Answer:
1/4845
Step-by-step explanation:
The probability of selecting a defective cog first is
1/5
The second cog is
3/19
The third cog is
1/9
And the fourth cog is
1/17
Multiplying these together we get
1/5 * 3/19* 1/9 * 1/17 = 1/4845
The probability of selecting 4 cogs from the 20 produced where all are defective is approximately 0.000206.
What is probability?Probability is a measure of how likely an event is to occur. Many events are impossible to predict with absolute certainty.
The probability of selecting 4 defective cogs from the 20 produced can be calculated as follows:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20)
The number of ways to select 4 defective cogs can be found by selecting 4 defective cogs out of the 4 defective cogs produced, and 0 non-defective cogs out of the remaining 20-4=16 non-defective cogs. This can be expressed mathematically as:
Number of ways to select 4 defective cogs = (4 choose 4) * (16 choose 0) = 1
The total number of ways to select 4 cogs from 20 can be found by selecting 4 cogs out of the 20 produced. This can be expressed mathematically as:
Total number of ways to select 4 cogs from 20 = (20 choose 4) = 4845
Therefore, the probability of selecting 4 defective cogs from the 20 produced is:
P(4 defective cogs) = (Number of ways to select 4 defective cogs) / (Total number of ways to select 4 cogs from 20) = 1/4845
Thus, the probability of selecting defective cogs is approximately 0.000206.
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Abena travelled 40% of the distance of her trip alone, went another 35 miles with Saralyn,
and then finished the last half of the journey alone. How many miles long was the journey?
Answer:
350 miles long.
Step-by-step explanation:
First, we analyze the breakdown of the journey
Abena travelled 40% of the distance of her trip alone.She went 35 miles with Saralyn.She finished the last half (50%) of the journey alone.Let the total distance of the journey =x
Therefore:
10% of the total distance of the journey =35 miles
10% of x=35
0.1x=35
Divide both sides by 0.1
x-350 miles
Therefore, the journey was 350 miles long.
Answer:
The journey was 350 miles long
Step-by-step explanation:
The parameters given are;
Distance traveled by Abena alone = 40% and the last half
∴ Distance traveled by Abena alone = 40% + 50% = 90%
Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%
Hence 10% of Abena's journey = 35 miles
The total distance of Abena's journey therefore, is given as follows
10% = 35 miles
Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%
10 × 10% = 10 × 35 miles = 350 miles
The total distance of Abena's journey = 350 miles.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
(0,34)
Step-by-step explanation:
I graphed the coordinates of the table on the graph below to find the y-intercept.
Solve Ixl >-9
No solution
All reals
(X|X<-9 or X>9)
Answer:
all reals
Step-by-step explanation:
all reals as |x| >= 0 for every x real
so |x| > -9 is always true
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny
Answer:
The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Step-by-step explanation:
Let us denote the events as follows:
Event 1: a sunny day
Event 2: a rainy day
From the provided data we know that the transition probability matrix is:
[tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]
[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex] [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]
In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.
This implies that we need to compute the value of P₁₁².
Compute the value of P² as follows:
[tex]P^{2}=P\cdot P[/tex]
[tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]
The value of P₁₁² is 0.86.
Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
Save and Exit
Next
Submit
Mark this and return
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
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Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.
Answer:
Step-by-step explanation:
Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 0
σ = 1
the probability that a given score is less than negative 1.15 is expressed as
P(x < - 1.15)
z = (- 1.15 - 0)/1 = - 1.15
Looking at the normal distribution table, the probability corresponding to the z score is 0.13
P(x < - 1.15) = 0.13
The sketch of the region is shown in the attached photo
How can I make the red segment less steep than the blue segment , and more steep than the green segment ?
solve 5(x+4)<75 sdsdsd
Answer:
x < 11
Step-by-step explanation:
[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]
[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]
[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]
The required solution of inequality is,
⇒ x < 11
We have to simplify the expression,
⇒ 5 (x + 4) < 75
We can simplify it by definition of inequality as,
⇒ 5 (x + 4) < 75
⇒ 5x + 20 < 75
Subtract 20 both side,
⇒ 5x + 20 - 20 < 75 - 20
⇒ 5x < 55
⇒ 5x - 55 < 0
⇒ 5 (x - 11) < 0
⇒ x - 11 < 0
⇒ x < 11
Therefore, The required solution of inequality is,
⇒ x < 11
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Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
Fiad the sample variance and standard deviation.
21, 10, 3, 7, 11
Answer:
SD = 5.987, Var(X) = 35.85
Step-by-step explanation:
Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.
Hope this helps!
please help me on this work please !
The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. in.3/min (b) Find the rate of change of the volume when r = 37 inches. in.3/min
Answer:
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Step-by-step explanation:
given data
radius r of a sphere is increasing at a rate = 3 inches per minute
[tex]\frac{dr}{dt}[/tex] = 3
solution
we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]
so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]
and when r = 9
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
and
when r = 37 inches
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Freddie put an empty bucket underneath a leaking pipe. After 34 hours, Freddie collected 12 cups of water. What is the rate, in cups per hour, at which the water is leaking from the pipe?
Answer:
0.35 cups/hour
Step-by-step explanation:
To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:
12 cups/34 hours= 0.35 cups/hour
According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.
Indicate in standard form equation of the line passing through the given 
Answer:
x - 3y= -14
Step-by-step explanation:
Slope is rise over run
m = (6-5)/(4-1) = 1/3
we write in slope-intercept form:
y = 1/3x + b
solve for b by plugging in either point
i'm going to plug in H
5 = 1/3 + b
b = 14/3
we get our equation
y = 1/3x + 14/3
now re-write it in standard form
-1/3x + y = 14/3
make it pretty
x - 3y = -14
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
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ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
B. 4x² - 20x + 26
Step-by-step explanation:
→Set it up, like so:
(2x - 5)² + 1
4x² - 20x + 25 + 1
→Add like terms (25 and 1):
4x² - 20x + 26
Please help me with this question, I need it to pass the class!!
Answer:
cos(20°)
Step-by-step explanation:
The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.
The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.
sin(70°) = cos(20°)
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
Since opposite angles of a quadrilateral inscribes in a circle add up to 180°
So,
<P + <N = 180°
2x+2x-12 = 180°
4x = 180+12
4x = 192
Dividing both sides by 4
x = 48
Now
<P = 2(48)
<P = 96
Now
<N = 2(48)-12
<N = 96-12
<N = 84
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
A researcher classifies firefighters according to whether their gloves fit well or poorly and by gender. They want to know if there is a difference in the proportion of poorly fitted gloves and gender. At alpha = 0.01, use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
Answer:
Step-by-step explanation:
Hello!
The objective is to test if the proportion of "X: gloves fitness, categorized: Fit poorly and Fit well" is the same for two populations of interest, "male firefighters" and "female firefighters"
To do this you have to conduct a Chi-Square test of Homogeneity.
In the null hypothesis you have to state that the proportion of the categories of the variable are the same for all the populations of interest.
Be
M: the firefighter is male
F: the firefighter is female
Y: represents the category that the gloves "fit poorly"
W: represents the category that the gloves "fit well"
The null hypothesis will be:
H₀: P(Y|M)=P(Y|F)=P(Y)
P(W|M)=P(W|F)=P(W)
H₁: At least one of the statements in the null hypothesis is false.
α: 0.01
To calculate the statistic under the null hypothesis you have to calculate the expected frequencies first:
[tex]E_{ij}= O_{.j}*\frac{O_{i.}}{n}[/tex]
O.j= total of the j-column
Oi.= total of the i-row
n= total of observations
[tex]E_{11}= 547*\frac{152}{586} = 141.88[/tex]
[tex]E_{12}=39*\frac{152}{586}= 10.12[/tex]
[tex]E_{21}= 547*\frac{434}{586} = 405.12[/tex]
[tex]E_{22}= 39*\frac{434}{586} = 28.88[/tex]
[tex]X^2= sum \frac{(O_{ij}-E_{ij})^2}{E_{ij}} ~~~X^2_{(r-1)(c-1)}[/tex]
r= number of rows (in this case 2)
c=number of columns (in this case 2)
[tex]X^2_{H_0}= \frac{(132-141.88)^2}{141.88} +\frac{(20-10.12)^2}{10.12} +\frac{(415-405.12)^2}{405.12} +\frac{(19-28.88)^2}{28.88} = 13.95[/tex]
Using the critical value approach, you have to remember that this test is always one-tailed to the right, meaning that you'll have only one critical value from which the rejection region is defined:
[tex]X^2_{(r-1)(c-1);1-\alpha }= X^2_{1;0.99}= 6.635[/tex]
The decision rule is then:
If [tex]X^2_{H_0}[/tex] ≥ 6.635, reject the null hypothesis.
If [tex]X^2_{H_0}[/tex] < 6.635, do not reject the null hypothesis.
The calculated value is greater than the critical value, the decision is to reject the null hypothesis.
So at a 1% level you can conclude that this test is significant. This means that the proportions of gloves fitness, categorized in "Fit poorly" and "Fit well" are different for the male and female firefighters populations.
I hope this helps!
Answer:
The Chi - Square Test Statistics is 13.98
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Step-by-step explanation:
From the information given ; the structure of the table can be well represented as follows;
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly
Gloves fit well
Total
The objective of this question is to use the chi-square test to determine if there is a difference in the population proportion of glove fitness for the two genders.
We call represent the hypothesis as follows:
The null hypothesis: [tex]H_o:[/tex] states that there is no difference in the population proportion of glove fitness for the two genders.
The alternative hypothesis: [tex]H_a[/tex] states that there is difference in the population proportion of glove fitness for the two genders.
The expected frequency of a particular cell can be calculated by multiplying the sum of the rows and columns together, then dividing it by the Total sum
For row 1 column 1 (gloves fit poorly (male) ; we have:
[tex]= \dfrac{547*152}{586} =141.884\\[/tex]
For row 2 column 1 (gloves fit well(male) ; we have:
[tex]= \dfrac{547*434}{586} =405.116[/tex]
For row 1 column 2 (gloves fit poorly (female)) ; we have:
[tex]= \dfrac{39*152}{586} =10.116[/tex]
For row 2 column 2 ( gloves fit well ( female ) ; we have:
[tex]= \dfrac{39*434}{586} =28.884[/tex]
Thus; we can have the complete table to now be:
Observed data Males Females Total
Gloves fit poorly 132 20 152
Gloves fit well 415 19 434
Total 547 39 586
Expected data Males Females Total
Gloves fit poorly 141.884 10.116 152
Gloves fit well 405.116 28.884 434
Total 547 39 586
The Chi - Square Test Statistics can be calculated via the formula:
[tex]X^2 = \dfrac{\sum (f_o-f_e)^2}{f_e}[/tex]
where;
[tex]f_o[/tex] = observed data frequency
[tex]f_e[/tex] = expected data frequency
∴
The Chi - Square Test Statistics is as follows:
[tex]=\dfrac{(131-141.884)^2}{141.884} + \dfrac{(20-10.116)^2}{10.116}+ \dfrac{(415-405.116)^2}{405.116}+ \dfrac{(39-28.884)^2}{28.884}[/tex]
= 0.68+9.6+0.2+3.5
= 13.98
We are given the level of significance ∝ to be = 0.01
numbers of rows = 2; number of column = 2
Thus; the degree of freedom = (2-1)(2-1) = 1×1 = 1
Using the Excel Function : [ = CHISQ.DIST.RT²(X²,df)]
p-value = 0.0002
CONCLUSION: Since the p-value is less than the level of significance ; (i.e p-value < ∝) we reject the null hypothesis and accept the alternative hypothesis.
Thus; there is a difference in the population proportion of glove fitness for the two genders.
Please answer this correctly
Answer:
4 pizza recipes
Step-by-step explanation:
It shows 4 Xs after the [tex]\frac{3}{4}[/tex] mark. So there are 4 recipes that use MORE than [tex]\frac{3}{4}[/tex] cups of cheese.
Answer:
4 cups of cheese
Step-by-step explanation:
More than 3/4 are (3+1) = 4 cups of cheese
Mark Wishing the Brainliest because he deserves it :)
What’s the correct answer for this question?
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean growth rate of sales. (Round your answer to 4 decimal places.)
Answer:
The geometric mean growth rate of sales is 1.4422.
Step-by-step explanation:
We have two sales values, one from 6 years ago and the other from now.
We have to calculate the geometric growth rate of sales.
We have:
[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]
We can write the relation between these two values as:
[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]
The geometric mean growth rate of sales is 1.4422.
In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.
a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
b. Roughly what proportion of vehicle speeds exceeded 57 mph?
Answer:
(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) Roughly 16% of vehicle speeds exceeded 57 mph.
Step-by-step explanation:
We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.
For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.
Let X = vehicle speed at impact
SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])
Here, [tex]\mu[/tex] = population average speed = 42 mph
[tex]\sigma[/tex] = standard deviation = 15 mph
Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;
68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;
[ [tex]\mu-\sigma , \mu+\sigma[/tex] ] = [42 + 15 , 42 - 15]
= [57 , 27]
So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.
It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.
This means that roughly 16% of vehicle speeds exceeded 57 mph.
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
What is 9/8 squaredto the power of 2 ?
Answer:
81/64
Step-by-step explanation:
(9/8)²=9²/8²=81/64
On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84
Answer:
b
Step-by-step explanation:
add the three numbers together then minus from the main total
Answer:
B. $899.15
Step-by-step explanation:
what equation results from completing the square and then factoring? x^2+24x=33
a.) (x+24)^2=57
b.) (x+12)^2=57
c.) (x+12)^2=177
d.) (x+24)^=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
The given equation is x²+24x=33.
We need to factorise the equation using completing the square method.
What is completing the square method?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Now, x²+24x-33=0
Add and subtract (b/2)²=144 to the equation.
x²+24x-33+144-144=0
⇒x²+24x+144-33-144=0
⇒(x+12)²-177=0
⇒(x+12)²=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
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