To find the probability of selecting the letter "C" or the coin landing tails up, we need to calculate the probability of each event individually and then add the probabilities of the two events together.
The probability of selecting the letter "C" is:
1/5
This is because there are 5 letters in total, A, B, C, D, and E, and "C" is one of them, so the probability of selecting "C" is 1/5.
The probability of the coin landing tails up is:
1/2
This is because there are two possible outcomes when flipping a coin, heads or tails, and since the coin is fair, the probability of getting heads or tails is 1/2.
To find the combined probability of the two events we need to add them together using the rule of "or" in probability which is defined as:
P(A or B) = P(A) + P(B) - P(A and B)
However in this case A and B are mutually exclusive events, meaning they can't happen at the same time. There is no way to have "C" and coin landing tails up at the same time. Then we don't have to subtract P(A and B)
Therefore, the probability of selecting the letter "C" or the coin landing tails up is:
1/5 + 1/2 = 2/5 + 1/2 = 7/10
So the probability of selecting the letter "C" or the coin landing tails up is 7/10
in ΔWXY, m∠W = (2x - 12)°, m∠X = (2x +17)°, and m∠Y = (9x - 7)°. Find m∠X.
Answer:
45°
Step-by-step explanation:
Angles in a triangle add to 180 degrees, so
2x - 12 + 2x + 17 + 9x - 7 = 18013x - 2 = 18013x = 182x = 14So, the measure of angle X is 2(14)+17=45°
Each container must hold exactly 1 litre of water Each container must have a minimum surface area
The containers must be spheres of radius = 6.2cm
How to minimize the surface area for the containers?
We know that the shape that minimizes the area for a fixed volume is the sphere.
Here, we want to get spheres of a volume of 1 liter. Where:
1 L = 1000 cm³
And remember that the volume of a sphere of radius R is:
[tex]V = \frac{4}{3}*3.14*R^3[/tex]
Then we must solve:
[tex]V = \frac{4}{3}*3.14*R^3 = 1000cm^3\\\\R =\sqrt[3]{ (1000cm^3*\frac{3}{4*3.14} )} = 6.2cm[/tex]
The containers must be spheres of radius = 6.2cm
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The graph shows the solution to a system of inequalities:
pe
Which of the following inequalities is modeled by the graph?
O 2x + 5y = 14; x = 0
O2x + 5y s 14; x 20
O2x - 5y 14; x 20
O-2x - 5y 14; x = 0
Answer: option (2)
Step-by-step explanation:
The slanted line has a negative slope.
Eliminate options 3 and 4.Also, the line is shaded below.
Eliminate option 1.This leaves option (2) as the correct answer.
If a 17-foot ladder makes a 71° angle with the ground, how many feet up a wall will it reach? Round your answer to the nearest tenth.
Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.
How many feet up the wall will the ladder reach?Given that;
Angle with the ground θ = 71°Length of the ladder / hypotenuse = 17ftLength of wall = xTo determine the length wall from the tip of the ladder to the ground level, we use trigonometric ratio since the scenario forms a right angle triangle.
Sinθ = Opposite / Hypotenuse
Sin( 71° ) = x / 17ft
x = Sin( 71° ) × 17ft
x = 0.9455 × 17ft
x = 16.1 ft
Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.
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the center of a circle is on the line y=2x and the line x=1 is tangent to the circle at (1,6).find the center and the radius
The radius and the center of the circle are 4 units and (1,2), respectively
How to determine the center and the radius?The center of the circle is on
y = 2x and x = 1
Substitute x = 1 in y = 2x
y = 2 * 1
Evaluate
y = 2
This means that the center is
Center = (1, 2)
Also, we have the point of tangency to be:
(x, y) = (1, 6)
This point and the center have the same x-coordinate.
So, the distance between this point and the center is
d = 6 - 2
d = 4
This represents the radius
Hence, the radius and the center of the circle are 4 units and (1,2), respectively
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15v - 2v + 29 = 5v - 27
Answer:
v=-7
Step-by-step explanation:
13v-5v=-27-29
8v=-56
v=-56/8=-7
suppose you are conducting a survey about the amount grocery store baggers are tipped for helping customers to their cars .for a similar simulated population with 50 respondents the population mean is $1.73 and the standard deviation is $0.657
about 68% of the sample mean fall with in the intervals $_______ and $________
about 99.7% of the sample mean fall with in the intervals of $-------- and $
Using the Empirical Rule and the Central Limit Theorem, we have that:
About 68% of the sample mean fall with in the intervals $1.64 and $1.82.About 99.7% of the sample mean fall with in the intervals $1.46 and $2.What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.What does the Central Limit Theorem state?By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, the standard deviation of the distribution of sample means is:
[tex]s = \frac{0.657}{\sqrt{50}} = 0.09[/tex]
68% of the means are within 1 standard deviation of the mean, hence the bounds are:
1.73 - 0.09 = $1.64.1.73 + 0.09 = $1.82.99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:
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Answer:
About 68% of the sample means fall within the interval $1.64 and $1.82.
About 99.7% of the sample means fall within the interval $1.45 and $2.01.
Step-by-step explanation:
To verify the given intervals, we need to calculate the standard error of the mean (SE) for a sample size of 50 using the population mean and standard deviation provided.
The standard error of the mean (SE) can be calculated as:
SE = population standard deviation / √(sample size)
Given that the population mean is $1.73 and the population standard deviation is $0.657, and the sample size is 50:
SE = $0.657 / √50 ≈ $0.09299 (rounded to 5 decimal places)
Now, we can calculate the intervals:
For the interval where about 68% of the sample means fall:
Interval = (Mean - 1 * SE, Mean + 1 * SE)
Interval = ($1.73 - $0.09299, $1.73 + $0.09299)
Interval ≈ ($1.63701, $1.82299)
So, about 68% of the sample means fall within the interval $1.64 and $1.82, which matches the given statement.
For the interval where about 99.7% of the sample means fall:
Interval = (Mean - 3 * SE, Mean + 3 * SE)
Interval = ($1.73 - 3 * $0.09299, $1.73 + 3 * $0.09299)
Interval ≈ ($1.54703, $1.91297)
So, about 99.7% of the sample means fall within the interval $1.55 and $1.91, which is different from the given statement.
The correct interval for about 99.7% of the sample means, rounded to the nearest hundredth, is $1.55 and $1.91, not $1.45 and $2.01 as mentioned in the statement.
Identify an equation in point-alope form for the line perpendicular to y-x-7 that passes through (-2,-6).
Answer:
[tex]y + 6 = -1(x + 2).[/tex]
Step-by-step explanation:
Let's find the general equation of the given line:
[tex]y - x - 7 = 0\\\\y = x + 7.[/tex]
We can see that [tex]m = 1.[/tex]
Thus, the slope of any perpendicular line to the line [tex]y = x + 7[/tex] is [tex]-1.[/tex]
Given that the perpendicular line passes through (-2, -6), its point-slope form equation is as given:
[tex]y - y_1 = m(x - x_1)\\\\y - (-6) = -1(x - (-2))\\\\y + 6 = -1(x + 2).[/tex]
PLEASE HELP WORTH 14 POINTS!
Answer:
180°
cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°
look at the picture
The interval where the function is increasing is (3, ∞)
Interval of a functionGiven the rational function shown below
g(x) = ∛x-3
For the function to be a positive function, the value in the square root must be positive such that;
x - 3 = 0
Add 3 to both sides
x = 0 + 3
x = 3
Hence the interval where the function is increasing is (3, ∞)
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Equilateral Triangle. 6in 6in 6in 5in
Point S is on line segment \overline{RT}
RT
. Given ST=2x,ST=2x, RT=4x,RT=4x, and RS=4x-4,RS=4x−4, determine the numerical length of \overline{RS}.
RS
.
[tex]\underset{\leftarrow \qquad \textit{\LARGE 4x}\qquad \to }{R\stackrel{4x-4}{\rule[0.35em]{7em}{0.25pt}} S\stackrel{2x}{\rule[0.35em]{20em}{0.25pt}}T} \\\\\\ RT~~ - ~~ST~~ = ~~RS\implies \stackrel{RT}{4x} - \stackrel{ST}{2x}~~ = ~~\stackrel{RS}{4x-4} \\\\\\ -2x=-4\implies x=\cfrac{-4}{-2}\implies \boxed{x=2}~\hfill \stackrel{4(2)~~ - ~~4}{RS=8}[/tex]
A train travels 600 kilometers in 1 hour. What is the train's velocity in meters/second?
lunch Then more students joined Jaden's
Answer:
166 2/3 meters/sec.
Step-by-step explanation:
1/1 =1 12 inches/1 foot =1 you are looking for equivalents that will cancel out the unit until you can get to meters and seconds. See work in the picture.
A bag contains 240 marbles that are either red, blue, or green. The ratio of red to blue to green marbles is 5:2:1. If one-third of the red marbles and two-thirds of the green marbles are removed, what fraction of the remaining marbles in the bag will be blue?
A. 6/17
B. 1/2
C. 6/13
D. 7/18
The fraction of the remaining marbles in the bag will be blue is 6/17.
What fraction of the remaining marbles in the bag will be blue?The first step is to determine the initial number of marbles in the bag:
Initial number of red marbles in the bag : (5/8) x 240 = 150
Initial number of blue marbles in the bag : (2/8) x 240 = 60
Initial number of green marbles in the bag : 240 - 150 - 60 = 30
Number of red marbles remaining after 1/3 is removed = (1 - 1/3) x 150
2/3 x 150 = 100
Number of green marbles remaining after 2/3 is removed = (1 - 2/3) x 30
1/3 x 30 = 10
Total number of marbles now in the bag : 100 + 10 + 60 = 170
Fraction of blue marbles = 60 / 170 = 6/17
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One solution to the problem below is 3.
What is the other solution?
b²-9=0
By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.
How to find the remaining root of second order polynomial
Herein we have a quadratic equation, that is, a second order polynomial, of the form b² - a² = 0. By algebra we know that the polynomial of such form have the following equivalence:
b² - a² = (b - a) · (b + a), which means that the roots of the interval are x₁ = a and x₂ = - a.
If we know that a² = 9, then the roots of the second order polynomial are:
b² - 9 = (b - 3) · (b + 3)
By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.
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Two trees are 120 m apart. From the point halfway between them, the angle of elevation to the top of the trees is 36 and 52. How much taller is one tree than the other.
One tree is 31.044 m taller than the other one in height.
Given Information and Formula Used:
The distance between the trees, BC (from the figure) = 120 m
Elevation of angles to the top of the trees,
∠AMB = 52°
∠DMC = 36°
In a right angled triangle,
tan x = Perpendicular/Height
Here, x is the angle opposite to the Perpendicular.
Calculating the Height Difference:
Let's compute the height of the taller tree first.
In ΔAMB,
tan 52° = AB / BM
Now, since M is the point halfway between the trees,
BM = CM = BC/2
BM = CM = 60 m
⇒ 1.2799 = AB / 60
AB = 1.2799 × 60
Thus, the height of the taller tree, AB = 76.794 m
Now, we will compute the height of the smaller tree.
In ΔDCM,
tan 36° = DC / CM
⇒ 0.7625 = DC / 60
DC = 0.7625 × 60
Thus, the height of the smaller tree, DC = 45.75 m
The difference in the heights of the trees, AP = AB - DC
AP = (76.794 - 45.75)m
AP = 31.044m
Hence one tree is 31.044m taller in height than the other.
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What is the y-intercept of the function f(x) = -2/9x + 1/3?
Answer: (0,1/3)
Step-by-step explanation:
Answer:
The y-intercept of the function f(x) = -2/9x + 1/3 is 1/3.
Step-by-step explanation:
Given, function is
f(x) = -2/9x + 1/3.
The y-intercept is the point where the graph intersects the y-axis.
The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.
We know that the x-coordinate of any point on the y-axis is 0.
So the x-coordinate of a y-intercept is 0.
To find the y - intercept set x = 0.
f(0) = (2/9 . 0) + 1/3
f(0) = 0 + 1/3
f(0) = 1/3.
what is 73 divdied by 84,649
Answer:
0.000862
Hope this helps :) If you have anymore questions just comment
Answer:
0.000862384670817 that is the answer
Find the recursive rule for the following sequence. -3, 2, 7, 12, 17,
Answer:
+5
Step-by-step explanation:
There is a length of 5 between all numbers, meaning that 5 is added to each number to get the next one.
I hope this helps!
The probability distribution for a
random variable x is given in the table.
x
-5 -3 -2 0
Probability 17
13 .33 16
2
.11
3
.10
Find the probability that -2 < x < 2
Answer:
0.6 or 60%
Step-by-step explanation:
According to the distribution table, the percent values within the interval of [- 2, 2] are:
0.33, 0.16, 0.11Add them together to get the required answer:
0.33 + 0.16 + 0.11 = 0.6 or 60%The answer is 0.6 or 60%.
The respective probabilities that lie in the interval [-2, 2] are 0.33, 0.16, and 0.11. Therefore, the probability it lies in the interval is equal to the sum of the probabilities.
0.33 + 0.16 + 0.110.49 + 0.110.6 = 60%Suppose you pay back $575 on a $525 loan you had for 75 days. What was your simple annual interest rate? State your result to the nearest hundredth of a percent.
The simple annual interest rate for the $ 525 loan is equal to 46.35 %.
What is the interest rate behind a pay back?
In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:
575 = 525 · (1 + r/100)
50 = 525 · r /100
5000 = 525 · r
r = 9.524
The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:
r' = 9.524 × 365/75
r' = 46.350
The simple annual interest rate for the $ 525 loan is equal to 46.35 %.
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Jed wants to prove that his test scores are greatly improving. He makes the graph shown here.
Explain why someone may think this graph is misleading.
Someone may think this graph is misleading because it does not start from the origin
How to determine the reason?As a general rule, graphs are to begin from the origin
The origin of a graph is
(x, y) = (0, 0)
From the given graph, the origin is
(x, y) = (0, 60)
This means that someone may think this graph is misleading because it does not start from the origin
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the square of a whole number is between 500 and 900. the number must be between...
A. 20 and 30
B. 30 and 40
C. 40 and 50
D. 50 and 60
The number must be between 20 and 30.
How to find the square of whole number?The square of the whole number can be found as follows;
The square of the whole number is between 500 and 900. The number must be between 20 and 30.
The number is an whole number.
Therefore, the number will be between 20 and 30.
20² = 400
30² = 900
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Triangles ABC and A''B''C'' are similar. Identify the type of reflection performed and the scale factor of dilation.
The type of reflection performed and the scale factor of dilation of the diagram are; Reflection over the x-axis and a scale factor dilation of 2.
How to Identify Transformation used on diagram?From the given diagram, we are told that triangle ABC is transformed into Triangle A"B"C".
Now, we are told that both triangles are similar and as such if they are similar then, it means each corresponding side has the same ratio. Thus, there was a dilation by a scale factor of 2.
Now, the reflection that took place after the dilation would be a reflection over the x-axis.
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adjoint of [1 0 2 -1] is
The adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
How to determine the adjoint?The matrix is given as:
[tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex]
For a matrix A be represented as:
[tex]A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
The adjoint is:
[tex]Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]
Using the above format, we have:
[tex]Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
Hence, the adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]
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Rotate the given triangle 270° counter-clockwise about the origin.
[tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-1&[?]&[?]\\1&[?]&[?]\end{array}\right][/tex]
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.
If a point (x, y) is rotated 270° counter-clockwise about the origin, the new point is (y, -x)
The rotation of the triangle [tex]\left[\begin{array}{ccc}-1&2&2\\-1&-1&3\end{array}\right][/tex] 270° counter-clockwise about the origin gives [tex]\left[\begin{array}{ccc}-1&-1&3\\1&-2&-2\end{array}\right][/tex]
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A company is reviewing a batch of 28 products to determine if any are defective. On average,3.2 of products are defective.
What is the probability that the company will find 2 or fewer defective products in this batch?
What is the probability that 4 or more defective products are found in this batch?
If the company finds 5 defective products in this batch, should the company stop production?
Using the Poisson distribution, it is found that:
There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.In this problem, the mean is:
[tex]\mu = 3.2[/tex]
The probability that the company will find 2 or fewer defective products in this batch is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
Then:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0408 + 0.1304 + 0.2087 = 0.3799[/tex]
There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.
The probability that 4 or more defective products are found in this batch is:
[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]
In which:
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]
P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0408 + 0.1304 + 0.2087 + 0.2226 = 0.6025
[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6025 = 0.3975[/tex]
There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.
For 5 or more, the probability is:
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which:
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]
[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]
[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]
[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]
[tex]P(X = 4) = \frac{e^{-3.2}3.2^{4}}{(4)!} = 0.1781[/tex]
P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0408 + 0.1304 + 0.2087 + 0.2226 + 0.1781 = 0.7806
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.7806 = 0.2194[/tex]
Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.
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25 mice were involved in a biology experiment involving exposure to chemicals found in ciggarette smoke. 15 developed at least 1 tumor, 9 suffered re[iratory failure, and 4 suffered from tumors and had respiratory failure
The number of mice that didn't get a tumor is 9 mice out of the 25 mice.
How to know how many mice didn't have a tumor?Identify the total mice who did not have any effects or the effects did not include a tumor.
Repiratory failure: 9 mice
Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.
Note: This question is incomplete; here is the missing section:
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4. (a)(i)Show that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix.
that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix
Please help me with this problem. Seriously desperate again !!
The dimensions are 7 inches by 17 inches.
What is the area of rectangle?
Let the length be l inches
Let the breadth be b inches
Area = l*b
We can find dimensions as shown below:
Let the length be x inches
Let the width be y inches
Area = 119 square inches
x=3+2y (1)
Area = l*w
119 = x*y
Putting value of x
119 = (3+2y) *y
119 = 3y+2y^2
2y^2+3y-119=0
2y^2-14y+17y-119=0
2y(y-7) +17(y-7) =0
(y-7) (2y+17) =0
y=7, -17/2
y cannot be negative
so, y = 7
Putting in equation (1)
x=3+2(7)
= 3+14
= 17
Hence, the dimensions are 7 inches by 17 inches.
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