Answer:
Step-by-step explanation:
45
Answer:
34
Step-by-step explanation:
1+4=5 2+5=12 3+6=21 5+8= ??
It is noticed that the previous solution is added to the unknowns and the cycle continues.
The previous solution is 5 which is added to 2 and 5 to give 12
5+2+5=12
12 is then added to the next set of unknowns 3+6 to give 21
12+3+6=21
21 is then added to the 5+8 to give 34
21+5+8= 34
a bag contains 6 white marbles and 4 black marbles. a marble is drawn without replacing the first one. what is the probability of drawing a white marble on the first draw, followed by a white marble on the second?
Answer:
6 = white marbles
4 = black marbles
10 = total marbles
6/10 - Pulling white marbles
4/10 - Pulling black marbles
10 - 4 = 6
2/6 - Pulling two white marbles
2/6 = 1/3 = 0.33 or 33%I hope this helped!
The probability of drawing a white marble on the first draw after following the second draw of white marble should be 0.33.
Given that
There are 6 white marbles.There are 4 black marbles.The total marbles are 10.Now based on the above information
Put white marbles be [tex]\frac{6}{10}[/tex]
And, black marbles be [tex]\frac{4}{10}[/tex]
So,
= 10 - 4
= 6
Now pull two white marbles i.e.
[tex]= \frac{2}{6} \\\\= \frac{1}{3}\\\\= 33\%\ or\ 0.33[/tex]
Therefore we can conclude that The probability of drawing a white marble on the first draw after following the second draw of white marble should be 0.33.
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Darin simplified 515+215 and got 15.7.
Martha simplified the same expression and
got 50. Use a calculator to determine who got
the correct answer.
There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.
How many milliliters of blood did the volunteers donate?
Answer:
470(32 - n)
Step-by-step explanation:
Here are the given:
> 32 volunteers
> n volunteers who didn't donate
> 470 mL each
So your expression is: 470(32 - n).
Why?
Subtract the 32 volunteers who want to donate blood from the volunteers who were not able to donate then multiply it by 470.
Hope this helps!
A regular octagon has an apothem measuring 10 in. and a perimeter of 66.3 in.
What is the area of the octagon, rounded to the nearest square inch?
Answer: 331.5 inches²
Step-by-step explanation:
To solve for the area of a regular octagon, we can use the formula that is shown below:
Area = 1/2 × apothem × perimeter
In this problem, we have been given the following values:
Apothem = 10 inches
Perimeter = 66.3 inches
To solve for the area,
Area = 1/2 × apothem × perimeter
Area = 1/2 × 10 × 66.3
Area = 331.5 inches²
What is the volume of the sphere? (Use 3.14 for π.) 28.26 in.3 113.04 in.3 339.12 in.3 452.16 in.3
Answer:
1.3 x 3.14 x 3 x 3 x 3 = 27 x 1.3 x 3.14 = 113.04
formula is 4/3 x pi x radius to the power of three
Step-by-step explanation:
I may have used google...
Answer:
It's 113.04 in. 3
Step-by-step explanation:
I used the formula from the person on top, credits to them ^^
I am a three digit number. I am number between 350 and 400. All my digits are different and they are all odd. The sum of my last two digits is 16. What number am I
Answer:
397
Explanation: 9+7 =16 and 3 is odd
Answer:
397
Step-by-step explanation:
379 or 397 with fit the criteria
Sadie decorated her horse with ribbons for the Memorial Day Parade. In the mane, she used 6 feet of ribbon. She used an additional 11 inches of ribbon around her front right leg. How many inches of ribbon did she use altogether for the horse?
Answer: 83 inches
Step-by-step explanation:
1 foot = 12 inches
In the mane, she used 6 feet of ribbon. 6×12 = 72 inches
She used an additional 11 inches of ribbon around her front right leg
Altogether she use 72 + 11 = 83 inches
Find the probability that a randomly selected student drives to school.
The probability that a randomly selected student drives to school is [tex]\( \frac{2}{45} \)[/tex].
Explanation:The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of sophomores who drive to school is 2, and the total number of sophomores is the sum of those who drive, take the bus, and walk: 2 + 25 + 3 = 30. Therefore, the probability for sophomores is [tex]\( \frac{2}{30} \)[/tex]. Similarly, for juniors, it is [tex]\( \frac{13}{35} \)[/tex], and for seniors, it is [tex]\( \frac{25}{35} \)[/tex]. To find the overall probability, we take the weighted average:
P(driver to school) = [tex]\frac{\text{(Number of sophomores)} \times P(\text{sophomores}) + \text{(Number of juniors)} \times P(\text{juniors}) + \text{(Number of seniors)} \times P(\text{seniors})}{\text{Total number of students}}[/tex]
[tex]\[ P(\text{driver to school}) = \frac{2 \times \frac{2}{30} + 13 \times \frac{13}{35} + 25 \times \frac{25}{35}}{30 + 35 + 35} \][/tex]
After calculating, the final answer is [tex]\( \frac{2}{45} \)[/tex], representing the probability that a randomly selected student drives to school. This approach considers the distribution of students across different grades, giving a more accurate representation of the overall likelihood.
Solve the equation. Two-thirds x = negative one-half x + 5 What is the first step to isolate the variable term on one side of the equation? What is the second step to solve for x?
Answer:
add 1/2x to both sides
multiply both sides by 6/7
Answer: Add 1/2x to both sides.
Multiply both sides by 6/7.
Step-by-step explanation: credit to the person above or below me
jsjsjjs jsjsjjs Help
Answer:
84,500
Step-by-step explanation:
8.45*10^4
8.45 * (10*10*10*10)
8.45 * 10000
84500
the decimal place moves to the right for however many zeros you have :)
i hope this helps :)
HELP PLZ THIS IS DUE TODAY
Answer:
1300π
Step-by-step explanation:
The volume of a cylinder is
V = Area of base * height
The base is a circle, so its area is
A = πr^2
The radius is half the diameter: 20/2 = 10 ft.
A = π10^2 = 100π
Plug this back into the volume formula:
V = 100π * height
= 100π * 13
= 1300π ft
Factor the quadratic expression completely.
-8x^2 -15x + 2 =
Answer:
Step 1: −8x2−15x+2
Step 2: (−8x+1)(x+2)
Step 3: Say thank you
The factors of quadratic equation are : (8x -1) and (x + 2)
Given ,
-8x² -15x + 2 = 0
Now,
Firstly multiply the equation with -1 to make the coefficient of x² positive .
8x² + 15x -2 = 0
Now taking the factors,
8x² + 16x - 1x -2 = 0
8x(x + 2) -1 (x + 2) = 0
(8x -1) (x + 2) = 0
Thus,
The factors are (8x -1) and (x + 2).
The values of x are 1/8 and -2 .
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Hannah's school hosted a book donation. There are 150150150 students at her school, and they donated a total of bbb books! Hannah donated 333 times as many as the average number of books each student donated. How many books did Hannah donate
Answer:
Hanna donated b/50 books
Step-by-step explanation:
In this problem, we have:
n = 150 number of students at Hanna's school
b = ? number of total books donated by the students
Also, Hannah has donated 3 times as many as the average number of books each student donated.
The average number of books each student donated can be written as:
[tex]\frac{b}{150}[/tex]
And calling
h = number of books donated by Hannah
This means that
[tex]h=3(\frac{b}{150})[/tex]
Simplifying, this can be rewritten as
[tex]h=\frac{b}{50}[/tex]
Answer:
b/50
Step-by-step explanation:
Please help me out please 10 point
Answer:
Its A.
Step-by-step explanation:
Please... I need help!
Some one to explain me plz
Answer:
See below where I explain line by line.
Step-by-step explanation:
If two lines are parallel, their slopes are equal.
Look at line 1: Both lines have slope 1/2. Since both slopes are 1/2, the slopes are equal, and the lines are parallel.
Look at line 7: slope 4/8, slope 1/2. Reduce 4/8. It reduces to 1/2. Both lines have slope 1/2. The lines have equal slopes, so they are parallel.
If two lines are perpendicular, then their slopes are opposite reciprocals. Reciprocals are two numbers that when when written as a fraction, when you flip one, you get the other. For example, 4/5 and 5/4. They are reciprocals because is you flip 4/5, you get 5/4. For two lines to be perpendicular, their slopes need to be reciprocals and opposites. That means their signs must be different (one positive and one negative) in addition to being reciprocals. For example, two lines with slope 5/8 and -8/5 are perpendicular since the slopes are both reciprocals and opposites.
Look at line 2: -2/3 and 3/2. If you flip -2/3, you get -3/2. The opposite of -3/2 is 3/2. That means each slope is the opposite reciprocal of the other, so they are perpendicular.
Line 5: slope 4, slope -1/4. Write 4 as a fraction. Now you have 4/1. Flip 4/1 to get 1/4. Then make it the opposite, -1/4. The second line does have slope -1/4, so they are perpendicular.
Line 6: slope -1/6, slope 6. Flip -1/6. You get -6/1. Find its opposite: 6/1. 6/1 is the same as 6. That means that -1/6 and 6 are opposite reciprocals and the lines are perpendicular.
Lines that are neither parallel nor perpendicular.
Look at line 3: 5/2 and 2/5. If you flip 5/2, you get 2/5. The slopes are reciprocals, but they are not opposites since they are both positive. The lines are not perpendicular. Also 5/2 is not equal to 2/5, so the lines are not parallel either.
Look at line 4: slope -3; slope -1/3. Start with -3. Write it as a fraction: -3/1. Now flip it: -1/3. Now find its opposite: 1/3. If the slopes were -3 and 1/3, the lines would be perpendicular because they'd be reciprocal and opposite. The second slope is -1/3, not 1/3, so they are not opposite, and the lines are not perpendicular. Also, -3 and -1/3 are not equal, so the lines are also not parallel.
Bob and John are 450 feet apart when they start running towards each other. Bob runs at a speed of 11 feet per second, and John runs at a speed of 14 feet per second. How soon will they meet?
Answer:
18 s
Step-by-step explanation:
We are given that
Distance between Bob and John=450 feet
Speed of Bob=11ft/s
Speed of John=14 ft/s
We have to find the time after they will meet when they are travel towards to each other.
Total distance traveled by Bob and John in 1 s=11+14=25 ft
25ft covered by Bob and John in 1 s
1 ft covered by Bob and John in [tex]\frac{1}{25}s[/tex]
450 ft covered by Bob and John in [tex]\frac{1}{25}\times 450=18 s[/tex]
Hence, they will meet after 18 s.
Answer:
18 seconds
Step-by-step explanation:
450 divided by 11+14=18
(09.01 MC)
Two quadratic functions are shown.
Function 2:
Function 1:
f(x) = 2x2 - 8x + 1
|x
g(x)
1
17
Which function has the least minimum value and what are its coordinates? (5 points)
Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2. - 7).
Function 2 has the least minimum value and its coordinates are (0,2).
Function 2 has the least minimum value and its coordinates are (-1.-3).
Answer:
Function 1 has the least minimum value and its coordinates are (2. - 7).Step-by-step explanation:
The first function is
[tex]f(x)=2x^{2} -8x+1[/tex]
The second function is
x g(x)
-2 2
-1 -3
0 2
1 17
The vertex has coordinates of [tex]V(h,k)[/tex], where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex].
Let's find the vertex for the first function where [tex]a=2[/tex] and [tex]b=-8[/tex].
[tex]h=-\frac{-8}{2(2)}=2[/tex]
[tex]k=f(2)=2(2)^{2} -8(2)+1=8-16+1=-8+1=-7[/tex]
Therefore, the vertex of the first function is at [tex](2,-7)[/tex].
Now, the minimum value of the second function can be deducted from its table, which is [tex](-1,-3)[/tex].
Therefore, [tex]f(x)[/tex] has -7 as minimum value and [tex]g(x)[/tex] has -3 as minimum vale.
So, the right answer is B, because -7 is less than -3.
Find the indicated probability. In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is between 1100 kWh and 1225 kWh.
Answer:
p=0.1971
Step-by-step explanation:
-Let X be the normally distributed random variable with mean=1050kWh and standard deviation=218kWh.
-We use the z-test to test for the probability of mean consumption being between 1100kWh and 1225kWh as:
[tex]P(1100<X<1225)=P(\frac{1100-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1225-\mu}{\sigma})\\\\=P(\frac{1100-1050}{218}<Z<\frac{1225-1050}{218})\\\\=P(0.2294<Z<0.8028)\\\\=P(Z<0.8028)-P(Z<0.2994)\\\\=0.7881-0.5910\\\\=0.1971[/tex]
Hence, the probability of mean consumption being between 1100 and 1225kWh is 0.1971
At 7am you drink a 12-ounce cup of coffee which has 140mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. How many milligrams of caffeine is in your body after 2 hours? Group of answer choices 136.4 106.2 178.4 33.8
Answer:
B. 106.2
Step-by-step explanation:
We have been given that at 7 am you drink a 12-ounce cup of coffee which has 140 mg of caffeine. The liver metabolizes caffeine at a rate of 12.9% per hour. We are asked to find the milligrams of caffeine left in your body after 2 hours.
We will use exponential decay formula to solve our given problem.
[tex]y=a\cdot (1-r)^x[/tex], where,
y = Final value,
a = Initial value,
r = Decay rate in decimal form,
x = Time.
Let us convert 12.9% in decimal form.
[tex]12.9\%=\frac{12.9}{100}=0.129[/tex]
Initial value is 140 mg.
[tex]y=140\cdot (1-0.129)^x[/tex]
[tex]y=140\cdot (0.871)^x[/tex]
Now we will substitute [tex]x=2[/tex] in our equation as:
[tex]y=140\cdot (0.871)^2[/tex]
[tex]y=140\cdot (0.758641)[/tex]
[tex]y=106.20974\approx 106.2[/tex]
Therefore, approximately 106.2 milligrams of caffeine will be in your body after 2 hours.
A certain appliance uses w watts to run. If you run it for m minutes, and the cost per kilowatt-hour is c, the cost of running the appliance for m minutes is given by the formula (w(m/60))/1000 c. Find the cost of running an appliance that requires 500 watts for 25 minutes at a cost of $0.125 per kWh.
Answer:
The cost for this appliance is $0.02604
Step-by-step explanation:
In order to solve this problem we need to apply the appliance's values to the provided formula as shown bellow:
cost = {[w*(m/60)]/1000}*c
cost = {[500*(25/60)]/1000}*0.125
cost = {[12500/60]/1000}*0.125
cost = {208.4/1000}*0.125
cost = 0.2084*0.125 = 0.02604
The cost for this appliance is $0.02604
Answer:
$1.68
Step-by-step explanation:
If the function modelled for finding the cost of running the appliance for m minutes is given by the formula (w(m/60))/1000 c, and the following datas are given:
W = 500watts
m = 25minutes
c = cost per kWhr = $0.125
Cost of running an appliance that requires 500 watts for 25 minutes at a cost of $0.125 per kWh will be gotten by substituting the given data in the modelled function.
C= {500(25/60)}/1000 (0.125)
C =(500×0.42)/125
C = 210/125
C = $1.68
The cost of running the appliance will be $1.68
A company has two large computers. The slower computer can send all the company's email in 35 minutes. The faster computer can complete the same job in 15 minutes. If both computers are working together, how long will it take them to do the job
It takes 10.5 minutes for both the computers to do the work by working together
What is a Fraction?
A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given data ,
The time for which the slower computer can send all the mails = 35 minutes
The time for which the faster computer can send all the mails = 15 minutes
So ,
The slower computer can complete the work in = 1 / 35 min
The faster computer can complete the work in = 1 / 15 min
Let the total work done by both computers together be = W
The total work completed when both the computers work together is 1 / W =
The work completed by slower computer + The work completed by slower computer
The total work completed when both the computers work together 1 / W =
1 / 35 + 1 / 15
And ,
1 / W = 1 / 35 + 1 / 15
1 / W = 10 / 105
Taking reciprocals , we get
W = 105 / 10
W = 10.5 minutes
Hence , The time taken by both the computers to do the work together is 10.5 minutes
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Final answer:
To find the combined time for two computers to complete a job, calculate their work rates individually and add them up.
Explanation:
To solve this problem, we can use the concept of work rates.
Calculate the work rate of each computer:
Slower computer's work rate = 1 job / 35 minutes = 1/35 job per minute
Faster computer's work rate = 1 job / 15 minutes = 1/15 job per minute
When both computers work together:
Total work rate = 1/35 + 1/15 = 5/105 + 7/105 = 12/105 jobs per minute
Calculating the time taken:
Time taken = 1 job / Total work rate = 105 / 12 = 8.75 minutes
Therefore, both computers working together will complete the job in 8.75 minutes.
Starting at the age of 40, an average man loses 5%of his hair every year. At what age should an average man expect to have half his hair left?
At the age of 53.5136 years, an average man expects to have half his hair left.
Given information:
Starting at the age of 40, an average man loses 5% of his hair every year.
So, at the age of 40 years, an average man will have 95% of total hairs left.
Let t be the number of years after the age of 40 years.
So, the value of t so that the man will have 50% of hairs left can be calculated as,
[tex]50\%=(1-5\%)^t\\0.5=(1-0.05)^t\\0.5=0.95^t\\log0.5=t\rm \;log0.95\\\it t=\rm 13.5136[/tex]
So, the age of the man with 50% hairs left will be 40+13.5136=53.5136 years.
Therefore, at the age of 53.5136 years, an average man expects to have half his hair left.
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Juan and Lizzy are in the final week of their training for a marathon. Juan's goal is to run one mile on the first day of the week and double the amount he runs each day for the next six days. Lizzy's goal is to run 10 miles on the first day of the week and increase the amount she runs by 3 miles each day for the next six days. 1: Juan's marathon training schedule is an example of a(n) : arithmetic or geometric 2: Lizzy's marathon training schedule is an example of a(n) : arithmetic or geometric 3: Who will be better prepared for the marathon: Juan or Lizzy
Answer:
1. Juan's marathon training schedule is an example of a geometric sequence
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
3. Lizzy will be better prepared for the marathon
Step-by-step explanation:
In the arithmetic sequence there is a common difference between each two consecutive terms
In the geometric sequence there is a common ratio between each two consecutive terms
Juan's Schedule
∵ Juan's will run one mile on the first day of the week
∴ [tex]a_{1}[/tex] = 1
∵ He will double the amount he runs each day for the next
6 days
- That means he multiplies each day by 2 to find how many miles
he will run next day
∴ [tex]a_{2}[/tex] = 1 × 2 = 2 miles
∴ [tex]a_{3}[/tex] = 2 × 2 = 4 miles
∴ [tex]a_{4}[/tex] = 4 × 2 = 8 miles
∴ [tex]a_{5}[/tex] = 8 × 2 = 16 miles
∴ [tex]a_{6}[/tex] = 16 × 2 = 32 miles
∴ [tex]a_{7}[/tex] = 32 × 2 = 64 miles
That means there is a common ratio 2 between each two consecutive days
1. Juan's marathon training schedule is an example of a geometric sequence
Lizzy's Schedule
∵ Lizzy's will run 10 miles on the first day of the week
∴ [tex]a_{1}[/tex] = 10
∵ She will increase the amount she runs by 3 miles each day for
the next six days
- That means she adds each day by 3 to find how many miles
she will run next day
∴ [tex]a_{2}[/tex] = 10 + 3 = 13 miles
∴ [tex]a_{3}[/tex] = 13 + 3 = 16 miles
∴ [tex]a_{4}[/tex] = 16 + 3 = 19 miles
∴ [tex]a_{5}[/tex] = 19 + 3 = 22 miles
∴ [tex]a_{6}[/tex] = 22 + 3 = 25 miles
∴ [tex]a_{7}[/tex] = 25 × 3 = 28 miles
That means there is a common difference 3 between each two consecutive days
2. Lizzy's marathon training schedule is an example of an arithmetic sequence
The rule of the sum of nth term in the geometric sequence is [tex]S_{n}=\frac{a_{1}(1-r^{n})}{1-r}[/tex]
∵ [tex]a_{1}[/tex] = 1 , r = 2 and n = 7
∴ [tex]S_{7}=\frac{1(1-2^{7})}{1-2}[/tex]
∴ [tex]S_{7}[/tex] = 127
∴ Juan will run 127 miles in the final week
The rule of the sum of nth term in the arithmetic sequence is [tex]S_{n}=\frac{n}{2}[a_{1}+a_{n}][/tex]
∵ n = 7, [tex]a_{1}[/tex] = 10 and [tex]a_{7}[/tex] = 28
∴ [tex]S_{7}=\frac{7}{2}(10+28)[/tex]
∴ [tex]S_{7}[/tex] = 133
∴ Lizzy will run 133 miles in the final week
∵ 133 miles > 127 miles
∴ Lizzy will run more miles than Juan
3. Lizzy will be better prepared for the marathon
RAMON SELLS CARS AND TRUCKS HE HAS ROOM ON HIS LOT FOR 521 VEHICLES. Ramon has 175 more more cars than trucks. How many of each vehicles should he have
Answer: he should have 348 cars and 173 trucks.
Step-by-step explanation:
Let x represent the number of cars that he should have.
Let y represent the number of trucks that he should have.
He has room on his lot for 521 vehicles. It means that
x + y = 521- - - - -- - - - -1
Ramon has 175 more more cars than trucks. It means that
x = y + 175
Substituting x = y + 175 into equation 1, it becomes
y + 175 + y = 521
2y = 521 - 175 = 346
y = 346/2
y = 173
x = y + 175 = 173 + 175
x = 348
To determine the number of cars and trucks on Ramon's lot, two equations were formed: T + C = 521 and C = T + 175. Solving these equations simultaneously, it was found that Ramon should have 173 trucks and 348 cars.
Explanation:Ramon's Car and Truck Problem
Let us define the number of trucks Ramon has as T and the number of cars as C. According to the problem, Ramon has room for 521 vehicles on his lot. The problem states that Ramon has 175 more cars than trucks, so we can express this as C = T + 175.
We know the total number of vehicles Ramon can have is 521, which leads us to the following equation: T + C = 521. Substituting the first equation into the second, we get T + (T + 175) = 521. Simplifying, 2T + 175 = 521. Subtracting 175 from both sides, 2T = 346. Dividing by 2, we find that T = 173. This means Ramon has 173 trucks on his lot.
Now, we substitute the value of T back into the equation for C: C = 173 + 175, which equals 348. So, Ramon should have 348 cars and 173 trucks on his lot.
the difference between circumference and area.
Answer:
The circumference of a circle is the length of its side, the area is the amount of space within it.
Step-by-step explanation:
Answer:
The circumference of a circle is the length of its side, the area is the amount of space within it.
Have a good day! (:
A computer chooses a random number
from 1 to 50. What is the probability of
you guessing the same number that the
computer chooses in 1 try?
Answer:
2% or less likely
Step-by-step explanation:
In magic squares, each row,
column, and diagonal adds up
to the same number. Complete
the magic square. Use each
number 1-9 only once.
Answer:
middle square top row =9 middle row left square= 7 middle row right square=3 bottom row left square =6 bottom row middle square 1
Step-by-step explanation:
every row = 15 so just start with the rows and columns that only need one square until you've filled it in enough that every row needs one and the solve from there
A magic square consists of a grid of numbers where each row, column, and diagonal add up to the same total. For a 3x3 magic square using numbers 1 through 9, this total is 15. Possible solutions include the rotations of the groupings 9, 5, 1 and 6, 2, 7.
A magic square is a grid of numbers where the values in each row, column, and diagonal add up to the same total. The key to solving such a puzzle is understanding that total. Since we are using the numbers 1 through 9, the total sum of these numbers is 45; because there are 3 rows (or columns or diagonals) in a 3x3 grid, each must add up to 15.
The only way to get 15 with three numbers in the 1-9 range is to either group 9, 5, and 1 or their rotations (such as 5, 1, 9 or 1, 9, 5) or use 6, 2, and 7 or their rotations. This leads to the following magic square:
8 1 6
3 5 7
4 9 2
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Complete the expressions to find the perimeter P of a rectangle that is 9 inches long by 4 inches wide. P=2l+2w =2⋅9+2⋅ ( ) =( )+( ) =( )in. AKA. ( ) = blank
Answer:
[tex]P= 26\text{ inches}[/tex]
Step-by-step explanation:
We are given the following in the question:
Dimensions of rectangle:
Length of rectangle,l = 9 inches
Width of rectangle, w = 4 inches
Perimeter of rectangle =
[tex]P= 2l + 2w[/tex]
Putting values, we get,
[tex]P= 2(9) + 2(4)\\P= (18) + (8)\\P= 26\text{ inches}[/tex]
Thus, the perimeter of rectangle is 26 inches.
The product of a number and five more than twice a number is 75. Find the number numbers
Assume number =x,
x(2x+5) = 75
=> 2x^2 + 5x -75 = 0
=> 2x^2+ 15x -10x -75 =0
=> x(2x+15)-5(2x+15)=0
=>(x-5)(2x+15)=0
x = 5, or x = -15/2
A shop sells packs of black pens, packs of red pens and packs of green pens.
There are:
3 pens in each pack of black pens
5 pens in each pack of red pens
6 pens in each pack of green pens
On Monday
number of packs sold of black, red and green pens = 7 : 2 : 4
A total of 220 were sold.
Work out the number of green pen sold. Show your working out.
Answer: There are 96 green pens sold.
Step-by-step explanation:
Since we have given that
Number of pens in each pack of black pens = 3
Number of pens in each pack of red pens = 5
Number of pens in each pack of green pens = 6
Ratio of number of packs sold of black, red and green pens = 7: 2: 4
Number of total pens sold = 220
So, ratio of pens in number of packs would be
[tex]7\times 3:2\times 5:4\times 6\\\\=21:10:24[/tex]
So, Number of green pens sold would be
[tex]\dfrac{24}{55}\times 220\\\\=24\times 4\\\\=96\ pens[/tex]
Hence, there are 96 green pens sold.
96 green pens were sold.
Since the number of packs sold of black, red and green pens are in the ratio 7 : 2 : 4
Also, a total 220 pens were sold. Let x represent the total number of packs, hence:
Number of black pens = 7x/13 * 3 = 21x/13
Number of red pens = 2x/13 * 5 = 10x/13
Number of green pens = 4x/13 * 6 = 24x/13
Hence:
21x/13 + 10x/13 + 24x/13 = 220
21x + 10x + 24x = 2860
55x = 2860
x = 52
Number of green pens = 24x/13 = 24(52)/13 = 96
Hence 96 green pens were sold.
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