The process of logarithmic functions in real-worlds problems is given below.
And an example of an application of logarithmic function is given.
What is Logarithmic?The inverse of exponentiation is the logarithm. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b.
We know,
logarithmic function and exponential function are inverse of each other.
So, whenever we solve the exponential function,
we use the help of logarithmic functions.
To compute the number with bigger exponents,
we use the logarithms.
Because it reduces the size of the numbers.
Let the bacteria is growing exponentially,
b = 2ⁿ.
We know that the bacteria grows every hour.
We want to find time.
Here, we will use the inverse function to the exponential function.
How long will it take them to get 1000 bacteria?
1000 = 2ⁿ
Taking log on both sides,
log(1000) = n log2
n = log(1000)/log(2)
n = 9.96
n ≈ 10 hours.
Therefore, an application of logarithmic function is given above.
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The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have an equal monthly salary of P7200, P7600, P6900, P8200, P7800 and P7400 respectively. What is the mean monthly salary of all the employees of the company?
The average monthly wage for the entire workforce of the business is $7489.09.
What is Mean?
The mathematical average of a group of two or more numbers is called the mean. There are two different sorts of means that can be calculated: the arithmetic mean and the geometric mean. The arithmetic mean is calculated by adding all of the numbers in a set and dividing by the total number of integers in the set.
Given, The six departments of a company consisting of 22, 32, 18, 16, 10, and 12 employees have equal monthly salaries of $7200, $7600, $6900, $8200, $7800, and $7400 respectively.
First, calculate the total monthly salary
22*7200 + 32*7600 + 18*6900 + 16*8200 + 10*7800 + 12*7200 dollars.
Total monthly salary = $823,800
Then divide this sum by the total number of employees
22 + 32 + 18 + 16 + 10 + 12
Total number of employees = 110
the mean monthly salary of all the employees = [tex]\frac{Total salary}{total number of employee}[/tex]
the mean monthly salary of all the employees = 823800/ 110
the mean monthly salary of all the employees = 7489.0909
Therefore, the mean monthly salary of all the employees of the company is $7489.09.
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Shana wants to buy a music player. She has $100 cash.
1. Can she afford a $79 unit plus HST? Yes or No?
Provide an estimate or a calculation to support your answer:
Answer:
Yes
Step-by-step explanation:
A $79 unit plus HST will be 89.27
A student made two patterns to show multiplication of a decimal by powers of ten. the equations shown for both patterns are incorrect. pattern A
3.675. 10 =3.7650
3.675. 100= 3.67500
3.675.1,000= 3.675000
pattern B
3.675. 10=3.0675
3.675.0.01= 3.00675
3.675. 0.001= 3.000675
explain why the equations in each of the patterns are false. Include in your explanation the values that should appear on the right side of each equation in both patterns to make the equations true.
If a student made two patterns to show multiplication of a decimal by powers of ten. All the value are incorrect. The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
How to find the correct value?Pattern A
3.675×10 =3.7650 Incorrect
3.675×10 = 36.75 Correct
3.675× 100= 3.67500 Incorrect
3.675×100= 367.5 Correct
3.675×1,000= 3.675000 Incorrect
3.675×1,000 = 3,675 Correct
Pattern B
3.675×10=3.0675 Incorrect
3.675× 10= 36.75 Correct
3.675×0.01= 3.00675 Incorrect
3.675×0.01= 0.03675 Correct
3.675×0.001= 3.000675 Incorrect
3.675×0.001= 0.003675 Correct
The correct value are: 36.75, 367.5, 3,675, 36.75, 0.03675, 0.003675.
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(3,-3) m= -2/3
Formula
Y-Y1= m(x-x1)
slope form -
y - y1 = m(x - x1)
y - (-3) = -2/3(x - 3)
y + 3 = -2/3x + 2
y = -2/3x - 1
Illustrate the effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream
The effect that a decrease in the price of milk and input to ice cream would have on the market for ice cream is that there will be more production and demand in the market.
What is Market?This is referred to as a place where buyers and sellers can meet to facilitate the exchange or transaction of goods and services.
A decrease in the price of milk and input to ice cream means that production costs would fall, which will cause the suppliers to produce more thereby shifting the supply curve to the right with the demand for the goods being increased which is therefore the effect on the market.
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Given:
f(x) = x² + x − 6
g(x) = x + 3
Find: (f/g)(x)
Answer:
x–2, x ≠ -3
Step-by-step explanation:
Solution in the diagram
1.171875 as a fraction
false
it is a decimal not a fraction
Consider all five-digit numbers that can be created from the digits 0-9 0 - 9 where the first and last digits must be odd and no digit can repeat. What is the probability of choosing a random number that starts with 7 7 from this group? Enter a fraction or round your answer to 4 4 decimal places, if necessary.
Teddy works part-time in the Sony Store. He has a base salary of $12.50/h plus a commission of 12% of the total sales he makes.
If Teddy works 10 hours and sells $1500 electronics, how much will he earn this week?
Answer: $305
Step-by-step explanation:
1) 12.50 multiplied by 10= 125
2) 12% of 1500 is 180
3) 125+180=305
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
What is the equation of C(t)?
C(t) = −(x − 5)2
C(t) = (x − 5)2
C(t) = −x2 + 5
C(t) = x2 + 5
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
What is the equation of the parabola?Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
The table represents a quadratic function C(t).
t C(t)
−2 1
−1 4
0 5
1 4
2 1
From the table, the coordinate of the vertex will be at (0, 5). Then the equation is given as,
C(t) = a(t - 0)² + 5
C(t) = at² + 5
The equation is passing through the point (1, 4), then we have
4 = a (1²) + 5
4 = a + 5
a = - 1
The equation that presents the table will be C(t) = - t² + 5. Then the correct option is C.
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An engine spins a wheel with radius 5 inches at 800 rpm. How fast is this wheel spinning in miles per hour?
The wheel is spinning at 23.80 miles per hour
How determine how fast the wheel spinning in miles per hour?The wheel speed in miles per hour can be calculated using the expression below:
Speed in miles per hour = Wheels RPM × 2 × π × r × (60 / 63360),
where r is the radius of wheel , 60 converts minute to hour and 63360
converts inches to miles
Speed in miles per hour = 800 × 2 × π × 5 × (60 / 63360)
Speed in miles per hour = 23.80 miles per hour
Thus, the wheel spins at 23.80 miles per hour
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Perry borrows $150 from his brother to fix his car. His brother doesn't like lending Perry money and so charges him 7% interest per month. a. Write a rule in the "y=..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments.
Answer: Let's say,
y = the amount of money Perry will owe his brother after n months.
x = the principal (the initial amount borrowed) = 150
r = the interest rate per month = 7/100 = 0.07
n = number of months.
We know that Interest on a loan is calculated by multiplying the principal by the interest rate.
Therefore, the interest for n months is (0.07*x)*n
So to find the total amount Perry will owe his brother after n months, we need to add the interest to the principal amount.
y = x + interest
y = x + (r*x)n
y = x(1 + rn)
Therefore, the rule in the "y =..." form that will give the amount of money, y, Perry will owe his brother after n months, assuming that he doesn't make any payments is:
y = 150(1 + 0.07*n)
It's worth noting that this formula can be used to calculate the amount he will owe after any number of months by changing the value of n, and It's assuming he doesn't make any payments, meaning if he makes any payments, the total amount he will owe will change.
Step-by-step explanation:
At a bakery, 55 chocolate chip cookies were burned. if that was 15% of the day's production, how many total cookie did they make that day?
The total number of cookies that was made that day given that 55 which is 15% was burnt is 360.
How to solve for the number of cookies madeWe know that the number of burned cookies is 55, and that this represents 15% of the total production for the day.
We can use this information to set up a proportion to find the total number of cookies made that day.
Burned cookies / Total cookies = 15% / 100%
55 / X = 15/100
To find the total number of cookies made, we can cross-multiply and divide:
X = (55 * 100) / 15
X = 365
So, the bakery made a total of 365 cookies that day.
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Jacob runs 2652 yards in 15 minutes. Michael runs 7920ft in .375 hours. who will win the race?
Answer:
I think Jacob wins the race
B. Higher Order Thinking For keeping business records, every three months of a year is called a quarter. How many months are equal to three-quarters of a year? Explain how you found your answer.
Answer:
9 months
Step-by-step explanation:
1 quarter is 3 months
3 quarters is 3 times 1 quarter, so it is 3 times 3 months.
3 x 3 months = 9 months
Answer: 9 months
Find the volume of a cone with a base radius of 3in and a height of 11in. Use the value 3.14 for π, and do not do anu rounding. Be Sure to include the correct unit in your answer.
So the formula to find the volume of a cone is,
[tex]V = \pi r^{2} \frac{h}{3}[/tex]
Given,
Base of the cone is 3 inchesHeight of the cone is given as 11 inchesTo Find : The Volume of the cone
Applying the values we get,
[tex]V = 3.14X(3)^{2} X \frac{11}{3}[/tex]
[tex]V = 28.26X\frac{11}{3}[/tex]
[tex]V = 103.62in^{3}[/tex]
Hence , the volume of the cone is 103.62in³
Express The Ratio 36 : 42 In it's Simplest Form ?
Answer:
6/7
Step-by-step explanation:
36/42 = 36:6/42:6 = 6/7
got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 24 cents per yard. If after that purchase there was $3.48 left on the card, how many yards of ribbon did
The length of ribbon is 48 yards.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Kala got a prepaid debit card with $15.
Price of Ribbon = 24 cents per yard.
After purchase money left $3.48.
So, Price of Ribbon purchased = 15 - 3.48 = $11.52 = 1152 cents
length of ribbon = 1152/ 24
= 48 yards
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Solve 2 < n +1| ≤ 7. Explain your reasoning and graph
the solution set.
Let n = the number
The solution set is {x | x > 10}. 2. 5 ≥ 7 + y.
What is the value of N?It's used to refer to the collection of all natural numbers. Positive whole numbers that are not zero make up the natural numbers. N = 1 , 2 , 3 , 4 . By multiplying the integers from 1 to n, the factorial of n is calculated and denoted by the symbol n!. n! = n (n - 1)! is the formula for n factorial. Example: What is9! if8, which is40,320, is?The sample size, or n, is the number of data points. described in Chapter 2 here. in a probability experiment using a binomial model, the total number of trials.Instead of the product n n, which is typically pronounced"n squared," the equivalent exponentiation n2 is used to represent a number's square.To learn more about exponentiation refer to:
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Can someone solve 18?
The piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
What is a piecewise function?A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function. Piecewise functions are implemented in the Wolfram Language as PiecewiseAdditional piecewise functions include the Heaviside step function, rectangle function, and triangle function.Given is the absolute value function -
f(x) = 1/2 |x|
We can write it as a piecewise function as follows. The given function is as follows :
f(x) = 1/2 |x|
The absolute value function is given as -
|x| = - x {x < 0}
|x| = x {x ≥ 0}
So, we can write the piecewise function as -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
Therefore, the piecewise function f(x) = 1/2 |x| is equivalent to -
1/2 |x| = {- x/2} {x < 0}
1/2 |x| = {x/2} {x ≥ 0}
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Refer to the diagram shown.
I need help with this please help me
Answer: Angle-Side-Angle Theorem
Step-by-step explanation:
The two triangles are shown to have congruent angles. By the Reflexive Property of Congruence, Side PM is shared and congruent between the two.
Because the angles are on either side (left and right) of the shared side, the triangles are congruent by the Angle-Side-Angle Theorem.
What is the probability of picking a month at random that starts with the letter “J”
Answer:
A 1 in 4 chance or a probability of 0.25
Step-by-step explanation:
There is only 3 months that start with J and 12 months in a year so simplify 3/12 you get 1/4 or 0.25
i’m not sure if the first one right but i need help
The formula is written as (3x+9)(x+9) of + 36x + 81 = 0. A second-degree polynomial equation can be used to define quadratics.
A quadratic equation is defined.Multiplying a variable by itself is the mathematical operation known as "squaring," which is frequently used to refer to a quadratic issue. This vocabulary is based on the notion that a square's area is equal to the sum of its side lengths. The word "quadratic" derives from the Latin quadratum, which meaning square.
here ,
[tex]= + 36x + 81 = 0\\= 3x^2 + 27x + 9x + 81\\= 3x(x+9) + 9(x+9)\\= (3x+9)(x+9)\\= 3(x+3)(x+9)[/tex]
factorized form is [tex](3x+9)(x+9) of + 36x + 81 = 0 .[/tex]
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A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,240 ft Determine the flag's width and length if the length is 460 ft greater than the width.
Answer:
the flag is 50 feet long and 160 feet wide
Answer: The width is 330 feet and the length is 790 feet.
Step-by-step explanation:
We will write a system of equations to help us solve. Let w be the width and l be the length.
2w + 2l = 2,240 ft
l = 460 ft + w
Now, we will solve for w, the width, by substituting one equation into the other.
2w + 2l = 2,240 ft, l = 460 ft + w
2w + 2(460 ft + w) = 2,240 ft
2w + 920 ft + 2w = 2,240 ft
4w + 920 ft = 2,240 ft
4w = 1,320 ft
w = 330 ft
The width is 330 feet.
Now, we will solve for l, the length.
l = 460 ft + w, w = 330 ft
l = 460 ft + 330 ft
l = 790 ft
The length is 790 feet.
What is the equation of the line that passes through the point (7, -4) and has an
undefined slope?
This tablet shows an example of
was first used by the
>
It
Answer: the answer is 1.cuneiform & 2.sumerians
Step-by-step explanation: searched it up
Maya went shopping for a new video game because of a sale. The store was offering a 40% discount. If the price on the tag was pp, which expression does NOT represent the price after the discount but before tax?
The expression that represents the price of the video game after the discount is
p - 0.4p
Where p is the original price of the video game.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Price of the video game = p
Discount = 40%
The price of the video game after the discount.
= p - (40% of p)
= p - (40/100)p
= p - 0.4p
Thus,
The expression is p - 0.4p.
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Convert to rectangular
When convert it into rectangular form we get x=-1/2 and y=0.
How to convert polar to rectangular form?To convert a point in polar coordinates (r, θ) to rectangular coordinates (x, y), you can use the following formulas:
[tex]x = r * cos(θ) \\y = r * sin(θ)[/tex]
Where r is the distance from the origin to the point, and θ is the angle in radians between the positive x-axis and the line connecting the point to the origin.
Alternatively, you can also convert from rectangular to polar coordinates using the following formulas:
[tex]r = sqrt(x^2 + y^2)\\θ = atan2(y, x)[/tex]
Where x, y are the rectangular coordinates and atan2 is a function that computes the angle of a point in a cartesian plane.
In general, it's worth noting that the polar coordinates are often used in some physics and engineering problems, while the rectangular coordinates are often used in computer graphics, analytic geometry and other fields.
What is 1 in polar co-ordinate?The angle of 1's inverse tangent is 45°. This is the outcome of translating to polar coordinates in the form (r,theta).
To convert it into rectangle equation we have
[tex]x=rcos(theta)\\y=rsin(theta)\\r=1\\theta= 3*pi/2\\x= cos(3*pi/2)\\x= -1/2\\y=sin(3*pi/2)\\y=0[/tex]
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If these two shapes are similar, what is the measure of the missing length j?
Step-by-step explanation:
since the 2 shapes are similar then their sides are proportional
9/18= j/90
then j equals 45
Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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