Answers
The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.
The logarithmic expression given is
log₃ 55 = x
To solve for x using the change of base formula, we can use the formula
logₐ b = log c / log a
where a, b, and c are positive real numbers and a ≠ 1.
Using this formula, we can rewrite the given expression as
log x / log 3 = log 55 / log 3
We can simplify this expression by canceling out log 3 on both sides
log x = log 55
Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get
x = 55
Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.
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Related Questions
Question 20 of 42
Which of the following is a type of data that is likely to be normally
distributed?
A. The weights of all the 5-year-olds in the United States
B. The outcomes of a fair die rolled 100 times
C. The number of students in a class who get a perfect score on a
test
D. The number of students in a class who get a B on a test
Answers
Answer: Option B, the outcomes of a fair die rolled 100 times, is likely to be normally distributed.
Step-by-step explanation:
Answer: Option B, The outcomes of a fair die rolled 100 times
Step-by-step explanation:
that would most likely be normally distributed.
hope it helped! Good luck!!! :)
a 110 minute meeting should have a 10 minute break in the middle of two equal parts. How long after the meeting start should the break begin
Answers
Answer: 24 minutes and 30 seconds after the meeting as started
Step-by-step explanation:
110 minutes into 2 equal parts = 55 minutes in each section.
In the middle of 55 minutes = subtract the 10 minutes for a break from the 55 minutes that leaves you with 45 minutes. 24 minutes and 30 seconds before and after the 10 minute break.
Total session minutes - 110
Two equal parts of session: 55 minutes in each session
10 minute break in each session: 55-10 =45.
24 minutes and 30 seconds + 10 min break (in middle) + 24 minutes and 30 seconds
After 50 minutes the break will start.
The metting is 110 minutes long. According to the Question the metting have 'a'(only one) break of 10 minutes in between of two equal parts of metting.
so, duration of metting without the break=100 minutes
duration of each part=50 minutes
Now, the break should be after First part which is of 50 minutes.
=> The break should 50 minutes after the starting of metting.
NEED HELP WILL GIVE BRAINLIEST AND WILL RATE. Show work and do all 3. :) (Do the one highlighted)
Answers
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions.
Which of the following is not an exponential function?To determine which option is not an exponential function, we will apply general equation of an exponential function.
f(x) = aⁿ
where;
a is the base of the functionn is the exponentSo from the given options;
(³/₅)ˣ is an exponential function, because ³/₅ is the base while x is the exponent.
4ˣ is an exponential function, because 4 is the base while x is the exponent.
(4ˣ/7)ˣ is not an exponential function, because the exponent is applicable to all the fractions, so there is no one base.
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prove the identity tan3x-tanx =2sinxsec3x
Answers
(Problem #1) 2sin(x)/cos(3x) = tan(3x) - tan(x)
Let's try to prove that 2sin(x) = sin(3x) - tan(x)cos(3x).
Using the identities sin(3x) ? 3sin(x) - 4sin³(x) and cos(3x) ? 4cos³(x) - 3cos(x),
sin(3x) - tan(x)cos(3x) = 3sin(x) - 4sin³(x) - tan(x)(4cos³(x) - 3cos(x))
= sin(x)(3 - 4sin²(x) - (4cos²(x) - 3))
= sin(x)(6 - 4(sin²(x) + cos²(x)))
= 2sin(x).
(The above is simpler than using the standard identity that gives tan(3x) in terms of tan(x).)
(Problem #2) (1 - tan²((?/4)-x))/(1 + tan²((?/4)-x)) = sin(2x)
Multiplying the numerator and denominator of the left-hand side by cos²((?/4)-x)) gives
(cos²((?/4)-x)) - sin²((?/4)-x)))/(cos²((?/4)-x)) + sin²((?/4)-x))),
which equals cos(2(?/4 - x))/1, i.e., cos(?/2 - 2x), i.e., sin(2x).
(Problem #3) (1 + sin(2x) - cos(2x))/(1 + sin(2x) + cos(2x)) = tan(x)
Hint: use the identities cos(2x) = 1 - 2sin²(x) = 2cos²(x) - 1 and sin(2x) = 2sin(x)cos(x) to express the left-hand side in terms of sin(x) and cos(x), then factorize the numerator and denominator.
(Problem #4) sin(2x) + (1/sin(2x)) = 5/2; for 0 ? x <2?
This is an equation you have to solve, not an identity. Start by treating it as a quadratic equation in sin(2x). The quadratic factorizes easily.
A quantity shrinks at a continuous rate of
per year. Its effective growth rate is
per year.
Answers
Answer:
Based on the information provided, there seems to be a discrepancy between the given information about the quantity shrinking at a continuous rate and the requested information about its effective growth rate. If a quantity is shrinking continuously, it is not experiencing growth, and therefore there is no effective growth rate. Nonetheless, assuming that the requested information was about the effective shrinkage rate of the quantity per year, this information can be extracted from the given information that "A quantity shrinks at a continuous rate of 33% per year." The effective shrinkage rate of the quantity can be calculated as follows:
Let r be the continuous shrinkage rate of the quantity
The effective shrinkage rate of the quantity is given by the expression (1 - r).
From the given information , r = 33% = 0.33.
Therefore, the effective shrinkage rate of the quantity is (1 - r) = (1 - 0.33) = 0.67 or 67% per year.
Note that if the phrase "effective growth rate" was a mistake, and the original intent was to ask for the shrinkage rate, then the above calculation gives the answer. Otherwise, further clarification is needed.
You may be interested in visiting A quantity's size after t years is given by A(t) =...
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Step-by-step explanation:
The question refers to the concept of continuous growth or shrinkage, and the effective growth rate in a financial context. Despite missing figures, assuming a quantity shrinks at a continuous rate of 3% and its effective growth rate is 2%, it implies a net shrinkage is 1% annually.
Explanation:The question pertains to the subject of compound interest in finance, but it appears that some of the figures and percentages are missing. However, generally speaking, continuous growth or shrinkage refers to the rate at which a quantity increases or decreases for a specific period of time. The effective growth rate is a term in finance that is used to compare the annual interest rates between financial products that have different compounding terms. For instance, if a quantity shrinks at a continuous rate of 3% per year, and its effective growth rate is 2% per year, it means that net shrinkage is 1% per year.
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Solve the following for θ, in radians, where 0≤θ<2π.
2cos2(θ)−8cos(θ)−1=0
Select all that apply:
1.07
1.69
4.59
2.49
2
2.33
Answers
Answer:correct answers 1.69
4.59
Step-by-step explanation:
We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):
2u^2 - 8u - 1 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 2, b = -8, and c = -1. Substituting these values, we get:
u = (8 ± sqrt(8^2 - 4(2)(-1))) / 2(2)
u = (8 ± sqrt(72)) / 4
u = 2 ± sqrt(18)
Therefore, either:
Pls help
The shape below contains a rectangle and four semi-circles.
Round your responses to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
Answers
Answer:
perimeter: 47.12 unitsarea: 151.60 square unitsStep-by-step explanation:
You want the perimeter and area of a figure consisting of a 4 × 11 rectangle with semicircles attached to each straight edge.
PerimeterIf you trace the perimeter of the figure, you see you are tracing the circumference of a circle 4 units in diameter and the circumference of a circle that is 11 units in diameter. The circumference of a circle is given by ...
C = πd
so the total circumference is ...
C1 +C2 = π(4) +π(11) = π(4+11) ≈ 47.12 . . . . units
The perimeter of the figure is about 47.12 units.
AreaThe area of two half-circles is the area of one whole circle of the same diameter. The area of a circle of diameter d is given by ...
A = (π/4)d²
The total area of the circles of diameters 4 and 11 is ...
A1 +A2 = (π/4)·4² +(π/4)·11² = (π/4)(4² +11²)
The area of the central rectangle is added to the areas of the semicircles. Its area is ...
A = LW
A = (11)(4)
TotalThe area of the entire figure is the sum of the circle areas and the rectangle area:
total area = (π/4)(4² +11²) +(4)(11) ≈ 151.60 . . . . square units
The area of the figure is about 151.60 square units.
__
Additional comment
You usually see the formula for the area of a circle as ...
A = πr²
Since r = d/2, we can express this using d as ...
A = π(d/2)² = π(d²)/(2²) = (π/4)d²
You may notice that a square that circumscribes the circle will have a side length of d, and an area of d². The fraction π/4 tells you the fraction of that enclosing square that is covered by the circle. This fact can help you estimate areas and volumes of circles and cylinders.
which equation represents a parabola opening downward with a vertex of the origin and a focus at (0,-1)?
y= -1/4x^2
y=1/4x^2
y=1/12x^2
y=-1/12x^2
Answers
y = -1/4x^2
The standard form of the equation of a parabola with vertex at the origin and focus (0, p) is given by:
y^2 = 4px
In this case, p = -1, so the equation becomes:
y^2 = -4x
Solving for y, we get:
y = ± √(-4x)
Since the parabola opens downward, we take the negative square root:
y = -√(-4x)
Simplifying, we get:
y = -2√(x)
Multiplying by a constant, we get:
y = -1/4(4√(x))^2
Therefore, the equation that represents a parabola opening downward with a vertex of the origin and a focus at (0,-1) is:
y = -1/4x^2.
So, the answer is "y = -1/4x^2."
Please help with this simple question (Large reward)
Answers
Answer:
H
Step-by-step explanation:
Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.
In F, the second number is 3 and 1/2.
In H, the second number is 3 and 1/4.
If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.
Please help !!!!!!!!!!!!!!!!!!!!!!
Answers
2) The way the coordinates show the given scale factor is that the ratio of both x and y coordinates to the mapped coordinate before dilation are all equal.
3) The coordinates after dilation are: (5.4, 27)
How to use scale factor dilation?2) The coordinates transformed points after dilation are completed as:
B(2, 4) → B'(3, 6)
K(4, -4) → K'(6, -6)
N(-6, 0) →N'(-9, 0)
The scale factor is same because using the ratio of the x coordinates gives:
3/2 = 1.5
6/4 = 1.5
-9/-6 = 1.5
3) The point W of the vertex of the polygon has coordinates as (2, 10)
Thus, if dilated by a scale factor of 2.7, we have the new coordinates as:
(2*2.7, 10*2.7) = (5.4, 27)
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what are the coordinates of the point that corresponds to -5pi/4 on the unit circle
Answers
The coordinates of the point that corresponds to -5π/4 on the unit circle is (-1/√2, 1/√2).
Given that,
We have to find the coordinates of the point that corresponds to -5π/4 on the unit circle.
We know that any point on the unit circle can be defined as,
(cos θ, sin θ)
where θ is the angle formed with the X axis.
-5π/4 will be the point the corresponds to -225°.
Cos(-5π/4) = cos (5π/4)
= cos (π + π/4)
= -cos (π/4)
= -1/√2
sin (-5π/4) = -sin (5π/4)
= -sin (π + π/4)
= sin (π/4)
= 1/√2
Hence the coordinate of the unit circle is (-1/√2, 1/√2).
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Subtract t⁴-3t²+7 from 5t³-9.
Answers
Answer:
t⁴+5t³-3t²-2
Step-by-step explanation:
You can't subtract a variable with a different exponent:
Example:
CAN'T BE SUBTRACTED - 3x²-3x⁴
CAN BE SUBTRACTED - 4x²-2x²=2x²
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Step-by-step explanation:1. Write the expression.[tex]\sf (5t^{3} -9)-(t^{4}-3t^{2} +7 )[/tex]
2. Remove the parenthesis.Beware of the terms of the right hand side parenthesis, as we'll have to change the symbol of all of them because of the minus (-) symbol infront of the parenthesis.
[tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
3. Work with like terms.Like terms are terms that contain the same variables and can be added and subtracted simply. For example, 7x and 2x are like terms, because they are both expressed in terms of x. However, 7x and x² are not like terms, because one os expressed in terms of x and the ither in terms of x².
• Note: All natural numbers not being multiplied by any variables are like terms.
So now let's identify those like terms:
From this expression: [tex]\sf 5t^{3} -9-t^{4}+3t^{2} -7[/tex]
Only -9 and -7 are like terms. And, since -9-7= -16, the resulting expression should be the following:
[tex]\sf 5t^{3} -t^{4}+3t^{2} -16[/tex]
4. Order the terms correctly.So even though the last expression is the answer to this problem, we can polish it a little bit by ordering the terms. In math and other exact sciences, terms are normally ordered alphabetically and from greatest to least of it's the same variable with different exponents. Therefore, the final answer is:
[tex]\sf -t^{4}+5t^{3} +3t^{2} -16.[/tex]
Given the unit circle what is the value of y PLEASE HELP
Answers
Answer: √35/6
Step-by-step explanation:
see image for explanation
∠1 and ∠2 are vertical angles. ∠2 has a measure of 31°.
What is the measure of ∠1?
Enter your answer in the box.
Answers
The measure of <1 is 31°.
What are vertical angles?Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.
In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;
<2 = 31° (given)
So that;
<1 = <2 = 31°
Thus,
<1 = 31°
Therefore, it can be concluded that the measure of <1 is 31°.
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Let p be the constant function p (z) = 1,000,000,000. Let q be the exponential function q (2) = 10
The product of the two functions is (pq) (z) = 10ª-2, where a is a constant. What is the value of a?
C2023 Illuminate Education, Inc.
P
C
Answers
[tex]\large \boxed{\mathrm{10}}[/tex]
The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.
Answer:
10 or 1b
Step-by-step explanation:
What meaning of the statement this?
Answers
We can see here that the statement means that H is a subgroup of a group, and aЄ H is an element of that subgroup.
What is a mathematical statement?We can define a mathematical statement to be a claim that, depending on the circumstances, may be true or false. It frequently incorporates mathematical objects and their relationships or characteristics, such as integers, sets, functions, or geometric shapes.
We can see here that it shows that a is an element of the subgroup of H.
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Which of the following is a statistical question that can result in numerical data?
What is the name of the librarian at your local library?
Which park is the best one to take your dogs to play?
What is the name of a local farm in your area?
How many students at your school ride horses?
Answers
Chantel is deciding which of two similar wallets she will buy. Both are rectangular, but she wants the one that will best fit in her purse. The larger wallet is 18 centimeters long and the smaller one is 10 centimeters long. What is the area of the larger wallet if the area of the smaller one is 60 square centimeters?
Answers
The requried area of the larger wallet is 194.4 square centimeters.
Since the two wallets are similar, their corresponding sides are proportional. Let x be the width of the smaller wallet, then the width of the larger wallet is 18/10 times x, or 9/5 times x. Therefore, the dimensions of the larger wallet are 9/5 times the dimensions of the smaller wallet.
The area of the smaller wallet is x times 10 (length times width), or 10x square centimeters. We are given that this area is 60 square centimeters, so:
10x = 60
x = 6
Therefore, the width of the smaller wallet is 6 centimeters. The width of the larger wallet is 9/5 times 6, or 10.8 centimeters. The length of the larger wallet is 18 centimeters.
The area of the larger wallet is 10.8 times 18, or 194.4 square centimeters. Therefore, the area of the larger wallet is 194.4 square centimeters.
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What types of polynomials do you think could factor using the relationship made
in the previous question?
If a is replaced with an x, and b is replaced with a 2, how would the equation
look, and what does it mean?
Create your own replacement of a and b and explain how your equations would
look and what would it mean?
Answers
The relationship in the previous question involves the difference of squares pattern, which applies to polynomials of the form:
a^2 - b^2
where a and b are any real numbers.
If we replace a with x and b with 2, the equation would look like:
x^2 - 2^2 = (x + 2)(x - 2)
This means that any polynomial of the form x^2 - 4 can be factored using the difference of squares pattern.
As for creating our own replacement of a and b, let's say we replace a with y and b with 3. Then the equation would look like:
y^2 - 3^2 = (y + 3)(y - 3)
This means that any polynomial of the form y^2 - 9 can be factored using the difference of squares pattern.
Determine which of the following statements is true concerning the values described in column #1 and column #2. (1 point)
Column #1
Column #2
The x-coordinate of the vertex of the graph of The x-coordinate of the vertex of the graph of
y=-2x² - 4x + 12
y=x²-4x+3
O The value found in column #1 is greater than the value found in column #2.
The value found in column #1 is less than the value found in column #2.
O The value found in column #1 is equivalent to the value found in column #2.
The relationship between column #1 and column #2 cannot be determined by the information given.
8
Answers
The statement which is true concerning the values described in column #1 and column #2 is: B. The value found in column #1 is less than the value found in column #2.
How to determine the x-coordinate of the vertex of the graph?In Mathematics, the axis of symmetry of a quadratic function can be calculated by using this mathematical expression:
Axis of symmetry, Xmax = -b/2a
Where:
a and b represents the coefficients of the first and second term in the quadratic function.
For the given quadratic function f(x) = -2x² - 4x + 12, we have:
Axis of symmetry, Xmax = -(-4)/2(-2)
Axis of symmetry, Xmax = 4/-4 = -1.
For the vertex of f(x) = -2x² - 4x + 12, we have:
f(-1) = -2(-1)² - 4(-1) + 12 = 14.
For the given quadratic function f(x) = x²-4x+3, we have:
Axis of symmetry, Xmax = -(-4)/2(1)
Axis of symmetry, Xmax = 4/2 = 2.
For the vertex of f(x) = x²-4x+3, we have:
f(2) = (2)²-4(2) +3 = -1.
Therefore, 2 is greater than -1.
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Financial aid letters show your aid and costs of attendance for
one year
O four years
the entire time you plan on attending
a semester
Answers
Financial aid letters display aid and attendance costs for one year only. Some schools offer a financial aid letter for four years of undergrad, aiding in budget planning for the program.
What is the Financial aid?A few schools may give a budgetary help letter that ventures aid and costs for all four a long time of an undergrad program. This could offer assistance understudies arrange and budget for their whole undergrad instruction.
In a few cases, Financial aid letters may show aid and costs for a single semester, instead of the complete scholarly year. This could be valuable for understudies who are as it were going to part-time or who got to take a semester off.
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A man has 16 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.50, how many dimes and how many quarters does he have?
Let d = number of dimes, q = number of quarters.
Step one:
A man has 16 coins in his pocket, all of which are dimes and quarters.
Set up the first equation for the number of dimes and quarters. Help PLS
Answers
Answer: 10 dimes and 6 quarters, see below for the equations.
Step-by-step explanation:
We know how much a dime is worth and how much a quarter is worth, and they give us the total number of coins and the total number of change.
This equation shows the total number of coins:
d + q = 16
This equation shows the worth of these coins:
0.10d + 0.25q = 2.5
Now, we can graph these equations. See attached. The point of intersection, where the lines cross, is our solution. In the graph, d = x and q = y.
This point is (10, 6) meaning he has 10 dimes and 6 quarters in his pocket.
Which equation represents a direct variation?
Oy - 4x = 8
Oy + 2 = 7x
Oy - 3x = 0
O y = 5x - 2
Answers
Answer:
The equation that represents a direct variation is y = 5x - 2.
In a direct variation, one variable is proportional to the other variable, which means that as one variable increases or decreases, the other variable also increases or decreases in direct proportion. The general form of an equation that represents direct variation is y = kx, where k is a constant of proportionality.
In this case, the equation y = 5x - 2 is in the form of y = kx, where k = 5. This means that as x increases or decreases, y will also increase or decrease proportionally, with a constant rate of change of 5. Therefore, this equation represents a direct variation.
what type of number is 15/10
Answers
Answer:
The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.
Step-by-step explanation:
Answer:
Fraction, 15/10 is written out as 15 Over 10
20x-12 factor out gcf in order to rewrite expression
Answers
20x - 12 = 4(5x - 3)
2y+3y-18=-83?????????????
Answers
Answer:
-13
Step-by-step explanation:
Claire got 17 out of 20 questions correct on her vocabulary quiz. What percent of the questions did she get wrong?
Answers
The percentage of the questions she got wrong is 15%
What is a Percentage?
Percentage is a number or ratio by dividing the value by the total value and then multiplying the result by 100.
How to determine this
Out of 20 questions, Claire got 17 questions
i.e the questions she got right = 17
The questions she got wrong = 20 - 17 = 3
To get the percentage she got wrong
= 3/20 *100%
= 300/20%
= 15%
Therefore, the percentage she got wrong is 15%
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Each triangle in the quilting square pattern shows has a base and height of 2 inches how much fabric is needed to create one quilting square
Answers
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Answer:
The amount of fabric needed to create one quilting square is 8 inches.
Step-by-step explanation:
What is the equation of the line shown in this graph?
Answers
Answer:
The equation is y=-3
Step-by-step explanation:
The line is horizontal, cutting across the y-axis, which means it will be a y= line. The point it hits the y-axis is -3, so it is y=-3.
geometry please help
Answers
A graph of triangle CAT is shown below.
A graph of triangle C'A'T, the image of ΔCAT after a reflection in the x-axis is shown below.
ΔC'A'T represents a rigid motion because the pre-image and the image are congruent.
What is a reflection over the x-axis?In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.
Next, we would apply a reflection over or across the x-axis;
(x, y) → (x, -y)
C (-1, 2) → (-1, -(2)) = C' (-1, -2)
A (-1, 4) → (-1, -(4)) = A' (-1, -4)
T (3, 2) → (3, -(2)) = T' (3, -2)
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