Solution :
[tex]\qquad \sf \dashrightarrow \: log(x) + 5 \: log(y) - 4 \: log(z) [/tex]
[tex]\qquad \sf \dashrightarrow \: log(x) + \: log(y {}^{5} ) - \: log(z {}^{4} ) [/tex]
( a log(x) = log(x^a) )
[tex]\qquad \sf \dashrightarrow \: log( x {y}^{5} ) - log(z {}^{4} )[/tex]
( log (a) + log (b) = log (ab) )
[tex]\qquad \sf \dashrightarrow \: log( \frac{ x {y}^{5} }{z {}^{4} }) [/tex]
( log (a) - log (b) = log (a/b) )
Add and simplify.
7/12 + 2/15
Ten men working 6 hours a day takes 12 days to complete a job.How long will it take 8 men working 12 hours a day to complete the same job
Answer:
It will take 7.5 days to complete the job.
Step-by-step explanation:
First, find how many total hours the ten men worked to complete the job
10 x 6 = 60 hours a day
12 x 60 = 720 hours total
Now compare that with the 8 men's hours
8 x 12 = 96 hours a day
720 / 96 = 7.5 days
PLEASE HELP! ALGEBRA 1 HW I WILL GIVE BRAINLYEST FOR ANSWER!!
please answer all questions (a, b, and c)
5 Math on the Spot Robin says, "I can find 6 × 9 by
multiplying 4 X 9 and doubling it." Does her statement
make sense? Justify your answer.
If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
What is distributive property?
The same outcome will be obtained by multiplying the sum of two or more addends by a number as it is by multiplying each addend separately by the number and then adding the resulting products.
A × (B + C) = AB + AC
A (B - C) = AB - AC
Here,
we can write 6 × 9 as,
= 6 × 9 = 6 × (6 + 3) = (6 × 6) + (6 × 3), by applying distributive property
Hence, If Robin says, "I can find 6 × 9 by multiplying 4 X 9 and doubling it, her statement didn't make any sense because it is not possible.
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2 step equation:12. Amy wants to start taking gymnastics. There is a one-time fee of $35 to sign up, then it costs $85 per month. If Amy saves up $225, how many months of gymnastics can she take?
The number of months Amy can take the Gymnastic = 2 months.
Amy wants to start taking gymnastics.
The fee structure of the gymnastics is divided into two parts.
There is a one time fee payment of 35$ and there is a monthly payment that costs 85$ per month.
So the first month fee of the gymnastics = 35 + 85 = 120$
Savings of Amy = 225$
If Amy pays the 1st month fee ,
then the she will be left with the savings = 225$ - 120$ = 105 $
It means Amy can join the gymnastics for one more month .
Hence the number of months Amy can take the Gymnastic = 2 months .
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what is meter × meter
[tex]meter^{1`} *meter^{1} \\=meter^{1+1} \\=meter^{2}[/tex]
⇒Mote I used the laws of exponents : [tex]=x^{m} *x^{n} \\=x^{m+n}[/tex]
A student raises the flag up at a steady speed of 3m/s. The flag is 2kg in mass. What is the average power exerted.
The average power exerted on the flag of mass 2 kg by the student is 58.8 Watt.
What is power?Power can defined as the rate at which work is done.
To calculate the average power exerted on the flag, we use the formula below.
Formula:
P = mgv............ Equation 1Where:
P = Power exertedm = Mass of the flagg = Acceleration due to gravityv = Velocity at which the flag was raisedFrom the question,
Given:
m = 2 kgv = 3 m/sg = 9.8 m/s²Substitute these values into equation 1
P = 2×3×9.8P = 58.8 WattHence, the average power exerted is 58.8 Watt.
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ABC has a right angle at C, BC=6.8 centimeters, and m
Answer:
your question is cutoff, cant read it
A study was commissioned to find the mean weight of the residents in certain town. The study found the mean weight to be 193 pounds with a margin of error of 9 pounds. Which of the following is not a reasonable value for the true mean weight of the residents of the town?
Considering the confidence interval, the non-reasonable value for the true mean weight of the residents of the town is:
A value that is less than 184 or more than 202.
How to obtain the confidence interval?The confidence interval for a population mean is given by the point estimate of this mean, which is the sample mean, plus/minus the margin of error.
For the context of this problem, these parameters are given as follows:
Point estimate: 193 pounds.Margin of error: 9 pounds.Hence the lower bound of the interval is:
193 pounds - 9 pounds = 174 pounds.
The upper bound of the interval is:
193 pounds + 9 pounds = 202 pounds.
All the values that are in the interval are reasonable values for the population mean, hence, in the context of this problem, the not reasonable values are given as follows:
A value that is less than 184 or more than 202.
(as they would be outside the confidence interval).
Missing InformationThe options are not given, hence the answer was given in general terms.
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In the fall of 2017, there were 48 thousand more female undergraduate students enrolled at a college than male
undergraduate students. If the total undergraduate enrollment was 414 thousand that fall, find the numbers of female
undergraduate students and male undergraduate students who were enrolled.
The number of female undergraduate students was
thousand.
Answer: 231 thousand
Step-by-step explanation:
given,
total number of undergraduate students enrolled = 414000
let us take number of total number of male students as, X
then, total number of female students will be X + 48000
now we get,
total number of male students + total number of female students = total number of students enrolled.
X + (X + 48000) = 414000
X + X + 48000 = 414000
2X = 414000 - 48000
X = 366000/2
X = 183000
total number of male students is 183000
total number of female students is
X + 48000
183000 + 48000 = 231000
In a class of 152 students, 100 are taking math (M), 77 are taking science (S), and 55 are taking both math and science. One student is picked at random. Find the probability.
P(taking math or science or both)
The probability of taking math or science or both is 123/152
The total number of students = 152 students
Number of students who take math = 100 students
Number of student who take science = 77 students
Number of students who take both math and science = 55 students
The probability = Number of favorable outcomes / Total number of outcomes
We have to find each term
The number of favorable outcomes =55+45+23
= 123
Total number of outcomes = 152
Substitute the values in the equation
Probability of taking math or science or both = 123/152
Hence, the probability of taking math or science or both is 123/152
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what is the present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now?
The present value of $2525 per year, at a discount rate of 10 percent, if the first payment is received 9 years from now and the last payment is received 24 years from now is; $9215.77
What is the Present Value of Annuity?
An annuity is defined as a fixed amount of cash that is received or paid periodically over a certain period of time. This would mean that the amount in each cash flow of the annuity would be equal and occur for a specific period of time.
The formula for present value is;
PV = P[1 - (1 + r)⁻ⁿ)/r]
where;
PV is present value
P is periodic cash flow
r is interest rate
n is time
We are given the following;
Periodic cash flow (P) = $2525 /Year
Interest rate (r) = 10% /Year = 0.1
Time (n) = 16 Year (from 9 years to 24 years)
Thus;
PV = 2525[1 - (1 + 0.1)⁻¹⁶)/0.1]
PV = $19754.86
This is the present value in 9 years
Thus, the present value in 24 years which is now will be expressed by the formula;
PV = FV/(1 + i)^(t)
where;
PV is present value
FV is future value
i is interest rate
t is time
Thus;
PV = 19754.86/(1 + 0.1)^(8)
PV = $9215.77
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Using the graph below, determine the employee's hourly wage.
Using the graph, the hourly wage of the employees is: $8 per hour.
How to Determine Hourly Wage From a Graph?Slope of a proportional graph is the unit rate between two variables, x and y, and it is calculated as: k = y/x.
To find the unit rate or slope of the graph, use any point on the graph (x, y).
The unit rate of the graph in the image above is the hourly wage of the employees.
Using any point on the line, say, (13, 104), we can find the slope/unit rate. Therefore:
Unit rate/slope, k = 104/13
Unit rate/slope, k = 8
Therefore, the hourly wage is: $8 per hour.
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Determine if the line segment YX is tangent to circle Z.
The segment XY is a tangent to circle Z.
What is tangent to a circle?
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle.
To check the segment YX is tangent to circle z, first we have to check that the triangle formed XYZ is right angle triangle or not.
If the triangle XYZ is a right triangle, then we have
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 it's true.
Therefore, the segment XY is a tangent to circle Z.
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Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of a person is 5.2ft in centimeter: 158.49cm
What are the Factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.So, the conversion of measurement from the unit feet to centimeters is provided by the feet-to-centimeter calculator.
The letters "ft" and "cm" stand for feet and centimeters, respectively. The centimeter is used in the International System of Units and is regarded as a component of the metric system. The US customary measurement system uses the unit foot.Approximately 30.48 cm makes up one foot.
1 ft = 30.48 cm
Now, the formula for 5.2 feet to centimeters is as follows:We are aware that 1 foot equals 30.48 centimeters.Therefore, 5.2 feet equals 5.2 x 30.48 centimeters.
5.2 ft = 158.49 cm.5.2 feet is therefore equal to 158.49 cm in centimeters.
Hence, the height of a person who is 5.2 feet tall to centimeters is 158.49cm.
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In your lab, a substance's temperature has been observed to follow the function T(x) = (x − 5)3 + 9. The turning point of the graph is where the substance changes from a liquid to a gas. Using complete sentences in your written answer, explain to your fellow scientists how to find the turning point of this function. Hint: The turning point of the graph is similar to the vertex of a quadratic function.
The turning point is at x = 5, and this means that the substance changes from liquid to gas when x = 5.
How to find the turning point?
Here we have the temperature function:
T(x) = (x - 5)^3 + 9
The turning point is the point where the curvature of the function changes, by differentiating the function two times and finding the zero, we can get the turning points.
T'(x) = 3*(x - 5)^2
T''(x) = 3*2*(x - 5) = 6*(x - 5)
This is zero when x = 5, then:
T''(5) = 6*(5 - 5) = 0
So the turning point is there.
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On a website that sells funny T-shirts, the number of customers has been falling 10% per month. If the site had 14,000 customers this month, then how many should it expect to have 10 months from now?
If necessary, round your answer to the nearest whole number.
customers
It should expect 4881 customers to have 10 months from now.
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given that T-shirts, the number of customers has been Falling 10% per month
There are 14,000 customers this month
Now Creating the function :
Let y be the remaining customers and x be the number of months from now
y = (14,000)(1 - 0.1)ˣ
y = (14,000)(0.9)ˣ
Solving :
y = (14,000)(0.9)¹⁰
y = (14,000)(0.34867844)
y = 4881 customers
(nearest whole person)
Hence, it should expect 4881 customers to have 10 months from now.
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Answer:
It should expect 4881 customers to have 10 months from now.
Whats ?? Also right an addition expression to get the same answer Answer ASAP
Answer:
p=-10
Step-by-step explanation:
-10-20=-30
Subtracting a negative from a negative will result in a higher negative, the same can be said for -10-20. Removing 10 from -20 will result in a lower answer. This is 20.
If f(x) = 3x and g(x)=1/x, what is the domain of (gof)(x)?
For the given functions f(x) = 3x and g(x) = 1/x then domain of
(gof)(x) =1/3x is all the real numbers excluding zero.
As given in the question,
Given functions are as follow:
f(x) = 3x
g(x) = 1/x
Now ,
(gof)(x)
= g(f(x))
Substitute f(x) = 3x in the above function we have,
=g(3x)
Replace the value of x by 3x in the given function g(x) we get,
= 1/ 3x
For x = 0 (gof)(x) =1/3x is undefined.
Domain include all the real numbers except zero.
Therefore, for the given functions f(x) = 3x and g(x) = 1/x then domain of (gof)(x) =1/3x is all the real numbers excluding zero.
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what is the expected value of x? where x/p equals 0/.15, 4/.05, 8/.25, 12/.05, 16/.5
The expected value of x is 10.8
How calculate the expected value of x?Expected value is defined as the predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence.
Given :
x| 0 4 8 12 16
p| 0.15 0.05 0.25 0.05 0.5
The expected value of x, E(x) =Σ xp
E(x) = (0×0.15) + (4×0.05) + (8×0.25) + (12×0.05) + (16×0.5)
E(x) = 0 + 0.2 + 2 + 0.6 + 8
E(x) = 10.8
Therefore, the expected value of x is 10.8
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K
Choose the measurement closest to 30 km: 10 mi, 20 mi or 30 mi.
Choose the correct answer below.
20 mi
30 mi
10 Ini
O
O
O 10
Answer:
20 miles
Step-by-step explanation:
1.6km is equivalent to 1 mile
so 30km / 1.6 = 18.75 miles
therefore 20 miles is the closest to 30km
a piece of pipe is 40in. long. It is cut in to 3 pieces. the longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece. Find the lengths of all 3 pieces of pipe.
The length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
According to the question,
We have the following information:
A piece of pipe is 40in. long. It is cut in to 3 pieces. The longest piece is 3 times as long as the middle sized piece and the shortest piece is 23 in. shorter than the longest piece.
Let's take the length of middle sized piece to be x inches.
Length of longest piece = 3x inches
Length of shortest piece = (3x-23) inches
Now, we have the following expression:
x+3x+3x-23 = 40
7x-23 = 40
Adding 23 on both the sides:
7x = 40+23
7x = 63
Dividing by 7 on both the sides:
x = 63/7
x = 9 inches
Length of longest piece = 3*9 inches
Length of longest piece = 27 inches
Length of shortest piece = (27-23) inches
Length of shortest piece = 4 inches
Hence, the length of shortest piece is 4 inches, middle sized piece is 9 inches and that of longest piece is 27 inches.
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The length of the segment is _____centimeters
The scale is __cm : __mm.
Answer:
I'm assuming it's just a conversion of mm into cm?? in that case it will be 2.4 cm
The adult daily dosage for a certain medicine is 260 mg (milligrams) of medicine for every 40 pounds of body weight. a. At this rate, find the daily dose for a man who weighs 195 pounds. b. If the man is to receive 600 mg of this medicine every 8 hours, is he receiving the proper dosage? a. The daily dose for a man who weighs 195 pounds is (Round to the nearest tenth as needed.) mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b)Here 422.5 mg is less than 600mg. Then, He doesn't receive proper dosage.
What is proportional ?
Any relationship that always has the same ratio is referred to be proportionality. For instance, the average number of apples per tree determines the proportionality between the quantity of apples in a crop and the number of trees in the orchard.
Here , The adult daily dosage for a certain medicine is 260 mg
=> [tex]\frac{40}{260} = \frac{195}{x}[/tex]
=> x = [tex]\frac{260*195}{40}[/tex]
=> x =1267.5 mg.
a) Daily dose for a man who weighs 195 pounds is 30 mg.
b) Here for 24 hours = 1267.5 then,
=> 8 hours = x
=> x = [tex]\frac{1267.5*8}{24}[/tex]
=> x = 422.5 mg.
Here 422.5 mg is less than 600mg. Then, He does'nt receive proper dosage.
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Select the correct answer. What is this equation rewritten in logarithmic form? 9x = 3
A. log9 3 = x
B. logx 3 = 9
C. log3 9 = x
D. log3 x = 9
Answer:
A. [tex]\log_9{3}=x[/tex]
Step-by-step explanation:
[tex]y=e^x\rightarrow\log_e{y}=x[/tex]
Therefore,
[tex]3=9^x\rightarrow\log_9{3}=x[/tex]
Jan works from 30 to 40 hours per week during the summer. She earns $12.00 per hour. Her friend Rachel also has a job. Rachel's pay for t hours is given by the function r(t) = 11t, where 20 ≤ t ≤ 30. Find the domain and range of each function. Compare their hourly wages and the amount they earn per week.
j(t) domain:
≤ t ≤
j(t) range:
≤ j(t) ≤
r(t) domain:
≤ t ≤
r(t) range:
≤ r(t) ≤
select: Jan or Rachel
earns more per hour than
select: Jan or Rachel
. Jan earns from $ (blank)
to (blank) $
per week and Rachel earns from (Blank) $
to (Blank) $
per week.
Jan earns more than Rachel. The range of what Jan earns is 360 dollars to 480 dollars per week. The range of what Rachel earns is 220 dollars to 330 dollars per week.
How to solve for the Range and the domain of the functionsJan's pay function is given as /(t) = 12 dollars this is the same as 12 dollars in one hour
the time that she has to work is given a 30 hours to 40 hours.
Hence the domain would be written as
domain : 30 ≤ t ≤ 40
we have to make use of the values of t
f(t) = 12 * 30 = 360
f(t) = 12 * 40 = 480
The range of Jan is going to be
range : 360 ≤ t ≤ 480
b. For Rachel, t is going to vary between 20 ≤ t ≤ 30
domain : 20 ≤ t ≤ 30
r*t = 11t
= 11 x 20 = 220
= 11 x 30 = 330
The range is given as
range: 220 ≤ t ≤ 330
Jan earns more per hour than Rachel
The amount earned is, Jan earns from 360 dollars to 480 dollars per week.
Rachel earns from 220 dollars to 330 dollars per week.
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A2 Lesson 3.2 Practice
1. Does the graph shown represent a function for 0 < x < 6? Explain.
Yes, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
What are the domain and range of the function?The domain of the function includes all possible x values of a function, and the range includes all possible y values of the function.
The function is given in the represented graph
According to the given graph, we can see the value of the domain of the given function f(x) when the function includes all possible variables of x values of a function.
Here the domain of the given function is 0 < x < 6
Therefore, the graph shown represents a function for 0 < x < 6 because its domain is true about the given interval.
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Anna makes a round pizza. She wants to put a cheese layer on the pizza. If the
pizza is 11 in in diameter, how many square cm of cheese layer does she need
to put on the pizza?
The number of square cm of cheese layers that Anna needs to put on the pizza is 30.25π square cm.
What is the area of a circle?
In geometry, the area of a circle is the space occupied by the circle.
To find the area of a circle having radius "r", we can use the formula.
Area of a circle = π×r².
In the given question, the diameter of the pizza is 11 cm.
so the radius will be = 11/2 = 5.5 cm.
Area of the pizza = π×r²
= π×(5.5)²
= 30.25π square cm.
Hence, the number of square cm of cheese layers that need to be put on the pizza is 30.25π square cm.
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a packet of crisps weighs 32 grams to the nearest gram. a multipack of crisps contains 10 packets. work out the least and the greatest weights of the multipack. you can ignore the weight of the multipack wrapper
If a multipack of crisps contains 10 packets. the least and the greatest weights of the multipack is 315, 325.
How to determine the least and greatest weight?Range = 31.5≤ x < 32.5
Range = 31.5≤ 10 < 32.5
Hence,
Lowest and greatest possible for 32 grams
Lowest possible = 31.5 grams
Greatest possible =32.4 grams
Since multipack of crisps contain is 10 packets hence.
Least weight = 31.5 grams × 10
Least weight =315
Greatest weight = 32.5 grams × 10
Greatest weight = 325
Therefore 315 and 325 are the weight.
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let o be the point of intersection for the diagnols of quadrilateral abcd prove that abcd could be a trapezoid (that is if it has one sides parallel) is Aaod = Aboc
From the given proof below, we have been able to show that quadrilateral ABCD is a Trapezoid.
How to identify a Trapezoid?A trapezoid is also called a trapezium and it is characterized by four straight sides and one set of parallel sides. The parallel sides are referred to as the base, while the non-parallel sides are referred to as the legs.
We are told that;
O is the point of intersection for the diagonals of quadrilateral ABCD;
where;
AO/BO = CO/DO
This can also be expressed as;
AO/CO = BO/DO
Thus, if we create line OE to be parallel to DC which is OE || DC. Then it means that point E lies on BC.
Using the Basic Proportionality Theory, in ΔBDC, we can say that;
BO/OD = BE/EC ............................1
We are also given that:
AO/CO = BO/DO ..........................2
Thus, from Equations 1 and 2, we have;
AO/CO = BE/EC
Using the converse form of the Basic Proportionality Theorem, we have;
OE || AB
Therefore, AB || OE || DC.
Therefore we can conclude that ABCD is a Trapezoid.
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