Using the properties of logarithm the value of the expression is [tex]log_{2} 96 - log_{2} 3 = 5[/tex]
A logarithm is the power to which a number must be raised in order to get some other number.
According to the question we have been given the expression as
= [tex]log_{2} 96 - log_{2} 3[/tex]
The properties of logarithm that we are going to use are :
[tex]log(\frac{x}{y} ) = logx - logy[/tex] and [tex]log_{a} a = 1[/tex]
Also we can see that the base are same so we can use the property of logarithm in the given equation.
Now solving this step by step using the properties of logarithm we get
[tex]= log_{2} \frac{96}{3} \\= log_{2} 32\\= log_{2} 2^{5}\\ = 5* log_{2} 2\\= 5*1\\= 5[/tex]
Hence using the properties of logarithm the value of the expression is
[tex]log_{2} 96 - log_{2} 3 = 5[/tex]
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How many minutes have passed, m, when Tank A contains the following amounts of water?
a. 151 liters
b. 191.5 liters
c. 270.25 liters
d. p liters
The minutes that have passed, m, when Tank A contains the following amounts of water will be:
151 liters = 3 minutes
191.5 liters = 7.5 minutes
270.25 liters = 16.25 minutes
p liters = (p-124) / 9 min
How to calculate the minutes?It should be noted that for 151 lit = (151 - 124)/9 = 3 min
Also, for 191.5 lit = (191.5-124) /9
= 67.5/9 = 7.5 min = 7 min 30 sec
It should be noted that for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 = 16 min 15 sec
For p lit = (p-124) / 9 min
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Tank A initially contained 124 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.
How many minutes have passed, m, when Tank A contains the following amounts of water?
151 liters
191.5 liters
270.25 liters
p liters
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Distance between (4,2) and (-3,4)
it is 22 units <3 your welcome
Death valley is a desert in northern california with many place of interest. one such place is the badwater basin, the elevation is
-282 feet. at another location, salt creek trail, the elevation is-220 feet. write an inequality to compare the elevations and state
which elevation is closer to sea level.
The inequality comparing the elevations is -220 > -282 and -220 feet is closer to sea level.
The elevation of Bad Water Basin = -282 feet
The elevation of the Salt Creek = -220 feet
We are asked to compare the elevations and find which is greater than the other.
So we know that on a number line -220 is greater than -282.
This can be understood in the same sense that -1 > -2 on the number line.
So the inequality comparing the elevations is -220 > -282.
Now consider the sea level as 0 on the number line.
Then clearly -220 is closer to 0 on number line.
Hence the elevation closer to the sea level = -220 feet.
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What’s the slope of the line that passes through the points (10,6) and (6,6)
Answer:
Slope is 0.
Step-by-step explanation:
If you graph these points, it is a horizontal line. Horizontal lines have ZERO slope.
Using slope formula:
subtract y's and put that on top of a fraction. Subtract x's and put that on the bottom of the fraction.
6-6 goes in top and 10-6 goes on the bottom.
slope = m = 0/4 = 0
Slope is zero.
What is the greatest common factor of 9 and 48?
Answer:
3 is the greatest common factor that can go into 9 and 48
The greatest common factor of 9 and 48 is 3.
What is the greatest common factor?The greatest common factor (GCF) is the largest positive integer that divides two or more numbers without leaving a remainder. In other words, it is the largest number that is a factor of both (or all) of the given numbers.
For example, the GCF of 12 and 18 is 6, beca
To find the greatest common factor (GCF) of 9 and 48, we need to determine the largest number that both 9 and 48 can be divided by evenly.
We can start by listing the factors of each number:
9: 1, 3, 9
48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Then we can look for the greatest factor that appears in both lists. In this case, the greatest common factor of 9 and 48 is 3, since it is the largest number that appears in both lists of factors.
Therefore, the GCF of 9 and 48 is 3.
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pls help me..................
Answer:
$142.60
Step-by-step explanation:
an increase of 15% on the original cost of 100% means
percentage increase = 100% + 15% = 115% , then
cost = 115% × $124 = [tex]\frac{115}{100}[/tex] × $124 = 1.15 × $124 = $142.60
Selena is making cookies. to make one dozen cookies, she needs 1/3 cup of brown sugar. how many cups of brown sugar does selena need to make 2 1/2 dozen cookies?
Answer:
5/6 cup
Step-by-step explanation:
[tex] \frac{1}{3} \times 2 \frac{1}{2} = \frac{1}{3} \times \frac{5}{2} = \frac{5}{6} [/tex]
Megan is thinking of a number that is divisible by both 9and 7. What is the smallest possible number that Megan is thinking?
Answer:
Step-by-step explanation:
63
because 9x7=63
and 7x9=63
Determine which line the point (2,-1) lies on.
Answer:
the point will not lie on any line. it will come in the first coordinate
Use the properties of exponential and logarithmic functions to solve each system. Check your answers.
2 x+y=16
4 x-y=1
The solved logarithmic function is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
What is a logarithmic and exponential function?
Logarithmic functions and exponential functions are inverses of each other. The logarithmic function is denoted by using the word log while exponential by using the alphabet, e. For example log 10 = 1 and e^2.
Solving the given expressions: 2x + y = 16 and 4x - y = 1
Applying given properties of logarithmic and exponential function;
log a + log b = log (ab)
4 log x = log x⁴
e^(log x) = 1
e^(x + y) = (e^x) × (e^y)
Take the expression, 2x + y = 16
Applying log on both sides, we get,
log (2x + y) = log (16)
log (2x + y) = log (2⁴)
log (2x + y) = 4 log (2)
To Check Results,
Taking exponential on both sides,
e^[log (2x + y)] = e^(4 log 2)
2x + y = e^(log 2⁴)
2x + y = 2⁴
2x + y = 16
Thus, the answer is verified.
Take expression, 4x - y = 1
Applying log on both sides, we get,
log (4x - y) = log 1
log (4x - y) = 0
To Check Results,
Taking exponential on both sides,
e^[log (4x - y)] = e^0
4x - y = 1
Thus, the answer is verified.
Hence, the solved expression is log (2x + y) = 4 log (2) and log (4x - y) = 0 for 2x + y = 2⁴ and 4x - y = 1 respectively.
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1.79 − 0.67 pls give me a answer
Answer: 1.12
Step-by-step explanation:
Answer:
1
1.12 is the exact value. 1 is an estimate.
Step-by-step explanation:
[tex]1.79 = 2\\0.67 = 1\\2 - 1 = 1\\\mathrm{(Estimate)~1 < 1.12~but > 0~and~1}\\\mathrm{Therefore,}\\= 1.12[/tex]
in science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution
When zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature, the change in temperature is 1/2 degree.
How to illustrate the information?It should be noted that from the information, science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 9/10 degrees as the. ending temperature.
Therefore,the change in temperature will be the subtraction of the temperature given. This will be illustrated as:
= 1/5 - (-3/10)
= 1/5 + 3/10
= 2/10 + 3/10
= 5/10
= 1/2
The change on temperature is 1/2 degree.
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In science class, zulaki recorded -3/10 degrees celcius as the starting temperature of a salt water solution and recorded 1/5 degrees as the. ending temperature. What was the change in temperature?
SOLVE THE FOLLOWING EQUATION FOR Y
Answer: 74
Step-by-step explanation: calculator
Which is a benefit of being an employee paid commission?
You receive more paid time off than other types of pay.
Excellent job performance is rewarded with higher pay.
The work schedule is typically weekdays 9:00 a.m. to 5:00 p.m.
Commission is typically paid monthly making budgeting easier.
Answer:b
Step-by-step explanation:
b
Are ∠2 and ∠5 vertical angles? Explain your reasoning.
Answer:
no
Step-by-step explanation
an example of vertical angles would be 6 and 8
pls give brainliest :)
The area of a rectangle is 132.99 in2 and the length is 14.3 in. Find the width.
4.6 in.
12.9 in.
9.3 in.
18.7 in.
Answer:9.3
Step-by-step explanation:
Area= length times width
132.99= 14.3xw
Divide by 14.3
W= 9.3
Need the answer for the function as stated in the photo
The average rate of change of [tex]f[/tex] over an interval [tex][a,b][/tex] is the difference quotient
[tex]\dfrac{f(b) - f(a)}{b - a}[/tex]
Over the interval [tex]3\le x\le5[/tex], we have
[tex]\dfrac{f(5) - f(3)}{5 - 3} = \dfrac{27 - 3}{5 - 3} = \dfrac{24}2 = \boxed{12}[/tex]
What is the remainder when 316 is divided by 13?
Answer:
24 reminder 4
Step-by-step explanation:
Reminder is 4
316/13 = 24 R 4
Four stores are having a sale on cans of Sprite. The sale prices are listed below:
Shop A: 6 cans for $5.10
Shop B: 6 cans for $5.70
Shop D: 12 cans for $10.80
Shop C: 12 cans for $9.60
Which store has the best buy?
Answer:
Shop C
Step-by-step explanation:
Without any calculations, you can eliminate stores B and D.
Shop A: $5.10/6 = $0.85/can
Shop C: $9.60/12 = $0.80/can
Answer:
It would be B
Step-by-step explanation:
Because A is 1.17 per can
B is 1.05 per can
D is 1.11 per can
and C is 1.25 per can
Solve each equation.
3x⁺²=27²x
After solving the equation, x = 2/5 is the value of x in [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = 27^{2x}[/tex]
⇒ [tex]3^{X+2} = ((3)^3)^{2x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ [tex]3^{X+2} = (3)^{6x}[/tex]
⇒ x+2 = 6x
⇒ 2 = 6x - x
⇒ 2 = 5x
⇒ x = 2/5
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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Which expression represents the model?
9*1/6
Step-by-step explanation:
1= 6/6 and there are 9 boxes so multiply 9*1/6
Find the average rate of change of g(2) = -4 + 4 between the points (-3,16) and (4,-12)
The average rate of change of the function between the points is -4/7
What are average rates of change?The constant average rates of change of a function is also regarded as the slope or the gradient of the function
How to determine the average rates of change?Here, we have the points to be
(-3, 16) and (4, 12)
The average rates of change between these points is calculated as
Average rate of change = [f(b) - f(a)]/[b - a]
So, we have
Average rate of change = [12 - 16]/[4 + 3]
Evaluate the sum and the difference
So, we have
Average rate of change = -4/7
Hence, the average rate of change between the points is -4/7
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#1 You are in charge of ordering hats for a youth
baseball team. Each hat costs $22.50. There are at
least 10 but no more than 16 players on the
baseball team. The total cost of ordering hats can
be modeled by the function f(x)=22.50x,
where x represents the number of hats ordered. answer
The range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the range of the function?The function is given as
f(x) = 2.250x
Where there are at least 10 but no more than 16 players on the baseball team
This means that the domain of the function is
10 <= x <= 16
Substitute the domain values in the given function
So, we have
f(x) = 2.250x
f(10) = 2.250 * 10
Evaluate
f(10) = 22.5
f(x) = 2.250x
f(16) = 2.250 * 16
Evaluate
f(16) = 36
The range of the function is then represented as
f(10) <= f(x) <= f(16)
So, we have
22.5 <= f(x) <= 36
Hence, the range of the function f(x) = 2.250x is 22.5 <= f(x) <= 36
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Complete question
ou are in charge of ordering hats for a youth baseball team. Each hat costs $22.50. There are at least 10 but no more than 16 players on the baseball team. The total cost of ordering hats can be modeled by the function f(x)=22.50x, where x represents the number of hats ordered.
What is the range of the function?
Multiply if possible. Then simplify. ∛9 .∛3
The answer is = 3
The phrase simplifies the way to make something less challenging to do or understand. So, by lowering or simplifying the fractions approach we make the fraction as easy as possible. We do this by dividing the numerator and the denominator by using the most important number which could divide into both numbers precisely.
Cross-cancellation is a simplification that may be executed earlier than. that is wonderful because simplifying earlier than the method while you do multiply, you'll have smaller numbers, and smaller numbers are easier to paint with.
Simplifying a rectangular root just means factoring out any best squares from the radicand, shifting them to the left of the unconventional image, and leaving the opposite factor within the radical image. If the variety is an ideal square, then the novel signal will disappear when you write down its root.
[tex]\sqrt[n]{a}[/tex][tex]\sqrt[n]{b}[/tex]=[tex]\sqrt[n]{ab}[/tex] , a[tex]\geq[/tex]0, b[tex]\geq[/tex]0
[tex]\sqrt[3]{9}[/tex][tex]\sqrt[3]{3}[/tex] = [tex]\sqrt[3]{9.3}[/tex]
[tex]\sqrt[3]{9.3}[/tex]
multiply the number 9.3 = 27
[tex]\sqrt[3]{27}[/tex]
[tex]\sqrt[3]{27}[/tex] =3
=3
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Aisha buys 2 packets of bread rolls costing £1.20 for each packet 1 bottle of ketchup costing £2.10 3 packets of biscuits Aisha pays with a £10 note. She gets 70p change. Work out the cost of one packet of biscuits. You must show how you get your answer. Optional working Answer: £|
The cost of one packet of biscuit is £1.60.
What is the cost of one packet of biscuit?The total amount that Aisha paid for the items she purchased is a function of the total cost of bread rolls, ketchup and biscuits.
Total cost of the items purchased = total cost of bread rolls + total cost of biscuits + total cost of ketchup
Total cost of bread rolls = cost per packet x number of packets bought
2 x £1.20 = £2.40
Total cost of ketchup = cost of one bottle x number of bottles bought
1 x £2.10 = £2.10
Total cost of biscuits = cost of one packet x number of packets bought
3 x b = 3b
Total cost = £2.40 + £2.10 + 3b = £4.50 + 3b
Total amount paid by Aisha = note given - change received
£10 - 70p
£10 - £0.70 = £9.30
Total amount paid by Aisha = total cost
£9.30 = £4.50 + 3b
£9.30 - £4.50 = 3b
£4.80 = 3b
b = £4.80 / 3
b = £1.60
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Do you think that the measures of central tendency (mean, median, mode) tell you the entire picture of a data set? Why or why not?
Answer:
Step-by-step explanation:
A measure of central tendency is a summary statistic that represents the center point or typical value of a dataset. These measures indicate where most
factor the following
the equation is f(x) = x^3+27
The factored form of the cubic equation x³ + 27 is equal to (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2). The roots of the cubic equation are - 3, 3 / 2 + i 3√3 / 2 and 3 / 2 - i 3√3 / 2.
How to factor a cubic equation
In this problem we find a cubic equation of the form x³ + a³, whose factor form can be found by using algebra properties:
f(x) = x³ + 27
f(x) = (x + 3) · (x² - 3 · x + 9)
f(x) = (x + 3) · (x - 3 / 2 - i 3√3 / 2) · (x - 3 / 2 + i 3√3 / 2)
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Let athe event of getting at least one defective calculator when four are randomly selected with replacement from a batch. Write a statement describing event
Answer: do you have a pic??
Step-by-step explanation:
What is the multiples of 2/5
Answer:
Step-by-step explanation: 2x5=10
:) have a good day
Show that the following equation is true for all values of a and b .
[(a-b)+1]⁵=a⁵ - 5a⁴ (b-1) + 10a³ (b-1)² - 10a² (b-1)³ + 5a(b-1)⁵- (b-1)⁵
8272936388272o274o4i49484i484748474
Step-by-step explanation:
2-2=Fish