9514 1404 393
Answer:
25
Step-by-step explanation:
To make this expression into a perfect square trinomial, we must add the square of half the coefficient of the linear term.
v^2 -10v +(-10/2)^2 = v^2 -10v +25
The missing constant is 25.
a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?
Answer:
No
Step-by-step explanation:
If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.
[tex]6^{2}+8^{2}=c^2[/tex]
If the triangle is a right triangle, c would equal 11
Solve.
[tex]36+64=100[/tex]
Then find the square root of 100.
The square root of 100 is 10, not 11.
So this is not a right triangle.
I hope this helps!
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2 gallons and the mean is 16 gallons per day. If they are using a 95% level of confidence, how large of a sample is required to estimate the mean usage of water
Answer:
A sample of 784 is required to estimate the mean usage of water.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
The standard deviation is 2 gallons
This means that [tex]\sigma = 2[/tex]
They would like the estimate to have a maximum error of 0.14 gallons. How large of a sample is required to estimate the mean usage of water?
This is n for which M = 0.14. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.14 = 1.96\frac{2}{\sqrt{n}}[/tex]
[tex]0.14\sqrt{n} = 1.96*2[/tex]
[tex]\sqrt{n} = \frac{1.96*2}{0.14}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*2}{0.14})^2[/tex]
[tex]n = 784[/tex]
A sample of 784 is required to estimate the mean usage of water.
The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.
Answer:
b. The actual count of bike riders is too small.
d. n*p is not greater than 10.
Step-by-step explanation:
Confidence interval for a proportion:
To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]
Of the 123 students surveyed 5 ride a bike to campus.
Less than 10 successes, that is:
The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.
Graph the inequality.
7 <= y - 2x < 12
Answer:
X(-12,-7)
Step-by-step explanation:
This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.
Below are the heights (in inches) of students in a third-grade class. Find the median height. 39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Given:
The heights (in inches) of students in a third-grade class are:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
To find:
The median height.
Solution:
The given data set is:
39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48
Arrange the data set in ascending order.
37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53
Here, the number of observations is 16. So, the median of the given data set is:
[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]
[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]
[tex]Median=\dfrac{47+48}{2}[/tex]
[tex]Median=\dfrac{95}{2}[/tex]
[tex]Median=47.5[/tex]
Therefore, the median height of the students is 47.5 inches.
Suppose point (4, −9) is translated according to the rule (, ) → ( + 3, − 2). What are the coordinates of ′? Explain
Which side of the polygon is exactly 6 units long?
Answer:
AB is correct as It is the shorter parallel line
as the line measures 6 units.
Step-by-step explanation:
The polygon is a trapezoid / (trapezium Eng/Europe)
We see the given coordinates (2, 6) - (-4, 6) = x-6 y 0 = x = 6units
as x always is shown as x - 6 as x= 6
We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6
y = 0 x = 6 = 6 units as its horizontal line.
when y is 6-6 = 0 then we know the line is horizontal for y = 0.
The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.
When looking at diagonal lines we still group the x's and y's and make the fraction whole.
When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.
2/3y = 1/4 what does y equal?
Answer:
Step-by-step explanation:
2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3
The 8th term in the arithmetic sequence is 17, the 12th term is 25. Find the first term, and the sum of the first 20 terms.
Answer:
First term a = 3
Sum of first 20 term = 440
Step-by-step explanation:
Given:
8th term of AP = 17
12th term of AP = 25
Find:
First term a
Sum of first 20 term
Computation:
8th term of AP = 17
a + 7d = 17 ....... EQ1
12th term of AP = 25
a + 11d = 25 ...... EQ2
From EQ1 and EQ2
4d = 8
d = 2
a + 7d = 17
a + 7(2) = 17
First term a = 3
Sum of first 20 term
Sn = [n/2][2a + (n-1)d]
S20 = [20/2][(2)(3) + (20-1)2]
S20 = [10][(6) + 38]
S20 = [10][44]
S20 = 440
Sum of first 20 term = 440
6. Find average of the following
expressions (4-2x), (-7-3x), and
(11x+6)
Answer:
2x + 1.
Step-by-step explanation:
Average = sum of the expression / number of expressions
= [(4 - 2x) + (-7 - 3x) + (11x + 6)] / 3
= (-2x - 3x + 11x + 4 - 7 + 6) / 3
= 6x + 3 / 3
= 2x + 1
Answer:
2x+1
Step-by-step explanation:
(4-2x), (-7-3x),(11x+6)
Add the three expressions
(4-2x)+ (-7-3x)+(11x+6)
Combine like terms
-2x-3x+11x+4-7+6
6x+3
Divide by the number of expressions which was 3
(6x+3)/3
2x+1
The average is 2x+1
What is the value of x?
Enter your answer in the box.
units
Answer:
25
Step-by-step explanation:
40/24 = x/15
x = 15•40/24
x = 25
Answer:
25
Step-by-step explanation:
just use the facts that both triangles are similar
Suppose a sample of 1453 new car buyers is drawn. Of those sampled, 363 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places
Answer:
"0.250" is the appropriate answer.
Step-by-step explanation:
Given:
New car sample,
= 1453
Preferred foreign,
= 363
Now,
The amount of new automobile purchasers preferring foreign cars will be approximated as:
= [tex]\frac{363}{1453}[/tex]
= [tex]0.250[/tex]
the point (-2,5) is reflected across the y-axis. which of these is the ordered pair of the image
Answer:(2,5)
Step-by-step explanation: watch this video
https://youtu.be/l78P2Xi68-k
Write the standard form of the equation of the circle with center (−7,10) that passes through the point (−7,7)
Answer:
(x+7)^2+(y-10)^2=9
Step-by-step explanation:
The distance between the two points is sqrt((-7+7)^2+(10-7)^2)=3 which is in turn the radius of the circle
If $6^x = 5,$ find $6^{3x+2}$.
If 6ˣ = 5, then
(6ˣ)³ = 6³ˣ = 5³ = 125,
and
6³ˣ⁺² = 6³ˣ × 6² = 125 × 6² = 125 × 36 = 4500
40% of what number is 16.6?
What is the measure of F?
G
65
10
H H
10
A. Cannot be determined
B. 55
C. 75
D65
Answer:
D. 65°
Step-by-step explanation:
It is so because the triangle is isosceles, two identical sides and two equal angles.
A sprinter travels a distance of 200 m in a time of 20.03 seconds.
What is the sprinter's average speed rounded to 4 sf?
Given:
Distance traveled by sprinter = 200 m
Time taken by sprinter = 20.03 seconds
To find:
The sprinter's average speed rounded to 4 sf.
Solution:
We know that,
[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]
It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.
[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]
[tex]\text{Average speed}=9.985022466[/tex]
[tex]\text{Average speed}\approx 9.985[/tex]
Therefore, the average speed of the sprinter is 9.985 m/sec.
Answer:
9.985
Step-by-step explanation:
Describe the transformation of f(x) to g(x). Pleaseee helllp thank youuuu!!!
The transformation set of [tex]y[/tex] values for function [tex]f[/tex] is [tex][-1,1][/tex] this is an interval to which sine function maps.
You can observe that the interval to which [tex]g[/tex] function maps equals to [tex][-2,0][/tex].
So let us take a look at the possible options.
Option A states that shifting [tex]f[/tex] up by [tex]\pi/2[/tex] would result in [tex]g[/tex] having an interval [tex][-1,1]+\frac{\pi}{2}\approx[0.57,2.57][/tex] which is clearly not true that means A is false.
Let's try option B. Shifting [tex]f[/tex] down by [tex]1[/tex] to get [tex]g[/tex] would mean that has a transformation interval of [tex][-1,1]-1=[-2,0][/tex]. This seems to fit our observation and it is correct.
So the answer would be B. If we shift [tex]f[/tex] down by one we get [tex]g[/tex], which means that [tex]f(x)=\sin(x)[/tex] and [tex]g(x)=f(x)-1=\sin(x)-1[/tex].
Hope this helps :)
If two marbles are selected in succession with replacement, find the probability that both marble is blue.
Answer:
1 / 9
Step-by-step explanation:
Choosing with replacement means that the first draw from the lot is replaced before another is picked '.
Number of Blue marbles = 2
Number of red marbles = 4
Total number of marbles = (2 + 4) = 6
Probability = required outcome / Total possible outcomes
1st draw :
Probability of picking blue = 2 / 6 = 1 /3
2nd draw :
Probability of picking blue = 2 / 6 = 1/3
P(1st draw) * P(2nd draw)
1/3 * 1/3 = 1/9
What is the complete factorization of the polynomial below?
x3 + 8x2 + 17x + 10
A. (x + 1)(x + 2)(x + 5)
B. (x + 1)(x-2)(x-5)
C. (x-1)(x+2)(x-5)
O D. (x-1)(x-2)(x + 5)
Answer: A (x+1)(x+2)(x+5)
Step-by-step explanation:
Pleaseee Help. What is the value of x in this simplified expression?
(-1) =
(-j)*
1
X
What is the value of y in this simplified expression?
1 1
ky
y =
-10
K+m
+
.10
m т
9514 1404 393
Answer:
x = 7
y = 5
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
__
For a=-j and b=7,
(-j)^-7 = 1/(-j)^7 ⇒ x = 7
For a=k and b=-5,
k^-5 = 1/k^5 ⇒ y = 5
(4-1) + (6 + 5) = help plz
The polynomial equation x cubed + x squared = negative 9 x minus 9 has complex roots plus-or-minus 3 i. What is the other root? Use a graphing calculator and a system of equations. –9 –1 0 1
9514 1404 393
Answer:
(b) -1
Step-by-step explanation:
The graph shows the difference between the two expressions is zero at x=-1.
__
Additional comment
For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.
Answer:
The answer is b: -1
Step-by-step explanation:
good luck!
As one once said Another one
Answer:
f
Step-by-step explanation:
Answer:
S = 62.9
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan S = opp side / adj side
tan S = sqrt(42)/ sqrt (11)
tan S = sqrt(42/11)
Taking the inverse tan of each side
tan ^ -1( tan S) = tan ^-1(sqrt(42/11))
S=62.89816
Rounding to the nearest tenth
S = 62.9
Prove the following identities : i) tan a + cot a = cosec a sec a
Step-by-step explanation:
[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]
[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]
[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]
Question :
tan alpha + cot Alpha = cosec alpha. sec alphaRequired solution :
Here we would be considering L.H.S. and solving.
Identities as we know that,
[tex] \red{\boxed{\sf{tan \: \alpha \: = \: \dfrac{sin \: \alpha }{cos \: \alpha} }}}[/tex][tex] \red{\boxed{\sf{cot \: \alpha \: = \: \dfrac{cos \: \alpha }{sin \: \alpha} }}}[/tex]By using the identities we gets,
[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]
[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]
Now, here we would be using the identity of square relations.
[tex]\red{\boxed{ \sf{sin {}^{2} \alpha \: + \: cos {}^{2} \alpha \: = \: 1}}}[/tex]By using the identity we gets,
[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]
[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]
[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]
Hence proved..!!According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50 and that a sample of 30 theaters was randomly selected. What is the probability that the sample mean will be between $7.75 and $8.20
Answer:
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.
This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]
Sample of 30:
This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]
What is the probability that the sample mean will be between $7.75 and $8.20?
This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.
X = 8.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = 2.63[/tex]
[tex]Z = 2.63[/tex] has a p-value of 0.9957
X = 7.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]
[tex]Z = -2.3[/tex]
[tex]Z = -2.3[/tex] has a p-value of 0.0107.
0.9957 - 0.0157 = 0.985
0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.
X+34>55
Solve the inequality and enter your solution as an inequality comparing the variable to a number
Answer:
x > 21
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
x + 34 > 55
Step 2: Solve for x
[Subtraction Property of Equality] Subtract 34 on both sides: x > 21Assuming that the sample mean carapace length is greater than 3.39 inches, what is the probability that the sample mean carapace length is more than 4.03 inches
Answer:
The answer is "".
Step-by-step explanation:
Please find the complete question in the attached file.
We select a sample size n from the confidence interval with the mean [tex]\mu[/tex]and default [tex]\sigma[/tex], then the mean take seriously given as the straight line with a z score given by the confidence interval
[tex]\mu=3.87\\\\\sigma=2.01\\\\n=110\\\\[/tex]
Using formula:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The probability that perhaps the mean shells length of the sample is over 4.03 pounds is
[tex]P(X>4.03)=P(z>\frac{4.03-3.87}{\frac{2.01}{\sqrt{110}}})=P(z>0.8349)[/tex]
Now, we utilize z to get the likelihood, and we use the Excel function for a more exact distribution
[tex]=\textup{NORM.S.DIST(0.8349,TRUE)}\\\\P(z<0.8349)=0.7981[/tex]
the required probability: [tex]P(z>0.8349)=1-P(z<0.8349)=1-0.7981=\boldsymbol{0.2019}[/tex]
A day trading firm closely monitors and evaluates the performance of its traders. For each $10,000 invested, the daily returns of traders at this company can be modeled by a Normal distribution with mean = $830 and standard deviation = $1,781.
(a) What is the probability of obtaining a negative daily return, on any given day? (Use 3 decimals.)
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row? (Use 3 decimals.)
(c) Give the boundaries of the interval containing the middle 80% of daily returns: (use 3 decimals) ( , )
(d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus? (Use 3 decimals.)
Answer:
a) 0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
b) 0.103 = 10.3% probability of having a negative daily return for two days in a row.
c) (-$1449.68, $3109.68)
d) A bonus of $4,488.174 is needed.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with mean = $830 and standard deviation = $1,781.
This means that [tex]\mu = 830, \sigma = 1781[/tex]
(a) What is the probability of obtaining a negative daily return, on any given day?
This is the p-value of Z when X = 0, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0 - 830}{1781}[/tex]
[tex]Z = -0.466[/tex]
[tex]Z = -0.466[/tex] has a p-value 0.321.
0.321 = 32.1% probability of obtaining a negative daily return, on any given day.
(b) Assuming the returns on successive days are independent of each other, what is the probability of having a negative daily return for two days in a row?
Each day, 0.3206 probability, so:
[tex](0.321)^2 = 0.103[/tex]
0.103 = 10.3% probability of having a negative daily return for two days in a row.
(c) Give the boundaries of the interval containing the middle 80% of daily returns
Between the 50 - (80/2) = 10th percentile and the 50 + (80/2) = 90th percentile.
10th percentile:
X when Z has a p-value of 0.1, so X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = -1.28*1781[/tex]
[tex]X = -1449.68[/tex]
90th percentile:
X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 1.28*1781[/tex]
[tex]X = 3109.68[/tex]
So
(-$1449.68, $3109.68)
d) As part of its incentive program, any trader who obtains a daily return in the top 2% of historical returns receives a special bonus. What daily return is needed to get this bonus?
The 100 - 2 = 98th percentile, which is X when Z has a p-value of 0.98, so X when Z = 2.054.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.054 = \frac{X - 830}{1781}[/tex]
[tex]X - 830 = 2.054*1781[/tex]
[tex]X = 4488.174 [/tex]
A bonus of $4,488.174 is needed.
