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 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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Solve the equation.
17=5k-2
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?
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 ?
27 students in all 4:5 packed lunch. how many students packed lunch
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
Angle XYZ is rotated 270 degrees counterclockwise about the origin to form angle X’Y’Z’. Which statement shows the measure of angle X’Y’Z’?
m∠X’Y’Z’ = m∠XYZ
m∠X’Y’Z’ = 180 degrees
m∠X’Y’Z’ = 270 degrees
m∠X’Y’Z’ = 2 × m∠XYZ
Answer:m∠X’Y’Z’ = m∠XYZ
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
marta took 48 pictures of flowers and 64 pictures of beautiful scenery. She wants to display the pictures so there is the same number of each kind of picture in each display. what is the greatest number of displays she can make?
there are 2 more than 3 times as many parrots as finches at the pet store, if there's a total of 18 parrots and finches, how many are parrots and how many are finches
Final answer:
To solve this problem, you can set up a system of equations. There are 4 finches and 14 parrots.
Explanation:
To solve this problem, we can set up a system of equations based on the given information. Let's assume that the number of finches is 'x'. According to the problem, there are 2 more than 3 times as many parrots as finches. This can be written as:
Parrots = 3x + 2
Since the total number of parrots and finches is 18, we can set up another equation:
Parrots + Finches = 18
Substituting the first equation into the second equation, we get:
(3x + 2) + x = 18
Combining like terms, we have:
4x + 2 = 18
Subtracting 2 from both sides, we get:
4x = 16
Dividing both sides by 4, we find that:
x = 4
So, there are 4 finches and 3(4) + 2 = 14 parrots.
Four sisters buy a total of 3 1/2 feet of ribbon. The sisters want to share the ribbon equally. How many feet of ribbon will each sister receive
divide 3 1/2 by 4
3 1/2 = 7/2
7/2 / 4 = 7/8 foot each
Answer:
[tex]\frac{7}{8}[/tex] feet.
Step-by-step explanation:
Four sister bought a total of ribbon = [tex]3\frac{1}{2}[/tex] feet
= [tex]\frac{7}{2}[/tex] feet
The sisters want to share the ribbon equally.
So we will divide the total length of the ribbon by 4.
= [tex]\frac{7}{2}[/tex] ÷ 4
= [tex]\frac{7}{2}[/tex] × [tex]\frac{1}{4}[/tex]
= [tex]\frac{7}{8}[/tex] feet.
Each sister will receive [tex]\frac{7}{8}[/tex] feet of ribbon.
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 sum of six consecutive integers is 387. what is the sixth number in the sequence
The elimination of paper-based documents between organizatins is made possible by
m−14.6=9.74 4.86 23.34 24.34 25.34 wich one
A painting crew bought 30 gal of paint for a job. The crew members used 3 gal of paint per hour until they used all the paint.
Which sketch represents this situation?
A) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 3 end ordered pair and begin ordered pair 30 comma 0 end ordered pair.
B) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 30 end ordered pair and begin ordered pair 10 comma 0 end ordered pair.
C) A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 10 end ordered pair and begin ordered pair 30 comma 0 end ordered pair.
D)A graph in the first quadrant containing a line segment. The x axis is labeled Hours and the y axis is labeled Gallons remaining. The endpoints of the line segment are begin ordered pair 0 comma 30 end ordered pair and begin ordered pair 3 comma 0 end ordered pair.
Answer:
Step-by-step explanation:
They have 30 gallons of paint and for each hour that passes, they use 3 gallons of paint. Therefore, we can express that as a function:
y = -3x + 30
where y = gallons left
and x = hours passed
Therefore, the end points are (0, 30) and (10, 0)
Using our function when 0 hours has passed:
y = -3(0) + 30
y = 30
Therefore one endpoint is when x = 0 y = 30 or (0,30)
Using our function when 10 hours has passed:
y = -3(10) + 30
y = -30 + 30
y = 0
Therefore one endpoint is when x = 10 y = 0 or (10, 0)
The graph can be seen in the picture below.
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.
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?
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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
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.
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.
Find the largest number δ such that if |x − 1| < δ, then |5x − 5| < ε, where ε = 0.1. δ ≤ repeat and determine δ with ε = 0.01.
Hi, here we want to "finish" a delta-epsilon proof.
We will find that the maximum delta is: δ = 0.02
We just want to find the value of δ such that:
[tex]|x - 1| < \delta[/tex]
Implies that:
[tex]|5x - 5| < \epsilon[/tex]
Well, let's start with the second expression:
[tex]|5x - 5| < \epsilon[/tex]
We can take the 5 out of the absolute value:
[tex]5*|x - 1| < \epsilon[/tex]
Now we can divide both sides by 5:
[tex]|x - 1| < \epsilon/5[/tex]
Now, if you look at the above expression, in the left side we have the same thing as in the delta inequality.
So for now we have:
[tex]|x - 1| < \epsilon/5[/tex]
[tex]|x - 1| < \delta[/tex]
From this is easy to conclude that the maximum value that delta can take is:
δ = ε/5
And we know that ε = 0.1, then we have:
δ = 0.1/5 = 0.02
δ = 0.02
The maximum value that delta can take is 0.02
Then we need to repeat it for ε = 0.01, so we get:
δ = 0.01/5 = 0.002
δ = 0.002
If you want to learn more, you can read:
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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
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.
on one of the day you went to the gym,the ratio of men to women was 3:2.if 120 men used the gym,how many women were there?
Answer:
80 women
Step-by-step explanation:
A ratio of men to women of 3:2 means that for 3 men that use the gym 2 women use the gym, so using a rule of three we can determinate how many women were on the gym that day if 120 men were there, like this:
3 men ------ 2 women
120 men ------ X
[tex]X = \frac{(120men)(2women)}{3men}=80 women[/tex]
Then, there were 80 women for the 120 men that were in the gym.
if the smaller of two consecutive intergers is subtracted from two times the larger then the result is 17 . find the intergers
Debra is on the swim team. Each day she swims 850m. How many kilometers does she swim each day?
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.
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.