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
15v - 2v + 29 = 5v - 27
Answer:
v=-7
Step-by-step explanation:
13v-5v=-27-29
8v=-56
v=-56/8=-7
A store is selling two mixtures of nuts in 20-ounce bags. The first mixture has 15 ounces of peanuts combined with five ounces of cashews, and costs $4.75. The second mixture has five ounces of peanuts and 15 ounces of cashews, and costs $6.25. How much does one ounce of peanuts and one ounce of cashews cost?
The cost of one ounce of peanuts is $0.20
The cost of one ounce of cashew is $0.35
What are the linear equations that represent the question?15p + 5c = 4.75 equation 1
5p + 15c = 6.25 equation 2
Where:
p = cost of one ounce of peanutsc = cost of one ounce of cashewWhat is the cost of one ounce of peanut and cashew?Multiply equation 2 by 3
15p + 45c = 18.75 equation 3
Subtract equation 1 from equation 3
40c = 14
c = 14/40
c = $0.35
Substitute for c in equation 1
15p + (5 x 0.35) = $4.75
15p + 1.75 = 4.75
15p = 4.75 - 1.75
15p = 3
p = 3/15
p = $0.20
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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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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°
I have tried finding the answer for this but 1.4 or anything like that is wrong and i dont know why, what is 2.1 / 1.488, and then rounded to the nearest tenth.
After rounding to the nearest tenth, we get:
[tex]\frac{2.1}{1.488} = 1.5[/tex]
How to get the quotient?We have the quotient:
[tex]\frac{2.1}{1.488}[/tex]
If you multiply the numerator and denominator by 1000, you will get the simpler quotient:
[tex]\frac{2100}{1488}[/tex]
It gives:
[tex]\frac{2100}{1488} = 1.45[/tex]
Now we want to round it to the nearest tenth, which is the first digit after the decimal point.
To do so, we need to look at the number at the right of it.
If is between 0 and 4, then we round down.If it is between 5 and 9, we round up.In this case, we can see a 5, so we should round up, then we have:
[tex]\frac{2100}{1488} = 1.5[/tex]
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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]
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!
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:
1.73 - 3 x 0.09 = $1.46.1.73 + 3 x 0.09 = $2.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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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.
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.
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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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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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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An individual is planning a trip to a baseball game for 15 people. Of the people planning to go to the baseball game, 10 can go on Saturday and 12 can go on Sunday, some of them can go on both days. How many people can only go to the game on Sunday?
The number of people who can go to the game only on Sunday by applying the concept of set theory is equal to 5.
Total number of people for a trip to a baseball game = 15
Number of people planning to go on Saturday = 10
Number of people planning to go Sunday = 12
Let x be the number of people who can go on both Saturday and Sunday.
Then, the number of people who can go only on Saturday is 10 - x.
And the number of people who can go only on Sunday is 12 - x.
Total of 15 people are going to the baseball game.
Using set theory we have,
Number of people going on Saturday only + number of people going on Sunday only + number of people going on both = 15
Substitute the value we have,
⇒(10 - x) + (12 - x) + x = 15
Simplifying the above equation, we get,
⇒22 - x = 15
⇒ x = 7
The number of people who can only go to the game on Sunday is
= 12 - x
= 12 - 7
= 5
Therefore, using set theory number of people can only go to the game on Sunday is equal to 5 .
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Complete the solution of the equation. Find
the value of y when x equals 4.
-3x + 9y = -57
Answer: -5
Step-by-step explanation:
-3x+9y=-57 x=4
-3(4)+9y=-57
-12+9y=-57
+12
9y=-45
9y
y=-5
Find the missing angle and side, A is 25 degrees, C is 90 degrees, and B is 16.
The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.
How to find all missing sides and angles of the triangle
In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:
B = 180° - A - C
B = 180° - 25° - 90°
B = 65°
a = 16 × (sin 25°/sin 65°)
a ≈ 7.461
c = 16 × (sin 25°/sin 90°)
c ≈ 6.762
The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.
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Find the measure of side a.
A = _ m
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 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.
Equilateral Triangle. 6in 6in 6in 5in
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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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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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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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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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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Shayla is 3 years older than Todd. If t represents Todd’s age, which expression represents Shayla’s age?
Answer:
t + 3
Step-by-step explanation:
adding 3 years onto t amount of years
4. G.CO.10 In the figure below, p ll q. What is the value of x? *
O A. 7
B. 68
C. 59
OD. 44
136
121
The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.
What is a perpendicular line?Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have two lines that are parallel to each other or p ll q
The angle made by transversal t is 136 degrees
The measure of the other angle = 180 - 136 = 44 degrees
Draw a line parallel to p and q and passes through the intersection point of line t and v
The angle made by the transversal and the line drawn is the same as 44 degrees.
The measure of the other angle = 121 - 44 = 77 degrees
Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.
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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.
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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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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