the sum of six consecutive integers is 387. what is the sixth number in the sequence
Mr. James wants to build a walkway around his school garden. The width of his garden is one-third the length. The perimeter of the school garden is 32 feet. What is the length and width of his garden?
L=3W
2(3W+W)=32 feet
8W=32 feet
W=4 feet
L=3W
L=3* 4 feet
L=12 feet
The width is 4 feet, the length is 12 feet.
The ling family wants to purchase a television that costs $449. The store that sells the television has multiple locations in different counties. The sales tax for each county is shown. Complete the table below by arranging the counties from least to greatest sales tax rate. Write each sale tax as a percent
Solve the equation.
17=5k-2
What is the volume in cubic yards of a greenhouse that is 35 feet long, 10 feet wide, and 10 feet high?
Final answer:
To determine the volume of a greenhouse, multiply its length, width, and height to find its volume in cubic feet, then convert to cubic yards using the conversion factor of 1 cubic yard being equivalent to 27 cubic feet. The volume for the given dimensions is approximately 129.63 cubic yards.
Explanation:
The volume of a structure, including a greenhouse, is calculated by multiplying its length by its width by its height. The first step is to calculate the volume in cubic feet, then convert cubic feet to cubic yards knowing that 1 cubic yard equals 27 cubic feet. Here's how to calculate the volume of the given greenhouse:
Multiply the length, width, and height in feet to get the volume in cubic feet: 35 ft x 10 ft x 10 ft = 3500 cubic feet.Convert cubic feet to cubic yards using the conversion factor (1 cubic yard = 27 cubic feet): 3500 cubic feetTherefore, the volume of the greenhouse is 129.63 cubic yards.
Nails cost $.13 per pound and screws cost $.21 per pound. Michelle bought 1.5 pounds of nails and 3.4 pounds of screws. How much did she pay for the nails and screws?
if the smaller of two consecutive intergers is subtracted from two times the larger then the result is 17 . find the intergers
What are the next three terms of the geometric sequence 32, -16, 8, …?
a.
2, 1, 1/2
c.
-8, 16, -32
b.
4, 2, 1
d.
-4, 2, -1
The remainder when aa is divided by 77 is 22 and the remainder when bb is divided by 77 is 55. (so a mod 7=2a mod 7=2, b mod 7=5b mod 7=5) find: (a+a) mod 7(a+a) mod 7 equation editor equation editor (a+b) mod 7(a+b) mod 7 equation editor equation editor (3a) mod 7(3a) mod 7 equation editorequation editor (2b) mod 7(2b) mod 7
The modulo of the expressions are computed as follows: (a+a) mod 7 = 4, (a+b) mod 7 = 0, (3a) mod 7 = 6, and (2b) mod 7 = 3.
Explanation:I'm sorry, but I'm afraid there might have been some confusion in your input. If you wanted the remainders of different expressions when divided by 7, here are the steps:
Given that a mod 7 = 2 and b mod 7 = 5, you can use modular arithmetic to compute the modulo of expressions including a and b:
(a+a) mod 7 = 2a mod 7. Since a mod 7 = 2, then 2a mod 7 = 4 mod 7.(a+b) mod 7 = 2+5 mod 7 = 7 mod 7 = 0.(3a) mod 7 = 6 mod 7.(2b) mod 7 = 10 mod 7 = 3.Learn more about Modular Arithmetic here:https://brainly.com/question/13089800
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The elimination of paper-based documents between organizatins is made possible by
Help me asap!
please help
cross multiply:
21*9 = 189
7*q = 7q
so you have 189/7q
divide 189 by 7 to get q
189 / 7 =27
q = 27
m−14.6=9.74 4.86 23.34 24.34 25.34 wich one
Lisa wants to buy a phone card for $5. Company X charges $0.49 for the first minute and $0.16 for each additional minute. Company Y charges $0.57 for the first minute and $0.12 for each additional minute. If Lisa makes just one call, which phone company gives her more minutes for $5? How many more minutes?
Rearrange the formula V = 1 3 πr2h for h.
Answer:
The answer is A. Thanks
Step-by-step explanation:
Making 'h' the subject , the expression obtained is h = 3V/ πr²
Given the volume formula :
V = 1/3 πr²hTo make 'h' the subject
multiply both sides by 3
3V = πr²h
divide both sides by πr² in other to isolate 'h'
3V/ πr² = πr²h/πr²
h = 3V/ πr²
Therefore, making 'h' the subject , the expression obtained is :
h = 3V/ πr²Learn more on equations :https://brainly.com/question/2972832
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An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.
Use
A=P(1+rn)nt
A=P(1+rn)nt where:
A = the amortized amount (total loan/investment amount over the life of the loan/investment)
P = the initial amount of the loan/investment
r = the annual rate of interest
n = the number of times interest is compounded each year
t = the time in years
Find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.
It will take ___ years. (Round answer to 3 decimal places.)
It will take approximately 1.459 years for a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly.
Explanation:To find how long it takes a $2,200.00 investment to earn $210.00 in interest if it is invested at 10% compounded monthly, we can use the formula A = P(1+rn)^(nt). Plug in the values: A = 2200 + 210 = 2410, P = 2200, r = 0.10 (10%), n = 12 (compounded monthly), and t = ?
2410 = 2200(1 + 0.10/12)^(12t). Divide both sides by 2200 to isolate the expression:
1.095 = (1 + 0.10/12)^(12t). Take the natural logarithm of both sides to remove the exponent:
ln(1.095) = 12t * ln(1 + 0.10/12). Solve for t:
t = ln(1.095) / (12 * ln(1 + 0.10/12)). Use a calculator to find the value of t, which is approximately 1.459 years when rounded to 3 decimal places.
A scientist studying bacteria begins with 20 cells. The bacteria population doubles every hour. Complete the table below to determine after how many hours there will be more than 500 bacteria cells. Time (hours) Number of bacteria cells 0 20 1 40 2 80 3 4 5 6 Write an exponential function to model this situation. Predict the bacteria population after 11 hours.
Answer:
1)
t=5 hours.
2)
40960 cells.
Step-by-step explanation:
A scientist studying bacteria begins with 20 cells.
The bacteria population doubles every hour.
Let P(t) determines the population of the bacteria in 't' hours.
Hence, by the given information our function P(t) is modeled as:
[tex]P(t)=20\times 2^t[/tex]
Now, we have to find the value of 't' such that:
P(t)>500
i.e.
[tex]20\times 2^t>500\\\\\\2^t>\dfrac{500}{20}\\\\2^t>25[/tex]
on taking logarithmic function on both side we get:
[tex]t\log 2>\log 25\\\\t>\dfrac{\log 25}{\log 2}\\\\t>4.64[/tex]
i.e. after 5 hours the population of the bacteria will exceed 500.
Now we have to find the value of function P(t) when t=11.
i.e.
[tex]P(11)=20\times 2^{11}\\\\P(11)=20\times 2048\\\\P(11)=40960[/tex]
Hence , the population of bacteria after 11 hours is:
40960 cells.
What is the exact volume of the cone?
28π in³
563π in³
1963π in³
196π in³
28π in^3
56/3π in^3
196/3π in^3
196π in^3
These are the numbers they meant to put and the answer is 196/3 in^3.
Allen is given three lengths of rope: 4 feet, 8 feet, and 15 feet. Can Allen form a triangle with side lengths of 4 feet, 8 feet, and 15 feet using these three pieces of rope
Answer:the answer is B No,set of side length does not satisfy triangle inequality theorem
Step-by-step explanation:
The initial number of views for a blog was 20. The number of views is growing exponentially at a rate of 20% per week. What is the number of views expected to be four weeks from now? Round to the nearest whole number.
Answer : The number of views expected to be four weeks from now is, 42
Step-by-step explanation :
Formula for exponential growth is :
[tex]y=a(1+r)^x[/tex]
where,
y = exponential growth = ?
a = initial amount of growth = 20
r = growth rate = 20% = 0.20
x = number of time intervals that have passed = 4
Now put all the given values in the above formula, we get:
[tex]y=20\times (1+0.20)^4[/tex]
[tex]y=41.475\aaprox 42[/tex]
Thus, the number of views expected to be four weeks from now is, 42
Lisa had 1750 stamps. Mark had 480 fewer stamps than Lisa. Lisa gave some stamps to Mark. Now Mark has three times as many stamps as Lisa. How many stamps did Mark have at first? How many stamps does Lisa have now? Explain.
Cases are normally sold full. There were three partially full cases that could be combined to make full cases. The cases were 11/16, 5/16 and 7/16 full.
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since angle 3 = 47, then angle 1 also = 47
this would mean that both angles 5 & 7 are also 47
so angle 5 = 47 degrees
27 students in all 4:5 packed lunch. how many students packed lunch
A 24-ounce mocha beverage with whipped cream has 25% of the calories allowed on a 2,000-calorie-per-day diet. What percentage of a 2,500-calorie-per-day diet would this same drink constitute?
Answer:
c
Step-by-step explanation:
The bookshelf was bought at a wholesale price of $147.00, and Gabriela Furniture Store Marie up all Furniture by 60%.At what price should the manager sell the bookshelf ?
Which planets diameter is approximately 1/200 of the sun's diameter?explain
Answer:
Mars
Step-by-step explanation:
Sun is the brightest object in the sky of the Earth. It is a giant spherical star, composed of hot plasma that is located at the center of the Solar System. The diameter of the Sun is about 1.391 million km.
Mars, also known as the Red Planet, is one of the four terrestrial planets. It is the fourth planet of the Solar System. It is the second-smallest planet having diameter of about 6,779 km.
Now, diameter of Mars ÷ diameter of the Sun ≈ 6,779 km ÷ 1391000 km ≈ 1 ÷ 200
⇒ diameter of Mars ≈ (1 ÷ 200) × diameter of the Sun
Therefore, the diameter of Mars is approximately 1/200 of the diameter of the Sun.
Shan's dumpling house can produce 100 dumplings using one worker and 175 dumplings using two workers. what is the marginal product of the second worker?
a.25 dumplings
b.75 dumplings
c.175 dumplings
d.275 dumplings
The marginal product of the second worker is b. 75 dumplings.
To find the marginal product of the second worker, we need to determine how many additional dumplings the second worker is able to produce compared to the first worker. The marginal product (MP) of a worker is calculated as follows
[tex]\[ MP = \text{Total production with two workers} - \text{Total production with one worker} \][/tex]
Given:[tex]\[\]\[ \text{Total production with one worker} = 100 \text{ dumplings} \]\[ \text{Total production with two workers} = 175 \text{ dumplings} \][/tex]
Substitute the given values into the formula:[tex]\[\]\[ MP = 175 \text{ dumplings} - 100 \text{ dumplings} \]\[ MP = 75 \text{ dumplings} \][/tex]
The weight of 10,000 identical samples of a substance is 10 pounds. What is the weight of 100 samples?
Answer: 0.1
Step-by-step explanation: Okay. So, the weight of 10,000 samples is 1 pound. To find the weight of each sample, we can do 10/10,000, which would give us 0.001. Each sample weighs 0.001 pound. We can multiply that times 100 to find the weight of 100 samples. 0.001 * 100 = 0.1. The weight of 100 samples is 0.1 pound.
Debra is on the swim team. Each day she swims 850m. How many kilometers does she swim each day?