How do you determine the base when solving for x by converting to a log?
The answer was supposed to be
x= ln(3/2) / 4ln(1.0125)
why is it ln?
Answers
[tex]$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
Solution:
Given expression:
[tex]$(1.0125)^{4 x}=\frac{3}{2}[/tex]
To solve the expression:
[tex]$(1.0125)^{4 x}=\frac{3}{2}[/tex]
If f(x) = g(x) then ln(f(x)) = ln(g(x)).
Using the above condition, we can write
[tex]$\ln \left(1.0125^{4 x}\right)=\ln \left(\frac{3}{2}\right)[/tex]
Apply log rule: [tex]\log _{a}\left(x^{b}\right)=b \cdot \log _{a}(x)[/tex]
[tex]$4 x \ln (1.0125)=\ln \left(\frac{3}{2}\right)[/tex]
Divide both side of the equation by [tex]4 \ln (1.0125)[/tex].
[tex]$\frac{4 x \ln (1.0125)}{4 \ln (1.0125)}=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
[tex]$x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex]
The answer is [tex]x=\frac{\ln \left(\frac{3}{2}\right)}{4 \ln (1.0125)}[/tex].
Final answer:
To solve for x by converting to a logarithm, the base used depends on the context and specific problem. In this case, the natural logarithm is used as the base is relevant to the equation.
Explanation:
To solve for x by converting to a logarithm, you need to determine the base of the logarithm. In this case, the answer is x = ln(3/2) / 4ln(1.0125), where ln represents the natural logarithm.
The natural logarithm, denoted by ln, is the logarithm with base e, where e is an irrational number approximately equal to 2.71828. It is commonly used in calculus and other fields of mathematics.
When converting to a logarithm, the base can be any positive number greater than 1. The choice of base depends on the context and the specific problem being solved. In this case, the natural logarithm is used because it is relevant to the given equation.
Related Questions
help! need asap! brainiest if right
Answers
Step-by-step explanation:
After the translation, rotation and reflection position of the image may differ but the side lengths, angle, orientation remains the same, so that the congruence is maintained, but in dilation the size of the image may get enlarged or reduced, so that congruence is not there.
Parallelograms are congruent when
Reflect across the y- axis and then translate 1 unit left.
Reflect across the y- axis then rotate 45° counterclockwise.
Translate 4 units up then rotate 180° counterclockwise
Parallelograms are non-congruent when
Translate 5 units right then dilate by a factor of 2
Rotate 90° clockwise then dilate by a factor of 6
Dilate by a factor of 3 then reflect across the x- axis
In the a science class Jodie pours 2 cups of water into one glass and 2 cups of milk into another glass. In her notebook, jorie writes that the liquid takes the shape of their containers. How many pints of liquid did jorie use for her experiment
Answers
Answer: she used 2 pints.
If we remember, 8 ounces = 1 cup, 2 cups = 1 pint (or 16 ounces = 1 pint).
and if we add two more cups that equals 2 pints!
have great day/ night!
Step-by-step explanation:
Final answer:
Jodie used 2 pints of liquid for her experiment, as she poured 2 cups each of water and milk and there are 2 cups in 1 pint.
Explanation:
Jodie used 4 cups of liquid for her experiment, with 2 cups of water and 2 cups of milk. To convert cups into pints, we use the conversion rate: 1 pint = 2 cups. Therefore, Jodie has used a total of 2 pints of liquid in her experiment (since 4 cups divided by 2 cups per pint equals 2 pints). This demonstrates understanding of volume, which is the amount of space a substance (such as a liquid) occupies and is typically measured in liters, but in this case, we are using pints as a unit of measure.
5(-3x - 2) - (x - 3) = -4 (4x +5) + 13
Answers
5(-3x - 2) - (x - 3) = -4(4x + 5) + 13
-15x - 10 - (x - 3) = -16x - 20 + 13
(Note: It's super important to be careful when opening up negative parentheses! -(x-3) is not just - x - 3, it is actually -x + 3 since the negative is distributed in every number!)
-15x - 10 - x + 3 = -16x - 20 + 13
-16x - 7 = -16x - 7
-16x = -16x
0 = 0
There is an infinite number of solutions in this equation.
(When you get 0=0 when solving for a variable, that means that said variable will have infinite solutions, that is, any number plugged into the equation will work)
Answer: No value for x
Step-by-step explanation:
Step 1: open the bracket
5(-3x - 2) - (x - 3) = -4 (4x +5) + 13
-15x + 10 - x +3= -16x - 20 +13
Step 2: combine like terms
-15x - x + 16x = -20 +13 -10 -3
-16× +16× = -20
0= -20
How do I find vertex
Answers
Answer:
Get the equation in the form y = ax2 + bx + c.
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
Step-by-step explanation:
I WILL MARK BRINLIEST FOR CORRECT ANSWER, PLEASE HELP.
Answers
Answer:
f(-2) = 4
f(0.5)= 0
f(1)=1
Step-by-step explanation:
Please help me figure this out explain it to me
Answers
Answer:
40yd
Step-by-step explanation:
area of total minus unshaded portion
What is the greatest area that you can make with a rectangle that has a perimeter of 24.
Answers
Answer:
Step-by-step explanation:
The greatest area of the rectangle with a perimeter of 24 units is in fact a square. So we take 24 units and divide by 4 to get a square of 6 units to a side. the area of that square is 6 units x 6 units = 36 square units
Find the product.
4(−12)(−3)
Answers
Answer:
144
Step-by-step explanation:
Answer:
-12/3
Step-by-step explanation:
It costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expression 100 + 4n. The cost for 20 people equals $ ___. (Input whole number only.)
Numerical Answers Expected!
Answers
Answer:$4 × 20 = 80 + 100 = 180
Step-by-step explanation:
$80 is how much it is for 20 people, then you add the $100 rent which equals 180
Answer:
180
Step-by-step explanation:
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is?
Answers
Hey there!
[tex]\large\boxed{25\%}[/tex]
Assuming that all the sections are the same size, there are four sections of equal size.
Blue would be one out of those four sections, so the probability is 1/4. In decimal form this is .25, and as a percent this is 25%.
Hope this helps!
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is 1/4.
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is 1/4 or 25%.
Total = 1+1+1+1 = 4
Number of blue =1
Therefore, probability =1/4
What is the image point of (-8,-1) after a translation left 3 units and up 4 units?
Answers
Answer:
(-11, 3)
Step-by-step explanation:
When you move -8 to the left its on the x-axis and it's on the negative side. Moving it to the left would mean the number is lower than -8. Moving it to the left 3 units would mean its -11. When you move -1 up 4 units it's on the y axis on the negative side in the beginning. Moving it up would mean the number is higher than -1. Moving -1 up 4 units would mean its 3.
A translation moves a point a constant distance in a given direction. Given the point (-8,-1), if it is translated left 3 units and up 4 units, the new point, or image point, is (-11,3).
Explanation:In mathematics, a translation refers to a geometric transformation that moves every point a constant distance in a specific direction. In this instance, the point (-8,-1) is being moved left 3 units and up 4 units. To implement this translation, you subtract 3 from the x-coordinate and add 4 to the y-coordinate.
So, start with the original point (-8,-1). Subtract 3 from the x-coordinate which gives you -8 - 3 = -11. Then, add 4 to the y-coordinate which gives you -1 + 4 = 3. After the translation, your new point, or image point, is (-11,3).
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(I NEED THIS ANSWERED QUICKLY! I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER!)
The coordinates of the vertices of quadrilateral ABCD are (7, -7), (4, -10), (1.5, -2.5), and (6, -3), respectively. If quadrilateral ABCD is rotated 180° counterclockwise about the origin, what are the coordinates of D’?
A. (6, 3)
B. (3, -6)
C. (-6, 3)
D. (-3, 6)
Answers
Answer:
D
Step-by-step explanation:
literlay just count
Answer:
i believe the answer is c
Step-by-step explanation:
A directed line segment on a gridded map shows the path of a hot air balloon from 1(0,0) to B(8,4). Each grid unit represents 1 mile. The balloon traveled at a constant speed of 20 miles per hour Point V divides line segment AB in the ratio 6 to 2.
a) What are the coordinates of point V? Round to the nearest tenth if necessary
b) Mary states that the distance from point A to point Vis 6 miles. What is Mary's mistake? What is the
correct distance? (Check)
Answers
Answer:
Step-by-step explanation:
There is a point V with ration 6 to 2, therefore we must find the coordinates of point V and the distance from A to V
According to the graph
[tex]c^{2}=x^{2}+y^{2}\\c^{2}=8^{2}+4^{2}\\c=\sqrt{64+16}=8.9.4\\sin\alpha =\frac{4}{8.94}[/tex]
α≅27°
V=2*8.94/6 (ratio 6:2)
V=2.98mile
[tex]sin27=\frac{y}{2.98}\\y=sin27*2.98=1.35\\cos27=\frac{x}{2.98}\\x=cos27*2.98=2.65[/tex]
coordinates of V = (2,65;1.35)
Distance from A to V
[tex]d_{AV}=2.98 miles[/tex]
finally
Mary's mistake is to take the 6 to 2 ratio as the distance traveled from the globe only in the x direction
Write an equation for the nth term of the geometric sequences-3,6,-12,......
Answers
Answer:
Write an equation for the nth term of the geometric sequences-3,6,-12,....
an= ar∩-1
a= first term
r= common ratio
an= nth term
an= -3 x (-2) (-12-1)
an= -3 x (-2) (-13)
an= -3 x (-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)
an= -3 x -16384
nth term= 49152
Step-by-step explanation:
What is (-7a^4bc^3)(5ab^4c^2)
Answers
Answer:=-35a^5b^5c^5
Step-by-step explanation:
Answer:
-35a^5b^5c^7
Step-by-step explanation:
Step 1: Distribute
(-7a^4bc^3)(5ab^4c^4)
(-7 * 5) * (a^4 * a) * (b * b^4) * (c^3 * c^4)
(-35) * (a^5) * (b^5) * (c^7)
-35a^5b^5c^7
Answer: -35a^5b^5c^7
3) Sadie used a container shaped like a cylinder to catch rainwater. The dimensions of the
container are shown below.
- 12 cm-
9 cm
Which measurement is closest to the volume of the container in cubic centimeters?
A 1,527 cm
B 4,072 cm
C 1,018 cm
D3,054 cm
Answers
The correct answer is option B which is [tex]4,072 cm^3[/tex]
Step-by-step explanation:
Given:
The dimensions of the cylinder,
Radius (r) = 12 cm
Height (h) = 9 cm
To find:
The volume of cylinder.
Formula:
Volume of the cylinder = [tex]\pi r^{2} h[/tex]
If r = 12 cm and h = 9 cm then the volume of the cylinder can be found by using the formula as,
Volume of the cylinder = [tex]\pi (12^{2}) (9)[/tex]
= [tex]4071.5 cm^3[/tex]
≈ 4072 cm³
So it is closest to the answer B, 4,072 cm³.
Answer:The answer is C , 1,018
Choose the equation that represents this situation. Use p to represent the
price of an item and tto represent its total cost with gift wrapping.
A store adds a $5 fee to the price of each item that a customer wants to have
gift-wrapped
O A. p=t+5
O B. t= 5p
OC. t= p +5
O D. t+p=5
Answers
Answer:
(c)t=p+5
Step-by-step explanation:
total price= item price + gift wrapping cost (given)
gift wrapping cost is constant/unchanged= 5
total price= t
item price=p
therefore by derivation t=p+5 (option c)
Final answer:
The correct equation to represent the store's $5 gift wrapping fee added to the price of an item is C. t = p + 5, where p is the price of the item and t is the total cost with gift wrapping.
Explanation:
The question is asking to find an equation that shows the relationship between the price of an item, represented by p, and its total cost with gift wrapping, represented by t. Given that the store adds a $5 fee for gift wrapping, the correct equation needs to include the original price of the item and the additional gift wrapping fee. Therefore, the total cost t is equal to the price of the item p plus the $5 wrapping fee.
The correct equation representing this situation is C. t = p + 5.
This is because when you start with the initial price of an item p and add a fixed gift wrapping fee of $5, you get the total cost t. It is the sum of the two values: the price of the item plus the additional fixed fee for gift wrapping.
Y=1/2+2 in standard form
Answers
Answer:
So Y would be 2 1/2, but in standard form it's 2.5
Step-by-step explanation:
So basically, you just have to add the numbers together. 2 + 1/2 = 2 1/2. 50 is half of 100, and this is 1/2 we're talking about. So we can change it to 2.5
You're welcome.
Answer:
y = 2.5
Step-by-step explanation:
[tex]y = \frac{1}{2} + 2[/tex]
[tex]( \frac{1}{2} = 0.5)[/tex]
[tex]y = 0.5 + 2[/tex]
[tex]y = 2.5[/tex]
Write a verbal expression for 2n+7
Answers
Because when it says “twice the number” it doesn’t give you what the number is so it has to be a variable which in “n” in this situation. And 7 more is obviously adding 7, so it is 7 more than twice a number
find the recursive formula.
-28, -35, -42, -49, ...
Answers
Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] - 7
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence, that is
d = - 35 - (- 28) = - 42 - (- 35) = - 49 - (- 42) = - 7
Thus to obtain a term in the sequence subtract 7 from the previous term
[tex]a_{n+1[/tex] = [tex]a_{n}[/tex] - 7 with a₁ = - 28
Which of the following are solutions to the equation below?
Check all that apply.
x2 - 2x - 24 = 0
Answers
Answer: there will be only one solution
x=6,-4
Answer:
[tex]x=-4[/tex] or [tex]x=6[/tex]
Step-by-step explanation:
[tex]x^2 - 2x - 24 = 0[/tex]
Factorizing the equation to find the value of 'x'
[tex]x^2+4x-6x-24=0[/tex]
Taking common from the equation:
[tex]x(x+4)-6(x+4)=0[/tex]
[tex](x+4)(x-6)=0[/tex]
[tex]x+4=0[/tex]
[tex]x=-4[/tex]
or
[tex]x-6=0[/tex]
[tex]x=6[/tex]
The solution for the equation is [tex]x=-4[/tex] or [tex]x=6[/tex]
Write an inequality to describe the relationship between -1 2/3 and -1/4.
Answers
Answer:
-14>-1 2/3
Step-by-step explanation:
Answer:
-14>-1 2/3
Step-by-step explanation:
An arc on a circle measures 125°. The measure of the central angle, in radians, is within which range? 0 to StartFraction pi Over 2 EndFraction radians StartFraction pi Over 2 EndFraction to π radians π to StartFraction 3 pi Over 2 EndFraction radians StartFraction 3 pi Over 2 EndFraction to 2π radians
Answers
Answer:
The answer is B or pi/2 to pi radians.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The area of a rectangle is 72^9^6 square yards. The length of the rectangle is 8^3^4 yards. What is the width of the rectangle in yards? Show how you found the variable expression to represent the width. (Hint: set this up as a division problem to find the missing measurement.)
Answers
Answer:
72^9^6 ÷ 8^3^4
72^3^12 ÷ 8^3^4
(9×8)^3^12 ÷ 8^3^4
9^3^12 × (8^3^12 ÷ 8^3^4)
9^3^12 × (8^3^(12-4))
9^3^12 × 8^3^8 feet
The sum of two numbers is 24.
Seven times the smaller number is
the same as 5 times the larger
number. Find the smaller number.
Answers
Create a chart to show how to use the distributive property to simplify the expression: 7 (5x +
10) – 10x.
Answers
Answer:
25x + 70
Step-by-step explanation:
Step 1: Distribute
7 (5x + 10) - 10x
7*5x + 7*10 - 10x
35x + 70 - 10x
25x + 70
Answer: 25x + 70
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts?
Answers
Answer:
2 1/4
Step-by-step explanation:
Why do you think George Washington wanted the us to avoid entangling alliances
Answers
The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 13.1 years; the
standard deviation is 1.5 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a meerkat living less than 14.6
years.
Answers
Using the Empirical Rule, it is found that there is a 84% probability of a meerkat living less than 14.6.
----------------------
The Empirical Rule states that in a normal distribution, 68% of the measures are within 1 standard deviation of the mean, 95% are within 2 standard deviations and 99.7% are within 3 standard deviations.----------------------
The mean is of 13.1 years, while the standard deviation is of 1.5 years.We have also consider that the normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.14.6 = 13.1 + 1.5, thus, one standard deviation above the mean.Of the 50% of the measures below the mean, all are below 14.6, while of the 50% above, 68% are below 14.6, thus:[tex]P = 50 + 0.68(50) = 50 + 34 = 84[/tex]
84% probability of a meerkat living less than 14.6.
A similar problem is given at https://brainly.com/question/13503878
To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Explanation:To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Given that the average lifespan is 13.1 years and the standard deviation is 1.5 years, we can calculate the z-score for 14.6 years using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for (14.6 years), μ is the mean (13.1 years), and σ is the standard deviation (1.5 years).
Substituting the values, we get:
z = (14.6 - 13.1) / 1.5 = 1.0
Now we can look up the probability corresponding to a z-score of 1.0 in a standard normal distribution table, which is approximately 0.8413. This means that the probability of a meerkat living less than 14.6 years is about 0.8413 or 84.13%.
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a regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches.
Approximately how many square centimeters of sheet will be left over a scraps?
A:32.9
B:93.5
C:113.1
D:126.2
Answers
Answer:
[tex]\large \boxed{\text{D. 126.2 cm}^{2}}[/tex]
Step-by-step explanation:
The area left over for scrap is the area of the circle minus the area of the hexagon.
1. Area of circle
The formula for the area of a circle is
A = πr²
A = π(6)² = 36π = 113.1 in²
2. Area of hexagon
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
(a) Height of a small triangle
Per the Pythagorean Theorem,
[tex]\begin{array}{rcr}h^{2} + 3^{2} & = & 6^{2}\\h^{2} + 9 & = & 36\\h^{2} & = & 27\\& = & 3\sqrt{3}\\\end{array}\\[/tex]
(b) Area of a small triangle
A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²
(c) Area of the hexagon
The hexagon contains 12 small triangles.
A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²
3. Area of scrap
A ≈ 113.1 in² - 93.53 in² = 19.6 in²
[tex]A = \text{19.6 in}^{2} \times \left(\dfrac{\text{2.54 cm}}{\text{1 in}}\right )^{2} = \text{126.2 cm}^{2}\\\\\text{The area of the scrap is $\large \boxed{\textbf{126.2 cm}^{\mathbf{2}}}$}[/tex]