Answer:
35 smaller trucks.
Step-by-step explanation:
Given:
i) The larger truck with a 2.5-ton payload, and smaller trucks with 1.5-ton payload.
ii) To unload a freight train 21 larger trucks are needed .
Total load of the freight train = 21 times 2.5 tons
= 21 × 2.5
= 52.5 tons
To find the number of small trucks needed, we need to divide 52.5 by 1.5
= 52.5 ÷ 1.5
= 35 small trucks needed.
So, to unload the freight, we need 35 smaller trucks.
Cynthia Besch wants to buy a rug for a room that is 20 ft wide and 31 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 350 square feet of carpeting. What dimensions should the rug have?
Final answer:
Cynthia should calculate the dimensions of the rug by solving the quadratic equation derived from the area she can afford and the dimensions of her room, taking into consideration the width of the uniform strip she wants to leave around the rug.After finding [tex]\( w \), the dimensions of the rug will be \( (20 - 2w) \) ft by \( (31 - 2w) \) ft.[/tex]
Explanation:
To find the dimensions of the rug, we need to subtract the width of the strip left around the rug from the width and length of the room.
The area of the room is given by [tex]\( A_{\text{room}} = W \times L \).[/tex]
Cynthia wants to leave a uniform strip of floor around the rug. This means that the dimensions of the rug will be reduced by twice the width of the strip. So, the dimensions of the rug will be [tex]\( (W - 2w) \times (L - 2w) \).[/tex]
Given that she can afford to buy 350 square feet of carpeting, the area of the rug must be equal to 350 square feet.
So, we have the equation:
[tex]\[ (W - 2w) \times (L - 2w) = 350 \][/tex]
Substituting the given values:
[tex]\[ (20 - 2w) \times (31 - 2w) = 350 \][/tex]
Expanding the equation:
[tex]\[ 620 - 82w - 40w + 4w^2 = 350 \][/tex]
Simplifying:
[tex]\[ 4w^2 - 122w + 620 = 350 \][/tex]
[tex]\[ 4w^2 - 122w + 270 = 0 \][/tex]
Now, we can solve this quadratic equation for w . Once we find the value of w , we can calculate the dimensions of the rug.
After finding [tex]\( w \), the dimensions of the rug will be \( (20 - 2w) \) ft by \( (31 - 2w) \) ft.[/tex]
what is the value of x
4.2x10^6+2.25x10^5+2.8x10^6
Max drives 348 miles in 6 hours. if Max drives at a constant speed. How many miles does he drive per hour?
What is a artafart and a Earth quack?
After the expression (x^16)3/4 is simplified as much as possible, x is raised to what exponent?
Mrs. Sanchez is given a $550 hiring bonus with a new job. She earns an average commission of $275 per week for the year. If $68 is subtracted each week for taxes and benefits, how much does she earn in commissions and bonus for the year?
Mrs. Sanchez earns a total of $11,314 in commissions and bonus for the year, calculated by adding her annual net commission of $10,764 to her hiring bonus of $550.
How much Mrs. Sanchez earns in commissions and bonus for the year:
1: Calculate her weekly net commission.
She earns $275 per week in commission.
However, $68 is deducted for taxes and benefits, leaving her with:
Weekly net commission = $275 - $68 = $207
2: Calculate her annual net commission.
Assuming she works 52 weeks a year (standard for full-time employment):
Annual net commission = $207/week * 52 weeks/year = $10,764
3: Add the hiring bonus to her net commission.
Her total earnings from commissions and bonus are:
Total earnings = $10,764 + $550 = $11,314
Therefore, Mrs. Sanchez earns $11,314 in commissions and bonus for the year.
You are adding two rational numbers with different signs.how can you tell if the sum will be postitive a negative or zero?
Katie is building a rectangle wall.the wall will be 332 bricks wide and 39 bricks tall. She has 15000 bricks.does she have enough bricks to build the wall?explain. Show your work
Write 4,857 in words
−20≤5/9(F−32)≤−15 I don't have a calc. for fractions, its at school
The simplified form of the inequality expression is −4 ≤ F ≤ 5
Using the inequality expression given:
−20≤5/9(F−32)≤−15multiply through by 9
−180 ≤ 5 (F−32) ≤ -135
−180 ≤ 5F - 160 ≤ -135
Add 160 to all sides of the expression
−20 ≤ 5F ≤ 25
divide through by 5 to isolate F
−4 ≤ F ≤ 5
The simplified form of the inequality expression is −4 ≤ F ≤ 5
Complete Question:
Simplify the inequality: −20 ≤ 5/9(F−32) ≤ -15
A snail traveled 2 feet in 90 minutes. How far would it travel in 6 hours
A seafood restaurant claims an increase of $1,750.00 over its average profit during a week where it introduced a special of baked clams
a. If this is true, how much extra profit did it receive per day?
b. if it had, instead, lost $150 per day, how much money would it have lost for the week?
c. If it's total loss was $490 for the week, what was its average daily change?
Molly has 24 muffins,18 breakfast bars,and 12 bottles of juice to be distributed evenly among a certain number of welcome baskets she wants to package the maximum number of welcome baskets that will contain the same combination of muffins breakfast bars and bottles of jucie which shows the correct number of muffins breakfast bars and juice bottles among with the proper explanation circle all that apply
Answer: Hello mate!
We want to distribute 24 muffins, 18 breakfast bars and 12 bottles of juice evenly into baskets, and we want to know the maximum amount of baskets that makes this possible.
This means that we are looking for the maximal common factor between 12, 18 and 24.
To find it, you can took the smallest number in the set, in this case, 12, and look at his divisors, then see if these divisors also divide the other numbers in the set.
Let's do it:
The biggest divisor of 12 is 6, because of 12/6 = 2.
Now 18/6 = 3, so 6 is also a divisor of 18.
24/6 = 4, then 6 is also a divisor of 24.
Then the maximal common factor of the numbers 12, 18 and 24 is 6.
This means that the maximum number of baskets that have an even distribution of the things is 6, where each basket has 2 bottles of juice, 3 breakfast bars, and 4 muffins.
There are 10 boys and 14 girls in your class.Three new students, 2 boys and 1 girl, join your class. Compare the ratio of boys to girls before and after the new students enrolled.Solve and give a short response explaining your answer.
answer a and b please......
Scientists were studying bears by catching, tagging, and releasing 24 bears. A month later, the scientists come back and catch 4 bears, of which 2 are tagged. Assuming that the catch is representative, how many bears are there?
Final answer:
The mark and recapture method is used to estimate the size of a population. In this case, 24 bears were initially tagged and 4 bears were recaptured, 2 of which were tagged. The estimated population size can be calculated using the mark and recapture formula as (24 * 4) / 2 = 48 bears.
Explanation:
The mark and recapture method is used to estimate the size of a population. By catching, tagging, and releasing a known number of individuals and then recapturing a second sample, scientists can calculate an estimate of the total population size. In this case, scientists initially tagged 24 bears and then recaptured 4 bears, 2 of which were tagged. Using the mark and recapture formula, the estimated population size can be calculated as follows:
Number of initial tagged individuals: 24
Total number of individuals in the second sample: 4
Number of tagged individuals recaptured in the second sample: 2
Estimated population size = (Number of initial tagged individuals * Total number of individuals in the second sample) / Number of tagged individuals recaptured in the second sample
Using this formula, the estimated population size of bears in this case would be (24 * 4) / 2 = 48 bears.
how can you compare and order rational and irrational numbers
To compare and order rational and irrational numbers, convert rational numbers to decimals and compare them directly, and for irrational numbers, compare their approximate decimal values.
Comparing and ordering rational and irrational numbers involves understanding their magnitude on the number line.
Let's compare 3 rational and irrational numbers: [tex]\( \frac{5}{3} \), \( \sqrt{2} \), and \( -\frac{4}{7} \).[/tex]
1. [tex]\( \frac{5}{3} \)[/tex] is a rational number, as it can be expressed as a fraction.
2. [tex]\( \sqrt{2} \)[/tex] is an irrational number, as it cannot be expressed as a fraction.
3. [tex]\( -\frac{4}{7} \)[/tex] is a rational number, a negative fraction.
To compare them:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Ordering them:
[tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
Calculation:
1. [tex]\( \frac{5}{3} = 1.67 \)[/tex]
2. [tex]\( \sqrt{2} = 1.414 \)[/tex]
3. [tex]\( -\frac{4}{7} = -0.57 \)[/tex]
Order: [tex]\( -\frac{4}{7} < \sqrt{2} < \frac{5}{3} \)[/tex]
So, [tex]\( -\frac{4}{7} \)[/tex] is the smallest, followed by [tex]\( \sqrt{2} \)[/tex], and [tex]\( \frac{5}{3} \)[/tex] is the largest. This is because irrational numbers lie between rational numbers and have a greater magnitude.
Complete Question:
How can you compare and order rational and irrational numbers ?
In the transit museum, there are 1,763 modern train paintings and 447 antique train paintings. There are 76 more paintings than sculpture. How many sculptures are in the museum?
To find the number of sculptures in the museum, we add the number of modern and antique train paintings and then subtract 76 from the total because there are 76 more paintings than sculptures. The museum has 2,134 sculptures.
The student asked how many sculptures are in the museum, given the number of modern train paintings and antique train paintings, and also knowing there are 76 more paintings than sculptures. To find out the number of sculptures, we first add the number of modern and antique paintings together: 1,763 + 447 = 2,210 paintings in total. Since there are 76 more paintings than sculptures, we subtract 76 from the total number of paintings to find the number of sculptures: 2,210 - 76 = 2,134 sculptures.
an art dealer makes a 17.5 percent commission on every painting sold if a painting sold for 1,500 dollars what was the commission
Help with the answer
z\12=10 what is it and there is no options to this
1/6(18x+24)=−14 solve for x
write each percent as a fraction in simplest form 45 1/2%
Function Question!!!!!!!!
We call a number special if every digit in the number either is a 1 or borders a 1. For example, 11111, 13, 141, 1441, 515151, and 101 are all special, but 10001, 222, 122, and 1333 are not special. How many positive 3-digit numbers are special?
Let us say that:
T = numbers from 2-9
Z = numbers from 0-9
X = all except 1 (0, 2-9)
If a number begins with 1:
1 _ _
Then we can have
1 1 Z (10 numbers)
1 X 1 (9 numbers)
So a total of 19.
Now if a number starts with 2-9
T _ _
The second digit must be 1
T 1 _
but the third can be anything so
T 1 Z = 8 * 1 * 10 = 90 numbers
Total = 99
Is this right here's what I did just in case you don't understand my rewriting
43,000. =43
43x 1,000
=43 x10^3 is this right or wrong this is scientific notion
Solve the equation; x/4-16=(-32)
Caffeine Castle buys bulk coffee to sell. The cost of 5 pounds of imported coffee is $60. What is the unit rate in cost per pound?
Simona si Andrei au impreuna 648 de lei. Andrei are o suma de trei ori mai mare decat a Simonei. Cei doi copii hotarascsa cumpere un joc Lego care costa 128 de lei. Afla cati bani ii raman fiecarui copil, stiind ca ei au cheltuit sume egale.
DATI-MI VA ROG RASPUNS SI EXPLICATIE XX DAU COROANA XX
If something starts out costing $500, and then is marked down by 25% on each of three separate occasions,what is the final price