Step-by-step explanation:
The art piece originally costs £600.
And it appreciates at a rate of 3.97% each year.
And we want to find the value of the art after 10 years.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]f(t)=a(r)^t[/tex]Where t is the time in years.
Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.
103.97% = 1.0397. So, r = 1.0397:
[tex]f(t)=a(1.0397)^t[/tex]Our a is the initial value. Therefore:
[tex]f(t)=600(1.0397)^t[/tex]Then the value of the piece of art after 10 years is:
[tex]f(10)=600(1.0397)^{10}=885.58793\approx885.59[/tex]Hence, It will be worth about £885.59 after 10 years.
How many triangles exist that fit the following criteria?B = 30°, a = 4, b = 3
Given:
B = 30°, a = 4, b = 3
We will solve the triangle to find how many triangles exist that fit the given data
We will use the sine rule to find the angle A as follows:
[tex]\begin{gathered} \frac{a}{sin(A)}=\frac{b}{sin(B)} \\ \\ \frac{4}{sin(A)}=\frac{3}{sin(30)} \\ \\ sin(A)=\frac{4}{3}sin(30)=\frac{2}{3} \\ \end{gathered}[/tex]So, the measure of angle A will be as follows:
[tex]A=sin^{-1}(\frac{2}{3})=41.81\degree,or,138.19\degree[/tex]Now, we will find the measure of angle C using the fact that the sum of the angles = 180
[tex]\begin{gathered} C=180-(A+B) \\ A=41.81\degree\rightarrow C=180-(30+41.81)=108.19\operatorname{\degree} \\ A=138.19\operatorname{\degree}\rightarrow C=180-(30+138.19)=11.81\operatorname{\degree} \end{gathered}[/tex]So, there are two triangles that can fit the given data
So, the answer will be Two
need help on value of f(5) for function[tex]f(x) = \frac{1}{4} \times {2}^{x} [/tex]
Given
The function,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]To find:
The value of f(5).
Explanation:
It is given that,
[tex]f(x)=\frac{1}{4}\times2^x[/tex]Then,
For x=5,
[tex]\begin{gathered} f(5)=\frac{1}{4}\times2^5 \\ f(5)=\frac{1}{4}\times32 \\ f(5)=8 \end{gathered}[/tex]Hence, the value of f(5) is 8.
Weight: How many grams does a 5 lb 8 oz roast weigh?The roast weighs ? grams.
Solution
For this case we have the following weight:
5 lb and 8 oz
Using the following conversion ratios
1lb = 453.592 gr
1 oz = 28.3495 gr
We need to convert into grams so we can do this:
[tex]5lb\cdot\frac{453.592gr}{1lb}=2267.96gr[/tex][tex]8oz\cdot\frac{28.3495gr}{1oz}=226.796gr[/tex]Then adding the two values we have:
2267.96gr + 226.796gr = 2494.756 gr
Identify the prime factorization for 75A 25x3B25x 3C 52x3
Given the number below;
[tex]75[/tex]We are asked to find the prime factorization of the number.
Step 1: Definition
"Prime Factorization" is finding which prime numbers multiply together to make the original number.
Step 2: We will use prime numbers to go through the given value until we can not divide further.
Since 75 is an odd number we will start with 3.
We can find above all the prime factors used to divide 75. Therefore;
[tex]75=3\times5\times5=3\times25^{}[/tex]Answer:
[tex]3\times25[/tex]a building has 63 apartments in 70 bathrooms what is the ratio Apartments to bathrooms in the building simplest form
ANSWER:
The ratio is 0.9 or 9:10
STEP-BY-STEP EXPLANATION:
We can calculate the ratio, calculating the quotient between the number of apartments and the number of bathrooms, just like this:
[tex]\begin{gathered} \frac{63}{70}=\frac{7\cdot9}{7\cdot10}=\frac{9}{10}=0.9 \\ 9\colon10 \end{gathered}[/tex]Use the following equation to solve for xf(x) = 2x-8f(6) =
Find the approximated area of a circle whose circumference is 7.85.
The formula of the circumference of a circle is given by:
[tex]C=2\pi r[/tex]Where r is the radius.
By replacing the C-value, we can solve for r:
[tex]\begin{gathered} 7.85=2\pi r \\ r=\frac{7.85}{2\pi} \\ r=1.25 \end{gathered}[/tex]Now, the formula of the area is given by:
[tex]A=\pi r^2[/tex]Replace the r-value and solve for A:
[tex]\begin{gathered} A=\pi(1.25)^2 \\ A=\pi\cdot1.56 \\ A=4.91 \end{gathered}[/tex]The area of the circle is 4.91
The triangle is a 45°-45°-90° triangle.x√2 = 66²36X =(√2)²x = 18Did not multiply the numerator by the radicalShould have squared the denominator only.No ErrorShould have squared the numerator onlyJUN1O6V2=82
Answer:
Did not multiply the numerator by the radical
Explanation:
The hypotenuse of a 45-45-90 triangle is equal to the leg times √2.
In this case, the leg is x and the hypotenuse is 6, so we have the following equation
hypotenuse = leg √2
6 = x √2
To solve for x, we get
[tex]\begin{gathered} x\sqrt{2}=6 \\ \\ x=\frac{6}{\sqrt{2}} \end{gathered}[/tex]Then, we need to multiply the numerator and denominator by √2, so
[tex]x=\frac{6}{\sqrt{2}}\cdot\frac{\sqrt{2}}{\sqrt{2}}=\frac{6\sqrt{2}}{(\sqrt{2})^2}[/tex]Therefore, the solution is equal to
[tex]x=\frac{6\sqrt{2}}{2}=3\sqrt{2}[/tex]Therefore, the error in the process was that they did not multiply the numerator by the radical
convert 2.5 years into hours
We are asked to convert 2.5 years into hours.
Step 1:
There are 365 days in a year so 2.5 years will have
[tex]2.5\cdot365=912.5\text{ days}[/tex]Step 2:
There are 24 hours in a day so 912.5 days will have
[tex]912.5\cdot24=21900\text{ hours}[/tex]Therefore, 2.5 years will have 21900 hours.
Can you explain to me why I got this wrong? And what are the correct answers
To get the true statements, we will be testing the options one by one in order.
First option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \cos (65)=0.4226 \\ \therefore\cos (25)\ne\cos (65) \end{gathered}[/tex]Second option
[tex]\begin{gathered} \cos (25)=0.9063 \\ \sin (65)=0.9063 \\ \therefore\cos (25)=\sin (65) \end{gathered}[/tex]Third option
[tex]\begin{gathered} \sin (25)=0.4226 \\ \cos (65)=0.4226 \\ \therefore\sin (25)=\cos (65) \end{gathered}[/tex]Fourth option
[tex]\begin{gathered} \tan (45)=1 \\ \tan (45)=1 \\ \therefore\tan (45)=\tan (45) \end{gathered}[/tex]Fifth option
[tex]\begin{gathered} \tan (65)=2.1445 \\ \tan (25)=0.4663 \\ \therefore\tan (65)=\tan (25) \end{gathered}[/tex]Hence, the correct options are Options 2, 3, 4.
proportional relationship. Vivian says that cannot be true because the constants ofMindy says that the equations p =1.59 and {o= q both represent the sameproportionality are different. Which student do you agree with? Explain.
We have two equations:
[tex]\begin{gathered} p=1.5q \\ \frac{2}{3}p=q \end{gathered}[/tex]We would like to know if those represent the same proportional relationship or don't.
For doing so, we remember that a constant of proportionality
Evaluate the expression −2ln(e^2 −12)+8
Solve
[tex]\begin{gathered} -2\ln (e^2-12)+18 \\ -2\ln (7.389-12)+18 \\ -2\ln (-4.611)+18 \end{gathered}[/tex]Answer: Undefined solution
HELP MEEEEisolate the variable to solve 4x + 4 > -20. what number line shows the solution set?
Given,
The expression is,
[tex]4x+4>-20[/tex]Required
The solution of the inequality.
Taking the given expression as,
[tex]\begin{gathered} 4x+4>-20 \\ 4x+4-4>-20-4 \\ 4x>-24 \\ \frac{4x}{4}>-\frac{24}{4} \\ x>-6 \end{gathered}[/tex]So, the solution of the inequality is x > -6.
Hence, option B is correct.
a sofa is on sale for $289, which is 32% less than the regular price what is the regular price
6149488990ay, this is the solution:
Let's use the Direct Rule of Three for answering this problem, this way:
Price Percentage
289 68
x 100
___________________
28,900 = 68x
68x/68 = 28,900/68
x = 425
The regular price of the sofa is $ 425, and you will save $ 136 if you buy it on sale.
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A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial10,500 + 3,9d, The revenue generated from the sale of d dog leashes will be given by the polynomial.d14,5 - 0,000030), Find a polynomial expression for the profit earned from producing and selling d dogleashes, Evaluate the expression for da 30,000.© $514,500© $295,650© $280,500© $535,500
Note that Profit = Revenue - Cost
From the problem, we have :
Revenue = d(14.5 - 0.00003d)
and
Cost = 10,500 + 3.9d
The profit function will be :
[tex]\begin{gathered} \text{Profit}=\text{Revenue}-\text{Cost} \\ \text{Profit}=d(14.5-0.00003d)-(10500+3.9d) \\ \text{Profit}=14.5d-0.00003d^2-10500-3.9d \\ \text{Profit}=-10500+10.6d-0.00003d^2 \end{gathered}[/tex]Substitute d = 30,000
[tex]\begin{gathered} \text{Profit}=-10500+10.6d-0.00003d^2 \\ \Rightarrow-10500+10.6(30000)-0.00003(30000)^2 \\ \Rightarrow280500 \end{gathered}[/tex]Answer :
C. $280,500
Find the 5 number summary for the data shownx2.72.97.27.58.511.215.418.3
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The minimum is the smallest number in the data : 2.7
The maximum is the largest number in the data : 18.3
Next, we find the median, which is the middle number in the data when arranged from smallest to largest. There are 8 numbers, so we will average the middle 2 numbers
2.7 ,2.9, 7.2, 7.5, 8.5, 11.2,15.4, 18.3
The middle is between the 4th and 5th numbers
( 7.5 + 8.5) / 2 = 16/2 = 8
The median(Q2) is 8
To find Q1 ( the 1st quartile), we take the numbers below the mean
2.7 ,2.9, 7.2, 7.5,
and find the median of these numbers
There are 4 numbers so the middle is between the 2nd and 3rd numbers
2.7 , 2.9, 7.2, 7.5,
(2.9+7.2) /2 =5.05
Q1 = 5.05
We will do the same process for Q3, which is the third quartile. We will use the numbers above the median
8.5, 11.2,15.4, 18.3
( 11.2 + 15.4) /2 =13.3
Q3 = 13.3
I need help on in the answer to this question
Using the 2 tangents line formula:
[tex]m\angle Q=\frac{1}{2}((360-mPR)-mPR)[/tex][tex]\begin{gathered} 81x-1=\frac{1}{2}(360-2(100x)) \\ 81x-1=\frac{1}{2}(360-200x) \\ 81x-1=180-100x \\ \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} 81x+100x=1+180 \\ 181x=181 \\ x=\frac{181}{181} \\ x=1 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} mPR=100(1)_{} \\ mPR=100 \end{gathered}[/tex]Answer:
A. 100
Please find entire surface are of a stereo receiver (question 17)
We could approach the stereo receiver to a rectangular prism, that has the formula of surface area (A):
[tex]A=2ab+2bc+2ac[/tex]As the dimensions are given: a = 18", b = 16", c = 9"; then we just have to replace these values in the formula:
[tex]A=2(18)(16)+2(16)(9)+2(18)(9)[/tex]Simplifying:
[tex]A=576+288+324[/tex][tex]A=1188[/tex]Answer: 1188 in²
Question 7 of 9Constance has an apple that weighs 85,000 milligrams and a peach that weighs 0.15 kilograms. Which fruit has the greater mass? Choose the words and numbers to complete the statements.Convert the masses of both fruits to the same unit.85,000 milligrams is the same asChoose...grams.0.15 kilograms is the same asChoose...grams.TheChoose...has the greater mass.
The Solution:
Given:
Apple weight = 85,000 milligrams
Peach weight = 0.15 kilograms.
Required:
To determine which fruit has a greater mass.
Converting 0.15 kilogram to milligrams, we get:
[tex]\begin{gathered} 0.15\times1000000=150\text{ milligrams} \\ 85000mg>150mg \end{gathered}[/tex]Clearly, Apple has a greater mass than a peach.
Therefore, the correct answer is Apple fruit.
if x + 9 equals 13 what is the value of x
X + 9 = 13
To know the value of x you have to subtract 9 from both sides of the equation
x+9-9= 13-9
x= 4
If PN = 2x + 5 ON =x + 3 and OS = 3x - 2. Solve for ps
Remember that
In a rectangle
opposite sides are parallel and congruent and the measure of the interior angles are 90 degrees
The diagonals are congruent
so
PS=ON
PO=SN
PN=OS
equate the equations of diagonals
PN=2x+5
OS=3x-2
2x+5=3x-2
solve for x
3x-2x=5+2
x=7
Find out PS
Remember that
PS=ON=x+3
substitute the value of x
PS=7+3
Ps=10 unitsfind the slope of the line through the giving points-1 -5 and 1 -1
the given points are
(x1 , y1) = (-1 , -5) and ()x2, y2) = (1 , -1)
the slope of the line is given as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{-1-(-5)}{1-(-1)} \\ m=\frac{-1+5}{1+1}=\frac{4}{2}=2 \end{gathered}[/tex]so the slope is m = 2
Persent to a decinal 7%.
To express a percentage as decimal numbers you have to make the following convertion:
Consider that 100% is equal to 1, use cross multiplication to convert 7%:
100%____1
7%____x
[tex]x=\frac{7\cdot1}{100}=\frac{7}{100}=0.07[/tex]So, remember, to transform any percentage in decimal numbers, just divide it by 100.
Find the compound interest and future value. Round your answers to the nearest cent. Do not round intermediate steps.Principal Rate Compounded Time$580 4.65% Quarterly6 yearsThe future value is $and the compound interest is $ХSCheck
Compound Interest
The Future Value of investment on compound interest can be calculated with the formula:
[tex]FV=PV(1+i)^n[/tex]Where PV is the present value or Principal, i is the adjusted interest rate and n is the number of compounding periods.
The principal is PV=$580.
The APR is 4.65% = 0.0465
The compounding period is quarterly.
Since there are 4 quarters in a year, the adjusted interest rate is:
i = 0.0465 / 4 = 0.011625.
The number of periods is n=6 years * 4 = 24 quarters
Now compute the future value:
[tex]FV=580(1+0.011625)^{24}[/tex]Calculating:
[tex]\begin{gathered} FV=\$580\cdot1.31968 \\ FV=\$765.42 \end{gathered}[/tex]The future value is $765.42 and the present value is $580, so the interest is:
I = $765.42 - $580
I = $185.42
Solve for R in I=PRTa.) What is the variable?b.) What is happing to the variable? (list the operations from the first thing to the last thing)c.) What is the inverse (opposite) of the last thing that happened to the variable. (Make a list of the steps to solve)
a) R is the variable
b) a product, the variable is being multiplied
[tex]R=\frac{I}{PT}[/tex]Explanation
Step 1
[tex]I=\text{PRT}[/tex]the value for I depends on the value for R, it means, that I depends on the value for R
so, R is the variable
Step 2
when you have
[tex]\begin{gathered} I=\text{PRT} \\ is\text{ equal to} \\ I=P\cdot R\cdot T \end{gathered}[/tex]it is a multiplication between P, R and T,the variable is being multiplied
Step 2
solve for R
[tex]\begin{gathered} I=\text{PRT} \\ \text{you n}eed\text{ to do the inverse operation } \\ \text{Multiplication}\Rightarrow opposite\Rightarrow Division \end{gathered}[/tex]then, opposite operation is division, divide both sides by PT
[tex]\begin{gathered} \frac{I}{PT}=\frac{PRT}{PT} \\ \frac{I}{PT}=R \\ R=\frac{I}{PT} \end{gathered}[/tex]I hope this helps you
How to find the domain of y=5√(2x-7) +10?
To find the domain for this function, we can see that the restriction we need to take into account is that the values in the radical must be values equal or greater than zero, so this function can have values in the Real set of numbers. Then, we have:
[tex]y=5\sqrt[]{2x-7}+10[/tex]We need to evaluate:
[tex]2x-7\ge0[/tex]Then, add 7 to both sides of the inequality, and then dividing the inequality by 2 (at both sides again) we have:
[tex]2x-7+7\ge0+7\Rightarrow2x+0\ge7\Rightarrow2x\ge7\Rightarrow\frac{2}{2}x\ge\frac{7}{2}_{}\Rightarrow x\ge\frac{7}{2}[/tex]We have that the values for the domain of this function are those for which are equal or greater than 7/2.
We can write the domain of this function in interval notation as follows:
[tex]D=\lbrack\frac{7}{2},\infty)[/tex]The important fact here is that for this function to have a domain and a range in the Real set, we need to have this restriction for this function.
The values of 5 and 10 are 'displacements' of a parent function and do not affect the values for this function to be in the Real Set of numbers.
For example, the value of 5 multiply the function, and the values for the range are greater (for x values) if the function was not multiplied by 5 ( and this does not affect, however, the values for the domain).
The value of 10 makes the function to be shifted 10 units above in the y-axis (and it does not affect the most important restriction found above). However, it does affect the values for the range in the function.
You deposit $75 in an account that earns simple interest at an annual rate of 5% . How much money is in the account after 3 years?
The account balance in the account $86.25 after 3 years by using simple interest.
What is the simple interest?
Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
The formula of the simple interest is I = PRt.
P = Principal
R = Rate of interest per year
t = time
In the given question Principal = $75, R = 5% = 0.05, t = 3 years.
I = 75 × 0.05 × 3 = 11.25
The account balance after 3 years will be sum of principal and interest.
The account balance after 3 years is = $(75 + 11.25) = $ 86.25.
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The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 80?
Answer:
25%
Explanation:
In the given box-and-whisker plot, the third quartile, Q3 = 80.
The percentage of data values that are greater than the third quartile is 25%.
Therefore, the percentage of the data values greater than 80 is 25%.
Ignore the second part where it has a question mark that was my attempt the question is on top.
The inverse function is [tex]f^-1(X)=5x+6[/tex],
Given,
[tex]y=\frac{x-6}{5}[/tex]
To find inverse function, first interchange the variables 'x' and 'y'
[tex]x=\frac{y-6}{5}[/tex]
solve for y,
[tex]5x=y-6\\\\5x+6=y\\\\y=5x+6[/tex]
Replace y with [tex]f^-1(x)[/tex]
[tex]f^-1(X)=5x+6[/tex]
Thus, the inverse function is [tex]f^-1(X)=5x+6[/tex]
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Three math classes at Sunview High School collected the most box tops for a school fundraiser, and so they won a $600 prize to share among them. Mr. Aceves’ class collected 3,760 box tops, Mrs. Baca’s class collected 2,301, and Mr. Canyon’s class collected 1,855. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of the box tops that they collected?
The total amount fundraised is given as follows:
[tex]3760+2301+1855=7916\text{ box tops}[/tex]The proportion of Mr. Aceves' class collected is given as follows:
[tex]\frac{3760}{7916}\text{ box tops}[/tex]The proportion of Mr. Baca's class collected is given as follows:
[tex]\frac{2301}{7916}\text{ box tops}[/tex]The proportion of Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\text{ box tops}[/tex]Now compute the amount for Mr. Aceves' class is given as follows:
[tex]\frac{3760}{7916}\times600\approx284.99[/tex]Again, compute the amount for Mr. Baca's class is given as follows:
[tex]\frac{2301}{7916}\times600\approx174.41[/tex]Again, compute the amount for Mr. Canyon's class is given as follows:
[tex]\frac{1855}{7916}\times600\approx140.60[/tex]As a result, $284.99 will go to Mr. Aceve's class, $174.41 will go to Mr. Baca's class, and $140.60 will go to Mr. Canyon's class.