Erin is buying floor tile to put in a room that is 10 ft. by 15 ft. She has chosen tiles that are 18 in by 18 in. Assuming that she needs to buy 10% extra to be safe, how many tiles will she need to buy?
Answers
so lets see what area we need. 10 ft by 15 ft = 150 ft^2
now out tile area is 1.5ft by 1.5 ft = 2.25 ft^2
150/2.25 =200/3=66+2/3, we need atleast 66 and 2/3rd of a tile, we must by atleast 10% to be extra safe so
10% of 66+2/3 is 6.6 + 2/30, so we will by 66+2/3 + 6.6+2/30 =73.3333333333, so we will by a total of 73 tiles.
Erin should buy 74 tiles to be safe.
Since Erin is buying floor tile to put in a room that is 10 ft. by 15 ft., and she has chosen tiles that are 18 in by 18 in., assuming that she needs to buy 10% extra to be safe, to determine how many tiles will she need to buy the following calculation must be performed:
The equality between feet and inches must be established, then the area of the room must be calculated, and then the area of each tile. Then, the area of the room must be divided by the area of the tile to know how many should be used.
1 foot = 12 inches 1.1 x ((10 x 12) x (15 x 12)) / (18 x 18) = X 1.1 x (120 x 180) / 324 = X 1.1 x 21,600 / 324 = X 23,760 / 324 = X 73.33 = X
Therefore, Erin should buy 74 tiles to be safe.
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Related Questions
dora reaches her goal of $ 400 in savings.she decide to set a new goal of $900.how many $100 bills will she need to reach $900 in savings? explain your answer using words pictures or numbers
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The sum of the length of l and 15
Answers
The number of students that hear a rumor on a small college campus t days after the rumor starts is modeled by the logistic function R(t)= 3,000 1+Bekt. If 5 students initially heard the rumor and 149 students heard the rumor after 1 day, then how long will it take 2,700 students to hear the rumor?
Answers
The information given:
R(0) = 5
R(1) = 149
will allow us to do this.
First plug in initial point R(0) = 5 and solve for B (e^0 = 1)
[tex] \frac{3000}{1+ B} = 5 [/tex]
[tex]1+B = \frac{3000}{5} = 600 [/tex]
[tex] B = 599 [/tex]
Next plug in R(1) = 149 and solve for k (actually only solve for e^k)
[tex] \frac{3000}{1+599e^k} = 149 [/tex]
[tex]e^k = \frac{3000-149}{(599)(149)} [/tex]
Finally we can solve for t when R(t) = 2700.
Plug in the fraction for e^k since e^(kt) = (e^k)^t
[tex]\frac{3000}{1 +599( \frac{3000-149}{(599)(149)})^t } = 2700[/tex]
[tex]599 (\frac{3000-149}{(599)(149)})^t = \frac{3000}{2700} - 1 = \frac{1}{9}[/tex]
[tex]t = \frac{ln ( \frac{1}{(599)(9)}) }{ln(\frac{3000-149}{(599)(149)})} = 2.495[/tex]
The logistic function is [tex]S[/tex] shaped curve which use to determine the statistical distribution over the energy states of a system.
The time will take for 2,700 student to hear the rumor is 2.495 days.
Given:
The given logistic function is,
[tex]R(t)=\frac{3000}{1+Be^{kt}}[/tex]
As per the question, at initial stage 5 students heard the rumor. At initial stage [tex]t=0[/tex].
Calculate the constant [tex]B[/tex] at initial stage.
[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(0)=\frac{3000}{1+Be^{k\times 0}}\\R(0)=\frac{3000}{1+B}[/tex]
Substitute [tex]R(0)=5[/tex].
[tex]\begin{aligned}5=\frac{3000}{1+B}\\1+B= \frac{3000}{5}\\B=599\\\end[/tex]
As per the question, after 1 day 149 students heard the rumor. After 1 day stage [tex]t=1[/tex].
[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(1)=\frac{3000}{1+Be^{k\times 1}}\\R(1)=\frac{3000}{1+B^k}[/tex]
Substitute [tex]R(1)=149[/tex] and [tex]B=599[/tex].
[tex]\begin{aligned}149=\frac{3000}{1+599e^k}\\e^k=\frac{(3000-1149)}{(599)(149)} \\\end{aligned}[/tex]
Calculate the time take to hear rumor by 2,7000 students.
[tex]\begin {aligned}2700=\frac{3000}{1+599(\frac{3000-149}{599\times 149})^t }\\\frac{3000}{2700}-1 =599(\frac{3000-149}{599\times 149})^t }\\t=\frac{ln(\frac{1}{(599)(9)})}{ln(\frac{3000-149}{599\times 149}) }\\t=2.495\:\rm days\\\end{aligned}[/tex]
Thus, the time will take for 2,700 student to hear the rumor is 2.495 days.
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how many different ways can you make 82 cents using current u.s. currency
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You need non-negative integer solutions to p+5n+10d+25q = 82.
If p = leftovers, then you simply need 5n + 10d + 25q ≤ 80.
So this is the same as n + 2d + 5q ≤ 16
So now you simply have to "crank out" the cases.
Case q=0 [ n + 2d ≤ 16 ]
Case (q=0,d=0) → n = 0 through 16 [17 possibilities]
Case (q=0,d=1) → n = 0 through 14 [15 possibilities]
...
Case (q=0,d=7) → n = 0 through 2 [3 possibilities]
Case (q=0,d=8) → n = 0 [1 possibility]
Total from q=0 case: 1 + 3 + ... + 15 + 17 = 81
Case q=1 [ n + 2d ≤ 11 ]
Case (q=1,d=0) → n = 0 through 11 [12]
Case (q=1,d=1) → n = 0 through 9 [10]
...
Case (q=1,d=5) → n = 0 through 1 [2]
Total from q=1 case: 2 + 4 + ... + 10 + 12 = 42
Case q=2 [ n + 2 ≤ 6 ]
Case (q=2,d=0) → n = 0 through 6 [7]
Case (q=2,d=1) → n = 0 through 4 [5]
Case (q=2,d=2) → n = 0 through 2 [3]
Case (q=2,d=3) → n = 0 [1]
Total from case q=2: 1 + 3 + 5 + 7 = 16
Case q=3 [ n + 2d ≤ 1 ]
Here d must be 0, so there is only the case:
Case (q=3,d=0) → n = 0 through 1 [2]
So the case q=3 only has 2.
Grand total: 2 + 16 + 42 + 81 = 141
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets _____ interest rates to find willing buyers.
Answers
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets greater than interest rates to find willing buyers.
Final answer:
At an interest rate of 2%, below the equilibrium rate of 5%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers and reach the equilibrium.
Explanation:
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers. This situation outlines how the market responds when the interest rate is below the equilibrium level. If the interest rate is below equilibrium, there is an excess demand for financial capital; too many borrowers and not enough lenders at this low rate. To attract more lenders (sellers of financial assets), the interest rate would need to be increased. Conversely, when the interest rate is above the equilibrium, there is an excess supply, meaning there are more suppliers of loans than there are borrowers. Sellers in this scenario lower interest rates to attract more borrowers, bringing the market back to equilibrium.
This concept is parallel to the example where, at an interest rate of 21%, the supplied funds increase greatly while the demand falls sharply, leading to excess supply. Suppliers of financial capital, such as credit card companies, will then reduce their rates to encourage more borrowing, pushing the interest rate back toward the equilibrium. In the case of a government borrowing increase, if it leads to a higher demand for financial capital, this would cause the demand curve to shift to the right and result in a higher interest rate, potentially crowding out private investment.
Write a number from 20 to 50 that has both tens and ones
Answers
Answer:
45
Step-by-step explanation:
We know that,
If we have the numbers of the form xyz.
This gives that, x is placed at the hundredth place, y is placed at the tens place and z is located at ones place.
Since, we need a number between 20 and 50 having both tens and ones place.
We can take any number from 20 to 50.
For e.g. Let us take 45.
In 45, 4 is placed at the tens place and 5 is placed at the ones place.
Hence, 45 is the number between 20 to 50 having both tens and ones place.
Suppose a culture of bacteria starts with 8000 bacteria. After one hour, the count is 9000. Find an exponential equation that models the number of bacteria in hours. Keep at least 4 decimal places in your formula for rounded values. Find the doubling time of the bacteria. Round the doubling time to the nearest 0.01 hours.
Answers
1) 1.125^t = 2
2) log_1.125(2) = t
3) t = 5.8849491924
Rounding the time to the nearest 0.01 hours would give you 5.88 hours.
The exponential equation that models the number of bacteria in hours is N = 8000 * (1 + 0.125)^t. The doubling time of the bacteria is 5.55 hours.
Explanation:To find an exponential equation that models the number of bacteria in hours, we can use the formula: N = N0 * (1 + r)^t.
Where:
N is the final count of bacteria (9000)N0 is the initial count of bacteria (8000)r is the growth rate (unknown)t is the time in hours (1)Plugging in the values, we have:
9000 = 8000 * (1 + r)^1
Dividing both sides by 8000, we get:
1.125 = 1 + r
Subtracting 1 from both sides, we find:
0.125 = r
Therefore, the exponential equation that models the number of bacteria in hours is: N = 8000 * (1 + 0.125)^t.
To find the doubling time of the bacteria, we can use the formula: t = log(2)/log(1 + r).
Plugging in the value of r (0.125), we have:
t = log(2)/log(1 + 0.125)
Using a calculator, we find that t is approximately 5.5452 hours. Rounded to the nearest 0.01 hours, the doubling time of the bacteria is 5.55 hours.
A building in a city has a rectangular base. The length of the base measures 70ft less than twice the width. The perimeter of the base is 910 ft. What are the dimensions of the base?
Answers
width=x
perimeter of a rectangle=2(base)+2(width)
We can suggest the next equation:
2(2x-70)+2x=910
4x-140+2x=910
6x=910+140
6x=1050
x=1050/6
x=175
base: 2x-70=2(175)-70=350-70=280
Answer,: the length of the base would be 280 ft.
insted of telling carmen her age ,sora gave this clue:my age is one-tenth of one-tenth of one-tenth of 3,000.
Answers
A=3+10
A=13
A department store holds a year-end clearance sale that includes a 14.5% discount on cosmetics. Find the sales price of the bottle of perfume if it's original price was 56.69
Answers
56.69 - 0.145(56.69)
= 56.69 - 8.22
= 48.47
How to calculate discount and sale price?Find the original price (for example $90 )Get the discount percentage (for example 20% )Calculate the savings: 20% of $90 = $18.Subtract the savings from the original price to get the sale price: $90 - $18 = $72.the formula for discount price
Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.
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three men and four women stand in line at a checkout counter at a store. in how many ways can they stand in the line if we consider only their gender
Answers
there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.
To determine the number of ways the three men and four women can stand in line at the checkout counter if we only consider their gender, we can use the concept of permutations.
There are 3 men and 4 women, so there are a total of (3 + 4 = 7) people in line.
We need to arrange these 7 people in a line. Since the order matters, we use permutations.
The number of ways to arrange (n) objects is given by (n) (n factorial).
So, the number of ways the 7 people can stand in line is [tex]\(7\).[/tex]
[tex]\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \][/tex]
Therefore, there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.
In our solar system, 666 of the 888 planets have moons. What percentage of the planets have moons?
Answers
Answer:
75% of the planets have moons
Step-by-step explanation:
In order to calculate this you just have to do a simple rule of three, in which you will use 888 as the 100 percent and you want to discover what percentage of that does 666 represents:
[tex]\frac{888}{100} \frac{666}{x} \\x=\frac{666*100}{888}\\ x=75\\[/tex]
So you have that 666 is the 75% of 888, that means that 75% of the planets have moons.
A 200 centimeter-long wire is cut into three pieces. The second piece is 3 times as long as the first. The third piece is 2 times as long as the second. How long is each piece?
Answers
x + y + z = 200 since the sum of the lengths equals the total length of the wire
y = 3x since piece two is 3 times longer than piece one
z = 2y = (2)(3)(x) = 6x since piece three is 2 times longer than piece two
Now we have (x,y,z) in terms of x alone, so we can substitute into the first equation:
x + 3x + 6x = 10x = 200 which means x = 20.
Then, substitute this value into all the other equations.
y = 3(20) = 60
z = 6(20) = 120
This can be checked by summing them up like this: 20 + 60 + 120 = 200.
The lengths of the three wire pieces are 20 cm for the first piece, 60 cm for the second piece, and 120 cm for the third piece.
Explanation:A wire that is 200 cm long is cut into three pieces.
We are told that the second piece is 3 times as long as the first piece and the third piece is 2 times as long as the second piece.
Let's denote the first piece's length as x centimeters.
According to the problem, the second piece will then be 3x centimeters long, and the third piece will be 2 * 3x = 6x centimeters long.
To find the length of each piece, we need to set up the following equation based on the total length of the wire:
x + 3x + 6x = 200
Combining terms, we have:
10x = 200
Dividing both sides by 10, we find:
x = 20
Therefore, the first piece is 20 cm long, the second piece is 3 * 20 cm = 60 cm long, and the third piece is 6 * 20 cm = 120 cm long.
How to change 2/3 to eighteenths
Answers
What is the GCF of 3 and 18
3: 1,3
18: 1,2,3,6,9,18
GCF-3
Therefore, 2/3 = 12/18 because 3 × 6= 18
what you do to the denominator you have to do the numerator
so 2 × 6= 12
The eighteenths of 2/3 is 12/18.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
let,
2/3 = n/18
What is the GCF of 3 and 18
3: 1,3
18: 1,2,3,6,9,18
GCF-3
Therefore, 2/3 = 12/18
because 3 × 6= 18
what you do to the denominator you have to do the numerator
so 2 × 6= 12.
hence, eighteenths of 2/3 is 12/18.
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A cupcake recipe asks for 3/4 of a cup of butter. Rob wants to make 1/3 of the original recipe. How many cups of butter will Rob need?
Answers
Find the value of I given that p=300,r=0.14,andt=2
Answers
P = 300
R = 0.14
T = 2
now it is just a matter of subbing and doing the math
I = (300)(0.14)(2)
I = 84 <==
From a marginal analysis perspective, what is the inventory carry cost for Andrews if the company carries one additional unit of Able in inventory at the end? Select: 1Save Answer $9.98 $1.20 $1.92 $3.85
Answers
49 percent of all people who buy running shoes don't run at all. Assuming 340,000 people buy running shoes, how many will use them to run in?
Answers
A brace for a shelf has the shape of a right triangle. Its hypotenuse is 10 inches long and the two legs are equal in length. How long are the legs of the triangle?
Answers
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2 Hope this helps!!
Suppose that the mean GRE score for the USA is 500 and the standard deviation is 75. Use the Empirical Rule (also called the 68-95-99.7 Rule) to determine the percentage of students likely to get a score between 350 and 650? What percentage of students will get a score above 500?
Answers
Find how many std deviations 350 and 650 are from the mean of 500.
350 - 500 = -150 ----> -150/75 = -2
650 - 500 = 150 ----> 150/75 = 2
Each are 2 std deviations from the mean. This means that about 95% of students are between 350 and 650.
By definition, 50% will be above the mean and below the mean.
Therefore 50% of the students will get a score above 500.
Using the Empirical Rule, it is determined that 95% of students are likely to get a GRE score between 350 and 650, and 50% of students will get a score above 500.
According to the Empirical Rule (also known as the 68-95-99.7 Rule), about 95% of the values in a data set with a normal distribution will fall within two standard deviations of the mean. In this case, the mean GRE score is 500 and the standard deviation is 75. Using this rule, we can determine that 95% of the students would likely score between 500 - (2 imes 75) and 500 + (2 imes 75), equating to scores between 350 and 650.
Regarding the percentage of students that will get a score above 500, the distribution is symmetric around the mean in a normal distribution. Since the mean is 500, 50% of the values will lie above the mean and 50% will lie below. Therefore, 50% of students are expected to score above 500.
a printer charges a fixed setup cost plus $0.40 for every 40 copies. if 320 copies cost $43.20 how much will it cost to print 1200 copies
Answers
The cost to print 1200 copies is $52.00.
The given data tells us that 320 copies cost $43.20. Each set of 40 copies costs $0.40, so 320 copies are 8 sets (320/40). The variable cost for 320 copies is 8 × $0.40 = $3.20.
We can then determine the fixed setup cost by subtracting the variable cost from the total cost for 320 copies: $43.20 - $3.20 = $40.00.
The total cost C for printing x copies can be expressed as:
C = fixed setup cost + variable cost per set × (x/40)
So the total cost for 1200 copies is:
C = $40.00 + $0.40 × (1200/40)
Calculating this, we get:
C = $40.00 + $0.40 × 30 = $40.00 + $12.00 = $52.00
Therefore, the cost to print 1200 copies is $52.00.
two angles are supplementary. their difference is 22°. find the angles
Answers
x+y = 180 (supplementary)
x - y = 22(given) so x = 22 + y
22+ y + y = 180
2y + 22 = 180
2y =180 -22
2y = 158
y = 158/2
y = 79
x = 22 + y = 22 + 79 = 101
answer:Two angles are supplementary angles are 101 and 79
A person randomly selects one of six envelopes. Each envelope contains a check that the person gets to keep. Determine the person's expectation if three envelopes contain a $533 check and three envelopes contain a $1039 check.
Answers
envelopes- $1039 × 3 = $3117
so you add $1599 + $3117= $4716.00
Answer with explanation:
Number of Envelopes possessed by the person = 6
Probability of selecting an Envelope is equal to [tex]/frac{1}{6}[/tex].
It is given that,three envelopes contains $ 533 check and another 3 Envelope contain $ 1039 check.We can consider that any of three checks contain $ 533 and another three $ 1089.
Expectation
[tex]E(x)=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}+x_{4}p_{4}+x_{5}p_{5}+x_{6}p_{6}\\\\\frac{1}{6} \times [533+533+533+1039+1039+1039]\\\\=\frac{1}{6} \times [4716]\\\\=786[\tex]
E(x)=786
Certain gases in the atmosphere trap heat on Earth.
What is the name of this phenomenon?
A.
the greenhouse effect
B.
global warming
C.
glacial melting
D.
cooling period
this is science not mathematics
Answers
glacial melting<<<<<<<<<<<<<<<
Answer:
the answer is a
Step-by-step explanation:
Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible
Answers
Write the given expression in terms of x and y only.
sin(sin−1(x) + cos−1(y))
Answers
_______________
Write the expression below in terms of x and y only:
(I'm going to call it "E")
[tex]\mathsf{E=sin\!\left[sin^{-1}(x)+cos^{-1}(y)\right]\qquad\quad(i)}[/tex]
Let
[tex]\begin{array}{lcl} \mathsf{\alpha=sin^{-1}(x)}&\qquad&\mathsf{then~-\,\dfrac{\pi}{2}\le \alpha\le \dfrac{\pi}{2}}\\\\\\ \mathsf{\beta=cos^{-1}(x)}&\qquad&\mathsf{then~0\le \beta\le \pi.} \end{array}[/tex]
so the expression becomes
[tex]\mathsf{E=sin(\alpha+\beta)}\\\\ \mathsf{E=sin\,\alpha\,cos\,\beta+sin\,\beta\,cos\,\alpha\qquad\quad(ii)}[/tex]
• Finding [tex]\mathsf{sin\,\alpha:}[/tex]
[tex]\mathsf{sin\,\alpha=sin\!\left[sin^{-1}(x)\right]}\\\\ \mathsf{sin\,\alpha=x\qquad\quad\checkmark}[/tex]
• Finding [tex]\mathsf{cos\,\alpha:}[/tex]
[tex]\mathsf{sin^2\,\alpha=x^2}\\\\ \mathsf{1-cos^2\,\alpha=x^2}\\\\ \mathsf{cos^2\,\alpha=1-x^2}\\\\ \mathsf{cos\,\alpha=\sqrt{1-x^2}\qquad\quad\checkmark}[/tex]
because [tex]\mathsf{cos\,\alpha}[/tex] is positive for [tex]\mathsf{\alpha\in \left[-\frac{\pi}{2},\,\frac{\pi}{2}\right].}[/tex]
• Finding [tex]\mathsf{cos\,\beta:}[/tex]
[tex]\mathsf{cos\,\beta=cos\!\left[cos^{-1}(y)\right]}\\\\ \mathsf{cos\,\beta=y\qquad\quad\checkmark}[/tex]
• Finding [tex]\mathsf{sin\,\beta:}[/tex]
[tex]\mathsf{cos^2\,\alpha=y^2}\\\\ \mathsf{1-sin^2\,\beta=y^2}\\\\ \mathsf{sin^2\,\beta=1-y^2}\\\\ \mathsf{sin\,\beta=\sqrt{1-y^2}\qquad\quad\checkmark}[/tex]
because [tex]\mathsf{sin\,\beta}[/tex] is positive for [tex]\mathsf{\beta\in [0,\,\pi].}[/tex]
Finally, you get
[tex]\mathsf{E=x\cdot y +\sqrt{1-y^2}\cdot \sqrt{1-x^2}}\\\\\\ \therefore~~\mathsf{sin\!\left[sin^{-1}(x)+cos^{-1}(y)\right]=x\cdot y +\sqrt{1-y^2}\cdot \sqrt{1-x^2}\qquad\quad\checkmark}[/tex]
I hope this helps. =)
Tags: inverse trigonometric trig function sine cosine sin cos arcsin arccos sum angles trigonometry
the kilo-prefix in the metric system means __________________ units
Answers
Crafty grandma Edith set her family down during Thanksgiving and told them they couldn't have any pet can pass until they worked out this puzzle are six-year-old granddaughter was the first to solve it can you work out what 9183 equals
8809=6 3590=2
7111=0 6855=3
9881=5 1012=1
6660=4 5731=0
5531=0 9191=2
2516=1 9193=?
Answers
You 495 miles from home and you are driving toward home at an average of 45mph. How long will it take to drive home if you maintain the same speed? (Hint: When you reach home, the x-value is zero.)
Answers
it will take 11 hours
Answer:
f(x)=45x
Step-by-step explanation:
if the home is 495 miles away, 11 hours would take to drive home.
f(11)=45X11=495
whats between 0 and [tex] \pi /2[/tex]