Answers
EXPLANATION:
Given;
We are given the following equation;
[tex]1.12^x=20[/tex]Required;
We are required to describe two methods which can be used to solve for x in this equation.
Step-by-step solution;
We can solve for the variable x by taking the natural log of both sides of the equation. This is shown below;
[tex]1.12^x=20[/tex]We take the natural log of both sides;
[tex]ln1.12^x=ln20[/tex]Next we apply the log rule;
[tex]\begin{gathered} If: \\ log_bx^a \\ Then: \\ alog_bx \end{gathered}[/tex]Therefore, our equation is now refined and becomes;
[tex]xln1.12=ln20[/tex]Divide both sides by ln(1.12);
[tex]x=\frac{ln(20)}{ln(1.12)}[/tex]A second method is to express it as a logarithmic equation;
[tex]1.12^x=20[/tex]We shall apply the log rule which is;
[tex]\begin{gathered} If: \\ log_bx=a \end{gathered}[/tex][tex]\begin{gathered} Then: \\ b^a=x \end{gathered}[/tex]For example;
[tex]\begin{gathered} If: \\ log_{10}100=2 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ 10^2=100 \end{gathered}[/tex]Therefore, for the equation given;
[tex]\begin{gathered} If: \\ 1.12^x=20 \end{gathered}[/tex][tex]\begin{gathered} Then: \\ log_{1.12}20=x \end{gathered}[/tex]Note that both solutions can be simplified eventually with the use of a calculator.
ANSWER:
(1) By taking the natural log of both sides
(2) By expressing the equation as a logarithmic equation
Related Questions
???????????????????
Answers
The domain is the set of all possible inputs that would satify the function while the range is the set of possible output values
Looking at the given graph,
Domain = ( - infinity, 4)
Range = (- 5, 2)
radical 9 cubed times radical -24 cubed=?
Answers
we can easily calculate that -6 times -6 times- 6 =- 216 it is why we can do this equality
because we have an exponent 3 and a cubic root we can cancel both so the answer of
[tex]\sqrt[3]{9}\text{ }\cdot\sqrt[3]{-24}=\text{ -6}[/tex]Use an alternative method to express the following set: {y:y is a person in your math class and also more than 100 years old.}
Answers
Let's use the letter M to label the math class. The fact that person y is in that class can be expressed by:
[tex]y\in M[/tex]We also have to show that is older than 100 so we have:
[tex]y>100[/tex]If we put all this information together we get:
[tex]\mleft\lbrace y\colon y\in M,y>100\mright\rbrace[/tex]And that's an alternative way to express the set.
12. One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.%
Answers
One year ago the median price for a home was $342,000. Now the current median price for a home is $215,000. What was the percent decrease in the median price of a home over the last year? Give your answer to at least one decimal place.
In this problem
$342,000 ------> represents 100%
so
Applying proportion
Find out how much percentage represents the difference (342,000-215,000=127,000)
100/342,000=x/127,000
solve for x
x=(100/342,000)*127,000
x=37.1%uueJUU Telp Find the area of the polygon. The area of the polygon is (Type a whole number.) 4 cm 7 cm 7 cm -14 cm 14 cm יד 4 cm
Answers
The area of the polygon = Sum of area of eight triangles + area of a square.
Area of the square
[tex]\begin{gathered} \\ \text{Length = 14cm} \\ \text{Area of the square = Length}^2 \\ \text{ = 14}^2 \\ =196cm^2 \end{gathered}[/tex]Area of one triangle
[tex]\begin{gathered} =\text{ }\frac{Base\text{ x Height}}{2} \\ \text{Base = 4cm} \\ \text{Height = 7cm} \\ =\text{ }\frac{4\text{ x 7}}{2} \\ =\text{ }\frac{28}{2} \\ =14cm^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the eight triangles = 8 x 14 } \\ \text{ = 112 cm}^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Area of the polygon = 196 + 112} \\ \text{ = 308 cm}^2 \end{gathered}[/tex]Simplify the expression 8h + (-7.3d) - 14 + 5d - 3.2h
Answers
The expression is:
8h + (-7.3d) - 14 + 5d - 3.2h
collecting like terms, we have:
8h - 3.2h +(-7.3d) + 5d - 14
= 4.8h - 7.3d + 5d - 14
= 4.8h - 2.3d - 14
That is the expression simplified
PLEASE HELP ME !!!!!!!!
Find and describe the error in the following problem
Answers
Answer:
When multiplying the bottom equation, they did not multiply 4y by -2, but instead by 2.
9. Alberta Emery can sew a dress in 3 days. Allison Taylor requires only 2 days. If theycombine efforts to fill one order to sew 30 dresses, how long will they take to fill the order?Answer
Answers
Given that Alberta Emery can sew 1 dress in 3 days. so the efficiency of Alverta Emery is given by,
[tex]=\frac{1}{3}\text{ work per day}[/tex]Similarly, given that Allison Taylor takes 2 days to sew 1 dress, so the efficiency of Allison Taylor is given by,
[tex]=\frac{1}{2}\text{ work per day}[/tex]When they combine their efforts, the amount of work done per day is given by,
[tex]\begin{gathered} =\frac{1}{3}+\frac{1}{2} \\ =\frac{2+3}{6} \\ =\frac{5}{6}\text{ work per day} \end{gathered}[/tex]So the number of days required to sew 30 dresses when both of them work together, is calculated as,
[tex]\begin{gathered} =\frac{30}{\frac{5}{6}} \\ =30\cdot\frac{6}{5} \\ =6\cdot6 \\ =36 \end{gathered}[/tex]Thus, they will take 36 days to sew 30 dresses.
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
Answers
Tracey paid $145 for an item that was originally priced at $550. What percent of the original price did Tracey pay?
we know that
$550 represent 100%
so
Applying proportion
100/550=x/145
solve for x
x=(100/550)*145
x=26.36%Mr. Cumme bought the amount of clay listed for his class.- 2.2 kilograms- 1.5 kilograms- 850 grams - 700 gramshow many grams of clay did Mr.Cumme buy?
Answers
Hello there. To solve this question, we have to remember how to convert kilograms to grams.
Given an amount in kilograms, to determine its value in grams, we simply multiply it by 1000.
In this case, we know that Mr. Cume bought the amount of clay listed for his class:
- 2.2 kilograms
- 1.5 kilograms
- 850 grams
- 700 grams
To determine how many grams of clay he bought, we start converting the values from kilograms to grams
2.2 kilograms * 1000 = 2200 grams and
1.5 kilograms * 1000 = 1500 grams
Now, we add everything
2200 + 1500 + 850 + 700 = 5250 grams
This is the final answer to this question.
A credit union client deposits $2,700 in an account earning 6% interest, compounded annually. What will the balance of the account be at the end of 31 years?
Enter the answer in dollars and cents, and round to the nearest cent, if needed. Do not include the dollar sign. For example, if the answer is $0.61, only the number 0.61 should be entered.
Balance ≈ $________ after 31 years.
Answers
Answer:
Balance ≈ $7,722 after 31 years
Step-by-step explanation:
multiply your deposit by your interestMultiply by how longAdd your base deposit to the interestEx.
2, 700(0.06) =$162.
162(31)= $5,022.
5,022 + 2,700 = $7,722.
Convert 15% to a fraction. Write in lowest terms.Convert 26% to a fraction. Write in lowest terms.Read the "Fractions, Decimals & Percents" lesson. Then answer each of the following questions to practice converting between fractions, decimals and percents.
Answers
Convert 15% to a fraction. Write in the lowest terms.
So,
[tex]15\%=\frac{15}{100}=\frac{5\times3}{5\times20}=\frac{3}{20}[/tex]So, the answer will be 15% = 3/20
=========================================================
Convert 26% to a fraction. Write in the lowest terms.
So,
[tex]\frac{26}{100}=\frac{2\times13}{2\times50}=\frac{13}{50}[/tex]So, the answer will be 26% = 13/50
5. * 20 points Rotate 180° about the origin. 3 Y 4 5 3
Answers
In order to rotate these point 180° about the origin, we just need to change the signal of all coordinates.
So we have that:
[tex]\begin{gathered} X(-1,3)\to X^{\prime}(1,-3) \\ W(-2,5)\to W^{\prime}(2,-5) \\ V(-5,5)\to V^{\prime}(5,-5) \\ T(-4,3)\to T^{\prime}(4,-3) \end{gathered}[/tex]Looking at the options, the correct one is c. (the third one).
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds
worth of pie, and has 7 people to feed, including herself. How much does each
person get if Charlotte is finished making pies?
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more
people to feed, how much pie will each person get from Charlotte's 5.04
pounds?
Answers
Step-by-step explanation:
Charlotte is making pies for her whole family. So far, she has made 5.04 pounds worth of pie, and has 7 people to feed, including herself. How much does each person get if Charlotte is finished making pies?
5.04 / 7 = 0.72 pounds per person
a) Charlotte's aunt and uncle decide to visit her unexpectedly. With 2 more people to feed, how much pie will each person get from Charlotte's 5.04 pounds?
7 + 2 = 9 people now
5.04 / 9 = 0.56 pounds per person
Question 6: a study of several cities show a positive correlation between the percent of people biking to work and percent of people spending their vacation time at home.What statement is most likely true? A. Correlation implies causation; therefore vacationing at home make people want to ride their bike.B. Correlation implies causation; therefore, bike riding makes people want to vacation at home.C. Correlstion does not imply causation; therefore,the correlation is due to a third. variable: cost of milk.D. Correlation does not imply correlation, therefore is due to a third variable: cost of gas.
Answers
If the study shows a positive correlation means that as people bike to work increase also the percentage of people spending their vacation time at home increases
since work happens before vacation one of the statemens that is most likely to be true will be B.
The table summarizes results from 977 pedestrian deaths that were caused by automobile accidents.Pedestrian DeathsDriverPedestrian Intoxicated?Intoxicated?YesNoYes4885No260584If one of the pedestrian deaths is randomly selected, find the probability that neither the pedestrian nor the driver wasintoxicated. Please enter a decimal to 4 places.Probability
Answers
We are asked to find the probability that neither the pedestrian nor the driver was intoxicated.
Probability is given by
P = number of desired outcomes/total number of outcomes
From the given table we know that
Total number of pedestrian deaths = 977
The desired outcomes are
Driver intoxicated = No and Pedestrian intoxicated = No (584)
So the probability is
P = 584/977
P = 0.5977
Therefore, the probability that neither the pedestrian nor the driver was intoxicated is 0.5977
Determine the domain and range of the function shown below. Assume the entire function is shown. Domain: Range:
Answers
The function is made of the following ordered pairs:
(-1,-3) (1, -5) (2, 3) (3, 6) (5, 6) (7, -1)
The first coordinate of the ordered pairs is the input value and the second coordinate is the output value of the function.
The domain is the set of all the input values as shown below:
Domain: {-1, 1, 2, 3, 5, 7}
Range: {-3, -5, 3, 6, -1}
Sorting the values of the range.
Range: {-5, -3, -1, 3, 6}
Vihaan got 38/48 on his geography test. Sahaj got 80% on his geography test. Jada got 0.8125 on her geography test. Quinn thinks that Vihaan got a higher mark on his test than Sahaj and Jada.Is Quinn right? Prove whether he is right or wrong by showing your work (5 marks)
Answers
Vihaan got 38 in her geography test
Since the geography test has a total score of 48
Since Sahaj got 80% of it, then multiply 80/100 by 48 to find his score
[tex]\frac{80}{100}\times48=38.4[/tex]Sahaj got 38.4 on the geography test
Since Jada got 0.8125 on her geography test, then multiply 0.8125 by 48 to find her score
[tex]0.8125\times48=39[/tex]Jada got 39 on the geography test
The greatest one is Jada, then Sahaj, then Vihaan
Quinn thinks that Vihaan got the higher score
But Jada the one who got the higher score
Then Quinn is not right
What are lim f(x) and lim f(x) if they exist?
Answers
SOLUTION:
Case: Limits
Method:
Right and left-sided limits.
The right sided limits is gotten from the right-hand side and gives an f(x) of 0 while the left sided limits gives an f(x) of 1.
Final answer: Option
[tex]\begin{gathered} \lim_{x\to0^-}f(x)=1 \\ \lim_{x\to0^+}f(x)=0 \end{gathered}[/tex]The half-life of a certain substance is 27 years. How long will it take for a sample of this substance to decay to 66% of its original amount? for the sample of the substance to decay to 66% of its original amount
Answers
This is a type of radioactive decay problem. Given an initial amount of N0, the amount at t years is given by
[tex]N(t)=N_0e^{-\lambda t}[/tex]The information "27 years is the half-life of the substance" means that if we replace t by 27, we will get exactly half of the initial amount we had. That is
[tex]N_0e^{-\lambda\cdot27}=\frac{N_0}{2}[/tex]We can cancell out N0 on both sides, so we get
[tex]e^{-\lambda\cdot27}=\frac{1}{2}[/tex]using the properties of exponentials, we have the equivalent equation
[tex]\frac{1}{2}=\frac{1}{e^{\lambda\cdot27}}[/tex]which is also equivalent to
[tex]e^{\lambda\cdot27}=2[/tex]If we apply natural logarithm on both sides, we get
[tex]\ln (e^{\lambda\cdot27})=\lambda\cdot27=\ln (2)[/tex]Finally, we can divide both sides by 27, to get
[tex]\lambda=\frac{\ln (2)}{27}[/tex]So, the function that describes the amount of the subtances at time t is given as
[tex]N(t)=N_0e^{\frac{-\ln (2)\cdot t}{27}}[/tex]Now, we want to calculate the value of t, for which the amount we have at year t is exactly 66% of what we have at t=0. That is
[tex]\frac{N_0e^{-\frac{\ln (2)\cdot t}{27}}}{N_0}=0.66[/tex]We can cancell out N0 and, by equivalence by using the properties of exponents, we get
[tex]\frac{1}{e^{\frac{\ln(2)}{27}\cdot t}}=0.66[/tex]which is also equivalent to
[tex]\frac{1}{0.66}=e^{\frac{\ln (2)t}{27}}[/tex]if we apply the natural logarithm on both sides, we get
[tex]\ln (\frac{1}{0.66})=\ln (e^{\frac{\ln(2)\cdot t}{27}})=\ln (2)\cdot\frac{t}{27}[/tex]Finally, we want to solve for t. To do so, we can multiply by 27 and then divide by ln(2). So we get
[tex]t=\frac{27}{\ln(2)}\cdot\ln (\frac{1}{0.66})[/tex]with help of a calculator, we have that t is approximately 16.185. That is, about after 16 years, we will have 66% of the initial amount.
-4x-2y = -6a. y = -2x + 3b. y = 2x-3C. y = 2x + 3d. y = -2x - 3
Answers
A store makes a profit of $25 on each watch it sells. What solution setwill represent how many watches the store must sell to make a profitof at least $375?US
Answers
Here, the variable is the number of watches.
The profit on each watch it sells is, $25.
The least profit to be made is, $375.
Let x be the number of watches, Then we have, the total profit as,
[tex]25x[/tex]This profit should be atleast 375, therefore, we have,
[tex]\begin{gathered} 25x\ge375 \\ \frac{25x}{25}\ge\frac{375}{25} \\ x\ge15 \end{gathered}[/tex]what do factors 12 and 24 have in common
Answers
Mcd (max common divisor) of 12, 24 = 12
(Because 24/12= 2 )
are
2,3,4,6,12
can you please solve this problem then tell me what was wrong with the answer
Answers
Given:
[tex]64^{\circ\text{ }}and\text{ }x^{\circ}[/tex]Sum of the angles of Same side interior angles is 180 degree.
[tex]\begin{gathered} 64+x=180 \\ x=180-64 \\ x=116^{\circ} \end{gathered}[/tex]Can you please help me out with a question
Answers
The volume of the figure = volume of first cone + volume of second cone + volume of a hemisphere
Formula
Volume of a cone = 1/3πr²h
The volume of hemisphere = 2/3πr³
Therefore
r = radius , h = height
where h1 = 20in , h2 = 18in and r = 15in
Volume of the first cone = 1/3πr²h1
= 1/3 x π x (15)² x 20
= 1500π in³
Volume of the second cone = 1/3πr²h2
= 1/3 x π x (15)² x 18
= 1350π in³
Volume of hemisphere = 2/3πr³
= 2/3 x π x (15)³
= 2250π in³
Therefore
The volume of the figure = 1500π in³ + 1350π in³ + 2250π in³
= 5100π in³
Hence the volume of the figure = 5100π in³
i need help with this problem Find rate of change.
Answers
Step 1:
First, pick two points where the line intercept with both the horizontal and the vertical axis.
( 0 , 300 ) and (
The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 69?
Answers
Given:
The box-and-whisker plot below represents some data set.
As shown:
The median = 65
The value of Q1 = 61
The value of Q3 = 69
The percentage of the data values that are greater than 69 will be the percentage of the data that are greater than Q3
So, the answer will be 25%
7. Simplify28120.51 +423) + (222 +7.51).
Answers
Answer: 581.5i + 140.64
Explanation:
574i + 118.44 + 22.2 +7.5i
grouping the terms yield
574i + 7.5i + 118.44 + 22.2
⇒
Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)
Answers
To obtain the expression for the composition of the function of the inverse function of x, the following steps are necessary:
Step 1: Write out the expression for the function of x and the inverse function of x, as below:
[tex]\begin{gathered} f(x)=\sqrt[5]{5-4x} \\ ^{}f^{-1}(x)=\frac{5-x^5}{4} \end{gathered}[/tex]Step 2: Write out the expression for the composition of the function of the inverse function of x, as below:
[tex](f^{-1}Of))(x)=^{}\frac{5-(\sqrt[5]{5-4x})^5}{4}[/tex]Thus, the above is how the expression for the composition of the function of the inverse function of x is to be written out
fill in the blanks.30x8=3x_____x840x7=_____x10x7
Answers
Answer:
30x8=3x_10_x8
40x7=_4_x10x7
First one: 10
Second one: 4