Answer: The speed of the faster lane is 800 km/hour and the slower plane is 600 km/hour
Step-by-step explanation:
The speed of the faster plane is 800 km/h and the speed of the slower plane is 600 km/h.
The given parameters:
Distance traveled by both planes, d = 3600 km
Let the speed of the faster plane = vThe speed of the slower plane, u = v - 200 km/hLet the time taken for the faster plane = t hoursTime taken for the slower plane to arrive = t + 1.5 hours
The distance traveled by both planes is the same;
d = u(t + 1.5) ---(1)
d = (v - 200) (t + 1.5)
3600 = vt + 1.5v - 200t - 300
d = vt ----(2)
3600 = vt
[tex]v = \frac{3600}{t}[/tex]
[tex]3600 = \frac{3600}{t} t \ +\ 1.5 (\frac{3600}{t} ) \ - \ 200 t - 300\\\\3600 = 3600 + \frac{5400}{t} - 200t - 300\\\\300 = \frac{5400}{t} - 200t\\\\300t = 5400 - 200t^2\\\\200t^2 +300t - 5400 = 0\\\\2t^2 + 3t- 54= 0\\\\(2t - 9)(t + 6)= 0\\\\t = 4.5 \ \ or \ \ -6 \ \\\\t = 4.5 \ hours[/tex]
The speed of the faster plane is calculated as;
[tex]v = \frac{3600}{t} \\\\v = \frac{3600}{4.5} \\\\v = 800 \ km/h[/tex]
The speed of the slower plane is calculated as follows;
[tex]u = v- 200\\\\u = 800 - 200\\\\u = 600 \ km/h[/tex]
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factor 1/2 out of 1/2x - 33/2
Answer:
Step-by-step explanation:
1/2x-33/2=1/2(x-33)
The process of factoring 1/2 out of the equation 1/2x - 33/2 involves dividing each term in the expression by 1/2. This process yields the result x - 33.
Explanation:To factor 1/2 out of the expression 1/2x - 33/2, you perform the factoring by dividing every term in the expression by 1/2. In mathematics, factoring is a crucial concept and is widely used in simplifying expressions, solving quadratic equations, and multiple other scenarios. So, the factoring works as follows:
Divide the term 1/2x by 1/2. This results in x. Divide the term 33/2 by 1/2. This results in -33.
Hence, when you factor 1/2 out of 1/2x - 33/2, the result is x - 33.
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How do you simplify this expression using
properties of logarithms?
1/4 log4 16
Step-by-step explanation:
[tex] \frac{1}{4} \: log_4 16 \\ \\ = \frac{1}{4} \: log_4 {4}^{2} \\ \\ = \frac{1}{4} \times 2\: log_4 {4} \\ \\ = \frac{1}{4} \times 2\: \times 1 \\ \\ = \frac{1}{2} \\ \\ \huge \blue{ \boxed{\therefore \: \frac{1}{4} \: log_4 16= \frac{1}{2} }}\\ [/tex]
What is negative 3/11 as a decimal
Answer: - 0.2727
Step-by-step explanation:
Homework counts as 10%, quizzes as 20% and tests as 70%. If the homework grade is 92, quiz grade is 68 and test grade 81 what’s the final grade?
Answer:
[tex]Final\ grade=79.5[/tex]
Step-by-step explanation:
[tex]Homework\ grade=92\\\\quiz\ grade=68\\\\Test\ grade=81\\\\Final\ Grade=10\%\ of\ homework\ grade+20\%\ of\ quizzes\ grade+70\%\ of\ test\ grade\\\\Final\ Grade=\frac{10}{100}\times 92+\frac{20}{100}\times 68+\frac{70}{100}\times 81\\\\Final\ grade=0.1\times 92+0.2\times 68+0.7\times 81\\\\Final\ grade=9.2+13.6+56.7\\\\Final\ grade=79.5[/tex]
Final answer:
The final grade, calculated by weighting the individual grades for homework, quizzes, and tests, and then applying standard rounding rules, would be a rounded grade of 80.
Explanation:
To calculate the final grade based on the given weights, multiply each individual grade by its respective percentage and then add the results together. Here's a step-by-step calculation:
Homework: 92 (weight 10%) -> 92 x 0.10 = 9.2
Quizzes: 68 (weight 20%) -> 68 x 0.20 = 13.6
Tests: 81 (weight 70%) -> 81 x 0.70 = 56.7
Add these results together to get the final grade:
9.2 (Homework) + 13.6 (Quizzes) + 56.7 (Tests) = 79.5
Using standard rules for rounding, 79.5 would be rounded to 80, which is typically a 'B' grade.
complete the table for the given rule: y=1/4+1
Answer:
there is no table :)
Step-by-Step Explanation:
y = 1/4x +1
X Y
4 2
8 3
12 4
write the ratio as a fra tion in the lowest term
8. Teacher-to-student ratio in a school is
8 teachers to 160 students.
elimination using addition and subtraction
-7x= y - 4
5x - y = 8
Answer:
look at the picture shown
In art class, Kerion is coloring a patter where half of the squares on her paper are being colored blue. Of the blue squares,1/3 of them will also have stripes. What fraction of squares will be blue blue with stripes?
if you add Natalie's age and Fred's age, the result is 45. if you add Fred's age to 3 times Natalie's age, the result is 73. Find how old Fred and Natalie are.
Answer:
Fred is 31 years old and Natalie is 14 years old.
Step-by-step explanation:
Given:
If you add Natalie's age and Fred's age, the result is 45.
If you add Fred's age to 3 times Natalie's age, the result is 73.
Now, to find the age of Fred and Natalie.
Let the age of Fred be [tex]x.[/tex]
And the age of Natalie be [tex]y.[/tex]
As, given If you add Natalie's age and Fred's age, the result is 45.
[tex]x+y=45[/tex] ......(1)
Now, if you add Fred's age to 3 times Natalie's age, the result is 73.
[tex]x+3y=73[/tex] ......(2)
So, to solve the equations by using elimination method.
Now, subtracting both the equations (1) and (2):
[tex]x+y-(x+3y)=45-73[/tex]
[tex]x+y-x-3y=-28[/tex]
[tex]-2y=-28[/tex]
Dividing both sides by -2 we get:
[tex]y=14.[/tex]
Natalie's age = 14 years.
Now, to get the age of Fred by substituting the value of [tex]y[/tex] in equation (1):
[tex]x+y=45\\\\x+14=45[/tex]
Subtracting both sides by 14 we get:
[tex]x=31.[/tex]
Fred age = 31 years.
Therefore, Fred is 31 years old and Natalie is 14 years old.
1. $239 television; 10% discount 2. $72 game; 20% discount
3. $18.95 football; 15% discount 4. $10.99 CD; 25% discount
5. $149 MP3 player; 40% discount 6. $213 ski jacket; 30% discount
7. $595 refrigerator; 20% discount 8. $64 video game; 25% discount
9. $119 croquet set; 50% discount 10. $14.99 clock; 10% discount
11. A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel? Hint: need to use a proportion to find the whole.
12. A box of laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the original price to the nearest cent?
13. Determine the price of a $35 basketball that is on sale for 50% off the regular price.
14. Dominic bought a new alarm clock that was on sale for $18.75. If this price represents a 30% discount from the original price, what is the original price to the nearest cent?
15. Michael bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sales tax of 3% is applied to the discounted total. What was the sale price with tax of Michael’s fishing rod to the nearest cent?
16. Jaylynn was buying new mascara. She bought it on sale for $5.56. If the price represents a 20% discount from the original price, what is the original price to the nearest cent?
Please help! It is due TOMORROW!!! :[I] HELP!!
These are 16 questions and 16 answers
Answer:
See below and the attachment.Explanation:
From 1 to 10, find the sale price to the nearest cent:
1. $239 television; 10% discount
[tex]Sale\text{ }price=Orignal\text{ }price-discount\\ \\ Sale\text{ }price=\$239-10\%\times \$239=\\\\ Sale\text{ }price=\$239-0.10\times \$239=\\\\ Sale\text{ }price=\$239-\$23.9=\$215.10[/tex]
2. $72 game; 20% discount
You can also multiply by the factor (1 - % discount);
For instance for 20% discount, the factor is 1 - 20% = 1 -0.20 = 0.80. Which means that you can multiply the original price by the factor 0.80 to get the sale price:
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$72\times(1-0.20)=\\\\ Sale\text{ }price=\$72\times0.80=\\\\ Sale\text{ }price=\$57.60[/tex]
3. $18.95 football; 15% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$18.95\times(1-0.15)=\\\\ Sale\text{ }price=\$18.95\times0.85=\\\\ Sale\text{ }price=\$16.11[/tex]
4. $10.99 CD; 25% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$10.99\times(1-0.25)=\\\\ Sale\text{ }price=\$10.99\times0.75=\\\\ Sale\text{ }price=\$8.24[/tex]
5. $149 MP3 player; 40% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$149\times(1-0.40)=\\\\ Sale\text{ }price=\$149\times0.60=\\\\ Sale\text{ }price=\$89.40[/tex]
6. $213 ski jacket; 30% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$213\times(1-0.30)=\\\\ Sale\text{ }price=\$213\times0.70=\\\\ Sale\text{ }price=\$149.10[/tex]
7. $595 refrigerator; 20% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$595\times(1-0.20)=\\\\ Sale\text{ }price=\$595\times0.80=\\\\ Sale\text{ }price=\$476.00[/tex]
8. $64 video game; 25% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$64\times(1-0.25)=\\\\ Sale\text{ }price=\$64\times0.75=\\\\ Sale\text{ }price=\$48.00[/tex]
9. $119 croquet set; 50% discount
You should not have problems with this: 50% discount means that you will pay half the price.
Hence, the sale price is:
[tex]Sale\text{ }price=Orignal\text{ }price/2 \\\\ Sale\text{ }price=\$59.50[/tex]
10. $14.99 clock; 10% discount
[tex]Sale\text{ }price=Orignal\text{ }price\times factor\\ \\ Sale\text{ }price=\$14.99\times(1-0.10)=\\\\ Sale\text{ }price=\$14.99\times0.90=\\\\ Sale\text{ }price=\$13.49[/tex]
11. A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the nearest nickel? Hint: need to use a proportion to find the whole.
First note that if the discount is 10%, the sale price is 100% - 10% = 90% of the original price.
Let's set the proportion that represents the proportionality between the two ratios, starting with the fact that $ is the 90% and original price is the 100% (the whole part):
First ratio: $50/90Second ratio: x /100Proportion: first ratio = second ratio[tex]\$50/90=x/100[/tex]
Solve for x:[tex]x=100\times\$50/90=\$55.55[/tex]
Hence, the original price is $55.55
12. A box of laundry detergent is on sale for $6.50. If this price represents a 40% discount from the original price, what is the original price to the nearest cent?
Use the same hint used in the question above: set a proportion.
Remember a 40% discount means that the sale price is 60% of the original price:
[tex]\$6.50/60=x/100\\ \\ x=100\times\$6.50/60=\$10.83[/tex]
13. Determine the price of a $35 basketball that is on sale for 50% off the regular price.
Again, 50% discount means that the sale price will be half of the original price, or the original price will be double of the sale price.
Here, the original price is $35, hence the sale price is $35/2 = $17.50
14. Dominic bought a new alarm clock that was on sale for $18.75. If this price represents a 30% discount from the original price, what is the original price to the nearest cent?
Since the price is after a 30% discount, the sale price is a 70% of the original price, and you set the proportion:
[tex]\$18.75/70=x/100[/tex]
Solve for x:
[tex]x=100\times\$18.75/70=\$26.79[/tex]
15. Michael bought a new fishing rod. The regular price of the fishing rod was $125.99. He bought it on sale with a 15% discount. Sales tax of 3% is applied to the discounted total. What was the sale price with tax of Michael’s fishing rod to the nearest cent?
First find the the sale price after the 15% discount:[tex]\$125.99\times(1-0.15)=\$125.99\times0.85=\$107.09[/tex]
Now add the 3% tax:[tex]\$107.09\times1.03=\$110.30[/tex]
Hence, the sale price with tax is $110.30
The last answer (# 16) is in the attached file, since this already exceeds the number of characters allowed.
As a salesperson you are paid $70 per week plus $6 per sale. This week you want your pay to be at least $150. Write an inequality to represent the number of sales you need to make to achieve your goal. Then solve the inequality algebraically, showing all work on your paper.
The inequality is:
[tex]70+6x\geq 150[/tex]
You must do more than 14 sales to get at least $ 150
Solution:
Given that,
As a salesperson you are paid $70 per week plus $6 per sale
Let "x" be the number of sales
This week you want your pay to be at least $150
We have to frame a inequality to represent the number of sales you need to make to achieve your goal
This week he must earn at least $ 150
Thus, he can spend $ 150 or more then 150 also
So we have to use "greater than or equal to" symbol
From given,
[tex]70 + 6(\text{number of sales})\geq 150[/tex]
[tex]70+6x\geq 150[/tex]
Thus the inequality is found
Solve the inequality
[tex]70+6x\geq 150\\\\Subtract\ 70\ from\ both\ sides\\\\6x\geq 150-70\\\\6x\geq 80\\\\Divide\ both\ sides\ by\ 6\\\\x\geq 13.3\\\\Thus\ approximately\ we\ get\\\\x\geq 14[/tex]
So he must do more than 14 sales to get at least $ 150
Lucy and Judy each had a pie of equal size Lucy divided her pie into 6 equal slices and ate 2 of them. Judy divided her pie into 4 equal slices and ate 3 of them who ate more
Answer:
Judy
Step-by-step explanation:
Use two points on the graph to find the slope. How does the slope relate to the unit cost?
Create a problem for the equation 3 + x equals 8 then solve the equation and write the answer to your problem
Answer:
Andy had 3 apples, and his mom surprised him with x apples. His mom told him that he had 8 apples in total. As he counted the apples he found out his mom gave him 5 apples By subtracting 8 and 3.
Step-by-step explanation:
Graph the linear function described by the equation
y = -3x - 2
X
y
Step 1: Identify the slope and y-intercept.
slope =
NA
Check
What is 3 divided by 260
Answer:
86.666666 or 0.01153846153
Answer:
0.0115
Step-by-step explanation:
Ms. Killikelly added 33 and 48 by first
taking 2 from 33 and adding the 2 to 48
making 50. She likes making friendly
numbers when adding! What does she now
need to add to 50 to find the sum?
Answer:
31+2+48=31+50
30+50+1=81
Step-by-step explanation:
Ms. Killikelly is trying to add two 2-digits numbers by making the groups of tens
So she first tried to make 48 as 50 (i.e. group of five tens) by adding digit 2 of the number 33 to the number 48.
Now she needs to add 31 and 50. She needs to add three groups of tens (i.e. 30) with five groups of tens (i.e. 50) and then add 1(i.e. the remaining 1 of 31) as following
:
[tex]10+10+10+10+10+10+10+10+1=30+50+1=81[tex]
(because 30=10+10+10 and 50=10+10+10+10+10)
OR simply as follow
30+50+1=81
You estimate that a box contains 141 envelopes the actual number of envelopes is 150 find the percent error
sally draws a triangle with one side 6 inches long and another side 8 inches long. which is NOT a possible length for the third side ? A) 4 in B)10 in C) 12 in D) 14 in
When constructing a triangle with given side lengths, the possible range for the third side can be determined by adding and subtracting the lengths of the existing sides. Side lengths of 4, 10, and 14 inches are not possible choices for the third side length.
Explanation:The third side of a triangle must be less than the sum but greater than the difference of the other two sides. Given sides of 6 inches and 8 inches:
6 + 8 = 14 inches8 - 6 = 2 inchesTherefore, the lengths of the sides 4, 10, and 14 inches are not possible.
9. Anya and Sue each have $90.
Anya spends 5 over 8 of her money.
Sue spends 60% of her money.
Who has spent the most money?
Answer:
Anya spend the most money
Combine likes terms to create an equivalent expression 1/7 - 3(3/7h -2/7)
[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7}) = \frac{7-9h}{7}[/tex]
Solution:
Given expression is:
[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]
We have to combine the like terms
From given expression,
[tex]\frac{1}{7} -3(\frac{3}{7}h -\frac{2}{7})[/tex]
By distributive property,
The distributive property lets you multiply a sum by multiplying each addend separately and then add the products.
a(b + c) = ab + bc
Therefore,
Solve for brackets using distributive property
[tex]\frac{1}{7} - (3 \times \frac{3}{7}h) + (3 \times \frac{2}{7})\\\\\frac{1}{7} - \frac{9h}{7} + \frac{6}{7}[/tex]
Add 1/7 and 6/7
[tex]\frac{1}{7} + \frac{6}{7} -\frac{9h}{7}\\\\\frac{1+6}{7} -\frac{9h}{7}\\\\Simplify\\\\\frac{7}{7}-\frac{9h}{7}\\\\1-\frac{9h}{7}\\\\Simplify\\\\\frac{7-9h}{7}[/tex]
Thus the equivalent expression is found
PLEASE GIVE A CORRECT ANSWER NOT JUST ANYTHING!!!!!!
Answer:
£28+£16(each half hour)
£28+£48= £76
What’s the absolute value of 13
Answer:
The absolute value of 13 is (-13)
Step-by-step explanation:
It just is lol
Answer: 13
Explanation: The absolute value of an integer it its distance from zero on a number line. Since 13 is 13 units from zero, the absolute value of 13 is 13.
To represent the absolute value of a number, we use a vertical bar on either side of the number so we say that |13| = 13.
I have drawn a number line and also showed you in the image attached.
Write the expression in standard form.
(4f-3+2g)-(-4g+2)
Answer:
Apply the distributive property.
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−
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4
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Simplify by adding terms.
Tap for fewer steps...
Subtract
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Step-by-step explanation:
How many sides does a polygon have if the sum on the interior angle measures 3600
Answer:
22
Step-by-step explanation:
What decimal is greater than 0.15 and less than 0.7?
Any decimal number that lies between 0.15 and 0.7 meets the criteria, such as 0.6, 0.20 or 0.30. In mathematics, there can be infinite possibilities between these values as you can always add more digits after the decimal point.
Explanation:In mathematics, a decimal number greater than 0.15 and less than 0.7 could be any number that falls within these two boundaries. For example, 0.6 is a decimal number that would meet these criteria. Alternatively, a number like 0.20 or 0.30 would also satisfy the conditions specified in the question.
Remember, a decimal between two numbers can have infinite possibilities. That's because you can always add more digits after the decimal point (for example, 0.601, 0.602, 0.603, ..., and so on).
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Which property would be used to solve the expression x + 12 = 47 ?
Select one:
A. Inverse
B. Distributive
C. Associative
D. Commutative
A. Inverse
Explanation:Basically, inverse Property of Addition states that if you add any number added to its opposite the result will be equal zero. So, here we have the following equation:
[tex]x + 12 = 47[/tex]
Adding -12 to both sides we get:
[tex]x + 12 - 12= 47-12 \\ \\ \\ But \ 12+(-12)=0 \\ \\ \\ So: \\ \\ x + 0= 35 \\ \\ Finally: \\ \\ \boxed{x=35}[/tex]
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Answer:
A. Inverse
Step-by-step explanation:
The given equation is [tex]x+12=47[/tex]
To solve this equation, we use the inverse property of addition.
We add the additive inverse of 12 to both sides to get:
[tex]x+12-12=47-12[/tex]
We then simplify to obtain:
[tex]x+0=35[/tex]
This gives us x=35.
The correct answer is A
A box of expo markers are priced $10.99. How much will I pay after a 10% teacher discount and 6.5% sales tax
On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
Number of adults = 264
Number of children= 127
Step-by-step explanation:
Let the number of adults be......x
Let the number of children be.....y
The total number of people that used the public swimming pool is given as 391. This means
x+y=391
The total cost per the receipt is : $752.75
This means, 2.25 x+ 1.25 y = 752.75
The two equations are;
x+y=391 ...........(i)
2.25 x+ 1.25 y = 752.75...........(ii)
Making the x variable equal to eliminate x
2.25x + 2.25 y = 879.75
2.25x + 1.25 y = 752.75
Apply subtraction as
1.00 y = 127.00
y=127
Use the value of y in equation (i)
x+y=391
x+127=391
x=391-127=264
Number of adults = 264
Number of children= 127
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Keywords ; public, swiming pool, prices, daily, adults, children, receipt, admission
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Loretta is a single mom with two kids. In 2009 her gross income was $61,840. She filed
her taxes as Head of the Household and claimed herself and her 2 children. Using the tables
above find Loretta's taxable income.
Answer:
$7300
Step-by-step explanation:
Loretta's taxable income in 2009 is $42,540. Calculation involves subtracting allowable deductions from gross income.
Explanation:Loretta's taxable income can be calculated by subtracting her allowable deductions from her gross income. As Head of the Household, Loretta is eligible for a higher standard deduction compared to single individuals. For tax year 2009, the standard deduction for Head of the Household was $8,350. Loretta can also claim deductions for herself and her two children. The personal exemption for each individual was $3,650 in 2009. Therefore, Loretta's total deductions would be $8,350 (standard deduction) + $3,650 (personal exemption for herself) + $3,650 (personal exemption for child 1) + $3,650 (personal exemption for child 2) = $19,300.
To find Loretta's taxable income, we subtract her total deductions from her gross income: $61,840 - $19,300 = $42,540. Therefore, Loretta's taxable income is $42,540 in 2009.
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