The length of Rectangle is 81 feet's.
We have a rectangle which has a length of 27 feet less than nine times its width and the area of the rectangle is 972.
We have the length of the rectangle.
State the formula to calculate the Perimeter and Area of Rectangle?The Area of a Rectangle = A = L x B
The Perimeter of a Rectangle = P = 2(L + B)
According to the question, we have -
Area = 972 square feet's.
Let the length of rectangle be x and width be y.
Then -
x = 9y - 27
Now -
Area = 972
xy = 972
y(9y - 27) = 972
9y(y - 3) = 972
y(y - 3) = 108
[tex]$y^{2} -3y -108 = 0[/tex]
(y - 12)(y + 9) = 0
y - 12 = 0 or y + 9 = 0
y = 12 or y = - 9
But width cannot be negative. Therefore -
y = 12.
Now, length = x = 9y - 27 = 12 x 9 - 27 = 108 - 27 = 81.
Hence, the length is 81 feet's.
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How to solve a+5=-5a+5
The solution to the equation a+5=-5a+5 is a=0.
We are given that;
The expression a+5=-5a+5
Now,
To solve the equation a+5=-5a+5, we need to isolate the variable a on one side of the equation.
We can do this by adding 5a to both sides of the equation:
a + 5 + 5a = -5a + 5 + 5a
Combining like terms gives:
6a + 5 = 5
Subtracting 5 from both sides of the equation gives:
6a = 0
Dividing both sides of the equation by 6 gives:
a = 0
Therefore, by algebra the answer will be a=0.
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What is the measure of an interior angle of a regular octagon?
135°
45°
22°
180°
Answer:
135
Step-by-step explanation:
Answer: if theres 1080 degrees in a octagon and 8 sides. Id suppose that a regular angle in the octagon would all equal the same weighting it to 1080/8=135 degrees. Correct me if im wrong.
Answer:
135°
Step-by-step explanation:
the eights angles is 1080 degrees and there are eughts angles so yhe mesure of yhe interior amgle of a regular octagon is 135 degrees
Round 12.695 to the nearest hundredth
Answer:
12.700
or 12.7
or 12.70
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made. 0.7744 0.7733 0.0144 0.176
Answer:
The probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made is 0.7744
Solution:
Total number of coils = number of good coils + defective coils = 88 + 12 = 100
p(getting two good coils for two selection) = p( getting 2 good coils for first selection ) [tex]\times[/tex] p(getting 2 good coils for second selection)
p(first selection) = p(second selection) = [tex]\frac{\text { number of good coils }}{\text { total number of coils }}[/tex]
Hence, p(getting 2 good coil for two selection) = [tex]\frac{88}{100} \times \frac{88}{100} =\bold{0.7744}[/tex]
Probability of selecting two good coils with replacement: [tex]\(0.88 \times 0.88 = 0.7744\)[/tex]. Correct answer is D) 0.7744.
To solve this problem, we need to calculate the probability of selecting two good coils when the first selection is replaced before the second is made. This means the selections are independent.
Here are the steps:
1. Calculate the total number of coils:
12 defective +88 good $=100$ total
2. Determine the probability of selecting a good coil on the first draw:
[tex]\[ P(\text{good on first draw}) = \frac{88}{100} = 0.88 \][/tex]
3. Since the first coil is replaced, the probability of selecting a good coil on the second draw is the same:
[tex]\[ P(\text{good on second draw}) = \frac{88}{100} = 0.88 \][/tex]
4. Calculate the probability of both events (selecting two good coils):
[tex]\[ P(\text{two good coils}) = P(\text{good on first draw}) \times P(\text{good on second draw}) \][/tex]
[tex]\[ P(\text{two good coils}) = 0.88 \times 0.88 = 0.7744 \][/tex]
Therefore, the probability of getting two good coils when two coils are randomly selected with replacement is:
[tex]\[\boxed{0.7744}\][/tex]
So the correct answer is:
D) 0.7744
The correct question is:
A batch consists of 12 defective coils and 88 good ones. Find the probability of getting two good coils when two coils are randomly selected if the first selection is replaced before the second is made.
A) 0.176
B) 0.0144
C) 0.7733
D) 0.7744
Help pls! It’s really easy but hard haha
Answer:
Step-by-step explanation:
Domain is your x values. So it's your input and independent variable.
Range is your y values. So it's your output and dependent variable.
What is 21=6r+5-7r someone please help thank you
Answer:
r=-16
Step-by-step explanation:
21=6r+5-7r
1) Combine alike terms on the right side (6r and -7r):
21=-r+5
2) Subtract a 5 from both sides:
16=-r
3) Divide both sides by -1:
r=-16
Step-by-step explanation:
first combine like terms : 6r and -7r = -1r
21=5 -1r
cancellation cancel the same terms on both sides of the equation by inverse operations:
subtract 5 from both sides 21-5= 16 5-5=0
16=-1r
divide both ends of the equation by -1
16÷1 = 16 1÷ -1= 1
16=r
Rachel spends 1/4 of her money
on chocolate, 1/8 on pizza.
She has $40 remaining.
How much did she have
at the beginning?
Step-by-step explanation:
Let's start by defining our term:
How much she had at the beginning = B
Now let's edit that value like the problem says
B - B/4 - B/8 = 40
Let's multiply everything by 8 to get rid of any denominators
8B - 2B - B = 320
5B = 320
B = 64
Answer:
Rachel had $64 at the beginning.
What is the surface area of this right circular cone?
Answer:
○ B) 624π mm.²
Step-by-step explanation:
[tex]\pi r(r + \sqrt{ {r}^{2} + {h}^{2}}) = S. A. \\ \\ \pi (12)(12 + \sqrt{{12}^{2} + {40}^{2}}) \\ \\ 12\pi(12 + \sqrt{1744}) = 12\pi(12 + 38) = 12\pi(50) = 600\pi \\ \\ 600\pi ≈ 624\pi[/tex]
I am joyous to assist you anytime.
Can someone please help me with this problem, I have been trying to do it for about an hour, but my math always comes out badly... Thanks!
Answer:
800000000000
Step-by-step explanation:
i think
Answer:
the minimum distance from earth to mars is about 54.6 million kilometers. The farthest apart they can be is about 401 million km. the average distance is about 225 million km
Step-by-step explanation: you divide 230,000,00,00 by two and then add 1.5 + 10/11.
What is the circumference of a circle with a radius of 9.2 inches?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
Answer:
What is the circumference of a circle with a radius of 9.2 inches?
Use 3.14 for pi.
Enter your answer as a decimal in the box.
57.776 in.
What is the simplified form of the following expression? Assume x = 0 ^5 sqrt 10x / 3x^3
Answer:
[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]
Step-by-step explanation:
We are given that an expression
[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]
We have to simplify the given expression.
[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]
Multiply numerator and denominator by [tex]81x^2[/tex]
[tex]\sqrt[5]{\frac{10\cdot 81x^3}{243x^5}}[/tex]
After multiplying ,then we get
[tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]
Hence, option d is true.
Answer:[tex]\frac{\sqrt[5]{810x^3}}{3x}[/tex]
Answer:it’s D. On edge
Step-by-step explanation:
What is 336 divided by 7 the long way
Answer: the answer is 48 with a remander of 0 my friend
Step-by-step explanation:
The race speeds for the top eight cars in a 200-mile race are listed below. Use the range rule of thumb
to estimate the standard deviation. Round results to the nearest tenth.
185.9 179.5 189.2 176.7 1758 188.7. 188.3 177.9
Answer:The standard deviation is about 3.6.
Step-by-step explanation:
According to the Range Rule of Thumb : The range is about four times the standard deviation.
i.e. [tex]R\approx4\sigma\Rightarrow\ \sigma\approx\dfrac{R}{4}[/tex] (i)
Given , The race speeds for the top eight cars in a 200-mile race are :
185.9 179.5 189.2 176.7 175.8 188.7. 188.3 177.9
Here , minimum speed = 175.8 and maximum speed = 189.2
Range = maximum speed - minimum speed
i.e. R = 189.2-175.8 =13.4
from (i),
[tex]\sigma\approx\dfrac{13.4}{4}\\\\\Rightarrow\sigma\approx3.6[/tex]
Hence, the standard deviation is about 3.6.
there are 12 people in cafe. half of them are drinking coffee. How many people are drinking coffee?
Is the following relation a function
The relation given yields the following points:
(6, -1), (-1, -2), (4,3), (0,3)
Because every x-value is mapped exactly to one y-value, this relation is a function.
However, because y has two repeated values of 3, it is not one-to-one.
Yes, a function.
In a bank account a paid out expense is called a debit and a deposit is called a credit. Would you use positive or negative integers to represent credits? Debits?
Debits are represented using negative integers, while credits are represented using positive integers.
How are debits and credits represented using integers?In the context of accounting, debits are expressed as negative integers, and credits are denoted with positive integers. This numerical representation helps maintain consistency in recording financial transactions.
Debits indicate the reduction of an account balance, while credits signify an increase. This system ensures accurate bookkeeping and financial reporting.
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(04.05 LC)
The number of protons in an atom is equal to its
atomic number
atomic mass
atomic model
atomic medium
Answer:
atomic number (Z)
thats how they are organized in the periodic table
Answer:
The number of protons in an atom is equal to its atomic number
Step-by-step explanation:
Molly read a few books each week during the summer. How many books did she read over four weeks
To find out how many books Molly read over four weeks during the summer, multiply the number of books she read in one week by four.
Molly read a few books each week during the summer. To calculate how many books she read over four weeks, we can multiply the number of books she read in one week by four.
If she read 'x' books per week, then over four weeks she would have read 4x books.
Therefore, if she read 5 books per week, Molly would have read a total of 20 books over four weeks.
Could anyone please find the quotient? I'm horrible at math.
Answer:
2x-4 is the answer if you multiply 2x-4 by 4x-3 you get 8x squared minus 10x -12
Step-by-step explanation:
Triangle ABC is reflected over the x-axis. What are the coordinates of the image of the vertex A?
A. A’(2, 5)
B. A’(-2, 5)
C. A’(5, -2)
D. A’(2, -5)
Answer:
D. A'(2, -5)
Step-by-step explanation:
Since point A is at (2, 5), and you are reflecting it across the x-axis, you take a look at the y-coordinate. Since it is five above the x-axis, you go five below the x-axis, or just give the OPPOSITE of 5, which is -5.
So, A' is at (2, -5).
I am delighted to assist you anytime.
When point A(2, 5) is reflected over the x-axis, its y-coordinate becomes -5 while the x-coordinate remains the same, resulting in the image point A'(2, -5).
The correct answer is option B.
When a point is reflected over the x-axis, its y-coordinate changes sign while the x-coordinate remains the same.
Let's apply this reflection to point A(2, 5):
Original point A(2, 5) has an x-coordinate of 2 and a y-coordinate of 5. When reflected over the x-axis, the x-coordinate remains 2, but the y-coordinate changes sign to -5. Therefore, the image of point A after the reflection is A'(2, -5).
So, the correct answer is:
D. A’(2, -5)
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What is the solution to this equation?
X- 13 = -4
O
A. x = 17
o
O
B. x= -17
o
OC. x = 9
O
D
. = -9
Answer:
9. This is because you have to add 13 to -4, which gives you positive 9. Hope this helped!
the width of a rectangle is 8 inchs shorter than its length.The perimeter of the rectangle is 18 onchs what are the width and length
Answer:
width= 0.5 per side, 1 in total; length= 8.5 per side, 17 in total
Step-by-step explanation:
because 8.5*2=17, then 8.5-8=0.5. so then 0.5*2=1 and 17+1=18. I CAN EXPLAIN FURTHER
demonstrate on a number line 33.61 and 36.13 which is greater
Answer:the answer is 36.13 because it is greater than 33.61
Step-by-step explanation:
Fernando invested money in a 3–yr CD (certificate of deposit) that returned the equivalent of 3.8% simple interest. He invested $1000 less in a 6–month CD that had a 2% simple interest return. If the total amount of interest from these investments was $424.00, determine how much was invested in each CD.
Answer:
The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600
Step-by-step explanation:
Let
x -----> the amount invested at 3–yr CD
x-$1,000 ----> the amount invested at 6–month CD
we know that
The simple interest formula is equal to
[tex]I=P(rt)[/tex]
where
I is the Final Interest Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
3–yr CD
[tex]t=3\ years\\P=x\\r=0.038[/tex]
substitute in the formula above
[tex]I1=x(0.038*3)[/tex]
[tex]I1=0.114x[/tex]
6–month CD
[tex]t=6/12=0.5\ years\\P=x-1,000\\r=0.02[/tex]
substitute in the formula above
[tex]I2=(1,000-x)(0.02*0.5)[/tex]
[tex]I2=10-0.01x[/tex]
Remember that
the total amount of interest from these investments was $424.00
so
[tex]I1+I2=424[/tex]
substitute and solve for x
[tex]0.114x+10+0.01x=424[/tex]
[tex]0.115x=414[/tex]
[tex]x=\$3,600[/tex]
[tex]x-\$1,000=\$2,600[/tex]
therefore
The amount invested at 3–yr CD was $3,600 and the amount invested at 6–month CD was $2,600
What is the 30th term of the linear sequence below?
-4, -1,2,5,8,...
Answer:
The 30th term is 83
Step-by-step explanation:
we know that
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant called the common difference d
in this problem
[tex]a_1=-4\\a_2=-1\\a_3=2\\a_4=5\\a_5=8[/tex]
so
[tex]a_2-a_1=-1-(-4)=3\\a_3-a_2=-2-(-1)=3\\a_4-a_3=-5-2=3\\a_5-a_4=-8-5=3[/tex]
The common difference d is 3
We can write an Arithmetic Sequence as a rule:
[tex]a_n=a_1+d(n-1)[/tex]
Find out the 30th term
we have
[tex]n=30\\d=3\\a_1=-4[/tex]
substitute
[tex]a_n=-4+(3)(30-1)[/tex]
[tex]a_n=-4+(3)(29)[/tex]
[tex]a_n=83[/tex]
Final answer:
The 30th term of the linear sequence is 83, found using the formula for the nth term of a linear sequence an = a1 + (n - 1)d, with a common difference of 3.
Explanation:
To find the 30th term of the linear sequence given by -4, -1, 2, 5, 8,..., first identify the common difference between consecutive terms. In this sequence, each term increases by 3. So, the common difference (d) is 3.
To find the nth term of a linear sequence, use the formula:
an = a1 + (n - 1)d, where
an is the nth term,
a1 is the first term, and
d is the common difference.
For our sequence:
a1 = -4 (the first term),
d = 3,
n = 30 (since we are finding the 30th term).
Plugging into the formula gives:
a30 = -4 + (30 - 1) × 3
a30 = -4 + 29 × 3
a30 = -4 + 87
a30 = 83
Therefore, the 30th term of the sequence is 83.
Alejandria has four shirts and three pairs of pants. She says that she has seven possible combinations.
Answer: False, there are 12 possible combinations.
Step-by-step explanation:
Each pair of pants matches to each shirt.
She has 3 pairs of pants (1, 2, & 3) and 4 shirts (A, B, C, & D).
Here are all of the combinations:
1A 1B 1C 1D
2A 2B 2C 2D
3A 3B 3C 3D
There are 3 pants × 4 shirts = 12 different combinations
Bryan took a taxi home from the opera. The taxi fare was $2.50 per mile, and he gave the driver a tip of $3. Bryan paid a total of $35.50. The equation 2.50x + 3 = 35.5 can be used to find the distance in miles (x) between the opera house and Bryan's home.
How many miles is it between the opera house and Bryan's home?
Answer:
There are 13 miles between the opera house and Bryan's home.
Step-by-step explanation:
The equation [tex]2.50x+3=35.5[/tex] can be used to find the distance in miles (x) between the opera house and Bryan's home.
We will solve this to get the value of x.
[tex]2.50x+3=35.5[/tex]
=> [tex]2.50x=35.5-3[/tex]
=> [tex]2.50x=32.50[/tex]
we get x = 13
Hence, there are 13 miles between the opera house and Bryan's home.
If Jay ran 1 mile in 10 minutes on Monday, 2 miles in 20 minutes on Tuesday,
and 3 miles in 30 minutes on Wednesday, how many miles do you think he
might run in 40 minutes on Thursday?
Answer:
4 miles
Step-by-step explanation:
4t + 10t
PLEASE HELP ASAP!
Answer:
answer is 14t as 4t +10t =14t
3+g=1/4
Solve each equation.
Answer:
g= - 4/11 in 3+g=1/4
Step-by-step explanation:
Use the site that I will comment . But it won't show you the step to the answer if you each month. I can't submit the answer with the site's name.