How would you explain the relationship between an exponential function and a logarithmic function to an English major you are tutoring in math? Can you give me a real life example of it?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay.
The logarithmic function [tex]\bold{y=log_ax}[/tex] is defined to be equivalent to the exponential equation x = ay.
Real life example:
Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity)
Three of the most common applications of exponential and logarithmic functions have to do with interest earned on an investment, population growth, and carbon dating.
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The price of a product increased by $75, which was a 15% increase. What was the product's original price
The correct answer is: The original price is = x = $500
Explanation:
Mathematically, we can write it as:
[tex] \frac{15}{100} * x = 75 [/tex]
x = Original Price
The above equation can be read as: "The 15% of the original price is $75."
Now we need to find the value of x:
[tex] x =\frac{75 * 100}{15} = 500 [/tex]
Hence,
The original price is = x = $500
Using the letters A and B, the following two-letter code words can be formed: AA, AB, BB,Ba. Using the letters A, B, and C, how many different three-letter code words can be formed?
I know that the answer is 27 from the answer sheet, but how? Can you please list the combinations? Thanks!
Answer:
27
Step-by-step explanation:
Make a tree-diagram for all three-letter code words starting with A. Each path from the top to the bottom contains 3 letters, which is one of the code words beginning with A. There are 9 such code words. Clearly, there are 9 code words starting with B and 9 starting with C. In all, there are 27 code words.
Rock musician Donny West is paid 15% on his CD sales and tour video sales. Last year, he sold one million CDs and $550000 videos. The CDs were sold to the music store for $5 each. The videos were sold to the music store for $6 each.
a.) What was the total amount of CD sales?
b.) What was the total amount of video sales?
c.) What was the combined total of CD and video sales?
d.) How much did he receive in royalties last year?
is 12x=7y-10y a linear equation?
The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function is a function that varies linearly with respect to the changing variable.
Given the line,
12x = 7y - 10y
12x = -3y
-3y = 12x
Divide both sides by -3
y = -4x
The slope of any function is given as dy/dx or first differential
dydx = -4 so the slope is constant thus the line will be a linear equation.
The graph of the line also has been attached for refernce.
Hence "The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation".
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The equation 12x = 7y - 10y simplifies to 12x = -3y and is a linear equation because it can be rewritten in the form y = mx + b, where m is the slope (-4) and b is the y-intercept (0).
Explanation:The equation 12x = 7y - 10y simplifies to 12x = -3y, which can then be written in the slope-intercept form as y = -4x. This is a linear equation because it can be expressed in the standard form y = mx + b, where m represents the slope and b is the y-intercept. In this equation, m equals -4 and b equals 0, indicating that the line crosses the y-axis at the origin (0,0).
Similar examples of linear equations include 7y = 6x + 8, 4y = 8, and y + 7 = 3x. These equations all have a constant rate of change, which is characteristic of linear relationships, where one variable is a constant multiple of the other plus a constant (y = a + bx). As a real-life example, the equation y = 55x + 75 represents the total labor charges to fix a car, with y being the dependent variable and x the independent variable, showcasing the linear relationship between hours worked and total charges.
if there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it, how much pizza does she want
The amount of pizza she wants is:
[tex]\dfrac{1}{6}[/tex] of the pizza.
Step-by-step explanation:If there is 1/3 of a pizza left, and Becky only wants to eat 1/2 of it.
Then the amount of pizza she wants is:
1/2 of the amount of the pizza left.
i.e. she wants:
[tex]\dfrac{1}{2}\times \dfrac{1}{3}=\dfrac{1}{6}[/tex]
This means that Becky wants 1/6 parts of the whole pizza.
A _______ is a group of people who agree to save their money together and to make loans to each other at a relatively low rate of interest. A. credit union B. mutual fund C. investment firm D. commercial bank
What is the quotient for 2 and 4/7 divided by 1 and 3/6?
Find w(4) for the function w(x) = 3x + 7.
Use parallelogram JKLM to find the length of JK.
Answer:
JK = 6
Step-by-step explanation:
Given: We are given a parallelogram JKLM and ML = 6 units. and m∠K = 109°
We need to find length of JK.
Here we use the properties of parallelogram to find the length of Jk.
In a parallelogram, the opposite sides are parallel and equal in measures.
Therefore, ML = JK
Given: ML = 6
So, 6 = JK
Therefore, the length of JK = 6
Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
What did you include in your response? Check all that apply.
Louise is missing the term 30x3.
Louise could have used the formula for a perfect square trinomial.
Louise squared each term in the binomial rather then using the distributive property.
Using the square of the sum notable product, it is found that Louise's answer is not correct, as she forgot to add the multiplication of 2 by both terms.
What is the square of the sum notable product?It is represented by the following relation:
[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]
Hence, for Louise's expression, we have that:
[tex](5x^3 + 3)^2 = (5x^3)^2 + 2(5x^3)(3) + 3^2 = 25x^6 + 30x^3 + 9[/tex]
She forgot the middle term, hence her answer is not correct.
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HELP ME PLEASEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
For the past 5 years, Frank and Peggy have deposited $15,000 in a retirement account with a simple interest rate of 7%. They plan to continue to make annual deposits for the next 20 years. Explain how their money will grow over time. Note: You do not need to extend their entire savings for 25 years in your explanation. Focus on the earning for the first several years and explain how their money will grow.
circle of the radius of 3 an arc of a circle has a central angle of 340 degrees what is the length of the arc
Final answer:
The length of the arc of a circle with a radius of 3 and a central angle of 340 degrees is 17π. This is calculated by converting the angle to radians and finding the proportion of this angle to the full circle's circumference (2πr).
Explanation:
To find the length of the arc of a circle with a radius of 3 and a central angle of 340 degrees, we first need to understand that arc length (Δs) is proportional to the central angle when measured in radians. The circumference (Δ4) of a circle is given by the formula Δ = 2πr. Since there are 360 degrees in a complete circle, which corresponds to 2π radians, we can set up a proportion to solve for the arc length of the 340-degree angle.
The proportion will look like this:
Convert the central angle from degrees to radians by multiplying it by π/180.
340 degrees * π/180 = 340π/180 radians.
Use the ratio of the angle in radians to the entire circle in radians (2π) to find the arc length: Δs = (Angle in radians/2π) * Circumference.
Δs = (340π/180) / (2π) * 2π * 3.
Simplify to find the arc length Δs.
The final step yields the arc length for the given central angle and radius:
Δs = (340/360) * 2π * 3 = (17/18) * 2π * 3.
Therefore, the length of the arc is Δs = 17π.
72 divided by 9 4 x 4 =
three apples and two bananas cost 2.00. four apples and four bananas cost 3.00. what is the cost of one apple?
HELP PLS
a)1
b)0.75
c)0.50
d)0.25
The cost of one apple is 0.5, option C is correct.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let A represents cost of one apple and B represents cost of one banana
Three apples and two bananas cost 2.00
3A+2B=2...(1)
Four apples and four bananas cost 3.00.
4A+4B=3..(2)
Let us multiply equation 1 with 2
6A+4B=4...(3)
Subtract equation 3 from 2
4A+4B-6A-4B=3-4
-2A=-1
A=1/2
A=0.5
Hence, the cost of one apple is 0.5, option C is correct.
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Determine which choice best shows the distributive property of multiplication.
The distributive property is demonstrated best by equations in the form a(b + c) = ab + ac. The correct choices that illustrate this property are: 1. C, 2. B, 3. A, 4. A, 5. A, 6. B, 7. C, and 8. C.
To determine which choice best shows the distributive property of multiplication, we need to find the equation that demonstrates the format a(b + c) = ab + ac. This property states that you can distribute the multiplication over addition inside the parentheses.
1 Correct choice: C. (7 × 2) + (7 × 4) = 7 × (2 + 4)
2 Correct choice: B. (7 × 3) + (7 × 2) = 7 × (3 + 2)
3 Correct choice: A. (2 × 10) + (2 × 8) = 2 × (10 + 8)
4 Correct choice: A. (9 × 4) + (9 × 5) = 9 × (4 + 5)
5 Correct choice: A. 2 × (3 + 5) = (2 × 3) + (2 × 5)
6 Correct choice: B. 9 × (3 + 7) = (9 × 3) + (9 × 7)
7 Correct choice: C. 5 × (4 + 6) = (5 × 4) + (5 × 6)
8 Correct choice: C. (2 × 6) + (2 × 0) = 2 × (6 + 0)
This demonstrates the distributive property effectively.
Complete question:
Determine which choice best shows the distributive property of multiplication.
1) A. 7 × 1 = 7, B. 7 × 2 = 2 × 7, C. (7 × 2) + (7 × 4)=7 × (2 + 4), D. (7 × 2) × 4 = 7 × (2 × 4)
2) A. (7 × 3) × 2 = 7 × (3 × 2), B. (7 × 3) + (7 × 2) = 7 × (3 + 2), C. 7 × 1 = 7, D. 7 × 3=3 × 7
3) A. (2 × 10) + (2 × 8) = 2 × (10 + 8), B. (2 × 10) × 8 = 2 × (10 × 8), C. 2 × 1 = 2, D. 2 × 10 = 10 × 2
4) A. (9 × 4) + (9 × 5) = 9 × (4 + 5), B. (9 × 4) × 5 = 9 × (4 × 5), C. 9 × 1 = 9, D. 9 × 4 = 4 × 9
5) A. 2 × (3 + 5) = (2 × 3) + (2 × 5), B. 2 × 3 = 3 × 2, C. 2 × (3 × 5) = (2 × 3) × 5, D. 1 × 2 = 2
6) A. 9 × (3 × 7) = (9 × 3) × 7, B. 9 × (3 + 7) = (9 × 3) + (9 × 7), C. 9 × 3 = 3 × 9, D. 1 × 9 = 9
7) A. 5 × (4 × 6) = (5 × 4) × 6, B. 1 × 5 = 5, C. 5 × (4 + 6) = (5 × 4) + (5 × 6), D. 5 × 4 = 4 × 5
8) A. 2 × 1 = 2, B. 2 × 6 = 6 × 2, C. (2 × 6) + (2 × 0) = 2 × (6 + 0), D (2 × 6) × 0 = 2 × (6 × 0)
Match the given equation with the verbal description of the surface:
A. Cone
B. Elliptic or Circular Paraboloid
C. Plane
D. Half plane
E. Circular Cylinder
F. Sphere
1. r = 4
2. θ = [(π)/3]
3. ρ = 2cos(φ)
4. r = 2cos(θ)
5. ρ = 4
6. r2 + z2 = 16
7. ρcos(φ) = 4
8. φ = [(π)/3]
9. z = r2
Each equation matches with a surface as follows: A. Cone - ρ = 2cos(φ); B. Elliptic or Circular Paraboloid - z = r²; C. Plane - ρcos(φ) = 4; D. Half plane - θ = [(π)/3]; E. Circular Cylinder - r = 2cos(θ); and F. Sphere - r² + z² = 16 or r = 4.
Explanation:In order to match each equation with the verbal description of the surface, it's important to recognize their respective characteristics.
A. Cone matches with 3. ρ = 2cos(φ). This is because this polar equation describes a cone in spherical coordinates, where ρ represents the radius, φ is the angular altitude, and cos(φ) describes the height-to-radius ratio of the cone.B. Elliptic or Circular Paraboloid is linked to 9. z = r². This equation represents a paraboloid in cylindrical coordinates. Here, z elevation varies quadratically with the distance from the z-axis, r.The C. Plane can be matched with 7. ρcos(φ) = 4. In spherical coordinates, if ρcos(φ) equals a constant, a plane is obtained where it cuts the z-axis at that constant.D. Half plane corresponds to 2. θ = [(π)/3]. This polar equation with θ as a constant represents a half plane.The E. Circular Cylinder links to 4. r = 2cos(θ). This equation represents a circular cylinder in cylindrical coordinates.F. Sphere is matched with 6. r² + z² = 16 and 1. r = 4 which represent a sphere in cylindrical and polar coordinates, respectively.Learn more about Surface Equations here:https://brainly.com/question/28482933
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a, 2a, 4a, 8a
If a < 0, which of the four numbers above is the greatest?
A. a
B. 2a
C. 4a
D. 8a
E. It cannot be determined from the information given.
Suppose a normal distribution has a mean of 20 and a standard deviation of 4. A value of 26 is how many standard deviations away from the mean?
**URGENT HELP???!!!*
Suppose that b(x) varies directly with x and b(x) = 4325 when x= 25.
What is b(x) when x =19?
A.) 4325
B.) 3287
C.) 173
D.) 9.1
I can't remember how problems like these are suppose to go and how to write them out, could you tell me how you got the answer once you get it. Thanks ;)
Answer:
B.3287
Step-by-step explanation:
We are given that
b(x) varies directly with x.
b(x)=4325 when x=25
We have to find the value of b(x) when x=19
According to question
[tex]b(x)\propto x[/tex]
[tex]b(x)=kx[/tex]
Where k=Proportionality constant
Substitute the values then we get
[tex]4325=k(25)[/tex]
[tex]k=\frac{4325}{25}=173[/tex]
[tex]k=173[/tex]
Now, substitute the value of k then, we get
[tex]b(x)=173 x[/tex]
Substitute the value of x=19
Then, we get
[tex]b(x)=173 \times 19=3287[/tex]
Hence, option B is true.
Susan wants to make 2 square flags to sell at a crafts fair. The fabric she wants to buy is 3 meters wide. She doesn't want any fabric left over. What's the least amount of fabric she should buy?
Which equation will help Susan solve her problem?
Let x= the length of one side of the flag.
A.) 3x^2-2x=0
B.) 2x^2=3x
C.) 2*2=3*2
D.) 6+2x=2(4x)
Answer:
Option. B) 2x² = 3x
Step-by-step explanation:
Susan wants to make 2 square flags to sell at a craft fair.
She wants to buy a fabric of 3 meters wide. She doesn't want any fabric left over.
It means area of fabric purchased should be same as area of the flags.
Since x = length of one side of the flag
So area of one flag = x² meter²
Area of 2 flags = 2x² meter²
Area of the fabric = length × width
Area of fabric = x.3 = 3x
Now as per question both the areas should be same
2x² = 3x
Option B. is the correct option.
Saturated hydrocarbons are relatively unreactive except in the presence of _____.
high temperatures and oxygen
other alkanes
alkenes
oxygen
Answer:
Saturated hydrocarbons are relatively unreactive except in the presence of high temperatures and oxygen.
Step-by-step explanation:
we have to choose the option in which saturated hydrocarbons react.
Saturated hydrocarbons do contain double and triple bonds that make molecule reactive. They only contains sigma bonds, which are very stable and difficult to break and hence these are unreactive.
In saturated hydrocarbons the percentage of carbon is lower which gets easily oxidised in oxygen of the air to form [tex]CO_2[/tex] completely.
Saturated hydrocarbons are generally unreactive, but when exposed to high temperatures and oxygen they react in a combustion reaction to produce Carbon Dioxide and Water.
Hence, Saturated hydrocarbons are relatively unreactive except in the presence of high temperatures and oxygen.
Option option 1 is correct.
What percent of 77 is 7?
The value "7" is approximately 9.09 percent of the number "77".
To calculate what percent of 77 is 7, we need to find the proportion of 7 in relation to 77. The concept of percent is based on the idea of expressing a fraction of a whole as a value out of 100.
To find the percentage, we divide the given value (7) by the total value (77) and multiply by 100.
⇒ (7/77) × 100 = 0.0909 × 100 ≈ 9.09%,
Therefore, 7 is approximately 9.09% of 77. This means that 7 represents about 9.09% of the total value of 77. It reflects the proportion of 7 within the whole value of 77, expressed as a percentage.
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Find Dxy using the rules for finding derivatives.
=(5x^2−8)(9x^2−3x+5)
(x+f)+2=j solve for x ...?
(x + f) + 2 = j subtract 2 from both sides
x + f = j - 2 subtract f from both sides
x = j - f - 2
Divide £42 in a ratio of 4:6
Explanation on dividing £42 in the ratio of 4:6 into two parts accurately.
Divide £42 in a ratio of 4:6:
Calculate the total parts in the ratio, which is 4 + 6 = 10.
Divide £42 by 10 to find the value of one part: £42 ÷ 10 = £4.20.
Multiply £4.20 by the parts in each ratio: £4.20 x 4 = £16.80 for the first part (4 parts),
£4.20 x 6 = £25.20 for the second part (6 parts).
Round off 0.065 to one significant figure
The formula to find the area of a triangle is
A = ½bh. Solve the formula for h.
Which is not a way to solve 4÷15=n4÷15=n??
The sum of the measures of the interior angles of a triangle is equal to A. 90 B.180 C. 270 D. 360