The value of the given expression is 16.
The expression we are interested in is:
logₐ ((x²y)/(z³))
To simplify this expression, we can use the properties of logarithms. In particular, we can use the fact that the logarithm of a quotient is equal to the difference of the logarithms of the numerator and denominator. Similarly, the logarithm of a power is equal to the product of the logarithm of the base and the exponent.
Using these properties, we can rewrite the expression as follows:
log ₐ ((x²y)/(z³)) = log ₐ (x²) + log ₐ (y) - log ₐ (z³)
Now, we can substitute the given values of the logarithms of x, y, and z:
log ₐ (x²) = 2 log ₐ (x) = 2 * 5 = 10 log ₐ (y) = 3 log ₐ (z³) = 3 log ₐ (z) = 3 * (-1) = -3
Substituting these values back into the expression, we get:
log ₐ ((x²y)/(z³)) = 10 + 3 - (-3) = 16
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What is -2 1/3 x 5/4
Answer:
-2 11/12
Step-by-step explanation:
-2 1/3 x 5/4
-7/3 x 5/4 = -35/ 12
-35/-12= -2 11/12
In a survey conducted by a website, employers were asked if they had ever sent an employee home because they were dressed inappropriately. A total of 2765 employers responded to the survey, with 964 saying that they had sent an employee home for inappropriate attire. In a press release, the website makes the claim that more than one-third of employers have sent an employee home to change clothes.
A button hyperlink to the SALT program that reads: Use SALT.
Do the sample data provide convincing evidence in support of this claim? Test the relevant hypotheses using
= 0.05.
For purposes of this exercise, assume that it is reasonable to regard the sample as representative of employers in the United States. (Round your test statistic to two decimal places and your P-value to four decimal places.)
z =
P-value =
find an equation of a parabola with a vertex at the origin and directrix y=-1.5.
x=-1/6y^2
x=1/6y^2
y=-1/6x^2
y=1/6x^2
Step-by-step explanation:
We know that the vertex of the parabola is at the origin, so the equation must have the form:
y = a x^2
where a is a constant.
We also know that the directrix is y = -1.5, which means that the focus is located at (0, 1.5).
Using the formula for the distance between a point (x, y) and a line ax + by + c = 0, which is given by:
d = |ax + by + c| / sqrt(a^2 + b^2)
we can find the value of a. The distance from the vertex (0, 0) to the directrix y = -1.5 is equal to the distance from the vertex to the focus (0, 1.5), so we have:
d = |y - (-1.5)| / sqrt(1^2 + 0^2) = sqrt(x^2 + (y - 1.5)^2) / sqrt(0^2 + 1^2)
Simplifying this equation, we get:
sqrt(x^2 + (y - 1.5)^2) = |y + 1.5|
Squaring both sides, we get:
x^2 + (y - 1.5)^2 = (y + 1.5)^2
Expanding and simplifying, we get:
x^2 = 3y
So the equation of the parabola with vertex at the origin and directrix y = -1.5 is:
y = (1/3)x^2
Therefore, the correct answer is: y = (1/3)x^2.
Need help with this problem. I don’t quite understand this!
The value of cos 2θ is determined as 0.442.
What is the value of cos 2θ?The value of cos 2θ is calculated by applying the following trig identities.
sin θ = 28/53
The value of θ is calculated as;
θ = sin ⁻¹ (28/53)
θ = 31.89⁰
The value of cos 2θ is calculated as follows;
cos 2θ = cos (2 x 31.89)
cos 2θ = cos (63.78)
cos (63.78) = 0.442
Thus, the value of cos 2θ is determined by first calculating the value of θ based on the sine function given.
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Find the value of x.
a. 53°
b. 72°
c. 48°
d. 39°
Answer:
Step-by-step explanation:
yes it is b
Find the equation of a line parallel to −5x+y=−4that passes through the point (−7,−9).
The equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.
Given that, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9).
The given equation can be written as y=5x-4.
Now, compare y=5x-4 with y=mx+c, we m=5
The slope of a line parallel to given line is m1=m2
So, the slope of the line parallel to the given line is 5.
Now, substitute m=5 and (x, y)=(-7, -9) in y=mx+c, we get
-9=5(-7)+c
c=-9+35
c=26
So, the equation is y=5x+26
Therefore, the equation of the line is parallel to -5x+y=-4 and passes through the point (−7,−9) is y=5x+26.
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* Required Problem Set 1 A swimming pool has 150 gallons of water in it. It fills up at a constant rate of 30 gallons every 2 hours. The initial value is 30 gallons every 2 hours * O True O False
False. The initial value is 0 gallons every 2 hours because the pool already has 150 gallons of water in it.
Calculate the area of the shaded region for the given figure.
The area of the shaded region of the given figure would be = 47.1.
How to calculate the area of the shaded figure?To calculate the area of the shaded figure, the formula of the area of a sector of a circle is used such as;
area of sector = ∅/360πr²
∅ = 40°
r = 12
area = 40/360 × 3.14× 12×12
= 18086.4/360
= 50.24
Area of the unshaded portion
radius = 12-9 = 3
area = 40/360×3.14×3×3
= 1130.4/360
= 3.14
Therefore area of the shaded portion;
= 50.24- 3.14
= 47.1
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The number of students earning master's degrees in mathe
g(x) = 7x² -226x + 4941, where x represents the number o
mathematics or statistics in that country in 2009.
The number of students earning master’s degrees in mathematics or statistics in the country in 2009 was 4474.
We are given that;
g(x) = 7x² -226x + 4941
Now,
To find the number of students in 2009, we need to plug in x = 9 into the function g(x), since 2009 is 9 years after 2000.
g(9) = 7(9)² -226(9) + 4941
g(9) = 7(81) -2034 + 4941
g(9) = 567 -2034 + 4941
g(9) = 4474
Therefore, according to the function g(x) the answer will be 4474.
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A metallurgist has one alloy containg 34% aluminum and another containing 69% aluminum. How many pounds of each alloy must he use to make 45 pounds of a third alloy containing 56% aluminum?
The metallurgist needs to use 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.
How to find the how many pounds of each alloy must he use to make 45 pounds of a third alloy containing 56% aluminumLet x: the number of pounds of the alloy containing 34% aluminum that the metallurgist needs to use,
Let y: be the number of pounds of the alloy containing 69% aluminum.
We want to find values for x and y such that when they are mixed together, they will produce 45 pounds of an alloy containing 56% aluminum.
To solve for x and y, lets set up a system of two equations
x + y = 45 (total weight of the final alloy)....eqn 1
0.34x + 0.69y = 0.56(45) (total amount of aluminum in the final alloy)....eqn 2
Simplifying Eqn 2, we get:
0.34x + 0.69y = 25.2
Now we can solve the system of equations by substitution method
Solve Equation 1 for x in terms of y:
x = 45 - y
Substitute x = 45 - y into Equation 2:
0.34(45 - y) + 0.69y = 25.2
Distribute the 0.34:
15.3 - 0.34y + 0.69y = 25.2
Combine like terms:
0.35y = 9.9
Solve for y:
y = 28.2857... (rounded to 3 d.p)
Now we can use this value of y to find x:
x = 45 - y
x = 16.7142... (rounded to 3 decimal places)
Therefore, the metallurgist needs to use approximately 16.714 pounds of the alloy containing 34% aluminum and 28.286 pounds of the alloy containing 69% aluminum to make 45 pounds of a third alloy containing 56% aluminum.
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A pack of 12 pens cost $3.25 what is the cost of one pen
Therefore, using simple division, the price of one pen is calculated to be around $0.27.
Describe Division.In mathematics, division is the process of dividing an integer into equal pieces or groups. It performs multiplication in the other direction. To obtain the quotient or outcome in division, an even number has been divided by another integer, known as the divisor.
We must divide the total expense of the 12-pen pack by the quantity of pens in the box in order to figure out the price of one pen:
Price of one pen is equal to the sum of the pack's pen costs divided by the number of markers in the pack.
In this instance, we may substitute these values as we are aware that the set of 12 pens costs $3.25.
In this instance, we may enter the following values into the calculation as we are aware that the set of 12 markers costs $3.25:
One pen costs $3.25 divided by 12
Long division or using a calculator, we obtain:
One pen costs $0.27.
Consequently, the price of a pen is roughly $0.27.
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Which of the following exponential functions represents the graph below?
Answer:
A
Step-by-step explanation:
I used desmos to graph the equations and A matches
Michelle has four credit cards with the balances and interest rates listed below. She would like to consolidate all of her credit cards in a single credit card with an interest rate of 16% and pay off the balance in 36 months. If she did so, what would Michelle’s monthly credit card payment be?
Credit Card
Balance
APR
#1
$4,380
17%
#2
$1,365
19%
#3
$2,480
23%
#4
$5,000
15%
a.
$367.36
b.
$464.95
c.
$685.23
d.
$826.56
Answer:
mark me brilliant
Step-by-step explanation:
To calculate Michelle’s monthly credit card payment, we need to find the total amount she owes and then divide it by the number of months she has to pay it off.
First, we need to find the total balance on Michelle’s credit cards:
$4,380 + $1,365 + $2,480 + $5,000 = $13,225
Next, we need to find the weighted average interest rate of her credit cards. To do this, we multiply each balance by its corresponding APR and add up the results. Then we divide by the total balance:
($4,380 x 0.17) + ($1,365 x 0.19) + ($2,480 x 0.23) + ($5,000 x 0.15) = $1,038.55
$1,038.55 ÷ $13,225 = 0.0785, or 7.85%
Now we can use the total balance and the weighted average interest rate to calculate Michelle’s monthly payment using the formula for a fixed payment on a loan:
P = (r(PV)) / (1 - (1 + r)^-n)
Where:
P = monthly payment
r = monthly interest rate (as a decimal)
PV = present value of the loan
n = number of payments
r = 0.16 ÷ 12 = 0.01333 (monthly interest rate)
PV = $13,225
n = 36
P = (0.01333(13,225)) / (1 - (1 + 0.01333)^-36) = $367.36
Therefore, Michelle’s monthly credit card payment would be $367.36 if she consolidated all of her credit card debt into a single credit card with an interest rate of 16% and paid it off in 36 months. The answer is (a) $367.36.
matt had 4/6 bag of peanuts. He ate a quarter of what was in the bag. How much of a full bag of peanuts did Matt eat?
Matt ate 1/6 of the bag of peanut
Matt had 4/6 bag of peanut
He ate a quarter of what was in the bag
The amount of peanut he ate can be calculated as follows
= 4/6 × 1/4
= 4/24
= 1/6
Hence Matt ate 1/6 of the bag of peanut
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It is hypothesized that the total sales of a corporation should vary more in an industry with active price competition than in one with duopoly and tacit collusion. In a study of the merchant ship production industry it was found that in 4 years of active price competition, the variance of company A’s total sales was 114.09. In the following 7 years, during which there was duopoly and tacit collusion, this variance was 16.08. Assume that the data can be regarded as independent random sample from two normal distributions. Test at the 5% level the null hypothesis that the two population variances are equal against the alternative that the variance of total sales is higher in years of active price competition.
Since the calculated F-value of 7.098 is greater than the critical value of 5.79, we reject the null hypothesis and conclude that the population variance of total sales during active price competition is higher than during duopoly and tacit collusion at the 5% level of significance.
How can we explain the above?For the above issue, the null and alternate hypotheses are as follows:
The population variations of total sales under duopoly, active price competition, and tacit cooperation are all identical.
In contrast to duopoly and implicit collusion, total sales population variance is larger under active price competition.
To test the null hypothesis, we must use a two-tailed F- test with a 5 % threshold of significance. The ratio of the sample variances is used to determine the F- statistic.
F = s1² / s2²
Where:
s1² - Sample Variance (Active price competition)
s2² - SAmple variance (Duopoy and Tacit collusion)
Since n1-1 = 3
and n2-1 = 6
F = 114.09 / 16.08
F = 7.098
Having derived same, we know that the critical values of F for a two-tailed test with 3 and 6 degrees of freedom at 5% level of significance are:
Critical Value (3) = 5.14
Critical Value (6) = 5.79
Therefore, since the F-value > Critical Value in both cases, we must reject the null hypothesis.
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Determine the interval(s) for which the function shown below is increasing.
Answer:
Step-by-step explanation:
When x≥2 the function is increasing. you read the graph from left to right
Can also be written [-2, +∞)
Solving exponential equations with the same base
Solve for x:
(-3)* = (-3) 13
O 13
Ox+13
0-3
Ox-13
Answer:
x = 13 is the solution.
Step-by-step explanation:
Here is how it looks for this problem:
(-3)* = (-3) 13 Ignore the base and write an equation for the exponents: x = 13 Solve for x by subtracting 13 from both sides: x - 13 = 0 Add 13 to both sides: x = 13 Check your work by plugging x = 13 into the original equation: (-3)* = (-3) 13 (-3) 13 = (-3) 13 True
Write the solution set to x ≥ 2 in interval notation.
Answer:
[2, ∞)
Step-by-step explanation:
We Know
The solution set to x ≥ 2, meaning the 2 ≤ x < ∞
So, the interval notation is [2, ∞)
A proportional relationship is shown in the table below:
�
xx
0
00
1.3
1.31, point, 3
2.6
2.62, point, 6
3.9
3.93, point, 9
5.2
5.25, point, 2
�
yy
0
00
1
11
2
22
3
33
4
44
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
The slope of the line that represents the relationship is 0.76.
What is slope of a line?Slope in mathematics relates to how steep a line is. It measures how much the y-coordinate shifts upward or downward for every unit increment in the x-coordinate. The ratio of the vertical change (rise) to the horizontal change (run) between any two locations on a line is, in other words, the slope of the line.
The following equation can be used to determine a line's slope: slope = (y2 - y1) / (x2 - x1).
where any two points on the line (x1, y1) and (x2, y2).
Positive, negative, zero, or undefinable slopes are all possible. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.
The slope of the line is given by the formula:
slope = (change in y) / (change in x)
Substituting the point from the table we have (0, 0) , (1.3, 1) thus:
m = 1 - 0 / 1.3 - 0
m = 1 / 1.3 = 0.76
Now, using the slope intercept form we have:
y - y1 = m(x - x1)
For (0, 0) we have:
y = 0.76x
Hence, the slope of the line that represents the relationship is 0.76.
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The complete question is:
the length of rectangular hall is two times of its breadth and 3 times it height. If the volume. of the hall is 36000m³ find the area of its floor.
Answer: The area of the floor of the hall is approximately 599.2448 square meters.
Step-by-step explanation: Let's assume the breadth of the hall be x meters. Then, the length of the hall will be 2x meters and the height will be 3x meters.
The volume of the hall can be found as follows:
Volume = Length × Breadth × Height
36000 = 2x × x × 3x
36000 = 6x³
x³ = 6000
x = ∛6000 ≈ 17.32 meters
Therefore, the breadth is approximately 17.32 meters, the length is 2 × 17.32 = 34.64 meters, and the height is 3 × 17.32 = 51.96 meters.
The area of the floor can be found by multiplying the length and breadth:
Area = Length × Breadth
Area = 34.64 × 17.32
Area = 599.2448 m²
Therefore, the area of the floor of the hall is approximately 599.2448 square meters.
pls help me with this
The expression of the perimeter of the triangle is 15h - 6k + 12m.
How to find the perimeter of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The perimeter of a triangle is the sum of the whole three sides of the triangle.
Therefore, let's find the perimeter of the triangle with side length (5h - 4k), (10h + 7m) and (5m - 2k).
Therefore,
perimeter of a triangle = 5h - 4k + 10h + 7m + 5m - 2k
collect like terms
perimeter of a triangle = 5h + 10h - 4k - 2k + 7m + 5m
Therefore,
perimeter of a triangle = 15h - 6k + 12m
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Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.
please help also explain how you got the answer
Answer:
The Answer may be D
Step-by-step explanation:
The answer is D because it's an one step equation. For something to be linear it must be one step.
9) Find the 10th term in the
sequence.
9) 2, 4, 12, 48, 240, ...
A) a
5828046
a 10
B) a = 3765310
10
C) a = 4678865
10
D) a = 7257600
10
The 10th term of the sequence is 7,257,600. Option D.
Arithmetic sequenceTo find the 10th term in the sequence, we can use the pattern to generate the next terms:
The first term is 2.
To get the second term, we multiply the first term by 2: 2 × 2 = 4.To get the third term, we multiply the second term by 3: 4 × 3 = 12.To get the fourth term, we multiply the third term by 4: 12 × 4 = 48.To get the fifth term, we multiply the fourth term by 5: 48 × 5 = 240.Therefore, to get the 10th term, we can multiply the fifth term by 6, then by 7, then by 8, and then by 9:
5th term = 2406th term = 240 × 6 = 14407th term = 1440 × 7 = 100808th term = 10080 × 8 = 806409th term = 80640 × 9 = 72576010th term = 725760 × 10 = 7257600Therefore, the 10th term in the sequence is 7,257,600.
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What is the decimal equivalent of 7/12? A. 0.583 B. 0.58 C. 0.583 D. 5.83
who ever answers the question right i will make them a brainlest
Answer:
c
Step-by-step explanation:
I hope it help :)
which radian measure is equivalent to 300°?
• 5/3
• 11pi/6
• 5pi/6
• 5pi/3
The radian measure that is equivalent to 300° is equal to 5π/3. So, correct option is D.
To convert degrees to radians, we use the conversion factor of π/180, which means that one degree is equal to π/180 radians. Therefore, to convert 300° to radians, we multiply 300 by π/180:
300° * π/180 = 5π/3
To understand this conversion, we need to remember that radians are a unit of measurement for angles, just like degrees. However, while degrees divide a circle into 360 equal parts, radians divide a circle into 2π equal parts. One full rotation is equal to 2π radians, which is also equal to 360°.
Since 5π/3 radians is less than one full rotation, it represents an angle that is less than 360°. In fact, 5π/3 radians is equivalent to 300°, which is a well-known angle used in many contexts, such as in geometry, trigonometry, and physics.
In summary, to convert 300° to radians, we multiply it by the conversion factor π/180, which gives us the equivalent angle measure of 5π/3 radians.
So, correct option is D.
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What is the distance between the coordinates (2, 9) and (10, 6)? Round your
answer to the nearest tenth.
Answer here
<>
SUBM
Answer:
8.54
Step-by-step explanation:
√(6-9)²+(10-2)2
=√(-3)²+8²
=√9+64
=√73=8.54
The answer is 8.54
Represent "the product of 3 and a number" algebraically Use n to represent "a number". DO NOT USE ANY SPACES! Use only +,-,*,/ for operation symbols
Answer:
The product of 3 and a number can be represented as:
[tex]3n[/tex]
Find the annual interest rate. (Round your answer to the nearest whole number.)
Principal
Balance
$4000
$62,702.95
Enter a number.
Need Help?
Submit Answer
X%
Read It
Time
20 years
Compounding
Quarterly
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Reque
Answer:
[tex]\text{Annual interest rate = 14 \%}[/tex]
Step-by-step explanation:
The formula for computing accrued amount(principal + interest) is given by
[tex]A = P\left (1 + \dfrac{r}{n}\right )^{nt}[/tex]
where
P =principal amount
r = annual interest rate as a decimal
n = number of times compounded per year
t = number of years
A = amount accrued at the end of t years
We are given
A = 62702.95
P = 4000
n = 4 since we are compounding quarterly, i.e. 4 times a year
t = 20
Plugging in known values into the equation we get
[tex]62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{4 \cdot 20}\\\\62702.95 = 4000\left(1 +\dfrac{r}{4}\right)^{80}\\\\[/tex]
Switch sides and divide both sides by 4000 to get
[tex]\left(1 +\dfrac{r}{4}\right)^{80} = \dfrac{62702.95}{4000}[/tex]
[tex]1 +\dfrac{r}{4}\right) = \left(\dfrac {62,702.95}{4000}\right)^{\dfrac{1}{80}}\\\\\text{Using a calculator,}\\1 +\dfrac{r}{4}\right) = 1.03499\dots \approx 1.035[/tex]
[tex]\dfrac{r}{4} = 1.035 - 1 = 0.035\\\\r = 4 \times 0.035\\\\\\r = 0.14\\\\\\[/tex]
As a percentage that would be
[tex]0.14 \times 100 = 14\%[/tex]
Can anyone tell me this worksheet and how to do it? Btw whenever I divide, I will have to turn it into a fraction and if the fraction isn’t simplified I will have to simplify it to a good looking fraction. Example: 0.75/1.25 would be 3/5in, scale drawing goes on top, actual goes on bottom. Remember you have to do proportional set up. it’s like that.
The scale factor of the given images above is as follows:
1.) 5/3
2.) 7/10
3.) 7/3
4.) 3/2
How to determine the scale factors of the given images?For image 1.), the image was scaled down.
scale factor = original image dimensions/scale drawing
= 1.25/0.75
proportional set up = 125/75 = 5/3
For image 2.) the image was scaled up.
scale factor = Bigger dimensions/smaller dimensions
= 3.5/2
proportional set up = 35/20 = 7/10
For image 3.) the image was scaled down.
scale factor = original image dimensions/scale drawing
= 1.75/0.75
proportional set up = 175/75 = 7/3
For image 4.) the image was scaled up.
scale factor = Bigger dimensions/smaller dimensions
= 6/4 = 3/2
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