive property,
For the numbers 28 and 49
GCF:
28 + 49
7(4) + 7(7)
7(4+7)
7(11)
77
Using as a product using gcf as a factor sipping distributive property For the numbers 28 and 49, GCF is 77.
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Please help me with these thank you
The value of (2/3) ÷ (1/4) is 8/3 and the value of 7 ÷ (2/3) is 21/2.
This is a question from the division of fractions.
We know the property of fractions is given by:-
(m/n) ÷ (a/b) = (m/n)*(b/a) = mb/na
Hence, we can write,
(2/3) ÷ (1/4) = (2/3) * (4/1) = 2*4/3*1 = 8/3
7 ÷ (2/3) = (7/1)*(3/2) = 7*3/ 1*2 = 21/2
Fractions
A fraction represents a part of a whole or, more generally, any number of equal parts. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.
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which is the correct answer ????
The correct way to replace equation 1 into equation 2 using the substitution method is 2x+(-5x+10) = 7.
According to the question,
We have the following two equations:
Equation 1: y = -5x+10
Equation 2: 2x+y = 7
Now, we will substitute the value of y from equation 1 in equation 2.
So, we have the following expression:
2x+(-5x+10) = 7
(More to know: we can also solve this equation to find the value of x and then the obtained value of x can be put in equation 1 to find the value of y.)
Hence, the correct option is B.
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y varies inversely with the square x. If y =
-4 when x =
-2, find y when x= 7.
The value of y is - 0.326 when x = 7.
What are ratio and proportion?A ratio is a divisional comparison of two quantities, and a proportion is the equality of two ratios. A ratio is typically expressed as x: y or x/y, although it may alternatively be read as x is to y.
Comparatively speaking, a proportional equation states that two ratios are comparable. A ratio is expressed as x: y: : z: w and is understood to mean that x is to y as z is to w. Here, w and y are not equal to 0, therefore x/y Equals z/w.
A connection between two quantities is said to be in inverse proportion if one quantity rises while the other falls, and vice versa. As a result, an inverse ratio is expressed as y ∝ 1/x.
The general equation of proportion is given by
y = k/x²
-4 = k/(-2)²
k = -4(4)=-16
y = -16/x²
When x=7, then
y= -16/49
y= - 0.326
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In how many ways can a committee of 5 men and 6 women be formed from a group of 8 men and 7 women?
By taking the product between the combinations of possible groups fo men and women we will see that the number of different committees is:
392
In how many ways can the committee be formed?For a set of N elements, the number of different sets of K elements that can be formed is:
C(N, K) = N!/(K!*(N - K)!)
Here we have 8 men and 7 women, and we want to make a committee of 5 men and 6 women
Then the total number of different committees is given by the product between the different sets of 5 men and the different sets of 6 women, these are:
for men:
C(8, 5) = 8!/( 5!*(8 - 5)!) = (8*7*6)/(3*2*1) = 56
for women:
C(7, 6) = 7!/(6!*(7 - 6)!) = 7
Then the total number of different committees is:
C = 56*7 = 392
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Ms. Jones is comparing two sets of scores. For Test A, the standard deviation is 7, and for Test B, the standard deviation is 12. This means that
The comparison done by Mr Jones means that Test A of standard deviation 7 is closer to the mean scores and Test B of standard deviation 12 is further apart from the mean score
What is standard deviation?The standard deviation is a statistic measure that expresses how much variance or dispersion there is in a group of numbers.
A high standard deviation suggests that the values are dispersed throughout a wider range,
A low standard deviation suggests that the values tend to be close to the established mean.
A positive value means the standard deviation is above the mean while a negative value means the standard deviation is below the mean
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Solve.
log3 (2x + 5) = 3
Enter your answer in the box.
X = ?
Answer:
x = 11
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]
given
[tex]log_{3}[/tex] (2x + 5) = 3 , then
2x + 5 = 3³ = 27 ( subtract 5 from both sides )
2x = 22 ( divide both sides by 2 )
x = 11
There are 17 counters in a bag. The table shows the number of counters of each colour. Colour Number of Counters Red 7 What fraction of the counters are blue? Blue 2 Yellow 5 Green 3
Answer: 2/17 or 2 over 17
Step-by-step explanation:
A statistician calculates that 8% of Americans own a Rolls Royce.
If the statistician is right, what is the probability that the proportion of Rolls Royce owners in a sample of 694 Americans would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of Rolls Royce owners in a sample of 694 Americans would differ from the population proportion by less than 3% is; 0.36%
How to use the central limit theorem?
The Central Limit Theorem states that, for a normally distributed random variable X, with mean μ and standard deviation σ, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean μ and standard deviation s = σ/√n
The standard deviation for proportion is given by the formula;
s = √(p(1 - p)/n)
We are given;
p = 8% = 0.08
n = 694
Thus;
s = √(0.08(1 - 0.08)/694)
s = 0.0103
Proportion above 8% + 3% = 11% or below 8% - 3% = 5%. Due to the fact that the normal distribution is symmetric, the probabilities will be equal, and as a result, we find one of them and multiply by 2.
Probability the proportion is less than 5%:
P-value of Z when X = 0.05.
z = (X - μ)/s
z = (0.05 - 0.08)/0.0103
z = -2.91
From p-value from z-score calculator, we have;
p-value = 0.001807
We multiply it by 2 to get the probability
Probability = 2 * 0.001807 = 0.0036 = 0.36%
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the population of white-tailed deer is growing rapidly in the united states. in 1905 the population was approximately 5x10^5 and in 2000 the population was approximately 2x10^7 how many times larger was the population of white tailed deer in 2000 than it was in 1905
Answer:
40
Step-by-step explanation:
2 x 10⁷/5 x 10⁵ = 2/5 x 10^5-7 = 2/5 x 10² = 2 x 100/5
There were 40 times more white-tailed deer in 2000 than in 1905
The equation m = 4b represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
Determine the constant of proportionality.
one fourth
1
4
8
For given equation, the constant of proportionality is 4
In this question, we have been given an equation m = 4b that represents the time in minutes (m) it takes a chef to cook a certain number of bacon cheeseburgers (b).
We need to determine the constant of proportionality.
We know that the the constant of proportionality is nothing but the ratio of two proportional values.
In this case the time a chef needs to cook depend on the number of bacon cheeseburgers (b).
So, m is directly proportional to the b
Therefore, the constant of proportionality is 4
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Answer:
The answer is 4
Step-by-step explanation:
I hope this helps!!
If you buy stock for $36.20 per share and sell that stock for $37.90 per share, what was your
return on investment?
Answer:
$1.70 per share
Step-by-step explanation:
37.90-36.20=1.70
Claire has sold 8 candy bars and sells 5 more each day. Ayden has sold 20 candy bars and sells 3 more each day. How many days (d) will it be before Claire sells as many candy bars (c) as Ayden.
It will take 7 days for Claire to sell as many candy bars as Ayden
Claire has sold 8 candy bars and sells 5 more each day
The first term = 8
Common difference = 5
nth term is = a+(n-1)d
= 8 +(n-1)5
= 8 + 5n - 5
= 3 +5n
Ayden has sold 20 candy bars and sells 3 more each day
The first term = 20
Common difference = 3
nth term = a+(n-1) d
= 20 +(n-1)3
= 20 + 3n -3
= 17 + 3n
Then,
3 + 5n = 17 + 3n
5n - 3n = 17 - 3
2n = 14
n = 14/2
n = 7
Hence, it will take 7 days for Claire to sell as many candy bars as Ayden
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Use the z-distribution table on pages A-1 and A-2 or technology to solve. Suppose a set of data is normally distributed. Below which z-score do approximately 34 of the data lie?
The z-score under which 3/4 of the data lies is of:
Z = 0.675.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The z-score under which 75% of the distribution lies is the 75th percentile, hence it is the value of Z with a p-value of 0.75.
Looking at the z-table, this value is of 0.675, as 0.675 is the mean of the p-values of Z = 0.67 and Z = 0.68.
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Factor the given number 102 Input the number's prime factors in ascending order.
What is the solution to the system graphed below? PLS ANSWER ASAP
The system of equations has its solutions to be (0, 3)
How to determine the solution to the system of equations?From the question, the system of equations is represented on the graph
On the graph, we have the following representations
Two lines of different colorsBoth lines intersect at a pointSay the functions are f(x) and g(x)
To determine the solution to the system of equations, we set both equations equal
i.e. f(x) = g(x)
This in other words mean that we determine the coordinates of the points where the graphs intersect
In this case, they intersect at point (0, 3)
This represents the solution
Hence, the solution to the system of equations is (0, 3)
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Solve: √x-4= -2
a) x=2
b) x=8
c) There is no solution.
d) x=0
Answer: There is no solution
Step-by-step explanation:
The formatting of the question isn't clear, but I'll still explore both possibilities. If the square root is only applied to x, we can solve for the variable by adding 4 to both sides and then squaring both sides, which would give us 4. Since that is not an answer choice, it means the square root applies to x-4. With this problem, we square both sides right away. That gives us x=0, but plug 0 back into the original equation. Doing so gives us the square root of -4, which is not possible with real numbers, only with imaginary numbers.
7 The profit function, p(x), for a company is the
cost function, c(x), subtracted from the revenue
function, (x). The profit function for the
Acme Corporation is p(x) = -0.5x² + 250x - 300
and the revenue function is r(x) = -0.3x² + 150x.
The cost function for the Acme Corporation is
1) c(x) = 0.2x² - 100x + 300
2) c(x) = 0.2x² + 100x + 300
3) c(x) = -0.2x² + 100x - 300
4) c(x) = -0.8x² + 400x - 300
The cost function for the Acme Corporation is -0.2x² + 100x - 300. a cost function, transfers an event or the values of one or more variables onto a real number that signifies the event's "cost" in real terms.
How to find cost function ?A loss function, also known as a cost function, is a function used in mathematical optimization and decision theory that transfers an event or the values of one or more variables onto a real number that intuitively represents some "cost" connected to the occurrence. A loss function is the goal of an optimization problem.
The event in question is some function of the difference between the estimated and true values for a particular instance of data, and in statistics, parameter estimation is typically done using a loss function.
Given that the profit function is
p(x) = 0.5x^2 + 250x+300
also given that the revenue is given as
r(x) = 0.3x^2 + 150x
we know that profit= revenue - cost
hence cost = revenue-profit
cost = r(x) -p(x)
cost= 0.3x^2 + 150x-(0.5x^2 + 250x+300)
cost= 0.3x^2 + 150x-0.5x^2 - 250x-300
collect like terms
cost=0.3x^2-0.5^2+150x-250x-300
The cost function for the Acme Corporation = -0.2x^2-100x-300
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(b)
The table below shows the cost price, selling price and profit or loss as a percentage of the cost
price.
Complete the table below, inserting the missing values at (i) and (ii).
(i)
(ii)
Cost Price
$55.00
(c) The table shows some rates of exchange :
Calculate the value of
(i) EC $ 1 in TT $......
(ii) US $80 in EC $ .
(iii) TT $648 in US $. .....
Selling Price
$44.00
$100.00
US $1.00 = EC $2.70
TT $1.00 = EC $ 0.40
Percentage
Profit or Loss
25% profit
(4 marks)
. (1 mark)
. (1 mark)
...... (3 marks)
Total 12 marks
Answer:
US$1.00=EC$2.70 TT$1.00=EC$0.40 calculate the value of : 1.EC$1in TT$ 2.US$80inEC$ 3.TT$648 in US$
Step-by-step explanation:
that what i've got is that I hope that helps you
The ratio of 7th grade students to 8th grade students in a soccer league is 7:13, if there are 100 students in all ,how many are in 7th grade ?
Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.
=====================================================
Explanation:
The equation y = 3x-1 is in slope-intercept form y = mx+b
m = 3 = slopeb = -1 = y interceptParallel lines have equal slopes, but different y intercepts.
The answer will also have a slope of m = 3.
Plug that slope value, and the coordinates of the given point [tex](x_1,y_1) = (1,5)[/tex] , into the point-slope formula below.
Solve for y.
[tex]y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\[/tex]
That's how we arrive at the answer of y = 3x+2
As a check, plugging x = 1 into that answer should get us y = 5.
It confirms that the point (1,5) is on this line.
What is the image of (0, -4) after a dilation by scale factor of 2 centered at the
origin?
The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)
What is the scale factor?
A scale factor is Scaling the shape of an object. it means the shape of the object remains the same but the size of the object is either increased or decreased. A scale factor greater than 1 means size is increased and less than one means size is decreased
We are given a point (0,-4)
Which is to be scaled by the factor of 2 at the center position
As the value is greater than 1 the size increase
We multiply the coordinate to find the new coordinates
We get (0,-8)
Hence, The image of of (0,-4) After the dilation by the scale factor of 2 at the center is (0,-8)
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Craig mows two lawns. The first lawn is 40 meters long and 20 meters wide. The second lawn has the same length, and a width that is 4 times as much as the first one. What is the total area of the two lawns??
The area of two lawns will be 4000 square meters.
According to the question,
We have the following information:
Craig mows two lawns. The first lawn is 40 meters long and 20 meters wide. The second lawn has the same length, and a width that is 4 times as much as the first one.
So, the width of the second lawn = 4*20
Width of second lawn = 80 m
Now, formula to find area of rectangle:
Length*width
Area of first lawn:
40*20
800 square meters
Area of second lawn:
40*80
3200 square meters
Now, the area of two lawns = area of first lawn+ area of second lawn
Area = 800+3200
Area = 4000 square meters
Hence, the total area of two lawns is 4000 square meters.
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