The value of the expression log₃54 is 3.6.
Given that the expression is log₃54.
We are required to find the value of the expression by using the change of base formula.
The change of base formula is the formula that will give us the answer of a log with a different base by using only log calculations with a base of 10.
The expression is log₃54.
log₃54= log (54)/log (3)
(We know that [tex]log_{a}b[/tex]=log b/ log a)
Now we have to use the values of logarithms in the above expression to find its value.
=1.73/0.48
=3.6
Hence the value of the expression log₃54 is 3.6.
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In 5-7 complete sentences, write a real world situation that can be modeled by the equation. Make it fun by using your name, if you want!
16x=14x+8
A possible real world scenario is that the product of your score in mathematics test and 16 is 8 more than the product of your score in mathematics test and 14
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to model the expression by a real world situation?The equation is given as
16x = 14x + 8
In the above equation, the variable of the equation is x while the number 8 is a constant
A possible real world scenario is that:
The product of your score in mathematics test and 16 is 8 more than the product of your score in mathematics test and 14
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If the reserve rate is 8% and a bank receives a deposit of $7000, how much of
the $7000 is the bank free to lend?
A. $6440
B. $1400
C. $5600
D. $560
The bank can borrow $6440 based on the $7000 deposit.
What is defined as the reserve rate?The reserve ratio is the proportion of a commercial bank's deposits that it has to keep in cash as a safeguard in the event of mass customer withdrawals, as determined by the central bank. The reserve ratio is a crucial monetary policy tool used by the Federal Reserve in the United States to continue increasing the economy's money supply.The following deposit amount: $7000
Because the reserve rate is 8%, the bank will reserve 8% of the 7000. The remaining funds can be lent by the bank.
7000 × (8/100) = amount set aside
= $560
Thus, the reserve deposit is $560.
Amount the bank is willing to lend = 7000 - 560 = $6440
Thus, the bank can lend $6440 based on a deposit of $7000.
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Jamie wants to share 18 ¾ inches of candy with two friends. How much will each person, including Jamie, receive if the candy is divided into equal amounts?.
Answer:
6 1/3
Step-by-step explanation:
18 3/4 divided by 3 is 6 1/3
What is the value of p?
Α. 45°
Β. 55°
C. 35°
D. 125°
Answer:
C I think would be the answer.
Simplify. (4/9)2
help
Answer:
8/9
Step-by-step explanation:
4/9 times 2 is 8/9 and 8/9 is already the simplest way to put it so the answer is 8/9
Answer:
8/9
Step-by-step explanation:
(4/9)(2/1)
(4)/(9)(2)/(1)
8/9
0.888 (decimal)
A roll of 50 pennies has a mass of 125 grams. What is the value of 1,000 grams of pennies?
$4.00
$3.50
$5.00
$8.00
$4.50
Answer:
$4.00
Step-by-step explanation:
make a proportion
50/125=x/1000
1000(50/125)=x
8(50)=x
400=x
400pennies=$4.00
or solve like this
50/125= 0.4 pennies per gram (p/g)
0.4p/g
0.4p/g*1000g=400p=$4.00
What is the equation of the line that passes through the point (8, 7) and has a slope
of 1?
Answer:
x - y - 1 = 0
Step-by-step explanation:
Using y-intercept
b = y - m × x
b = 7 - (1) × (8) = -1
y = mx + b/Flip expression, subtracting from all sides
assuming x ≠ 0 for x = 1
assuming y = 0
y = x - 1
x - y - 1 = 0
can someone please explain what a stem-and-leaf plot is? (10 points)
[tex]{\huge\color{red}{\boxed{\fcolorbox{green}{black}{꧁ANSWER ꧂}}}}[/tex]
A stem and leaf plot is a simple kind of graph that is made out of the numbers themselves.
It is a means of displaying the main features of a distribution.
If a stem and leaf plot is turned on its side.
it will resemble a bar graph or histogram and provide similar visual information.
Answer:
A stem and leaf plot is a simple kind of graph that is made out of the numbers by their selves.
The temperature of a city changed by a total of −20 degrees Celsius over a 4-week period. The temperature changed by the same amount each week.
Based on the change in the temperature of the city over the 4-week period, the expression to show the average change in temperature each week is -20 / 4
When the expression is simplified, the result if -5°C which means that the temperature reduced by 5°C every week.
What was the temperature change?The average temperature change of the city each week can be found by:
= Total change in temperature / Number of weeks
Solving gives:
= -20 / 4
= -5°C
This means each week for the 4-week period, the temperature of the city decreased by 5°C.
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PLEASE HELP!!!
The answer choices are:
A) −3 ≤ x ≤ 2
B). y ≥ 5.5
C). All Real Numbers
D). All real numbers less than −3 or greater than 2
Answer:
Step-by-step explanation:
cevap a ANSWER A
A machine can produce a nail every 2.4 seconds. If the machine keeps running for 3 days without stop, how many nails can be produced?
Answer:
Step-by-step explanation:
so 2.4 nails per second, multiply it by 60 (60 seconds in a minute) =144 so 144 nails per minute. 144 nails per minute times 60 minutes is 8640 nails per hour. If it’s running for 3 days non-stop it would be 72 hours, so 8640 multiplied by 72 (hours) 622,080 nails would be the total in 3 days.
Write a numerical expression using one of the properties that is equivalent to 2⁸
The numerical expression using commutative property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.
What is multiplication?Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. The result of a multiplication operation is called a product.
Now the given exponent is,
2⁸
Now, 8 can be written as using associative property of addition,
8 = 2 + 2 + 2 + 2
Thus we can write,
2⁸ = 2^( 2 + 2 + 2 + 2 )
Using exponential property
x^(a + b) = x^a . x^b
Thus we get,
2⁸ = 2^2 . 2^2 . 2^2 . 2^2
Thus numerical expression for 2^8 = 2^2 . 2^2 . 2^2 . 2^2
Solving we get,
2^8 = 4 x 4 x 4 x 4 = 256
Thus, the numerical expression using exponential property of multiplication that is equivalent to 2⁸ is 2² x 2² x 2² x 2² = 256.
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Simplify 0.1+3.7+5.9
A new club sent out 192 coupons to boost sales for next year's memberships. They provided 3 times as many to potential members
than to existing members. How many coupons did they send to existing members?
The number of coupons send by new club to existing members are 64.
What is defined as the product?The term product refers to the solution to a multiplication troubles.Multiplication is also known as repeated addition because the multiplication problem indicates that you have a particular number of groups about something, each of which contains a specific number.The commutative property states that when two numbers have been multiplied together, this same product remains the same regardless of how they are written.When three or even more numbers are magnified together, the product is the same no matter which two are multiplied first.For the given conditions in the question.
Let the existing number be 'x'.
3 times the number means do the multiplication of number by 3.
= 3x.
3 times as many to potential members than to existing members.
Thus,
3x = 192
x = 192/3
x = 64
Thus, the number of existing members are found to be 64.
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a) Evaluate the following calculation, giving your answer rounded to 3 decimal
places:
(4.01 +8.56)³ × (347-150) ½
b) Explain the steps you have taken in the calculation and why.
Answer:
Step-by-step explanation:
rewrite each expression in simpler terms. you may not use negative exponents
32x^3/ 16x^7
Answer:
[tex] \frac{2}{x {}^{4} } [/tex]
Step-by-step explanation:
[tex]1. \: \frac{32}{16} \times \frac{x {}^{3} }{x {}^{7} } \\ 2. \: 2 \times \frac{x {}^{3} }{x {}^{7} } \\ 3. \: 2x {}^{3 - 7} \\ 4. \: 2x {}^{ - 4} \\ 5. \: 2 \times \frac{1}{x {}^{4} } \\ 6. \: \frac{2}{x {}^{4} } [/tex]
What does x equal? −3(2x−3)=−6x+9
Answer: The answer for this question is x=1
Step-by-step explanation: -3(2x-3)=-6x+9 first you multiply -3x with 2x and -3 to get -6x+9=-6x+9 then subtract nine from both sides to leaves -6x=-6x then you divide -6 on both sides and you get x=1.
Any value of x makes the equation true. All real numbers
Interval Notation: (−∞,∞)
Because if you solve it
-3(2x-3)=-6x+9
distribute
-6x + 9 = -6x + 9
subtract 9 from both sides
-6x = -6x
simplify
0 = 0
I need help, thank you <3
Step-by-step explanation:
so, pre-image is then doing the opposite :
going up 2 units and left 4 units.
up/down changes y, left/right changes x.
up = positive y direction
down = negative y direction
right = positive x direction
left = negative x direction
just as indicated by the coordinate axes.
so,
going up 2 units = adding 2 to y
going left 4 units = subtracting 4 from x
giving us as pre-image point A
(4 - 4, -5 + 2) = (0, -3)
Find the inverse of each function. Is the inverse a function?
y=x²+4
If the equation be y = x² + 4 then the inverse function be [tex]f^{-1} (x)=[/tex] ± [tex]\sqrt{x - 4[/tex].
What is meant by inverse function?An inverse function, also known as an anti function, is a function that can be reversed into another function. Simply put, if any function " f " takes x to y, then its inverse will take y to x. The inverse function is denoted by f-1 or F-1 if the function is denoted by ' f ' or ' F '.
Let the equation be y = x² + 4
then the function be f(x) = x² + 4
y = x² + 4
⇒ x = y² + 4
simplifying the above equation, we get
x - 4 = y²
√y² = √x - 4
The value of y = ± √x - 4
Therefore, the inverse function be [tex]f^{-1} (x) =[/tex] ±√x - 4
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Identify the steps followed to solve the equation 5(3x+2)+7=6+2(3x−8)
Put responses in the correct input to answer the question.
15x+10+7 = 6+ 6x−16
15x+17=6x−10
9x+17=−10
9x=−27
x=−3
answer: x=3
5(3x+2)+7=6+2(3x−8)
1: Simplify both sides of the equation.
5(3x+2)+7=6+2(3x−8)
(5)(3x)+(5)(2)+7=6+(2)(3x)+(2)(−8)(Distribute)
15x+10+7=6+6x+−16
(15x)+(10+7)=(6x)+(6+−16)(Combine Like Terms)
15x+17=6x+−10
15x+17=6x−10
2: Subtract 6x from both sides.
15x+17−6x=6x−10−6x
9x+17=−10
3: Subtract 17 from both sides.
9x+17−17=−10−17
9x=−27
4: Divide both sides by 9.
9x/9=-27/9
x=−3
Wes wanted to bake cookies so he preheated the oven, the graph below shows the temperature of the oven over different periods of time
the temperature will be 2.5 degrees per second.
We are given the data:
Seconds Temperature (°F)
0 75
10 100
20 125
30 150
We need to find the temperature in degrees per second.
So, we get that:
Seconds Temperature (°F) degrees / sec
0 75 Nil
10 100 (100 - 75) / (10 - 0) = 2.5
20 125 (125 - 100) / (20 - 10) = 2.5
30 150 (150 - 125) / (30 - 20) = 2.5
Therefore, the temperature will be 2.5 degrees per second.
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Use the Commutative Property of Multiplication to write an expression equivalent to x•9.
Answer:
9 x x
Step-by-step explanation:
commutative property just means you can switch the numbers around
A student is finding the total cost of c, including sales tax, of a book that costs 9.95. the sales tax rate is 9%. find the students mistake and correct it.
The final cost of the book is 9.12
A sales tax is one that is levied on both the selling of products and services to businesses and on the purchases of those same goods and services by consumers. It's a form of consumption tax, which means it charges consumers for their purchases. Because sales taxes are typically passed on to customers at the moment of sale, it is classified as a consumption tax.
Solving the question:
Cost of the book = 9.95
Sale tax rate = 9%
Sale tax amount on 9.95 = 9.95/(9/100) = 9.12
Therefore, the final cost of the book is = 9.12
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The final cost of the book is 9.12
A sales tax is one that is levied on both the selling of products and services to businesses and on the purchases of those same goods and services by consumers. It's a form of consumption tax, which means it charges consumers for their purchases. Because sales taxes are typically passed on to customers at the moment of sale, it is classified as a consumption tax.
Solving the question:
Cost of the book = 9.95
Sale tax rate = 9%
Sale tax amount on 9.95 = 9.95/(9/100) = 9.12
Therefore, the final cost of the book is = 9.12
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It takes franklin 14 hours to make a 200-square-foot cement patio. it takes scott 10 hours to make the same size patio. which equation can be used to find x, the number of hours it would take franklin and scott to make the patio together? 14 x 10 x = 200 one-fourteenth x minus one-tenth x = 1 one-fourteenth x plus one-tenth x = 1 14 x minus 10 x = 200
The equation which can be used to find x is, [tex]\bold{\frac{1}{x} =\frac{1}{14} +\frac{1}{10} }[/tex]
The time taken by Franklin to make a 200 sq. foot cement patio = 14 hours
The time taken by Scott to make a 200 sq. foot cement patio = 10 hours.
Let x be the number of hours it would take Franklin and Scott to make the patio together.
Then x = 14 x 10 / (14 + 10)
⇒ 1 / x = (14+10)/(14 x 10)
⇒ 1/x = 1/14 +1/10
This is the equation to find the number of hours taken by Franklin and Scott together.
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Answer:
C
Edge2020
Step-by-step explanation:
Help now please!!
I dont understand at all and need help. pls dont comment if u dont know.
Answer:
I'm pretty sure it would be B
Step-by-step explanation:
X and Y
Answer:
am pretty sure it answer b
On a number line, suppose the coordinate of A is 0, and AR = 12. What are the possible coordinates of the midpoint of AR?
The possible coordinates for midpoints of the segment are
?
The midpoint of AR is (1/2 , 1).
Let the points be:
A(0,0) = (x₁,y₁)
B(1,2) = (x₂,y₂)
Midpoint = (x₁₊x₂/2) , (y₁₊y₂/2)
A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places.
= (0₊1/2) , (0₊2/2)
=(1/2 , 2/2)
= (1/2 , 1)
hence the midpoint of the number line is (1/2 , 1).
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When janelle woke up it was -3 degrees Fahrenheit outside.as the morning progressed,the temperature rose 2 degrees every hour.
W hitch line on the Garth could represent this scenario
The equation to illustrate the information regarding the temperature it the temperature rose 2 degrees every hour is -3 + 2h.
How to illustrate the information?It should be noted that an equation is used to show the relationship between the variables.
In this case, when janelle woke up it was -3 degrees Fahrenheit outside.as the morning progressed,the temperature rose 2 degrees every hour.
Let the number if hours be represented by h
Therefore, the equation to illustrate the information will be -3 + 2h
here h = number of hours.
Note that the complete information wasn't found and the equation was illustrated.
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A student has these scores on their assignments. the teacher is considering dropping a lowest score. what effect does eliminating the lowest value, 0, from the data set have on the mean and median? 0, 40, 60, 70, 75, 80, 85, 95, 95, 100 select all the true statements.
Mean = Sum of all observations/Number of observations
The value of the middlemost observation, obtained after arranging the data in ascending or descending order, is called the median of the data.
Given,
The set of scores = 0, 40, 60, 70, 75, 80, 85, 95, 95, 100
Mean without '0' = 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/9= 700/9
= 77.777
Median without '0' = 80Mean with ' 0' = 0+ 40+ 60+ 70+ 75+ 80+ 85+ 95+ 95+ 100/10 = 70Median with '0' = 80Learn more about mean and median here:
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Two out of every five cars are red.if there are 100 cars in the parking lot, how many are red
Answer: 10 Cars!!!!
Step-by-step explanation:
math.. HELP :(
A mountain goat is climbing to the top of a large cliff. The cliff is 50 feet higher than its starting point. If it takes the goat 22 minutes to climb this cliff, interpret the quotient to describe the rate of change in the goat’s elevation. Give your answer to the nearest hundredth.
The quotient that best represents the rate of change in the goat’s elevation is _
feet/minute.
The quotient that best represents the rate of change in the mountain goat’s elevation is 2.27 feet/minute.
What is quotient?Quotient can be defined as a mathematical expression that is simply used to represent the division of a number by another number.
What is the rate of change?The rate of change can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
Mathematically, the rate of change can be calculated by using this formula;
Rate of change = Δy/Δx = Change in height/Change in time
Substituting the given parameters into the formula, we have;
Rate of change = Quotient = 50 feet/22 minutes
Rate of change = Quotient = 2.27 feet/minute.
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