Answers
The value of the logarithmic equations when solved are :
a. x = 1 / 27b. x = -4, 1c. x = 6, -2d. m = 45.76How to solve the logarithmic equations?log₃(x) = -3
To solve this logarithmic equation, we can use the property:
x = b^(logₓ(y))
So, x = 3^(-3)
x = 1/(3^3) = 1/27
The solution for the equation is x = 1/27.
log₂(x² + 6x) = log₂(x - 4)
Since the bases are the same, we can set the arguments equal to each other:
x² + 6x = x - 4
Factor the quadratic equation:
(x + 4)(x - 1) = 0
x = -4, 1
2 * log₂(x) - log₂(x + 3) = 2
We can use the properties of logarithms to rewrite the equation:
log₂(x²) - log₂(x + 3) = 2
log₂(x² / (x + 3)) = 2
x² / (x + 3) = 2²
x² / (x + 3) = 4
x² - 4x - 12 = 0
(x - 6)(x + 2) = 0
x = 6, -2
log₇(m) = 1/3 * log₇(64) + 1/2 * log₇(121)
Using the power rule for logarithms, we can rewrite the equation as:
log₇(m) = 1/3 x (4 x log₇(2)) + 1/2 x (2 x log₇(11))
log₇(m) = (4/3) x log₇(2) + log₇(11)
log₇(m) = log₇(2^(4/3) x 11)
m = 2^(4/3) x 11
m = (2^(4/3)) x 11 ≈ 4.16 x 11 = 45.76
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Related Questions
Identify Central Ideas Explain how a country with little land and few natural resources could make up for such deficits-without depending on other countries-and have a healthy economy .
Answers
A country with little land and few natural resources could make up for such deficits without depending on other countries and having a healthy economy by developing its Human Capital.
What are examples of small countries with low natural resources and high GDP?Examples of small countries with low natural resources and high GDP are:
JapanVatican CityCosta Rica etc.It is to be noted that of all the factors of production, (Land, labor, Capital, and Entrepreneurship) Human Capital (Labor and Entrepreneurship) are the most valuable and yield the greatest return on investment.
The Democratic Republic of the Congo is commonly regarded as the world's richest country in terms of natural resources; its undiscovered stockpiles of raw minerals are estimated to be worth more than US $24 trillion.
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3/2 (x-5) - 3/2 = 9/2 x solve and verify
Answers
Answer:
x = -2
Step-by-step explanation:
3/2 (x-5) - 3/2 = 9x/2
3x/2 - 15/2 - 3/2 = 9x/2 ... alldenominator
are 2 so we can multiply all term by 2
2(3x/2 - 15/2 - 3/2 = 9x/2)
3x - 15 - 3 = 9x ... simplify it
3x - 12 = 9x
-12 = 9x - 3x ... take 3x to the left
-12 = 6x ... simplify
6x/6 = -12/6 ... dividing both side by 6
x = -2 ... simplify and solve x
Need help with 15 and show the work
Answers
Answer:
D
Step-by-step explanation:
In 2 hours they wash 8 cars total so...
8
16
24
The extra time is 15 mins for 2 cars
uno's has projected its Q1 sales at $46,000 and its Q2 sales at $48,000. Purchases equal 71 percent of the next quarter's sales. The accounts receivable period is 30 days and the accounts payable period is 45 days. At the beginning of Q1, the accounts receivable balance is $12,200 and the accounts payable balance is $14,800. The firm pays $1,500 a month in cash expenses and $400 a month in taxes. At the beginning Q1, the cash balance is $280 and the short-term loan balance is zero. The firm maintains a minimum cash balance of $250. Assume each month has 30 days. What is the cumulative cash surplus (deficit) at the end of the Q1, prior to any short-term borrowing?
Multiple Choice
$8,880
$8,633
$9,157
$9,210
$9,684
Answers
To calculate cumulative cash surplus/ deficit we need to consider cash flows during quarter, including sales, purchases, accounts receivable, accounts payable, cash expenses, taxes, initial cash,loan balances.
Calculate the total cash inflows from sales for Q1: $46,000 (Q1 sales) * 71% (purchases as a percentage of next quarter's sales) = $32,660.
Calculate the total cash outflows for Q1: $1,500 (monthly cash expenses) * 3 months + $400 (monthly taxes) * 3 months = $5,700 + $1,200 = $6,900.
Calculate the net cash flow from accounts receivable: $32,660 (total cash inflows from sales) - $12,200 (accounts receivable balance at the beginning of Q1) = $20,460.
Calculate the net cash flow from accounts payable: $48,000 (Q2 sales projection) * 45 days / 30 days = $72,000 (purchases for Q2) - $14,800 (accounts payable balance at the beginning of Q1) = $57,200.
Calculate the net cash flow from short-term borrowing: Since the short-term loan balance is zero at the beginning of Q1 and there is no mention of additional borrowing, the net cash flow from short-term borrowing is zero.
Calculate the net cash flow for Q1: Net cash flow = Cash inflows - Cash outflows = $20,460 (net cash flow from accounts receivable) - $6,900 (total cash outflows) + $57,200 (net cash flow from accounts payable) = $70,760.
Calculate the cumulative cash surplus/deficit at the end of Q1: Cumulative cash surplus/deficit = Initial cash balance + Net cash flow - Minimum cash balance = $280 (initial cash balance) + $70,760 (net cash flow) - $250 (minimum cash balance) = $71,790.
Therefore, the cumulative cash surplus (deficit) at the end of Q1, prior to any short-term borrowing, is $71,790.
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Why do we need to measure the volume?
Answers
We need to measure volume to check capacity of substance, to see that how much material it can hold inside it.
If the price of 3 apples is $1.95, what is the price of 14 apples?
O $6.50
O $7.80
O $9.10
O $9.75
Answers
Answer:
$9.10
Step-by-step explanation:
Answer:
9.10
Step-by-step explanation:
1.95/3=0.65
0.65x14=9.10
A health club charges a $50 initial fee plus $2 per visit. Brenda has spent a total of $144 at the health club this year. How many visits has she made?
Answers
144 = 2x + 50
94 = 2x
47 = x. i think
x = 47
Brenda has made 47 visits
Please tell me if it’s right
does someone know how to do this
Answers
Answer:
us
Step-by-step explanation:
(B)
bbbbbbbbbbbbbbbbbbbbbbbbbwhat’s the answer ??
Answers
Answer:
3132
Step-by-step explanation:
2.2% of 3500 is 77 which leaves you with 3423 after one year. At this rate you can take 2.2% of 3423. using this formula five times you reach a final answer of 3132.
3500
-77
3423
-75.306
3347.694
-73.649268
3274.044732
-72.028984104
3202.0157479
-70.4443464538
3131.57140145
and rounding up to a whole leaves you with 3132
What is the translation for this graph?
A.(x -3, y -4 ) B.( x + 4, y + 3) C.(x +3, y+4) D. (x -4, y- 3)
Answers
Answer:
ok so meet x-3 and y -4 in the middle were they meet if the y and x confuse you take them off and then do the same for the rest of them this - symbel means negitive and this one means + positive if you have more qeustions just ask
Step-by-step explanation:
Which of the following is equivalent to
4x2y - 2y2x - 5xy
Select one:
a. -2x2y - 5xy + 4xy2
b. 2xy2 - 5xy + 4x2y
c. -2xy2 + 5xy + 4x2y
d. -2xy2 - 5xy + 4x2y
e. 2x2y - 5xy
Answers
Answer:
1 Simplify 4x\times 2y4x×2y to 8xy8xy.
8xy-2y\times 2x-5xy
8xy−2y×2x−5xy
2 Simplify 2y\times 2x2y×2x to 4yx4yx.
8xy-4yx-5xy
8xy−4yx−5xy
3 Simplify.
-xy
−xy
Step-by-step explanation:
SOMEONE PLEASE HELP ME!!! PLEASE!!!!
Quadrilateral KLMN has points K(-1,1) , L(3,4) , M(6,0) , and N(2, -3)
Use the distance formula to find the side lengths of quadrilateral KLMN.
Use the slope formula to find and compare the slopes of quadrilateral KLMN.
Use the Properties of Shapes to identify what kind of quadrilateral KLMN must be
Answers
d=(x2−x1)2+(y2−y1)2
One pair of opposite sides are: KL and NM
KL=(4−−2)2+(6−3)2=45−−√=35–√
NM=(3−−3)2+(2−−1)2=45−−√=35–√
Using the substitution property KL=NM
The other pair is: KN and LM
KN=(−3−−2)2+(−1−3)2=17−−√
LM=(4−3)2+(6−2)2=17−−√
Using the substitution property KN=LM
Step-by-step explanation:
KN=(−3−−2)2+(−1−3)2=17−−√
LM=(4−3)2+(6−2)2=17−−√
The table below shows Zoey's earnings on the job
How much does she make in 18.2518.25 hours?
Answers
Answer:
she is going to make $408.90 in 18.2518.25 hours
suppose the mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars. if incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 73 million dollars? round your answer to four decimal places.
Answers
The probability that a randomly selected firm will earn less than 73 million dollars is 0.9842.
The mean income of firms in the industry for a year is 45 million dollars with a standard deviation of 13 million dollars, we need to find the probability that a randomly selected firm will earn less than 73 million dollars.
We can assume that the income distribution of firms is normal. Therefore, we can use the z-score formula to find the required probability.
We have, z = (X - μ) / σ, where X is the income of the firm, μ is the mean income, and σ is the standard deviation.
z = (73 - 45) / 13
z = 2.15
Using the z-table, we can find the area under the standard normal curve to the left of z = 2.15.
The area to the left of Z-score of 2.15 is 0.984, the probability that a randomly selected firm will earn less than 73 million dollars is 0.9842
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In the diagram below
Please help I’ll give brainliest
Answers
There are 7 people in a room. Each person shakes hands once. How many handshakes will there be?
A. 10
B. 15
C. 21
D. 29
Answers
7 people so first one shakes hand with the remaining people. that is 6
The 2nd person also shakes hand with 6 persons but we have already counted his handshake with first person. so we have to add 6-1 = 5 shakes for 2nd person
like wise 3rd person shakes hand with the remaining 6-2 = 4 people
4th person with 6-3=3 people
5th person with 6-4= 2 persons
6th person with 6-5=1 person
and 7th one with no one because already he has shaken his hand with everyone.
since these people shake their hands with others only once we just have to add the obtained values
6+5 +4+3+2+1= 21
totally 21 handshakes will be there in that room
Fill in the blank to make a perfect square trigeminal x^+18x+
Answers
The number that fills in the blank to make a perfect square trigeminal of the given expression is 81.
Given expression:
\(x^2+18x +\) _
We have to find the number that will fill the blank.
A perfect square trigeminal is an algebraic expression that is of the form ax 2 + bx + c, which has three terms. It is obtained by the multiplication of a binomial with itself.
Let the number that fills the blank be a.
Hence, the expression becomes:-
\(x^2+18x +a\)
To make it a perfect square geminal, the expression must be a perfect square of a binomial.
We know that,
\((x+y)^2=x^2+2xy+y^2\)
Comparing it with given expression, we get
2xy = 18x and,
\(y^2=a\)
Hence,
y = 9
a = \(9^2\) = 81
Hence, the number that fills the blank is 81.
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in the figure in angle abc point d on side BC is such that angle BAC is equal to angle abc prove that CA²=CB×CD
Answers
Answer: 2205
Step-by-step explanation CB is 45 and CD is 49 45x49 is 2205 hope this helps :)
find the exact length of the curve. x = y4 8 1 4y2 , 1 ≤ y ≤ 2
Answers
The length of the curve is (1/2) ∫(θ1 to θ2) (8sec^2(θ) - 8).
How to find length of the curve?To find the length of curve, we can use the formula for arc length:
L = ∫(a to b) √[1 + (dy/dx)^2] dx
First, we need to express x in terms of y and find dy/dx. We have:
x = y^4/(8 + 1/4y^2)
=> 8x + x/4y^2 = y^4
=> 8xy^2 + x = 4y^6
=> x = (4y^6 - 8xy^2)/(-1)
Differentiating both sides with respect to y, we get:
dx/dy = (24y^5 - 16xy)/(1)
Simplifying, we get:
dx/dy = 8y^4 - 16x/y
Substituting this into the formula for arc length, we get:
L = ∫(1 to 2) √[1 + (8y^4 - 16x/y)^2] dy
Next, we express x in terms of y and substitute into the integral. We have:
x = (4y^6 - 8xy^2)/(-1)
=> x = (4y^4 - 8y^2x)/(-y)
Substituting this into the integral, we get:
L = ∫(1 to 2) √[1 + (8y^4 + 16y^2x^2 - 16y^2x^2)/y^2] dy
= ∫(1 to 2)√[1 + 8y^2] dy
Use the substitution u = √(8)y, which gives us du/dy =√(8) and dy = du/√(8).
Substituting these into the integral, we get:
L = ∫(√(8) to 2√(8)) √[1 + u^2/8] du/√(8)
= (1/4) ∫(√(8) to 2√(8)) √(8 + u^2) du
Next, we can use the substitution u =√(8)tan(θ),
= √(8)sec^2(θ) d(θ).
Substituting these into the integral, we get:
L = (1/4) ∫(θ1 toθ2)√(8 + 8tan^2(θ)) √(8) sec^2(θ) d(θ)
= (1/2) ∫(θ1 toθ2) √(64 + 64tan^2(θ)) sec^2(θ) d(θ)
= (1/2) ∫(θ1 toθ2) 8sec^3(θ) d(θ)
We can use the trigonometric identity sec^2(θ) - 1 = tan^2(θ) to simplify the integrand:
L = (1/2) ∫(θ1 toθ2) (8sec^2(θ) - 8)
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if $850 grows to $1125 at an interest rate of 12.6% compounded continuously, how long has the money been in the account?
Answers
Answer:
22 years approx.
Step-by-step explanation:
Step one
Given data
Principal P= $850
final amount A= $1125
rate r= 12.6%
Calculate time, solve for t
t = ln(A/P) / r
Step two:
Substitute
t= ln (1125/850)/0.0126
t=ln 1.32/0.0126
t= 0.277/0.0126
t=21.9
t= 22 years approx.
HELPPPPPPPPPPPPPPPPPPPPPPP solving quadratics with the Calculator.
Answers
You are scuba diving at -8 feet. You dive 5 feet deeper. What is your position in the water?
Answers
Answer:
-13 feet
Step-by-step explanation:
Answer:
-13 feet
Step-by-step explanation:
We Start With -8 and we go 5 feet deeper so -8-5 is -13
What is the simplest form of the fraction below?
24/36
Answers
Answer:
2/3
Step-by-step explanation:
Please help I will mark brainliest
Answers
What is the rate he charges to mow?
OA. $1.50 per lawn
OB. $60.00 per lawn
OC. $15.00 per lawn
OD. $7.50 per lawn
Answers
SECTION A (20 MARKS) QUESTION 1 (a)Identify the relevant population for the below foci, and suggest the appropriate sampling design to investigate the issues, explaining why they are appropriate. Wherever necessary identify the sampling frame as well. 10 marks A public relations research department wants to investigate the initial reactions of heavy soft- drink users to a new all-natural soft drink'. (b) What type of sampling design is cluster sampling? What are the advantages and disadvantages of cluster sampling? Describe a situation where you would consider the use of cluster sampling. 10 marks
Answers
a) The relevant population is the heavy soft-drink users in the given case, and the appropriate sampling design that should be used is stratified random sampling. The list of all heavy soft-drink users is the sampling frame.
b) Cluster sampling refers to a sampling design where population is divided into naturally occurring groups and a random sample of clusters is chosen.
The advantages are efficient, easy to perform, and used when the population is widely dispersed. The disadvantages are sampling errors, have lower level of precision, and have the standard error of the estimate.
a) The relevant population for the public relations research department to investigate the initial reactions of heavy soft-drink users to a new all-natural soft drink is heavy soft-drink users. The appropriate sampling design that can be used to investigate the issues is stratified random sampling.
Stratified random sampling is a technique of sampling in which the entire population is divided into subgroups (or strata) based on a particular characteristic that the population shares. Then, simple random sampling is done from each stratum. Stratified random sampling is appropriate because it ensures that every member of the population has an equal chance of being selected.
Moreover, it ensures that every subgroup of the population is adequately represented, and reliable estimates can be made concerning the entire population. The list of all heavy soft-drink users can be the sampling frame.
b) Cluster sampling is a type of sampling design in which the population is divided into naturally occurring groups or clusters, and a random sample of clusters is chosen. The elements within each chosen cluster are then sampled.
The advantages of cluster sampling are:
Cluster sampling is an efficient method of sampling large populations. It is much cheaper than other types of sampling methods.Cluster sampling is relatively easy to perform compared to other methods of sampling, such as simple random sampling.Cluster sampling can be used when the population is widely dispersed, and it would be difficult to cover the entire population.The disadvantages of cluster sampling are:
Cluster sampling introduces sampling errors that could lead to biased results.Cluster sampling has a lower level of precision and accuracy compared to other types of sampling methods.Cluster sampling increases the standard error of the estimate, making it difficult to achieve the desired level of statistical significance.A situation where cluster sampling would be appropriate is in investigating the effects of a new medication on various groups of people. In this case, the population can be divided into different clinics, and a random sample of clinics can be selected. Then, all patients who meet the inclusion criteria from the selected clinics can be recruited for the study. This way, the study will be less expensive, and it will ensure that the sample is representative of the entire population.
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You bought a used truck for $15,000. The value of the truck will
decrease each year because of depreciation. The truck depreciates at the rate of 8% per year. Write an exponential decay model to represent the real-life problem.
Answers
Answer:
\(15000 \times {0.92}^{x} = y\)
x is the number of years and y is the value at x years
The exponential decay model to represent the real-life problem should be considered as the \(15000 \times 0.92^{x} = y\).
Calculation of the exponential decay model:Since the purchase value of the truck is $15,000
The depreciation rate is 8%
So here exponential decay model should be like
\(15000 \times 0.92^{x} = y\)
Hence, The exponential decay model to represent the real-life problem should be considered as the \(15000 \times 0.92^{x} = y\).
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can you guys help me please as much as you can ^^
Answers
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115
Express sin I as a fraction in simplest terms 28 21
Answers
Answer:
4/3
Step-by-step explanation:
First, you need to find the greatest common factor between the numerator and denominator. Then you divide the numerator and denominator by thetheir greatest common factor in order to simplify the fraction.
through Buzz under the assignment.
1. lan deposits $2,400 each quarter for 3 years. The annuity earns 10% interest and is compounded quarterly. Find the present value of the annuity.
Using the Present Value of Ordinary Annuity Table, the correct factor for 12 compounding periods at 2.5% interest is 10.25776.
Answers
Answer:
$56,577.12
Step-by-step explanation:
To find the present value of the annuity, we can use the formula for the present value of an ordinary annuity, which is:
PV = PMT x [1 - (1 + r/n)^(-n*t)] / (r/n)
Where:
PV = present value
PMT = payment amount per compounding period
r = annual interest rate
n = number of compounding periods per year
t = total number of years
Plugging in the given values, we get:
PV = 2400 x [1 - (1 + 0.10/4)^(-4*3)] / (0.10/4)
PV = 2400 x [1 - (1.025)^(-12)] / (0.025)
PV = 2400 x [1 - 0.610355] / 0.025
PV = 2400 x 23.5742
PV = $56,577.12 (rounded to the nearest cent)
Therefore, the present value of the annuity is $56,577.12, assuming the interest is compounded quarterly and the annuity earns a 10% interest rate.