Answer and Step-by-step explanation:
Part A: Exponential equation is the "opposite" of logarithmic equation, so:
[tex]y=log_{b}m[/tex]
[tex]b^{y}=m[/tex]
Part B: Using log with base c:
[tex]log_{c}b^{y}=log_{c}m[/tex]
Power property of logarithm states that if the anti-logarithm is elevated at a power, the elevated number can be pulled in front of the logarithm:
[tex]ylog_{c}b=log_{c}m[/tex]
Solving for y:
[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]
Part C: To facilitate the use of calculators, which only have values for the base-10 log and natural log, we use change of base formula, i.e., transform
[tex]y=log_{b}m[/tex]
into
[tex]y=\frac{log_{c}m}{log_{c}b}[/tex]
Part D: [tex](log_{3}z)(log_{z}27)[/tex]
Change of base will be:
[tex]log_{3}z=\frac{log_{10}z}{log_{10}3}[/tex]
[tex]log_{z}27=\frac{log_{10}27}{log_{10}z}[/tex]
Solving:
[tex](log_{3}z)(log_{z}27)[/tex] = [tex](\frac{log_{10}z}{log_{10}3})(\frac{log_{10}27}{log_{10}z} )[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}27}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{log_{10}3^{3}}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = [tex]\frac{3log_{10}3}{log_{10}3}[/tex]
[tex](log_{3}z)(log_{z}27)[/tex] = 3
Part E: [tex]log_{7}300[/tex]
Using change of base:
[tex]log_{7}300=\frac{log300}{log7}[/tex]
[tex]log_{7}300=\frac{2.48}{0.85}[/tex]
[tex]log_{7}300[/tex] ≈ 3
Jamie borrowed $361.75 from his uncle,
who has agreed to charge him a monthly
simple interest rate of 2.5%. Jamie pays
his uncle back in 7 months.
Answer:
Jamie will pay back a total of 370.79
Step-by-step explanation:
361.75 x 1.025
Simple interest is not compounded so just multiply the borrowed amount by
1 + .025
He pays 370.28125.
What is Simple Interest?Simple interest is a quick and easy method of calculating the interest charge on a loan. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
Given:
Jamie borrowed = $361.75
Simple interest = 2.5%
As, Simple interest is not compounded.
so,
361.75 x 1.025
=370.28125
Hence, he pays 370.28125.
Learn more about simple interest here:
https://brainly.com/question/25845758
#SPJ2
Planes S and R both intersect plane T Which statements are true based on the diagram? Select three options OPlane S contains points B and E. The line containing points A and B lies entirely in plane T B ULine v intersects lines x and y at the same point ULine z intersects plane S at point C OPlanes R and T intersections at line y.
Answer:
Options (2), (4) and (5)
Step-by-step explanation:
Option (1).
Planes S contains points B and F.
False.
(Point B lies on plane S and point F lies on plane R)
Option (2).
The line containing points A and B lie on the plane T.
True.
(points A and B lie on plane T)
Option (3).
Line v intersects lines x and y at the same plane.
False.
Option (4).
Line z intersects plane S at point C.
True.
Option (5).
Planes R and T intersect at line y.
True.
Answer:its b d e
Step-by-step explanation:
Determine whether the following probabilities are best categorized as subjective, empirical, or classical probabilities.
a. Before flipping a fair coin, Sunil assesses that he has a 50% chance of obtaining tails. Subjective probability Empirical probability Classical probability
b. At the beginning of the semester, John believes he has a 90% chance of receiving straight A’s. Subjective probability Empirical probability Classical probability
c. A political reporter announces that there is a 46% chance that the next person to come out of the conference room will be a Republican, since there are 80 Republicans and 93 Democrats in the room. Subjective probability Empirical probability Classical probability
a) Classical. This is because there are 2 sides and 1/2 = 0.50 = 50% is the chance of landing on tails. Classical probability is also known as theoretical probability.
b) Subjective. This is based off John's belief and his gut feeling. There doesn't seem to be any empirical data to back him up, unless he's looking back at previous semesters.
c) Empirical. When you have a finite set of data and you compute the probability based on it like what we're doing here, we're computing empirical probability. Another example would be that if you flipped a coin 30 times and got 17 heads, then the empirical probability of getting heads is 17/30 = 0.5667 approximately. Note how this is slightly different from the theoretical probability 0.50
Jacob is a scuba diver and is currently -15 meters below sea level. He continues to dive 7 meters down then swims up 11 meters. At what sea level does Jacob end at?
Answer:
-11
Step-by-step explanation:
Answer:
-11 meters down
Step-by-step explanation:
832 divided by 12
i also have to show my work in 2 different ways
Answer: 69
Step-by-step explanation:
duhhhhhhhhhhhh
Wendy and Mini earn $38 per week for delivering magazines. Wendy worked for x weeks and earned an additional total bonus of $15 Mini worked for y weeks. Which expression shows the total money, in dollars, that Wendy and Mini earned for delivering magazines
A: 53x + 38y
B: 38 + 15 + 38y
C: 38 - 15 + 38y
D: 38x + 53y
NEED ANSWER ASAP! !!!
3+2/3x=2/5 rewritten without fractions or decimals
Answer:
its c
Step-by-step explanation:
Find the value of f(15) if f(x) = 100x – 5x2.
this problem is to replace the variable (here "x" ) with a certain numerical value.
the given function is f(x) followed by the algebraic expression " 100x -5x^2 "
now u r asked to find f(15), mean u have to find the value of the "expression" with the numerical value "15" replacing "x"
so it looks like this:
f(x) = 100x -5x^2
f(15) = 100*15 - 5*(15)^2 [only "x" got replaced by it's numerical value "15"]
now u can calculate it
so
f(15) = 1500 - 5*225 = 1500 - 1125 = 375 (Ans.)
hope u got the basic idea.
feel free to ask if u have further queries.
all the best!
Which undefined geometric term is described as a two-dimensional set of points that has no beginning or end?
9+10....................................................................
Answer:
24234221111111111111111111111
Step-by-step explanation:
How much was the initial website fee? (from this equation)
Answer:
y= .75x + 3.75
Step-by-step explanation:
1. Distribute x:
Original Equation= y-2.25=.75(x-8)
So you just do .75 times x and .75 times -8= .75x - 6
2. Isolate the y Variable:
Add 2.25 to both sides. So -6 + 2.25= 3.75
Now you have left y= .75x + 3.75
when writing fraction from a graph does the x axis number go on top or bottom
Answer:
x ax-s can be horizontal and top
y axis is bottom
Step-by-step explanation:
please help!!!!!!!!!!!!! will give brainliest.
Answer:
x<9 and x>1/13
1/13<x<9
Step-by-step explanation:
First, let's find the value of x in the first equation:
6((x-1)/2-(x-3)/3)<2*6
(3x-3)-(2x-6)<12
3x-3-2x+6<12
x+3<12
x<9
Now, let's find the value of x in the second equation:
13x-1>0
13x>1
x>1/13
Since x has to satisfy both of these, the answer would be x<9 and x>1/13; in other words, 1/13<x<9.
Choose a linear function for the line represented by the point-slope equation y - 5 = 3(x - 2)
A) f(x) = 3x + 1
B) f(x) = 3x - 1
C) f(x) = 8x + 10
D) f(x) = 8x - 10
express the following into standard form
[tex] \frac{1}{3500000000} [/tex]
Answer:
350000
P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6P(-2,2), Q(4,2), R(2, -6), S(-4,-6
UCF is a major Metropolitan University located in Orlando Florida. UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13). The Director of Institutional Research at UCF is interested in testing this information. She decides to conduct a survey of 50 randomly selected recent graduate economic students. The sample mean is $43,350 and the sample standard deviation is 15,000. Alpha = 0.01
Answer:
The claim is rejected
Step-by-step explanation:
Claim: UCF is advertising their bachelor in Economics with the statistic that the starting salary of a graduate with a bachelor in economics is $ 48,500 according to Payscale (2013-13).
Null hypothesis: [tex]H_0: \mu = 48500[/tex]
Alternate hypothesis :[tex]H_a : \mu \neq 48500[/tex]
n = 50
Since n is more than 30 .
So we will use Z test
x=43350
Standard deviation = 15000
[tex]Z=\frac{x-\mu}{\frac{s}{\sqrt{n}}}\\Z=\frac{43350-48500}{\frac{15000}{\sqrt{50}}}\\Z=-2.42[/tex]
Refer the z table
p value = 0.00776
[tex]\alpha = 0.01[/tex]
p value < [tex]\alpha[/tex]
So, We are failed to accept null hypothesis
Hence The claim is rejected
In multiple regression analysis, the word linear in the term "general linear model" refers to the fact that β0, β1, . . ., βp all have exponents of a. at least 1. b. less than 0. c. 0. d. 1.
Answer:
d. 1
Step-by-step explanation:
it is called linear because β0, β1, . . ., βp all have their exponents to be 1. A multiple linear regression is a type of regression which has more than one independent variable. it tells us the existing relationship between 2 or more of these independent variables on the dependent variable. for it to be regarded to be linear, it is very important that the exponents be equal to 1. else it could be quadratic.
Calculate a point estimate of the mean pull-off force of all connectors in the population (Round the answer to four decimal places (e.g. 90.2353).) g
Answer:
The answer is "75.627"
Step-by-step explanation:
Please find the correct question in the attached file.
The mean displacement force among all connectors throughout the population calculates the point estimation.
[tex]\bold{ \bar x= \frac{\text{Sum of observation}}{\text{Amount of observations}}}[/tex]
[tex]= \frac{1966.88}{26}\\\\=75.627[/tex]
Jenna must run a total of 12 miles on Monday.
Jenna ran 3 5/6 miles in morning and 4 1/12 miles in the afternoon.
How many miles does Jenna still need to run before the end of the day?
•1 9/12
•4 1/12
•7 11/12
•5 5/12
You are a business owner and you want to know if you have made a profit
for the month. You are given the following information:
1. The monthly salary of your employees is Php 10000.00 each and you
have 5 employees.
2. The store rent is Php 40,000.
3. Utilities expenses amount to Php 20,000.00
4. 200 pieces of your product were sold at Php 1000.00 each.
Questions: Did your business make a profit for the month? How much?
Why?
Pleae help PLEASE
Answer: Yes the business made a profit for the month. They made $90,000 net profit. They made a profit of $90,000 after all the taxes were deducted.
Step-by-step explanation: 200 times $1000 = $200,000. $200,000 - $50,000 = $150,000. $150,000 - $40,000 = $110,000. $110,000 - $20,000 = $90,000
1. What is the value of 125 - 34 + 7 x 3?
a.) 294
c. 112
b. 252
d. 70
Answer:
c
Step-by-step explanation
7x3=21
125-34=91
91+21=112
Vincent is selling candy bars to raise money for his soccer team. He started with a full box of 20 candy bars and has sold 3/10 of them so far. If each candy bar costs $1.25, how much money has vincent raised?
Answer:
$7.25
Step-by-step explanation:
6*1.25
Answer:
7.50
Step-by-step explanation:
3) New Orleans, Louisiana, is 6 feet below sea
level. The highest point in Louisiana, Driskill
Mountain, is 541 feet higher than New Orleans.
How high is Driskill Mountain?
This is my hw lol i don’t understand it please help.
Answer:
-6+541=535
Step-by-step explanation:
g You measure 40 textbooks' weights, and find they have a mean weight of 73 ounces. Assume the population standard deviation is 11.7 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight.
Answer:
The confidence interval is 73 ± 4.8
Step-by-step explanation:
Here, we want to construct a 99% confidence interval
Mathematically;
mean ± Z * S.D/√n
From the question
mean = 73
SD = 11.7 ounces
Z score = 2.576 for 99% Confidence interval
n = sample size = 40
Thus;
73 ± (2.576 * 11.7)/√40
73 ± 4.8
So the range of values are;
73 + 4.8 and 73-4.8
= 77.8 and 68.2
The lower boundary is 68.2
The upper boundary is 77.8
Which one of these relationships is different than the other three?
Group of answer choices
A
B
C
D
help!!!1
Answer:
B
Step-by-step explanation:
I got this by looking at the graph and the numbers that I got vertically and horizontally I divided them .
find a formula for the nth partial sum of each series 4+(4/3)+(4/9) and use it to find the series’ sum of the series converges.
Answer:
We can see that:
a₀ = 4
a₁ = 4/3
a₂ = 4/9.
We easily can see that the n-th therm of this will be:
aₙ = 4/3^n.
Now, the denominator increases as n increases, then for a really large n, aₙ will tend asymptotically to zero. This means that this summation converges.
We can write this summation as:
4*∑(1/3)^n.
The sum for the first N-th therms is:
We know that for a summation:
1 + r + r^2 + r^3 + ... + r^N = (1 - r^(N + 1))/(1 - r)
4 + 4*(1/3) + 4*(1/3)^2 + ... + 4*(1/3)^N = 4*( 1 - (1/3)^(N + 1))/(1 - (1/3))
Now, for the complete sum we have that:
n = {0, 1, 2, ...}
We know that for a summation:
∑a*r^n
with n = {0, 1, ...}
the sum is = a/(1 + r).
in this case we have:
a = 4, r = 1/3.
Then the sum is:
S = 4/(1 - 1/3) = 4/(2/3) = 3*2 = 6
The net of a rectangular shipping box is shown.
What is the surface area, in square centimeters, of the box?
Answer:
It would be 376.
Hey I need help with this question:
6(x-3)^2-26 = 10
Answer:
x = 3 ±sqrt(6)
Step-by-step explanation:
6(x-3)^2-26 = 10
Add 26 to each side
6(x-3)^2-26+26 = 10+26
6(x-3)^2 = 36
Divide by 6
6/6(x-3)^2 = 36/6
(x-3)^2 = 6
Take the square root of each side
sqrt((x-3)^2) = ±sqrt(6)
x-3 = ±sqrt(6)
Add 3 to each side
x-3+3 =3 ±sqrt(6)
x = 3 ±sqrt(6)
- 7/8 k = -21
Please show the steps... :(
Answer:
Your answer is: k = 24
Solve for k by simplifying both sides of the equation, then isolating the variable.
Step-by-step explanation:
Hope this helped : )
-7/8k = -21
Step 1: Multiply both sides by 8/(-7).
(8/-7) x -7/8k = -21 x (8/-7)
Answer= k = 24