Answer:
a) 0.32 = 32% probability that your bid will be accepted
b) 0.72 = 72% probability that your bid will be accepted
c) An amount in excess of $15,400.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
This means that [tex]a = 10400, b = 15400[/tex]
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
You will win if the competitor bids less than 12000. So
[tex]P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32[/tex]
0.32 = 32% probability that your bid will be accepted
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
You will win if the competitor bids less than 14000. So
[tex]P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72[/tex]
0.72 = 72% probability that your bid will be accepted
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
His bid is uniformly distributed between $10,400 and $15,400.
So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.
A 2-pack of scented candles costs $0.95. What is the unit price, rounded to the nearest cent?i mark the 1st answer brainliest
Step-by-step explanation:
Cost of 2 pack = 0.95
Cost of 1 pack = 0.95 ÷ 2 = 0.475
Unit price = 0.475
Directions and Analysis
Task 1: Completing the Square
Look at the quadratic equation below.
2x^2-12x-16=0
This is not an equation that could be easily solved by factoring. Instead, you are going to use the method of completing the square to solve this equation. Follow each step in this task to complete the square and solve the equation.
a. To complete the square, the coefficient of the x2 term must be 1. Divide both sides of the equation by a value and rewrite the equation to meet this criteria.
Type your response here:
b. Rewrite the resulting equation so the constant term is on the right side of the equation and the variable terms are on the left.
Type your response here:
c. Identify the coefficient of the x term in the previous equation. Then divide it by half and square the result. What is the result?
Type your response here:
d. Add the value you identified in part c to both sides of the equation from part b and simplify the right side. Remember that when solving equations, whatever is done to one side of the equation must also be done to the other side the equation: that is why you must add the value to both sides.
Type your response here:
e. Notice that the left side of the equation now represents a perfect square quadratic expression. Use this fact to rewrite the left side of the previous equation as the square of a linear term and create a new equation.
Type your response here:
f. You have now completed the square. Starting with the result from part e, solve the equation for x. Show your work.
Type your response here:
g. Now that you know how to complete the square to solve a quadratic equation, solve the equation 3x^2 – 3x − 6 = 0. Show your work.
Type your response here:
Answer:
a. [tex]x^2-6x-8=0[/tex]
b. [tex]x^2-6x=8[/tex]
c.
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d. [tex]x^2-6x+9=17[/tex]
e. [tex](x-3)^2=17[/tex]
f, g. [tex]x=3\pm \sqrt{17}[/tex]
Step-by-step explanation:
Given: [tex]2x^2-12x-16=0[/tex]
To solve: the given equation
Solution:
a.
[tex]2x^2-12x-16=0[/tex]
Coefficient of [tex]x^2=2[/tex]
Divide both sides by 2
[tex]x^2-6x-8=0[/tex]
b.
[tex]x^2-6x=8[/tex]
c.
Coefficient of x = -6
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d.
Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]
[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]
e.
[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]
f.
[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]
g.
[tex]x=3\pm \sqrt{17}[/tex]
If the size of the sample to be used in a particular test of attributes has not been determined by utilizing statistical concepts, but the sample has been chosen in accordance with random selection procedures
A) No inferences can be drawn from the sample.
B) The auditor has committed a nonsampling error.
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
D) The auditor will have to evaluate the results by reference to the principles of discovery sampling.
E) The auditor may or may not achieve the desired
Answer:
C) The auditor may or may not achieve the desired risk of assessing control risk too low.
Step-by-step explanation:
In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.
This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean
Find the constant of variation k for the direct variation 3x+5y=0
Answer:
-3/5
Step-by-step explanation:
3x+5y=0
Subtract 3x from each side
3x+5y-3x=0-3x
5y = -3x
Divide each side by 5
5y/5 = -3x/5
y = -3/5 x
A direct variation is y = kx
y = -3/5 x
The constant of variation is -3/5
Which is equivalent to 8−+3
8
x
-
y
+
3
x
?
Answer:
DIDNT UNDERSTAND THE QUESTION PROPERLY BRO..
KEEP THE QUESTION AGAIN
A goat is tied to a peg in the ground. The rope is 3m long. What area of grass can the goat eat? (use the value 3.14 for pie)
Answer:
28.26 (Please mark as brainiest if you find it helpful )
Step-by-step explanation:Area the goat will eat is equal to the are of circle having radius 3m.
Area of circle = pi * r ^ 2
⇒ 3.14 * (3) ^ 2 → 3.14 * 9
⇒ 28.26
Which data collection method would provide an unbiased sample?
Answer:
The best data collection method or sampling method to provide an unbiased sample is the random sampling method.
Step-by-step explanation:
There are 5 popular known sampling methods or data collection methods.
1) Random Sampling
In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.
2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.
3) Convenience Sampling
This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.
4) Stratified Sampling
Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.
5) Cluster sampling
Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.
Hope this Helps!!!
A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketball Tournament. A random sample of 100 employees was selected. What is the probability that less than 80% of this sample will devote work time to follow games?
Answer:
4.18% probability that less than 80% of this sample will devote work time to follow games
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question, we have that:
[tex]p = 0.86, n = 100[/tex]
So
[tex]\mu = 0.86, s = \sqrt{\frac{0.86*0.14}{100}} = 0.0347[/tex]
What is the probability that less than 80% of this sample will devote work time to follow games?
This is the pvalue of Z when X = 0.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.8 - 0.86}{0.0347}[/tex]
[tex]Z = -1.73[/tex]
[tex]Z = -1.73[/tex] has a pvalue of 0.0418
4.18% probability that less than 80% of this sample will devote work time to follow games
the terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis. Describe how to find the measure of the angle in both degree and radian
Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
What is the terminal side of an angle?The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.
The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.
The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,
[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]
Multiply it with π/180 to find the measure of the angle in radian.
[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]
Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.
Learn more about the terminal side of an angle here
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A square of area 36cm2 is cut to make two rectangles, A and B The ratio of Area A to Area B is 2 : 1 Work out the dimensions of rectangle A and B
(Need help with this question)
Answer:
Given..hope it helps
Step-by-step explanation:
Area of square= 36cm2 = total area
Side of square= √36= 6cm
Ratio a:b = 2:1
so let's take total area as 3x
while a is 2x and b is 1x
3x= 36 (given)
x= 36/3 = 12
so area of each rectangle--
area A= 2x= 24cm2
area B= x= 12cm2
While finding the dimensions, they both have a common length since they are from the same square which will be 6cm (side)
So,
Dimensions of rectangle A= 6cm * 4cm
Dimensions of rectangle B= 6cm * 2cm
A tree that is 10 feet tall is growing at a rate of 2 foot each year. A tree that is 14 feet tall is growing at a rate of 2/3 foot each year. What is the number of years it will take for both trees to be the same height, and what will their height be?
Answer:
after three years
Step-by-step explanation:
3. The difference between two numbers is 5
Answer:
The difference of two numbers is 5 and the difference of their reciprocals is 1/10. find the no.s
Step-by-step explanation:
⇒ x(x-5) = 50
⇒ x2 - 5x - 50 = 0
⇒ x2 - 10x + 5x - 50 = 0
⇒ x (x - 10) + 5 (x - 10) = 0
⇒ (x+5) (x-10) = 0
⇒ (x+5) (x-10) = 0
⇒ x = -5 or 10
⇒ x = 10 (x = -5 , rejected)
There are 1760 yards in one mile about how many miles will a runner have to run
Answer:
3
I used to be an olimpic runner and I ran the 400 all the time and I did cross country
Do You Understand?
D
4.
1. Essential Question How does an equation
show the relationship between variables and
other quantities in a situation?
Answer:
An equation is basically a way to show a relationship of variables (x,y,a,b, etc) and numbers.
Step-by-step explanation:
Answer:
Shown by explanation.
Step-by-step explanation:
An equation shows a relationship between variables and other factors by defining the variables that are dependent and independent and how these dependent variables are related to the independent variables, this is usually as a result of a prescribed experiment where the relationship of this variables are investigated.
Also remember conditions that favour this experiment must be taken into consideration. And the experiment must always be performed under such conditions.
Use the drop-down menus to complete each equation so the statement about its solution is true.
No Solutions
No Solutions
2x+5+2x+3x= _ x +_
One Solution
2x+5+2x+3x=_ x + _
Infinitely Many Solutions
2x+5+2x+3x= _x +_
Answer:
7x+16x+17x+5Step-by-step explanation:
No Solutions
There will be no solutions when the left side is inconsistent with the right side:
2x +5 +2x +3x = 7x +1
7x +5 = 7x +1 . . . . . . no value of x will make this true
__
One Solution
There will be one solution when the left side and right side are not inconsistent and not the same.
2x +5 +2x +3x = 6x +1
7x +5 = 6x +1
x = -4 . . . . . . . . add -6x-5 to both sides
__
Infinitely Many Solutions
There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.
2x +5 +2x +3x = 7x +5
7x +5 = 7x +5 . . . . . true for all values of x
_____
Comment on these solutions
You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions." For "no solutions", the coefficient of x must be 7 and the constant must not be 5. For "one solution" the coefficient of x cannot be 7, and the constant can be anything.
Answer:
No Solutions: 7x+1
One Solution: 6x+1
Infinitely Many Solutions: 7x+5
A spherical gemstone just fits inside a plastic cube with edges 12cm. a) calculate the volume of gemstone, to the nearest cubic centimeter. b) how much empty space is there.
Answer:
a) (V) = 904.78 of a sphere = 288pi diameter = 12
(V) = 1728cm^3 of a cube = face diagonal = 16.9cm
b) Difference Volume = 1728-904.78 = 823.22cm^3
Step-by-step explanation:
To find volume of an inscribed sphere within a square cube
We use 4 π/3 * r^3 for the equation
As Radius = 6 = 6cm this is the only thing plugged into the equation to create a division first then a multiplication square of radius and then a multiplication. 4pi /3 * 6^3
r^3 = 216
4pi/3 = 4.18
4.18 * 216 = 904.78
This means the answer is 288 pi cm^3.
Answer:
volume of gemstone = 905 cm^3
volume of empty space = 823 cm^3
Step-by-step explanation:
volume of cube = s^3, where s = length of edge
volume of sphere = (4/3)(pi)r^3, where r = radius of sphere
The cube has a 12-cm edge. The sphere fits tightly inside the cube, so the diameter, d, of the sphere is 12 cm. The radius is half the diameter, so radius = r = diameter/2 = 12 cm/2 = 6 cm.
a)
volume of sphere = (4/3)(pi)r^3
volume of sphere = (4/3)(3.14159)(6 cm)^3
volume of sphere = 905 cm^3
b)
The empty space is the difference between the volume of the cube and the volume of the sphere.
volume of cube = s^3
volume of cube = (12 cm)^3
volume of cube = 1728 cm^3
empty space = volume of cube - volume of sphere
empty space = 1728 cm^3 - 905 cm^3
empty space = 823 cm^3
For circle O, and m∠ABC = 55°. In the figure, ∠ and ∠ have measures equal to 35°.
Answer:
In the figure ∠ABO and ∠BCO have measures equal to 35°.
Step-by-step explanation:
Measure of arc AD = 180-measure of arc CD= 180-125 =55
m<AOB= 55 ( measure of central angle is equal to intercepted arc)
<OAB= 90 degrees (Tangent makes an angle of 90 degrees with the radius)
In triangle AOB ,
< AB0 = 180-(90+55)= 35 degrees( angle sum property of triangle)
In triange BOC ,< BOC=125 ,
m<, BCO=35 degrees
Answer:
∠ABO and ∠BCO
Step-by-step explanation:
The functions r and s are defined as follows. r(x)=2x-1 s(x)=-2x^2-2 Find the value of s(r(-4)).
Answer:
s(r(-4)) = -164
Step-by-step explanation:
r(x) = 2x - 1
s(x) = -2x^2 - 2
r(-4) = 2(-4) - 1 = -8 - 1 = -9
s(r(-4)) = s(-9) = -2(-9)^2 - 2 = -2*81 - 2 = -162 - 2 = -164
Hope this helps!
What is the value of X ?
Answer:
D
Step-by-step explanation:
2² + 6² = x²
4 + 36 = x²
40 = x²
x = 2√10
A rectangular fish tank is 50 cm long, 40 cm wide, and 20 cm high. a) How many cubic centimeters of water will the tank hold? b) How many milliliters of water will the tank hold? c) How many liters of water will the tank hold?
Answer:
40 litres
Step-by-step explanation:
V = l x w x h
50 x 40 x 20 = 40000
40000 cm^3
1cm^3 = 1ml
40000 cm^3/ 1cm^3 = 40000ml
40000 x 10^-3 = 40 litres
what is the least common denominator of 4 7/9 and 2 2/3
Answer:
9
Equivalent Fractions with the LCD
4 7/9 = 43/9
2 2/3 = 24/9
For the denominators (9, 3) the least common multiple (LCM) is 9.
Therefore, the least common denominator (LCD) is 9.
4 7/9 = 43/9 × 1/1 = 43/9
2 2/3 = 8/3 × 3/3 = 24/9
Hope this helps :)
The least common denominator of 4 7/9 and 2 2/3 is 9.
Given data:
To find the least common denominator (LCD) of 4 7/9 and 2 2/3, we need to first convert both fractions to their equivalent forms with a common denominator.
The given fractions are:
4 7/9 = 4 + 7/9
2 2/3 = 2 + 2/3
To find a common denominator, we need to find the least common multiple (LCM) of the denominators 9 and 3, which is 9.
Now, let's convert the fractions to their equivalent forms with a denominator of 9:
4 7/9 = (4 * 9)/9 + (7/9) = 36/9 + 7/9 = 43/9
2 2/3 = (2 * 9)/9 + (2/3) = 18/9 + 2/3 = 20/9
The fractions 4 7/9 and 2 2/3 are now expressed with a common denominator of 9.
Hence, the least common denominator (LCD) of 4 7/9 and 2 2/3 is 9.
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What is the range of the function in the table
X Y
1 2
2 4
3 3
4 2
A) (1,2,3,4)
B) (1,2) (2,4) (3,3) (4,2)
C) (1,2)
D) (2,3,4)
Answer:
D. (2, 3, 4)
Step-by-step explanation:
The range is the y values. The y values, in numerical order, range from 2 to 4. The 2s do not need to be repeated.
I will give brainiest to the first to answer. The what
of the following set of data is 5.
13, 7, 9, 5, 2, 3, 5, 4, 10, 12
Answer:
it is the mode.
Step-by-step explanation:
i. e 5 is the most occuring number in the set of data listed above
Evaluate x - 2y when x = 5 and y = 5.
Determine whether the ordered pair satisfies the equation.
x - 2y = -5; (5,5)
Yes, the ordered pair satisfies the equation.
No, the ordered pair does not satisfy the equation.
Answer:
For the first question we just plug in the values so we get 5 - 2 * 5 = -5.
Again, for the second one we'll plug in the values and see if it's a true statement. 5 - 2 * 5 = -5 and -5 = -5 so the answer is yes.
Sarah wants to refurbish her shop.
She is quoted £2500 for the refurbishment, with a 20% discount to be taken off.
What is the final cost of the refurbishment after the discount?
Answer:
2000
Step-by-step explanation:
2500 / 100 = 25 (1%)
25 X 20 =500 (20%)
2500 - 500 =2000
The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs £60. What is the cost of a circular table with a radius of 75cm? Show all your working
Answer:
£135 is the correct answer.
Step-by-step explanation:
Let C be the cost of table.
And let R be the radius of table.
Cost of table is directly proportional to square of radius.
As per question statement:
[tex]C\propto R^{2}[/tex] or
[tex]C=a\times R^2 ....... (1)[/tex]
where [tex]a[/tex] is the constant to remove the [tex]\propto sign[/tex].
It is given that
[tex]C_1 =[/tex] £60 and [tex]R_1 = 50\ cm[/tex]
[tex]C_2 = ?[/tex] when [tex]R_2= 75\ cm[/tex]
Putting the values of [tex]C_1[/tex] and [tex]R_1[/tex] in equation (1):
[tex]60=a \times 50^2 ....... (2)[/tex]
Putting the values of [tex]C_2[/tex] and [tex]R_2[/tex] in equation (1):
[tex]C_2=a \times 75^2 ....... (3)[/tex]
Dividing equation (2) by (3):
[tex]\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135[/tex]
So, £135 is the correct answer.
Can someone please help me with this question the first one
A recipe submitted to a magazine by one of its subscribers’ states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed.
54 55 58 59 59 60 61 61 62 65
Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking time is 55 minutes against the alternative hypothesis μ > 55. Use α = .05.
Answer:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.
Step-by-step explanation:
Information given
We have the following data: 54 55 58 59 59 60 61 61 62 65
The sample mean and deviation can be calculated with the following formulas:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]
[tex]\bar X=59.4[/tex] represent the sample mean
[tex]s=3.239[/tex] represent the sample standard deviation
[tex]n=10[/tex] sample size
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to test if the true mean is higher than 55, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 55[/tex]
Alternative hypothesis:[tex]\mu > 55[/tex]
Replacing the info given we got:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing the info given we got:
[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The p value for this case is given by:
[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]
And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55
What is the square root of 100?
Answer:
10
Step-by-step explanation:
Answer:
10
Step-by-step explanation:
Square root is finding what number times what gets your goal.
10 x 10 = 100 so 100 squared is 10.
5 x 5 = 25 so 25 squared is 5.
4 x 4 = 16 so 15 squared is 4.
You get it? :)
Have a nice day!
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix Q. A. -67 B. -65 C. 65 D. 67
Answer: d) 67
Step-by-step explanation:
[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]
[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]
