write 125 as a power in base 5
[tex]q^3+5^3[/tex]then, apply the rule for the addition of cubes
[tex]\begin{gathered} a^3+b^3=(a+b)\cdot(a^2-a\cdot b+b^2) \\ \text{then, } \\ q^3+5^3=(q+5)\cdot(q^2-5x+5^2) \\ q^3+5^3=(q+5)\cdot(q^2-5x+25) \end{gathered}[/tex]A dart hits the square dartboard shown below at a random point. Find the probability that the dart lands in the shaded circular region. Each side of the dartboard is 12 in, and the radius of the shaded region is 5 in. Use the value 3.14 for n. Round your answer to the nearest hundredth.
For this problem, we are given the dimensions of a dashboard. We need to determine the probability a dart will hit the shaded area.
To solve this problem, we need to calculate the area of the whole board (square) and the area of the shaded area (circle). Then we need to divide the area of the shaded circle by the entire board.
The area of a circle can be found as shown below:
[tex]A_{shaded}=3.14\cdot(5)^2=78.5\text{ square inches}[/tex]The area of the square can be found as shown below:
[tex]A_{board}=12^2=144\text{ square inches}[/tex]Now we need to find the probability of the shaded area, which can be done by dividing the area of the circle by the area of the board.
[tex]P(shaded)=\frac{78.5}{144}=0.55[/tex]The probability is 0.55.
Please make this simple and easy, and help me quickly, thank you!
Given:
Total distance = 60 km
Upstream time = 5 hours
Downstream time = 3 hours
Find-:
The rate of boat in still water.
Explanation-:
Let
The speed of the boat in still water is"x"
The speed of the water is "y"
For upstream ( Against the current )
Speed of boat is:
[tex]=x-y[/tex][tex]\begin{gathered} \text{ Distance }=60\text{ km} \\ \\ \text{ Time }=5\text{ hours} \end{gathered}[/tex]Use the formula:
[tex]\text{ Speed}=\frac{\text{ Distance}}{\text{ Time}}[/tex]For upstream speed is:
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x-y=\frac{60}{5} \\ \\ x-y=12..............(1) \end{gathered}[/tex]For downstream,
[tex]\text{ Speed}=x+y[/tex][tex]\begin{gathered} \text{ Distance}=60\text{ km} \\ \\ \text{ Time}=3\text{ hours} \end{gathered}[/tex]Use the formula of distance
[tex]\begin{gathered} \text{ Speed}=\frac{\text{ Distance}}{\text{ Time}} \\ \\ x+y=\frac{60}{3} \\ \\ x+y=20 \\ \\ y=20-x................(2) \end{gathered}[/tex]From eq(2) put the value of "y" in eq(1) then the value is:
[tex]\begin{gathered} x-y=12...........(1) \\ \\ y=20-x...............(2) \end{gathered}[/tex][tex]\begin{gathered} x-y=12 \\ \\ x-(20-x)=12 \\ \\ x-20+x=12 \\ \\ 2x-20=12 \\ \\ 2x=12+20 \\ \\ 2x=32 \\ \\ x=\frac{32}{2} \\ \\ x=16 \end{gathered}[/tex]The rate of the boat in still water is 16 km/hour
Find the lowest common multiple of each group. show the factors you used.1) 5,22 and 121
Solution:
Given:
[tex]5,22,121[/tex]By prime factorization method:
[tex]\begin{gathered} 5=5 \\ 22=2\times11 \\ 121=11\times11 \\ \\ Hence,\text{ the LCM is:} \\ 2\times5\times11\times11 \\ LCM=1210 \end{gathered}[/tex]Therefore, the LCM is 1,210
Can you tell me What is 4x16=?
Hello
This is a multiplication question and we can easily use our calculator for this question.
[tex]4\times16=64[/tex]From the above, the answer to 4 * 16 is 64
Business that offers repayment plan for purchases are required by law to disclose the interest rate but that doesn’t mean they go out of their way to let you know what it is you have to read all the paperwork find the interest rate for the following purchaseTo finance a new laptop Emily is offered a five year payment plan with low monthly payments of $31 and50 Cent the cost of the laptop is $884.43 including tax round to the decimal place if necessary
Answer:
The number of years for the repayment is
[tex]t=5years[/tex]The amount to be repaid back monthly is
[tex]\text{ \$31.50}[/tex]The cost of the laptop given is
[tex]\text{ P=\$884.43}[/tex]Step 1:
Calculate the total amount of money to be repaid after 5 years
[tex]\begin{gathered} Amount\text{ repayable=monthly payments}\times number\text{ of years}\times12 \\ Amount\text{ repayable=31.50}\times5\times12 \\ Amount\text{ repayable=1890} \end{gathered}[/tex]Step 2:
Calculate the interest on the laptop
[tex]\begin{gathered} interest=Amount\text{ repayable-cost of the laptop} \\ interest=1890-884.43 \\ interest=1005.57 \end{gathered}[/tex]Step 3:
To calculate the interest rate, we will use the formula below
[tex]\begin{gathered} I=\frac{PRT}{100} \\ \frac{100I}{PT}=\frac{PRT}{PT} \\ R=\frac{100I}{PT} \\ T=5,P=884.43,I=1005.57 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} R=\frac{100I}{PT} \\ R=\frac{100\times1005.57}{884.43\times5} \\ R=\frac{100557}{4422.15} \\ R=22.7\% \end{gathered}[/tex]Hence,
The interest rate will be
[tex]\Rightarrow22.7\%[/tex]Which statement is true of the function flx) = -3/x? Select three options. The function is always increasing. The function has a domain of all real numbers. The function has a range of tyl-
Notice that the given function:
1.- has a domain of all real numbers because you can always compute the cube root for all real numbers,
2.- the function has a range of all real numbers, and
3.- the function is a reflection of
[tex]y=\sqrt[3]{x}[/tex]over the x-axis.
Answer: Options 2, 3, and 4.
For the function f(x) = x2 - 4. construct and simplify the difference quotient f(x+h)-f(x) h
From a group of 15 women and 16 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be selected?A. 300,540,195B. 778,377,600C. 19,305OD. 82,818,450
Since we are talking about a group of people the order is not going to matter when we select the different people, then, start to make the combination for the group of women and the group of men separately.
[tex]\begin{gathered} women=15C8 \\ women=\frac{15!}{(15-8)!8!} \\ women=\frac{15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ women=6435 \end{gathered}[/tex][tex]\begin{gathered} men=16C8 \\ men=\frac{16!}{(16-8)!8!} \\ men=\frac{16\cdot15\cdot14\cdot13\cdot12\cdot11\cdot10\cdot9}{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1} \\ men=12870 \end{gathered}[/tex]then, multiply the results
[tex]\begin{gathered} 16C8\cdot15C8 \\ 12870\cdot6435 \\ 82,818,450 \end{gathered}[/tex]You are designing a rectangda garden for the city park. The gardien is to have an area of 250 S feet, but you want to theamount of fending that you need to surround the garden. One length of the garden will not have a fence How many fees of lenong to you needto Surround the garden?
Consider the following picture
This is a sketch of the rectangular garden. We are given that the area of this rectangle is 200. Recall that the area of a rectangle is base * height. IN this case, we have the equation
[tex]\times\cdot\text{ y = 200}[/tex]Now, note that we want to minimize the amount of fence we use. This means, that we want to minimize the perimIn this case we are told that we are not putting fence on one side of the rectangle. Since we want the less amount of fence to be used, and since y is the lenght of the longest side, we will assume that we are not fencing one of the y sides. So the perimeter of this rectangle is sum of the three remaining sides. Hence the function we want to minimize is
[tex]y\text{ + 2x }[/tex]From the first equation, we can replace the value of y with 200/x. So the function we want to minimize is
[tex]\frac{200}{x}+2x[/tex]Since we want to find the minimum of this function, we proceed by calculating its' derivative, make it equal to zero and the find the value of x that makes the equation true.
So, recall that the derivative of a term x^n is n x ^(n-1). In the case of 1/x, the value of n is n=-1. Also, recall that the derivative of a sum is the sum of the derivatives. So, applying this rule we get that the derivative of the function is
[tex]200(-1)x^{^{\text{ -2}}}+2x^0=2\text{ - }\frac{200}{x^2}[/tex]No, we will make it equal to 0 and find the value of x that makes the equation true. So we get the equation
[tex]2\text{ - }\frac{200}{x^2}\text{ = 0 = }\frac{2x^2\text{ -200}}{x^2}[/tex]Since we have an equation of the form a/b =0 It must happen that a is 0. Then, we have the equation
[tex]2x^2\text{ -200 =0}[/tex]If we add 200 on both side, we get
[tex]2x^2\text{ = 200}[/tex]If we divide on both sides by 2, we get
[tex]\times^2\text{ = 100}[/tex]By taking the square root on both sides we get
[tex]\text{ x = 10 or x = -10}[/tex]Since x is a lenght, it should be positive. So we must have x = 10.
In this case, by replacing in the expression of y, we get that y = 200/10 = 20.
So we will need 2*10 + 20 = 40 feets long to surround the garden.
For the dinner special at a restaurant, the customer must choose an appetizer, a salad, an entree, a side dish, and a dessert.Here are the items to choose from.ChoicePossible items Appetizer Buffalo wings, Cheese sticks, Potato skins, Nachos Salad Caesar, Southwest, Garden Entree Lamb, Roast turkey, Salmon, Pot roast, Grilled chicken Side dish Mixed vegetables, Baked potato, Rice, French fries, Corn Dessert Chocolate cake, Brownies, Cheesecake How many dinner specials are possible?
Solution
Step 1:
There are 4 Appetizers, 3 Salad, 5 Entrees, 5 Side dishes, and 3 Desserts.
Step 2:
Possible dinner special
[tex]\begin{gathered} =\text{ 4 }\times\text{ 3 }\times\text{ 5 }\times\text{ 5 }\times\text{ 3} \\ \\ =\text{ 900 } \end{gathered}[/tex]Final answer
900 specials possible dinner.
900
Consider the following types of data that were obtained from a random sample of 49 credit card accounts. Identify all the averages (mean, median, or mode) that can be used to summarize the data.(Select all that apply.)(a) Outstanding balance on each account.A. modeB. medianC. mean(b) Name of credit card (e.g., MasterCard, Visa, American Express, etc.).A. modeB. medianC. mean(c) Dollar amount due on next payment.A. modeB. medianC. mean
Answer:
(a)A,B.C
(b)A
(c)A, B, C
Explanation:
Part A
The outstanding balance on each account can be summarized using the mean, median, and mode since it is quantitative data.
Options A, B, and C are correct here.
Part B
The name of credit cards can only be summarized by frequency. That is, how many belong to each company (i.e. MasterCard, Visa, American Express, etc.)
The only correct option here is Mode. (Option A).
Part C
The dollar amount due on the next payment is a numerical data, we can find the mean, median, and mode for any numerical data.
Options A, B, and C are correct here.
10 is what percent of 22 ?Round your answer to the nearest hundredth, if necessary. Type your answer in the box below.
Answer:
Explanation:
Answer:
We follow the s
Explanation:
To find out what percent of 10 is 22.
We follow the s
A local diner purchased a jukebox for $9400 the business makes a down payment of $1000 and agrees to 36 monthly payments of $275 each estimate the annual percentage rate to the nearest 10th of a percent
Given:-
Jukebox for $9400.
Payment done is $1000.
Agrees to make down payment for 36 months each month of $275.
To find
Special Right Triangles(Radical Answer) Problem I would appreciate the help:0
In order to determine the value of x, use the
list of financial formulas.Lisa invested $5300 in an account that pays an annual interest rate of 2.5%, compounded monthly. Answer each part. If necessary, refer to the(a) Find the amount in the account after one year, assuming no withdrawals are made.Do not round any intermediate computations, and round your answer to the nearest cent.X(b) Find the effective annual interest rate, expressed as a percentage.of a percent.Do not round any intermediate computations, and round your answer to the nearest hundredth%
Given:
Investment = $5300
annual interest rate = 2.5% compounded monthly
The amount A after time t can be computed using the formula:
[tex]\begin{gathered} A\text{ = P\lparen1 + }\frac{r}{n})^{nt}^ \\ \\ Where\text{ P is the principal} \\ r\text{ is the rate of interest} \\ n\text{ is the number of compounding periods } \\ and\text{ t is the time in years} \end{gathered}[/tex](a) The amount A after 1 year
Substituting the given values:
[tex]\begin{gathered} A\text{ = 5300\lparen1 + }\frac{0.025}{12})^{12\times1} \\ \text{= \$5434.0288} \end{gathered}[/tex]Answer:
Amount = $5434.03
AN Question 7 (5 points) A recent Nielson rating poll contact a random sample of Americans to determine the amount of time their family watched television on a Tuesday night. Exactly 250 people were involved in the poll with 37 people watching no television. 51 people watching 30 minutes of television. 17 people watching 45 minutes of television. 20 people watching 60 minutes of television. 19 people watching 75 minutes of television, 11 people watching 90 minutes of television. 50 people watching 120 minutes of television, and 45 people watching 240 minutes of television. Determine the mean from the given Nielson rating poli. Do not round your answer.
Mean = sum of the terms/number of terms
Replacing with data:
Mean = (37*0 + 51*30 + 17*45 + 20*60 + 19*75 + 11*90 + 50*120 + 45*240)/250
= 90.84 minutes
1 1/3 divided by 40 using the algorithm
the given expression is,
1 1/3 = 4/3
[tex]\frac{\frac{4}{3}}{40}=\frac{4}{120}[/tex]what might a postitive number mean in thid content ,what about a negatuve number
1.
A positive number might mean that the number of bottles in the machine is bigger than the number of bottles sold.
A negative number might mean that the number of bottles sold is bigger than the number of bottles in the machine.
2.
A cero might mean that the number of bottles sold is equal to the number of bottles in the machine.
Estimate the difference of the decimals below by rounding to the nearestwhole number. Enter your answer in the space provided.91.2764.310
The decimal number 91.276 is round off to the number 91 and number 4.310 is round off to the number 4.
Evaluate the difference between the number 91 and 4.
[tex]91-4=87[/tex]So answer is 87.
Whiteout graphing the function, describe what the graph would look like if b were 8.5
We have the function y=x+b.
This is a line with b as y-intercept.
When b gets larger, that graph moves parallel and up in the vertical axis.
That is because b is like a "floor" level when x=0, and, as the slope of the line stays the same, the lines stays parallel.
As b becomes negative, the graph goes in the opposite direction (down in the vertical axis).
The lines stays parallel, because the slope does not change.
4^4x - 1 = 8^2xSolve for x.
x = 1
Explanation:
[tex]4^{4x-1}=8^{2x}[/tex]Make the base have the same number:
8 = 2³
4 = 2²
The base becomes 2
[tex]2^{2(4x-1)}=2^{3(}^{2x)}[/tex]Then we simplify:
[tex]\begin{gathered} \text{The base cancels out:} \\ 2(4x-1)\text{ = 3(2x)} \\ 8x\text{ - 2 = 6x} \\ \text{collect like terms: } \\ 8x\text{ - 6x = 2} \\ 2x\text{ = 2} \\ x\text{ = 2/2} \\ x\text{ = 1} \end{gathered}[/tex]Therefore, x = 1
check:
[tex]\begin{gathered} 4^{4(1)-1}=8^{2(1)} \\ 4^{4-1}=8^2 \\ 4^3\text{ }=8^2 \\ 4\times4\times4=\text{ 64} \\ 8\times8\text{ = 64} \\ 64\text{ = 64 (x=1 is correct)} \end{gathered}[/tex]principal hernadez bought 640 t shirts for the student in his school. the t shirts came in packs of 20. how many packs did he buy
We know that
• Hernandez bought 640 t-shirts.
,• They came in packs of 20.
To know how many packs he bought, we just need to divide
[tex]\frac{640}{20}=32[/tex]Therefore, principal Hernandez bought 32 packs of t-shirts.Find the length of AB.A140/6 inAB = [ ? ]inBRound your answer to the nearest hundredth.
The length of AB is given by:
AB = θ*r
Basically AB = L
Where:
L = Arc length of the minor sector.
Now:
r = 6 in
θ = 140° = 7/9 π
Therefore:
AB = (7/9 π) * 6 = 14/3 π ≈ 14.66 in
May I please get help with this. I can’t seem to figure out the right answers for them
Given
Solution
Using similar triangles
[tex]\begin{gathered} \frac{35}{57}=\frac{22.8}{x} \\ \\ \text{cross multiply} \\ 35x=1299.6 \\ \text{Divide both sides by 35} \\ \frac{35x}{35}=\frac{1299.6}{35} \\ \\ x=37.1314\ldots \end{gathered}[/tex]The final answer
[tex]37m[/tex]Which shows the correct substitution for: "Evaluate f(6)"f(x) = x + 5
f(x) = x + 5
Evaluate the function for x = 6
f(6) = 6 + 5
f(6) = 11
How can you find a common denominator for one third and one fifth
Given to find the common denominator for one-third and one-fifth.
Here, the denominators of both fractions are 3 and 5. Since 3 and 5 do not have any factors common. So, the LCD will be the product of 3 and 5, which is equal to 15.
Thus, LCD of 1/3 and 1/5 is 15.
Graph the set on the number line. Then, write the set using interval notation.
(-5, 1)
Explanation:The given set:
{x | -5 < x < 1}
To draw the number line, the range of the line will be from -5 to 1.
Since there is no equal sign attached to the inequlaity, the dot or circle will not be shaded.
Plotting on the number line:
Writing the set in interval notation:
[tex]\begin{gathered} The\text{ parenthesis that will be used is ( ), since the inequality doesn't have equal sign attached} \\ \text{Hence, the interval is }(-5,\text{ 1)} \end{gathered}[/tex]How do I solve these?1) Evaluate the expression, 2b+(c-3a) when a= -1/2, b= 3/4, c= 1/4.2) A store manager uses a markup rate of 24% on all appliances. Find the cost of a coffee maker that sells for $77.50. Use formula S=C+r•C, where S is the selling price, C is the cost, and r is the markup rate.
To evaluate the expression
[tex]2b+(c-3a)[/tex]Plug in the corresponding values that are given and operate, as following:
[tex]\begin{gathered} 2b+(c-3a) \\ \\ \rightarrow2(\frac{3}{4})+(\frac{1}{4}-3(-\frac{1}{2})) \\ \\ \rightarrow\frac{3}{2}+(\frac{1}{4}+\frac{3}{2}) \\ \\ \rightarrow\frac{3}{2}+\frac{1}{4}+\frac{3}{2} \end{gathered}[/tex]At this point, we have to have all our fractions with the same denominator to add them up. To do so, let's find the LCM (Least Common Multiple) between our different denominators (In this case, 2 and 4)
The LCM is 4. Now, we need to find a way for all our fractions to have 4 as a denominator. Notice that we can do so by multiplying both 3/2 by 2 (both in the numerator and denominator), as following:
[tex]\begin{gathered} \frac{3}{2}+\frac{1}{4}+\frac{3}{2}\rightarrow\frac{2\cdot3}{2\cdot2}+\frac{1}{4}+\frac{2\cdot3}{2\cdot2} \\ \\ \rightarrow\frac{6}{4}+\frac{1}{4}+\frac{6}{4} \end{gathered}[/tex]Now, we can add them up:
[tex]\frac{6}{4}+\frac{1}{4}+\frac{6}{4}\rightarrow\frac{6+1+6}{4}\rightarrow\frac{13}{4}[/tex]This way, the answer is 13/4
22. Solve 3(5x – 4) < 15x.O x<4No solutionX >-4All Real Numbers
ANSWER
All real numbers
EXPLANATION
To solve this inequality, first, divide both sides by 3,
[tex]\begin{gathered} \frac{3\left(5x-4\right)}{3}\lt\frac{15x}{3} \\ \\ 5x-4\lt5x \end{gathered}[/tex]Then, subtract 5x from both sides of the inequality,
[tex]\begin{gathered} 5x-5x-4\lt5x-5x \\ \\ -4\lt0 \end{gathered}[/tex]-4 indeed is less than 0, and this is valid for any value of x in the real numbers - i.e. any real number for x satisfies the inequality.
Hence, the solution is all real numbers.
Find the slope from real world application. At pizza galore a two topping pizza costs $9. A pizza with four toppings costs $12. How much does each topping cost?
The slope is:
[tex]m=\frac{12-9}{4-2}[/tex][tex]m=\frac{3}{2}=1.5[/tex]Hence, each topping of the pizza cost $1.5