Answer: Choice B
[tex]2 = \log_{8}(64)[/tex]
======================================================
Explanation:
The original equation is [tex]8^2 = 64[/tex] with 8 as the base. That is also the base of the log when we get the final answer shown above. Logs are useful to isolate the exponent.
The general rule is that [tex]\text{y} = b^{\text{x}}[/tex] is equivalent to the log form of [tex]\text{x} = \log_{b}(\text{y})[/tex] where b is the base of each.
2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
The logarithmic equation equivalent to 82 = 64 is:
2 = log Subscript 64 Baseline 8
This is because the logarithmic equation relates the base (64) to the result of the exponentiation (8), which in this case is 2.
Hence, 2 = log Subscript 64 Baseline 8 is the logarithmic equation which is equivalent to 82 = 64.
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help!
Nora and Annie are raising money to purchase books for their school's library. The number of books they will be able to purchase for the library depends on the amount of money they raise.
b = the number of books Nora and Annie will be able to purchase
m = the amount of money Nora and Annie raise
Which of the variables is independent and which is dependent?
Answer: B is dependent and M is independent
Step-by-step explanation:
This is because the question says that they are raising money to buy books. In order to buy the books, they must raise money. So they raise money than buy the books which makes buying the books dependent on how much they raise.
ASAP PLEASE
Which point us the coordinate of the image of A under the transformation [0 1 1 0]
(-2,4)
(2,4)
(4,2)
(-4,-2)
Answer:
Step-by-step explanation:
(4, 2)
will you brainlyest?
Suppose we want to choose colors, without replacement, from the colors red, blue, green, and purple.
(a) How many ways can this be done, if the order of the choices is relevant?
(b) How many ways can this be done, if the order of the choices is not relevant?
The number of ways when the choice is not relevant is 4
How to determine the number of ways?The number of colors are:
Colors, n = 4
The color to choose are:
r = 3
Relevant choice
When the choice is relevant, we have:
[tex]Ways = ^nP_r[/tex]
This gives
[tex]Ways = ^4P_3[/tex]
Evaluate
Ways = 24
Hence, the number of ways when the choice is relevant is 24
Not relevant choice
When the choice is not relevant, we have:
[tex]Ways = ^nC_r[/tex]
This gives
[tex]Ways = ^4C_3[/tex]
Evaluate
Ways = 4
Hence, the number of ways when the choice is not relevant is 4
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ppose you have one quart of water/juice mix that is 40% juice, and you add 3
quarts of water. What percent juice is the final m
The final percent of juice is 10%
How to get the final percent?
We initially have one quart that is 40% juice and 60% water.
Then initially we have:
0.4 of quarts of juice.0.6 quarts of water.Then we add another 3 quarts of water, so the new mixture has:
0.4 quarts of juice.3.6 quarts of water.So we have 4 quarts of mixture.
The new percentage of juice will be:
P = (0.4 quarts/4 quarts)*100% = 10%
The final percent of juice is 10%
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please answer this i have tried lots of answers but they are all wrong urgent
(a). All four sides are equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is focused on spatial characteristics that relate to the proximity, size, shape, and relative placement of objects.
(a). Two features that make the shape square are all four sides equal and the angles are right-angled (90 degrees).
(b). A quadrilateral has no pairs of parallel sides is a Kite and irregular trapezium.
(c). A triangle having one pair of equal sides and one pair of equal angles is an isosceles Triangle.
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Equation that represents a line which is parallel to the line y=-2/3x+1
Answer:
- 2/3
Step-by-step explanation:
Answer:
Any equation that has the same slope as the line y = -2/3x + 1 but a different y-intercept will be parallel because the lines will never intersect. For example, y = -2/3x + 2 or y = -2/3x + 3.
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the equation y=ax describes the graph of a line.if the value of a is negative,the line
If the value of a is negative, the line is reflected across any of the axis
How to describe the line?The equation is given as:
y = ax
The new line is given as
y = -ax
The above implies that y = ax is transformed to y = -ax
The transformation can be any of:
reflection across the x-axisreflection across the y-axisHence, if the value of a is negative, the line is reflected across any of the axis
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Consider the graph of f(x) given below.
A curve labeled f of x declines through the points (negative 4, 7), (negative 3, 6), (negative 2, 5), (0, 3), (2, 1), (3, 0), (4, negative 1), (5, negative 2), (6, negative 3) and (7, negative 4) on the x y coordinate plane.
The function g(x) is a transformation of f(x). If g(x) has a y-intercept of -2, which of the following functions could represent g(x)?
A.
g(x) = f(x + 2)
B.
g(x) = f(x - 5)
C.
g(x) = f(x) - 2
D.
g(x) = f(x) - 5
The functions could represent g(x) is B. [tex]g(x) = f(x - 5)[/tex]
How can the function be determined?Using the general equation [tex]g(x) =f(x)+ b[/tex]
The g(x) has intercept of y=-2,
Then the y-intercept of f(x) is at y=3
If we find the difference between both y-intercepts, we have
( -2 -3) = -5
Then b=-5
Hence, [tex]g(x) = f(x - 5)[/tex] is correct.
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The figure below shows a triangular piece of cloth: B 35 8 in. What is the length of the portion BC of the cloth? 08 cos 35° sin35° 8 cos 35° 08 sin 35°
From the calculation, we can see that /BC/ is 8 sin 35. Option D
What is the length of the portion BC of the cloth?We can see the image of the triangular piece of cloth as shown in the image. This shows that we have to approach the problem by the use of the trigonometric ratios.
Hence;
/AC/ = 8 in
/BC/ = x
<A = 35 degrees
Sin 35 = /BC//8
/BC/ = 8 sin 35
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PLS HELP FAST THERE'S A TIMER WILL GIVE BRAINLIETS.
Which name accurately describes the figure shown below and why? A 4-sided figure with 2 parallel sides, 2 right angles, and 2 non-congruent sides. parallelogram, because the figure has two pairs of parallel sides parallelogram, because the figure has exactly one pair of parallel sides trapezoid, because the figure has two pairs of parallel sides trapezoid, because the figure has exactly one pair of parallel sides Mark this and return
Writing an Equation Representing a Real-World Example
Janelle is in charge of bringing in dry erase markers for everyone in her math group to use to work on a project. She brings 3 markers for each person in her group and 5 extra markers for everyone to share. If Janelle brings in 23 markers in all, which equation represents the information?
Let x represent the number of students in Janelle’s group.
3x = 23 + 5
3x = 23
3x – 5 = 23
3x + 5 = 23
The equation that represents the situation is 3x + 5 = 23
How to represents an equation?She is brings 3 markers for each person in her group and 5 extra markers for everyone to share.
She brings in 23 markers in all.
Therefore, the equation that represents this situation is as follows:
lets
x = number of students in the group
Therefore,
3x + 5 = 23
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Using the following accounts and balances, prepare the “Stockholders’ Equity” section of the balance sheet. 60,000 shares of common stock authorized, and 4,000 shares have been reacquired.
Common Stock, $50 par $2,400,000
Paid-In Capital from Sale of Treasury Stock 48,000
Paid-In Capital in Excess of Par—Common Stock 576,000
Retained Earnings 1,368,000
Treasury Stock 25,000
The total Stockholders’ Equity is $4,367,000
Total Stockholders’ EquityCommon Stock, $50 par $2,400,000
Paid-In Capital in Excess of Par—Common Stock $576,000
Paid-In Capital from Sale of Treasury Stock $48,000
Total paid in capital $3,024,000
Retained Earnings $1,368,000
Less Treasury stock $25,000
Total Stockholders’ Equity $4,367,000
Therefore the total Stockholders’ Equity is $4,367,000.
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en una fiesta hay 16 personas de las cuales el 25% son mujeres, luego llegan mas mujeres a la fiesta, de tal manera que ahora los hombres son el 60% ¿cuantas mujeres llegan a la fiesta?
Answer:
English (Ingles):
10 Women come to the party.
Spanish (Espanol):
10 Las mujeres vienen a la fiesta.
Step-by-step explanation:
English (Ingles):
We know that there are 16 people there at the start. 25% of those people are women. We can work out by subtracting 100 by 25 that 75% of the p-eople there are men. We need to do 25% of 16 so we can work out how many men and women there are there.
So we find 10% of 16 which is 1.6 then we take off 5% of 1.6 which is 0.08. We then double 1.6 to get 20% which gives us 3.2. We now add on the 5% to make it 25% which gives us 4.
This means 25% of 16 is 4.
This tells us that there are 4 women at the party and 12 men as 16 - 4 = 12.
It now says that more women arrive which makes the percentage for men go down to 60%. We now need to add 5% on to the 25% of women there are which will tell us how many more women there are now and it will let us work out how many women and men there are in total now.
As we can't do this without it giving us 4.8, we know that 25% of people is 4 women which means 50% of people would be 8 women and we make an estimate of how many women have joined which gives us 6 people which means the total amount of women at the party is 10.
Spanish (Espanol):
Sabemos que hay 16 personas allí al principio. El 25% de esas personas son mujeres. Podemos calcular restando 100 por 25 que el 75% de las personas son hombres. Necesitamos hacer el 25% de 16 para poder calcular cuántos hombres y mujeres hay allí.
Así que encontramos el 10 % de 16, que es 1,6, luego quitamos el 5 % de 1,6, que es 0,08. Luego duplicamos 1,6 para obtener el 20%, lo que nos da 3,2. Ahora sumamos el 5% para convertirlo en 25%, lo que nos da 4.
Esto significa que el 25% de 16 es 4.
Esto nos dice que hay 4 mujeres en la fiesta y 12 hombres como 16 - 4 = 12.
Ahora dice que llegan más mujeres lo que hace que el porcentaje de hombres baje al 60%. Ahora necesitamos agregar un 5% al 25% de mujeres que hay, lo que nos dirá cuántas mujeres más hay ahora y nos permitirá calcular cuántas mujeres y hombres hay en total ahora.
Como no podemos hacer esto sin que nos dé 4.8, sabemos que el 25% de las personas son 4 mujeres, lo que significa que el 50% de las personas serían 8 mujeres y hacemos una estimación de cuántas mujeres se han unido, lo que nos da 6 personas que significa que la cantidad total de mujeres en la fiesta es 10.
A wire is stretched from the ground to the top of an antenna tower. The wire is 15 feet long. The height of the tower is 3 feet greater than the distance d from the tower's base to the end of the wire. Find the distance d and the height of the tower.
The distance d is 9 ft and the height is 12ft.
How to find the distance and the height?
Here we can model the situation with a right triangle, where the length of the wire is the hypotenuse.
The height is one cathetus and the distance is the other catheti.
Let's define:
h = heightd = distance.hypotenuse = 15ftWe know that the height of the tower is 3 ft larger than the distance, then:
h = d + 3ft
Now we can use the Pythagorean theorem, it says that the sum of the squares of the cathetus is equal to the square of the hypotenuse.
Then:
[tex]d^2 + (d + 3ft)^2 = (15ft)^2[/tex]
Now we can solve this equation for d:
[tex]d^2 + d^2 + 6ft*d + 9ft^2 = (15ft)^2\\\\2d^2 + 6ft*d - 216 ft^2 = 0\\\\d^2 + 3ft*d - 108ft^2 = 0[/tex]
Then the solutions are:
[tex]d = \frac{-3ft \pm \sqrt{(3ft)^2 - 4*(-108ft^2)} }{2} \\\\d = \frac{-3ft \pm 21ft }{2}[/tex]
We only take the positive solution:
d = (-3ft + 21ft)/2 = 9ft
And the height is 3 ft more than that, so:
h = 9ft + 3ft = 12ft
The distance d is 9 ft and the height is 12ft.
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find m+n
pls help !!!
Answer:
m + n = 140===============
GivenTwo parallel lines,Included triangle between the parallel lines,Two interior angles of the triangle are m and n,Another angle of 40°.To find The sum of angles m and nSolutionAs per given, the missing interior angle is corresponding with 40° angle.
Since corresponding angles are equal, the third interior angle of the triangle is 40°.
Sum of three interior angles is 180°:
m + n + 40 = 180m + n = 180 - 40m + n = 140Apply angle sum property
m+n+40=180m+n=180-40m+n=140The answer is 140
Find the slope between the two points given. Then, use the slope and Point One to write the equation of the line in Point-Slope form. State the slope. Point One: (4,−3) Point Two: (−2,2)
The equation in point slope form is given as y+3 = -5/8(x-4)
Equation of a lineThe formula for calculating the equation of a line in point-slope form is expressed as:
y-y1= m(x-x1)
Given the coordinate point
Slope = 2-(-3)/-2-4
Slope = 5/-8
Determine the equation
y-(-3) =-5/8(x-4)
y+3 = -5/8(x-4)
Hence the equation in point slope form is given as y+3 = -5/8(x-4)
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The diameter of a pipe is normally distributed, with a mean of 0.8 inch and a variance of 0.0004. What is the probability that the diameter of a randomly selected pipe will exceed 0.84 inch? (You may need to use the standard normal distribution table. Round your answer to three decimal places.) . Hint: take the square root of the variance to find the standard deviation.
The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977
What is probability?Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events
How to determine the probability?The given parameters are:
Mean = 0.8
Variance = 0.0004
Calculate Standard deviation using
σ = √σ²
This gives
σ = √0.0004
Evaluate
σ = 0.2
Calculate the z-score at x = 0.84 using
z = (x - [tex]\bar x[/tex])/σ = √σ²
This gives
z = (0.84 - 0.8)/0.02
Evaluate
z = 2
The probability is then represented as:
P(x > 0.84) = P(z > 2)
Next, we look up the value of the z table of probabilities
From the z table of probabilities, we have:
P(x > 0.84) = 0.977
Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977
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Pls answer quick I rly need this.
Linking each equation with its equivalent equation below:
5 + 9x - 7 - 4x - 3x + 6 ≡ 2x + 4x + 8 + 4x - 3x - 4 ≡ 2x + 46x - 9 5x + 4 - x + 5x + 5 ≡ 5x3x + 5 - 2x - 5x + 9 + 8x ≡ 4x + 114x + x - 11 - 5x + 25 + 4x ≡ 4x + 11x - 3 + 2x + 3 + 2x ≡ 5xMeaning of Equivalent equationEquivalent equation can be defined as an equation that has the same value with another equation.
Equivalent equation are not directly the same but can be transformed to look like each other.
In conclusion, The equivalent equations have been matched in the list above.
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The diagonals of a rectangle enclose an angle of measure 78 degree
. If the perimeter of the rectangle is 36cm, what is its area?
the area of the rectangle is 80. 1 cm²
What is the area of a rectangle?
From the given information, let's say one side of rectangle = a
The other side = (36 - 2a)/2
= 18 - a cm
The angles between the diagonals of the rectangle is 78°
Then, the angle diagonal has with base will give
= (180° - 78°)/2
= 102/2
= 51°
We have the angle to be 51 degrees, using the tan ratio
Tan θ = opposite/ adjacent
Opposite of angle 51 degrees = a
Adjacent = 18 - a
Thus,
[tex]tan 51 = \frac{a}{18 - a}[/tex]
[tex]1. 2349 = \frac{a}{18-a }[/tex]
cross multiply
[tex]18 -a ( 1. 2349) = a[/tex]
[tex]22. 23 - 1. 2349a = a[/tex]
collect like terms
[tex]a + 1. 2349a = 22. 23[/tex]
[tex]2. 2349 a = 22. 23[/tex]
[tex]a = \frac{22. 23}{2. 2349}[/tex]
a = 9. 95
If a = 9. 95cm
Then, 18 - a = 18 - 9. 95 = 8. 05cm
The formula of area of a rectangle is given as;
Area = width × length
Area = 9.95 x 8.05
Area = 80. 1 cm²
Thus, the area of the rectangle is 80. 1 cm²
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An insurance company study shows that 9% of U. S. adults have diabetes. Suppose 8 US adults are selected at random. LetX be the number of US adults among the 8 selected that have diabetes. Find the mean and standard deviation of X.
Using the binomial distribution, it is found that:
The mean of X is of 0.72.The standard deviation of X is of 0.81.What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected value of the binomial distribution is:
E(X) = np
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
For this problem, the parameters are given as follows:
n = 8, p = 0.09.
Hence the mean and the standard deviation are, respectively:
E(X) = np = 8 x 0.09 = 0.72.[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8 \times 0.09 \times 0.91} = 0.81[/tex]More can be learned about the binomial distribution at https://brainly.com/question/24863377
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A recent survey points to the transformation underway in the automotive retail landscape. A study found that automobile executives believe the number of physical automotive retail outlets, as we know them today, will be reduced by 30% to 50%. Eighty-two percent of automobile executives strongly agree that the only viable option for physical retail outlets will be the transformation into service factories, used car hubs, or focusing on an ID-management approach, where the customer is recognized at every single touchpoint. What additional information would you want to know about the survey before you accepted the results of the study?
The additional information would you want to know about the survey before you accepted the results of the study will be:
What sampling design was used?What was the population from which the design was selected?What was the response rate?How to illustrate the information?In research of human subjects, a survey is a list of questions aimed for extracting specific data from a particular group of people.
Surveys may be conducted by phone, mail, through the internet or in malls. From the information, a recent survey points to the transformation underway in the automotive retail landscape.
It is important to know the sampling design that was used, the population from which the design was selected and the response rate.
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According to the Rational Root Theorem, which statement about f(x) = 12x3 – 5x2 + 6x + 9 is true?
Any rational root of f(x) is a multiple of 12 divided by a multiple of 9.
Any rational root of f(x) is a multiple of 9 divided by a multiple of 12.
Any rational root of f(x) is a factor of 12 divided by a factor of 9.
Any rational root of f(x) is a factor of 9 divided by a factor of 12.
The complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.
How to determine the rational roots?The polynomial is given as:
12x^3 - 5x^2 + 6x + 9
The first term in the above equation is 12 i.e. 12x^3, while the last term is 9
To determine the possible rational roots, we divide the factors of the last term i.e. 12 by the factors of the first term i.e. 12
Hence, the complete statement is (d) Any rational root of f(x) is a factor of 9 divided by a factor of 12.
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Answer:
D
Step-by-step explanation:
I took the test
If cot theta = 3/2, what is the value of csc theta?
The value of csc theta is [tex]\frac{3. 61}{2}[/tex]
How to determine the valueIt is important to note that the ratio for cot is given as;
Cot theta = adjacent/opposite
cosec theta = hypotenuse/opposite
If cot theta = 3/2, then
Adjacent = 3
Opposite = 2
Using Pythagoras theorem, we have
Hypotenuse square = opposite + adjacent square
[tex]H = \sqrt{2^2 + 3^2}[/tex]
[tex]H = \sqrt{4 + 9}[/tex]
[tex]H = 3. 61[/tex]
Cosec theta = [tex]\frac{3. 61}{2}[/tex]
Thus, the value of csc theta is [tex]\frac{3. 61}{2}[/tex]
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Answer:
3.16/2
Step-by-step explanation:
Have a great day
Write each equation in Slope-Intercept Form, if possible. Identify the slope and
y-intercept if they exist. Can you leave a detailed explanation please. Thank you
6x − 4y = 24
Answer:
slope intercept form: y = mx + b
6x - 4y = 24
4y = 6x - 24
y = 3/2x - 6
slope: 3/2
y intercept: - 6
Answer:
y = 3/2 x -6
The slope is 3/2 and the y intercept is -6
Step-by-step explanation:
6x-4y = 24
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
We need to solve the equation for y
6x-4y =24
Subtract 6x from each side
6x-4y-6x =-6x+24
-4y = -6x+24
Divide each side by -4
-4y/-4 = -6x/-4 + 24/-4
y = 3/2 x -6
The slope is 3/2 and the y intercept is -6
Find the dimensions of the rectangle
Answer:
length: 12 mwidth: 4.5 mStep-by-step explanation:
The given relation between length and width can be used with the area formula to write an equation for the dimensions of the rectangle.
SetupLet w represent the width of the rectangle. The length is 3 more than twice that, so is (2w+3). The area is the product of length and width.
A = LW
54 = (2w +3)(w)
SolutionRewriting this equation to standard form gives ...
2w² +3w -54 = 0
(2w -9)(w +6) = 0 . . . . factored
w = 9/2, -6 . . . . . . . . . values that make the equation true
Only the positive width makes sense in a geometry problem, so we have ...
w = 9/2
length = 2w +3 = 12
The length of the rectangle is 12 meters; its width is 4.5 meters.
What is the equivalent expression of 3x^2-4x-3
Answer:
C. 3(x+1)(x-1)-4x
Step-by-step explanation:
3(x+1)(x-1)-4x
(x+1)(x-1)=x^2-1
3(x^2-1)-4x
3x^2-4x-3
Select the correct answer. What is the domain of y = tan (x)?
At 90 degrees, the tangent of x is undefinable.
What does determining the domain mean?The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain. Keep in mind that a fraction's denominator (bottom) cannot be zero when determining the domain. The integer that comes after a square root symbol in this section needs to be positive.The domain of y = tan (x):
y = tan(x)
Except for 90, all sets of positive real numbers fall within the domain of y = tan(x).
At 90 degrees, the tangent of x is undefinable.
Due to the exclusion of 90, all sets of positive real numbers are included in the domain of y = tan(x).
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a bag contains 15 counters:7 red 4 blue and 4 green.a counter is taken out of the bag at random.what is the probability of choosing the following: a red or blue counter.
[tex]|\Omega|=15\\|A|=7+4=11\\\\P(A)=\dfrac{11}{15}\approx73.3\%[/tex]
Answer:
RED COUNTER: 7/15
BLUE COUNTER: 4/15
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solve for x by completing the square: x2 − 8x + 13 = 0. show all work
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
How to find the roots of a polynomial by completing the square
In this question we must apply algebraic handling to simplify a quadratic equation and find the roots that satisfy the expression. Completing the square consists in transforming part of the equation into a perfect square trinomial, and then we clear for x:
x² - 8 · x + 13 = 0
x² - 8 · x + 16 = 3
(x - 4)² = 3
x - 4 = ± √2
x = 4 ± √2
There are two real roots for the quadratic equation x² - 8 · x + 13 = 0, contained in the number x = 4 ± √2.
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Prove: An odd plus an odd
equals an even.
(2m + 1) + (2n + 1) = [ ? ]m + [ ]n + [ ]
= 2(m+n+ [])
= even
[tex](2m+1)+(2n+1)=2m+2n+2\\\\=2(m+n+1)[/tex]