Answer:
5,470,000
do the multiplication first and then add
When adding numbers in scientific notation, align the exponents and then add the coefficients. The sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.
Explanation:To add these two numbers in scientific notation, we need to first align the exponents. In this case, we can rewrite the first number as 0.12 x 10^6 and the second number as 5.35 x 10^6. Now, we can add the numbers together:
0.12 x 10^6 + 5.35 x 10^6 = 5.47 x 10^6. Thus, the sum of 1.2 x 10^5 and 5.35 x 10^6 is 5.47 x 10^6.
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The radius of Earth is 6378.1 km.
How long is the metal ring?
Answer:
12 756.2 kilometers
Step-by-step explanation:
12 756.2 kilometers
A metallurgist has one alloy containing 34% copper another containing 48% copper. How many pounds of each alloy must he use to make 46 pounds of the third alloy containing 37% copper
Answer:
36.14 pounds of 34% copper alloy and 9.86 pounds of 48% copper alloyStep-by-step explanation:
First alloy contains 34% copper and the second alloy contains 48% alloy.
We wish to make 46 pounds of a third alloy containing 37% copper.
Let the weight of first alloy used be [tex]x[/tex] in pounds and the weight of second alloy used be [tex]y[/tex] in pounds.
Total weight = [tex]46\text{ }pounds=x+y[/tex] [tex]-(i)[/tex]
Total weight of copper = [tex]37\%\text{ of 46 pounds = }34\%\text{ of }x\text{ pounds + }48\%\text{ of }y\text{ pounds }[/tex]
[tex]\dfrac{37\times 46}{100}=\dfrac{34x}{100}+\dfrac{48y}{100}\\\\ 34x+48y=1702[/tex] [tex]-(ii)[/tex]
Subtracting 34 times first equation from second equation,
[tex]34x+48y-34x-34y=1702-34\times46\\14y=138\\y=9.857\text{ }pounds \\x=36.143\text{ }pounds[/tex]
∴ 36.14 pounds of first alloy and 9.86 pounds of second alloy were used.
Final answer:
The metallurgist must use around 36.14 pounds of the 34% copper alloy and approximately 9.86 pounds of the 48% copper alloy to make 46 pounds of a 37% copper alloy.
Explanation:
To solve the problem involving an alloy containing copper, we can use a system of equations based on the percentages provided and the total weight required for the new alloy.
Let's denote x as the number of pounds of the 34% copper alloy, and y as the number of pounds of the 48% copper alloy. We are aiming to create 46 pounds of a 37% copper alloy.
The first equation represents the total weight of the mixture:
x + y = 46
The second equation represents the total amount of copper in the new alloy:
0.34x + 0.48y = 0.37 * 46
Solving this system of equations, we get:
Multiply the second equation by 100 to remove decimals: 34x + 48y = 37 * 46
Substitute y from the first equation into the second: 34x + 48(46 - x) = 37 * 46
Simplify and solve for x: 34x + 2208 - 48x = 1702
This yields -14x = -506, so x = 506 / 14 = 36.14
Using x to solve for y gives us y = 46 - 36.14 = 9.86
Therefore, the metallurgist must use around 36.14 pounds of the 34% copper alloy and approximately 9.86 pounds of the 48% copper alloy to make 46 pounds of the third alloy containing 37% copper.
A textile factory in the United States plays 300 workers a total of $9 million each year to produce 4.5 million shirts. A foreign factory employs 225 workers at a total cost of $1,050,000 to produce 2,500,00 shirts. How do the labor costs per shirt of the American and foreign factory compare
Answer:
The labor cost per shirt of the American factory is 0.36 times the labor cost per shirt of the foreign company.
Step-by-step explanation:
A textile factory in the United States plays 300 workers a total of $9 million each year to produce 4.5 million shirts.
Therefore, the labor cost per shirt will be
[tex]\frac{9 \times 10^{6}}{300 \times 4.5 \times 10^{6}} = 0.0067[/tex]
Again, a foreign factory employs 225 workers at a total cost of $1,050,000 to produce 2,500,00 shirts.
Therefore, the labor cost per shirt will be
[tex]\frac{1050000}{250000 \times 225} = 0.01867[/tex]
Therefore, the labor cost per shirt of the American factory is 0.36 times (Approximate) the labor cost per shirt of the foreign company. (Answer)
How do I find the coordinates of the point P that lies along the directed segment from C(-3,-2) to D(6,1) and partitions the segment in the ratio 2 to 1?
[tex]\bf \textit{internal division of a line segment using ratios} \\\\\\ C(-3,-2)\qquad D(6,1)\qquad \qquad \stackrel{\textit{ratio from C to D}}{2:1} \\\\\\ \cfrac{C\underline{P}}{\underline{P} D} = \cfrac{2}{1}\implies \cfrac{C}{D} = \cfrac{2}{1}\implies 1C=2D\implies 1(-3,-2)=2(6,1)\\\\[-0.35em] ~\dotfill\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf P=\left(\cfrac{(1\cdot -3)+(2\cdot 6)}{2+1}\quad ,\quad \cfrac{(1\cdot -2)+(2\cdot 1)}{2+1}\right) \\\\\\ P=\left( \cfrac{-3+12}{3}~~,~~\cfrac{-2+2}{3} \right)\implies P=\left( \cfrac{9}{3}~~,~~\cfrac{0}{3} \right)\implies P=(3~~,~~0)[/tex]
Find the area and circumference of a circle with radius 2 cm use 3.14 for pie do not round answers
Answer:
The area is 12.56, and the circumference is 12.56.
Step-by-step explanation:
For the area,
We need to use the formula A=3.14*radius*radius
So we plug it in, and we get 3.14*2*2, which is 12.56 centimeters squared.
For circumference, we need to do,
C = 3.14*diameter
To find the diameter we need to do 2 (radius) x 2 which is 4
Plugging it in that would be 3.14 * 4 which is 12.56
So, in this case, the area is 12.56, and the circumference is also 12.56.
The area of a circle with a radius of 2 cm is 12.56 cm², and the circumference is 12.56 cm, using 3.14 for pi.
Explanation:To find the area and circumference of a circle with a radius of 2 cm, we can use the formulas A = πr² for the area and C = 2πr for the circumference, where π (pi) is approximately 3.14.
Area of the Circle
The area of the circle is calculated using the formula A = πr². Plugging in the radius:
A = 3.14 × (2 cm)²
A = 3.14 × 4 cm²
A = 12.56 cm²
Circumference of the Circle
The circumference of the circle is calculated using the formula C = 2πr. Plugging in the radius:
C = 2 × 3.14 × 2 cm
C = 12.56 cm
I need help on these three.
Step-by-step explanation:
I think it 1,180 yeah I think it is
Data scored 42 points in 3 games. How many points would you expect him to make in an 11 game season?
Answer:
He would score 154 points because he averages 14 points per game and 11 times 14 is 154
Data scored 42 points in 3 games, then points scored in 11 games will be equal to 154 points.
What is an arithmetic operation?The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.
As per information obtained from the question,
Let x points will be obtained in 11 games.
Data scored,
42 points = 3 games
Points earned in 1 game = 42/3 = 14
Then,
Points obtained in 11 games = 14 × 11
x = 154 points.
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Which does not show a direct variation between x and y ?
A) y = 5x
B) y = 6/x
C) y - 0.7x
D) y = x/9
Answer:
B
Step-by-step explanation:
in B, the expression can be writting in variation form as
y∝1/x
this indicate an inverse variation
Answer:
B) y=6/x
Step-by-step explanation:
I took the test.
meghan wants to go to prem. the dress she wants cost her 78.99, the shoes are 32.50 the tickets are $25 and the dinner will be $50 .meghan babysitdms and has put $52 in savings so far she earns $12/hour babysitting meghan would like to have some money left over in her savings after she pays for everything
Answer:
Meghan should babysit for 12 hoursStep-by-step explanation:
Meghan is soon going to have to spend $78.99 on a dress, $32.50 on shoes, $25 for the ticket and $50 for dinner.
Meghan already has $52 from her savings to spend. She earns money from babysitting at $12 each hour.
Let the number of hours Meghan babysits be denoted by [tex]x[/tex].
From [tex]x[/tex] hours of babysitting, Meghan earns $([tex]x\times12[/tex]).
So, her total earnings sum up to [tex]12x+52[/tex]. This should be greater than total spendings.
[tex]12x+52\geq 78.99+32.50+25+50\\12x\geq 134.49\\x\geq 11.208[/tex]
So, Meghan must work for 12 hours so she has something left after spendings.
∴ Meghan must babysit for 12 hours.
If 4x < 24, then x < 6
Answer:
x is less than 6 so that is correct because 24 divided by 4 is 6
When do you need to rationalize the denominator? My physics teacher says that you don't have to if you are isolating a variable.
Answer:
When the denominator is an irrational number in order to make the denominator a rational number we rationalize the denominator.
Step-by-step explanation:
For example,
[tex]\frac{1}{1+\sqrt{2} }[/tex] (here the denominator is an irrational number)
Multiply the numerator and denominator by [tex]1-\sqrt{2}[/tex]
We get [tex]\frac{1-\sqrt{2} }{(1+\sqrt{2})(1-\sqrt{2}) }[/tex]
Here (1+\sqrt{2})(1-\sqrt{2}) = -1
Thus we get [tex]\sqrt{2} -1[/tex]
Here the denominator has become a rational number.
When we are isolating a variable we are only taking the required variables to one side thus it doesn't require rationalization.
[tex]a = \frac{x}{1+\sqrt{2} }[/tex]
Then we can say,
[tex]x = a(1+\sqrt{2})[/tex]
No rationalisation required
To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest. Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest. The total interest earned on both accounts for 1 year was $676. How much money was deposited in the CD?
$
The amount deposited in CD is $660
Solution:Given that , To save for the purchase of a new car, a deposit was made into an account that earns 8% annual simple interest.
Let the amount deposited in new car be $ n
Another deposit, $1700 less than the first deposit, was placed in a certificate of deposit (CD) earning 12% annual simple interest.
Then, amount deposited in CD will be $ (n – 1700)
The total interest earned on both accounts for 1 year was $676
The simple interest is given as:
[tex]\text { Simple interest }=\frac{\text { principal } \times \text {rate} \times \text {time}}{100}[/tex]
Simple interest for purchase of new car:
[tex]\text { S. } \mathrm{I}=\frac{n \times 8 \times 1}{100}=\frac{8 n}{100}[/tex]
Simple interest for CD:
[tex]\text { S.I } =\frac{(n-1700) \times 12 \times 1}{100}=\frac{12(n-1700)}{100}[/tex]
Now, given that S.I for new car + S.I for CD = 676
[tex]\begin{array}{l}{\frac{8 n}{100}+\frac{12(n-1700)}{100}=676} \\\\ {\frac{8 n+12 n-12 \times 1700}{100}=676}\end{array}[/tex]
20n = 67600 – 20400
n = 2360
So money deposited in CD = n - 1700 = 2360 – 1700 = 660
Hence, the CD deposit amount is $660
To find the amount deposited in the CD, set up an equation using the given information. Solve for x to find the amount of the first deposit. Subtract $1700 from the first deposit to find the amount deposited in the CD.
Explanation:To find the amount of money deposited in the CD, we can set up an equation using the given information.
Let the amount of the first deposit be x.
The second deposit is $1700 less than the first deposit, so it is x - $1700.
Using the formula for simple interest, the interest earned on the first deposit is x * 0.08.
The interest earned on the second deposit is (x - $1700) * 0.12.
According to the given information, the total interest earned is $676. Therefore, we can set up the equation: x * 0.08 + (x - $1700) * 0.12 = $676.
Simplifying and solving for x:
0.08x + 0.12x - $204 = $676
0.20x - $204 = $676
0.20x = $880
x = $4400
Therefore, the amount of money deposited in the CD is $4400 - $1700 = $2700.
walter's salary this year is $23,400. If this is $1,700 more than he made last year, what was his salary last year?
Answer:
21700
Step-by-step explanation:
23400 - 1700 = 21700
Walter's salary last year can be found by subtracting the increase from his current salary. After calculating, we find that Walter's salary last year was $21,700.
Explanation:To calculate Walter's salary last year, we need to subtract the amount his salary increased this year from his current salary. Walter's current salary is $23,400, and it has increased by $1,700 from last year. Thus, his salary last year was:
$23,400 (current salary) - $1,700 (increase) = $21,700
Therefore, Walter's salary last year was $21,700.
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Richard bought six pounds of sliced ham for $2.79 per pound. How much did he spend?
$8.79
$16.74
$12.24
$16.24
Answer:
$16.74
Step-by-step explanation:
so for every pound is 2.79 so just so
6 times 2.79
if the area of a parallelogram is 86cm and the height is 12cm write an equation that relates the height,base and area of the parallelogram
Answer:
The relation to find base is, [tex]base=\frac{area\ of\ the \ parallelogram}{height}=\frac{86}{12}=7.16\ cm[/tex]
Step-by-step explanation:
Given
Area of the parallelogram [tex]=86\ cm^2[/tex]
Height of the parallelogram [tex]=12\ cm[/tex]
We know that the area of the parallelogram [tex]=base\times height[/tex]
So
To find base we have to divide the height on both sides of the equation.
[tex]base=\frac{area\ of\ the \ parallelogram}{height}[/tex]
Plugging the values.
[tex]base=\frac{86}{12} =7.1\ cm[/tex]
So the base in terms of area of the parallelogram and its height is [tex]b=\frac{area}{height} =\frac{86}{12}=7.16\ cm[/tex]
5/6 is equivalent to a percent that is larger than 100%.
True or False
13 pts.
I think it's false.... 5/6 is 83.33% as a percent so I don't think it's true.
6/6 ......... 100%
5/6 ..............x%
x = 5/6*100/6/6 = 500/6 = 83,(3)%
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality
_____<√74 <____
Answer:
8<74 square root<9
Step-by-step explanation:
The first thing we have to do is to find the lowest number that can be squared to 74. 1,4,9,16,25,36,49,64,81,100.
As we see, 64 is the lowest closest number to 74 and the square root of 64 is 8. So right now, is 8<square root of 74<___.
Now, we have to find the highest number closest to 74. As we look back at our square roots, 81 is the closest number to 74 in the square roots and the square root is 9 and voila. 8<sqrt74<9
The inequality is -
8 < √74 < 9.
We have the following inequality -
_____<√74 <____.
We have to fill in the blanks with two consecutive integers to complete the above inequality.
What is inequality ?In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question -
Let A = √74
Then - A² = 74
The nearest integers, square of between which A² lies is between 8 and 9. So -
8² < A² < 9²
Therefore, the two consecutive integers will be - 8 and 9.
Hence, the inequality is -
8 < √74 < 9
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Describe the pattern 0.13, 0.65, 3.25, 16.25
Answer:
multiply by 5
Step-by-step explanation:
Note the ratio between consecutive terms is constant, that is
[tex]\frac{0.65}{0.13}[/tex] = [tex]\frac{3.25}{0.65}[/tex] = [tex]\frac{16.25}{3.25}[/tex] = 5
Thus the pattern is multiply by 5
Answer:Multiply by 5
Step-by-step explanation:
6 people voted, and it ended up 84% to 16%. How many people voted for each option?
Answer:
see the explanation
Step-by-step explanation:
we know that
To find out how many people voted for each option multiply the percentage in decimal form of each option by the total number of people
so
[tex]84\%=84/100=0.84[/tex] ---> [tex]0.84(6)=5.04=5\ people[/tex]
[tex]16\%=16/100=0.16[/tex] ---> [tex]0.16(6)=0.96=1\ people[/tex]
0.812
In to a fraction
Answer:812/1000
Step-by-step explanation:
What is the eighth term of the geometric sequence whose first three terms are 3, 6, and
12?
Answer:
The answer is 384.
Step-by-step explanation:
It starts at 3 going up by three to 6 then from there it adds 6 equaling 12 then so forth so it would be 3, 6, 12, 24, 48, 96, 192, 384
Long-Term Mehlum
The boiling point of water T
by the function T(a) = -0
water T (measured in degrees), at altitude a (measured in feet) is mod
-0.0018a + 212. In terms of altitude and temperature, which
nt describes the meaning of the slope?
A. The boiling point decreases by
B. The boiling point decrea
C. The boiling point decreases by 10
D. The boiling point decrea:
decreases by 18 degrees as the altitude Increases by 1,000 feet.
reases by 1.8 degrees as the altitude increases by 1,000 feet.
decreases by 18 degrees as the altitude Increases by 1,000 feet.
t decreases by 1.8 degrees as the altitude increases by 1,000 feet.
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
EDGE 2021
Through: (-1,-5), slope=3
Answer:
y + 5 = 3(x + 1) → point-slope form
y = 3x - 2 → slope-intercept form
3x - y = 2 → standard form
Step-by-step explanation:
The point-slope form of an equation of a line:
y - y₁ = m(x - x₁)
m - a slope
(x₁, y₁) - a point on a line
We have
m = 3, (-1, -5) → x₁ = -1, y₁ = -5
Substitute:
y - (-5) = 3(x - (-1))
y + 5 = 3(x + 1) → point-slope form
convert to the slope-intercept form y = mx + b:
y + 5 = 3(x + 1) use the distributive property: a(b + c) = ab + ac
y + 5 = 3x + 3 subtract 5 from both sides
y = 3x - 2 → slope-intercept form
convert to the standard form Ax + By = C:
y = 3x - 2 subtract 3x from both sides
-3x + y = -2 change the signs
3x - y = 2 → standard form
It takes 60 minutes to make 2000 copies on an old copy machine. The newer copier works with the old copier to create 2000 sheets and it only takes 15 minutes. How many minutes would the new copier need to create the 2000 copies on its own?
The new copier can create 2000 copies in 20 minutes.
Step-by-step explanation:
Given,
It takes 60 minutes to make 2000 copies by old printer and 15 minutes to made x number of copies, therefore, using proportion
[tex]60:2000::15:x[/tex]
Product of mean = Product of extreme
[tex]2000*15=60*x\\30000=60x\\60x=30000[/tex]
Dividing both sides by 60
[tex]\frac{60x}{60}=\frac{30000}{60}\\x=500[/tex]
As the new copier is working with old copier, therefore,
Copies made by new printer = 2000 - 500 = 1500
New copier can make 1500 copies in 15 minutes and 2000 copies in x minutes, using proportion
[tex]1500:15::2000:x\\1500*x=15*2000\\1500x=30000[/tex]
Dividing both sides by 1500;
[tex]\frac{1500x}{1500}=\frac{30000}{1500}\\x=20[/tex]
The new copier can create 2000 copies in 20 minutes.
Keywords: ratio, proportion
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HELP I NEED YOUR HELP MATH ONE PROBLEM 10 POINTS HELP
Answer:
The Value of x is 40.
Step-by-step explanation:
Given:
∠SRT ≅ ∠STR
∠SRT = 20
m∠SRT = 4x
To find: Value of x
Solution:
From the given data,
m ∠SRT = 20
Also ∠SRT ≅ ∠STR
Hence from congruence and equality property we can say that;
m∠STR= 20
m∠STU= 4x
Now by straight angle property which states that sum of two angles which are created by a straight line is always 180.
Hence,
∠STR +∠STU =180
Now Substituting the given values we get;
[tex]20+4x=180\\4x=180-20\\4x=160\\\\x=\frac{160}{4} =40[/tex]
Hence m∠STU = 4x =4 ×40 = 160°
Hence the value of x = 40.
Cousin Hector drove 1,851 miles to the reunion. He lives in Mexico and drove 747 miles through that country to the United States border. How many miles did he drive in the United States?
Answer:
1104 miles
Step-by-step explanation:
Given
Hector drove 1851 miles totallyHector drove 747 miles from mexico till US borderLet x be the miles he drove in the United States
⇒
The total distance traveled by him= distance traveled in mexico + distance traveled in US
1851=747+x
x=1104 miles
⇒distance traveled in US= 1104 miles
Kiera is buying the items shown at the right
for her kitchen. Will $35 be enough to purchase all three items?
Explain your reasoning.
mixing bowl
14.95
spatula
8.49
measuring cups
10.75
Answer:
Yes
Step-by-step explanation:
Total Price of all 3 items - $34.19
35 > 34.19
Yes, Kiera will have enough to purchase all three items.
No, $35 will not be enough to purchase all three items.
To determine if $35 is enough to purchase all three items, we need to calculate the total cost of the items and compare it to the amount of money Kiera has.
The cost of each item is as follows:
- Mixing bowl: $14.95
- Spatula: $8.49
- Measuring cups: $10.75
Now, let's add up the costs of these items to find the total cost:
Total cost = Cost of mixing bowl + Cost of spatula + Cost of measuring cups
Total cost = $14.95 + $8.49 + $10.75
To make the calculation easier, we can round each price to the nearest whole number:
- Mixing bowl: $14.95 ≈ $15.00
- Spatula: $8.49 ≈ $8.50
- Measuring cups: $10.75 ≈ $10.75 (already a whole number)
Now, let's calculate the total cost with these rounded numbers:
Total cost ≈ $15.00 + $8.50 + $10.75
Total cost ≈ $34.25
However, even with rounding, the total cost is $34.25, which is still less than $35. Therefore, we need to calculate the exact total cost without rounding:
Total cost = $14.95 + $8.49 + $10.75
Total cost = $34.19
Since the total cost of $34.19 is less than $35, it appears that Kiera has enough money to purchase all three items. However, we must also consider sales tax, which is not included in the given prices. Sales tax rates vary by location, but let's assume a standard rate of 7%.
To calculate the total cost including sales tax:
Total cost with tax = Total cost before tax + (Total cost before tax × Sales tax rate)
Total cost with tax = $34.19 + ($34.19 × 0.07)
Total cost with tax = $34.19 + $2.3933
Total cost with tax ≈ $34.19 + $2.40 (rounded to the nearest cent)
Total cost with tax ≈ $36.59
After including the sales tax, the total cost is approximately $36.59, which is more than the $35 Kiera has. Therefore, $35 will not be enough to purchase all three items once sales tax is included.
A car originally priced at $8,900 is on sale at 15% off. If the sales tax rate is 8.25%, what is the sale price of the car?
Answer:
8189.11
Step-by-step explanation:
If 8900 is 100% and we need to find 15% we would multiply 8900 and 15 then divide by 100 and that equal 1335 so we would then subtract 1335 from 8900 because it is 15% off, which equals 7565, so now 7565 is 100% and we need to add the 8.25% tax, so we multiply 7565 and 8.25 then divide by 100 which equals 625.11 then we add 7565 and 625.11 which equals 8189.11
The sale price of the car is $8,188.36.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed.
We have,
A car originally priced at $8,900 is on sale at 15% off.
If the sales tax rate is 8.25%.
So, Discount
= 15% of $8,900
= 0.15 x $8,900
= $1,335
Now, Price after discount
= $8,900 - $1,335
= $7,565
and, Sales tax
= 8.25% of $7,565
= 0.0825 x $7,565
= $623.36
So, Sale price of the car
= $7,565 + $623.36
= $8,188.36
Therefore, the sale price of the car is $8,188.36.
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A lawn has a perimeter of 300 ft and width of 60ft and a bag of grass seeds cover 270ft how many seeds are needed for the new lawn
Answer:
Multiply the length by the width to find the area in square metres and then multiply that figure by 0.03 Kg to find out how much seed you'll need.
Step-by-step explanation:
Answer:
20 bags of seed is needed for the new lawn
Step-by-step explanation:
To answer this question, first find the area of the lawn and divide the area calculated by the number of square feet per bag of seed.
A lawn is assumed to have a rectangular shape, the area (A) of the lawn therefore is
A = L x W
Where: A = Area of lawn
L = Length of lawn
W = Width of lawn
A = L x W
L = ?
W = 60 ft
To find the length, use the formula for the perimeter of a rectangle since the lawn is assumed to a rectangular shape
Perimeter (P) = 2(L+W)
P = 300 ft
300 = 2(L + 60) ft
300 = 2L + 120
Subtract 120 from both sides
300 - 120 = 2L + 120 - 120
180 = 2L
Divide both sides of the equation by the coefficient of L which is 2
180/2 = 2L/2
90 = L
L = 90 ft
That is, the length of the lawn is 90 ft
To calculate the area of the lawn
A = L x W
L = 90 ft
W = 60 ft
A = 90 ft x 60 ft
A = 5400 square feet
This means that the area of the lawn is 5,400 square feet
To get the number of bags of seed that will cover the lawn, divide the area of the lawn by the number square feet that a bag will cover.
Number of bags of seed = Total Area of lawn/Number square feet per bag.
Total Area = 5400 square feet
Number square
feet per bag = 270
Number of bags = 5400/270
= 20 bags of grass seed
20 bags of seed is needed for the new lawn
8. You are a computer technician for Data Control. You earn a regular hourly
rate of $15.40. You earn time and a half for overtime work on Saturdays and
double time on Sundays. This week you worked 38 hours from Monday
through Friday, 8 hours on Saturday, and 5 hours on Sunday. What is your
total pay for the week?
Answer:
Total pay for the week is $924.
Step-by-step explanation:
The per hour rate of weekdays from Monday to Friday = $15.40
The rate for Saturday = One and Half ( $15.40)
Now, [tex]1\frac{1}{2} \times (15.40) = \frac{3}{2} (15.40) = 23.1[/tex]
So, the per hourly rate for work on Saturday = $23.1
The rate for Sunday = 2 x ( $15.40) = $30.80
So, the per hourly rate for work on Sunday = $30.80
Now, total hours worked in weekday = 38
So, the rate of 38 hours = 38 x ( Per hour rate) = 38 x ($15.40)
= $585.2
Now, total hours worked on Saturday = 8
So, the rate of 8 hours = 8 x ( Per hour rate) = 8 x ($23.1) = $184.8
Now, total hours worked on Sunday = 5
So, the rate of 5 hours = 5 x ( Per hour rate) = 5 x ($30.80) = $154
Hence the total pay = Payment of ( weekday + Saturday +Sunday)
= $585.2 + $184.8 + $154 = $924
Hence, total pay for the week is $924.