Answer:
30 mph
Step-by-step explanation:
Let d = distance (in miles)
Let t = time (in hours)
Let v = average speed driving to the airport (in mph)
⇒ v + 15 = average speed driving from the airport (in mph)
Using: distance = speed x time
[tex]\implies t=\dfrac{d}{v}[/tex]
Create two equations for the journey to and from the airport, given that the distance one way is 18 miles:
[tex]\implies t=\dfrac{18}{v} \ \ \textsf{and} \ \ t=\dfrac{18}{v+15}[/tex]
We are told that the total driving time is 1 hour, so the sum of these expressions equals 1 hour:
[tex]\implies \dfrac{18}{v} +\dfrac{18}{v+15}=1[/tex]
Now all we have to do is solve the equation for v:
[tex]\implies \dfrac{18(v+15)}{v(v+15)} +\dfrac{18v}{v(v+15)}=1[/tex]
[tex]\implies \dfrac{18(v+15)+18v}{v(v+15)}=1[/tex]
[tex]\implies 18(v+15)+18v=v(v+15)[/tex]
[tex]\implies 18v+270+18v=v^2+15v[/tex]
[tex]\implies v^2-21v-270=0[/tex]
[tex]\implies (v-30)(v+9)=0[/tex]
[tex]\implies v=30, v=-9[/tex]
As v is positive, v = 30 only
So the average speed driving to the airport was 30 mph
(and the average speed driving from the airport was 45 mph)
Let s represent the speed on the return trip
So, The initial speed will be (s-15)
Equation of time:
[tex] \boxed{ \tt \: time = \frac{distance}{speed} }[/tex]
return time + initial time = 1 hr
[tex] \sf\frac{18}{s} + \frac{18}{s - 15} = 1[/tex]
⚘Solution for the complete equation in attachment!!~
[tex]\rule{300pt}{2pt}[/tex]
His average speed is 30 km/hr...~In a village 200 persons out of 450 were found to be alcoholic. Can you conclude that minority of persons in this village are alcoholic assuming the persons being alcoholic and non-alcoholic are equal?
Step-by-step explanation:
Step 1 total number of person =450
Step 2 number of people who are alcholic =200
Step 3 now subtract them like: 450 - 200
Answer=200 people are non alcholic
Can someone help please
Answer:
1=1/2
2=8 times the square root of 3 over 25 8xsuare root 3/25
3=16
4=7 times square root of 3 over 4 7x square root 3/4
5=square root of 2 over 2
6=square root 3
7=square root 2
8=1/3
9=10/7
Step-by-step explanation:
you can also use algebrator square root calculator!!
Find the surface area of rectangular prism
Fractions math help me pls and thanks !!!
Answer:
A
Step-by-step explanation:
All the other options have arrows at the ends. This means they continue forever. A segment starts and stops at points. Line A starts and stops at 2 points.
The ratio of dogs to cats is __3:4______. For every ________ dogs, there are ________ cats.
For every 3 dogs, there are 4 cats.
There are 4 cats and 3 dogs, so that means for every 3 dogs, there will be 4 cats.
For every ___3_____ dogs, there are _____4___ cats.
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given,
ratio of dogs to cats = 3:4
which means there are 3 dogs per 4 cats.
Hence, there are 4 cats for every 3 dogs.
Learn more about ratio here:
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Problem 2: Use the Laplace Transforms to solve:
[tex]y'' - y' - 2y= 1 - x , \\ y(0) =y'(0) =1[/tex]
Using the given table of transforms,
[tex]L\left\{ y'' - y' - 2y \right\} = L\left\{ 1-x \right\}[/tex]
[tex](s^2 Y(s) - sy(0) - y'(0)) - (s Y(s) - y(0)) - 2 Y(s) = \dfrac1s - \dfrac1{s^2}[/tex]
(where Y(s) is the Laplace transform of y(x))
Solve for Y(s) :
[tex](s^2 - s - 2) Y(s) - s = \dfrac1s - \dfrac1{s^2}[/tex]
[tex](s^2 - s - 2) Y(s) - s = \dfrac{s-1}{s^2}[/tex]
[tex](s^2 - s - 2) Y(s) = \dfrac{s-1}{s^2} + s[/tex]
[tex](s^2 - s - 2) Y(s) = \dfrac{s^3 + s - 1}{s^2}[/tex]
[tex]Y(s) = \dfrac{s^3 + s - 1}{s^2 (s^2 - s - 2)}[/tex]
[tex]Y(s) = \dfrac{s^3 + s - 1}{s^2 (s + 1) (s - 2)}[/tex]
Decompose the right side into partial fractions:
[tex]Y(s) = \dfrac as + \dfrac b{s^2} + \dfrac c{s+1} + \dfrac d{s-2}[/tex]
Solve for the coefficients.
[tex]\implies s^3 + s - 1 = as(s+1)(s-2) + b(s+1)(s-2) + cs^2(s-2) + ds^2(s+1)[/tex]
[tex]\implies s^3 + s - 1 = -2 b + (-2 a - b) s + (-a + b - 2 c + d) s^2 + (a + c + d) s^3[/tex]
[tex]\implies \begin{cases}-2b = -1 \\ -2a-b = 1 \\ -a+b-2c+d = 0 \\ a+c+d = 1 \end{cases} \implies a=-\dfrac34, b=\dfrac12, c=1, d=\dfrac34[/tex]
Then
[tex]Y(s) = -\dfrac34 \times \dfrac1s + \dfrac12 \times \dfrac1{s^2} + \dfrac1{s+1} + \dfrac34 \times\dfrac1{s-2}[/tex]
Take the inverse transform and solve for y(x) :
[tex]F(s) = \dfrac1s \implies f(x) = 1[/tex]
[tex]F(s) = \dfrac1{s^2} \implies f(x) = x[/tex]
Using the frequency-shifting property,
[tex]F(s) = \dfrac1{s+1} \implies f(x) = e^{-x}[/tex]
[tex]F(s) = \dfrac1{s-2} \implies f(x) = e^{2x}[/tex]
So, the particular solution to the ODE is
[tex]\boxed{y(x) = -\dfrac34 + \dfrac x2 + e^{-x} + \dfrac{3e^{2x}}4}[/tex]
It takes a snail 10 seconds to move 1 centimeter.
Answer:
you would still have 10 snles
simplify: 4/5 - 1/3
A. 3/15
B. 5/15
C. 7/15
D. 3/2
Answer:
7/15
Step-by-step explanation:
4/5 - 1/3
multiply one side by 3 and the other by 5
12/15 - 5/15
7/15
Write 350 as a product of primes. Use index notation when giving your answer
Answer: 2 x 5 x 5 x 7 = 350. =2¹ x 5²x 7¹
Step-by-step explanation:
Is 8,397 divisible by 9? If it is, write the number as the product of 9 and another factor. If not, explain
Answer:
311 x 27 = 8397
Step-by-step explanation:
first find the factors of your number 8 397 by dividing continuously starting with the smallest value
8397/3 = 2799
2799/3 = 933
933/3 = 311
311/311 = 1
therefore 311 x (3 x3 x3) = 8397
311 x 27 = 8397
help asap will mark brainliest to the correct answer and 5 star it
Answer:
50°
Step-by-step explanation:
The missing angle would equal the formula:
180°- a - b= x
a and b are the two angles given.
180- 110 -20 = 50
So the missing angle is 50 °
The bill at a restaurant
is $37.52. Helen wants
to leave a 15% tip. If
Helen has $40, will she
have enough money to
pay the bill? Justify
your answer.
Show Work:
Answer:
no, she won't have enough money to pay the bill
Step-by-step explanation:
$37.52×15/100
=$5.63
therefore:$37.52 + $5.63
= $43.15
•she wont have enough money to pay the bill as her bill will be $43.15 and she has $40.
The numbers 38 and 41 are rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 38 × 41 based on this method?
1,200
1,600
2,000
2,500
The numbers 38 and 41 are rounded to the nearest ten and then multiplied to estimate the product. What is the best estimate of 38 × 41 based on this method?
1,200
1,600
2,000
2,500
What is the product of 21 × 3?
21
24
60
63
Yusef wants to buy 20 pairs of sneakers to donate to a local shelter. Each pair costs $23. How much money will Yusef spend on all the sneakers?
$100
$200
$360
$460
The product of 42 × 31 is
.
A basketball team has 22 games this season. At each game, 95 raffle tickets are sold. How many raffle tickets are sold during all 22 games?
1,900
1,980
2,080
2,090
Carter rewrites 28 × 2 in expanded form to find the product.
28 × 2
= (20 × 2) + (8 × 2)
What is the next step to find the product?
adding the product of 20 × 2 to the product of 8 × 2
subtracting the product of 20 × 2 from the product of
8 × 2
multiplying the product of 20 × 2 by the product of 8 × 2
dividing the product of 20 × 2 by the product of 8 × 2
What is the product of 33 × 2?
31
33
60
66
What is the product?
57 × 4
228
232
240
285
Marta has 128 stamps. Kelli has 11 times as many as Marta. Marta estimates the total they have altogether by rounding each amount to the nearest ten and then multiplying.
What is the best estimate of 128 × 11 using this method?
1,200
1,300
1,408
1,508
pls hurry first one right gets brainlist
Answer:
Jeez this is a big question
Step-by-step explanation:
1. if they are rounded to the nearest 10 that would mean that it is actually
40 * 40
40 * 40 is 1600. The answer for #1 is 1600
2. its just asking what 21 x3 is, 21x3 is 63
3. All you do for this is 20*23
20 * 23 is 460
4. 42 * 31 is 1302
5. 22 * 95 = 2090
6. You do 20x2 which is 40 and then you do 8x2 which is 16
Adding
then you have 40 + 16 = 56
Subtracting
40 - 16 = 24
Multiplying
40 * 16 = 640
Dividing
40/16 = 2.5
7. 33x2 is 66
8. 57* 4 is 228
9. 128 * 11 is 1408 but if you round the 11 to the nearest 10, that would be 10, then if you round the 128 to the nearest 10, that would be 130, and then 130 * 10 is 1300
38 × 41 can be estimated by rounding 38 and 41 to the nearest ten, which gives us 40 and 40. Multiplying these two numbers gives us 1600. So the answer is 1,600.
21 × 3 is equal to 63.
How to solveYusef wants to buy 20 pairs of sneakers to donate to a local shelter. Each pair costs $23. How much money will Yusef spend on all the sneakers? The answer is $460.
The product of 42 × 31 is 1,262.
A basketball team has 22 games this season. At each game, 95 raffle tickets are sold. How many raffle tickets are sold during all 22 games? The answer is 2,090.
Carter rewrites 28 × 2 in expanded form to find the product.
28 × 2
= (20 × 2) + (8 × 2)
The next step to find the product is to multiply the product of 20 × 2 by the product of 8 × 2.
= 20 × 2 + 8 × 2
= 40 + 16
= 56
What is the product of 33 × 2? The answer is 66.
What is the product?
57 × 4
= 228
Marta has 128 stamps. Kelli has 11 times as many as Marta. Marta estimates the total they have altogether by rounding each amount to the nearest ten and then multiplying.
What is the best estimate of 128 × 11 using this method? The answer is 1,300.
Read more about algebra here:
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Assume you earn $41,250 per year in take-home pay. Can you afford the house with a $625.95 per month total mortgage payment that you have been considering in the previous example?
Jenny randomly selects 20 boxes of crayons from the shelf and finds two boxes with at least one broken crayon. If the shelf holds 130 boxes, how many would you expect to have at least one broken crayon?
The angles of a triangle are in a ratio 1:3:8. What are the angles?
Answer:
15° , 45°, 120°
Step-by-step explanation:
sum the parts of the ratio, 1 + 3 + 8 = 12 parts
the sum of the 3 angles in a triangle = 180° , then
180° ÷ 12 = 15° ← value of 1 part of the ratio, then
3 parts = 3 × 15° = 45°
8 parts = 8 × 15° = 120°
the 3 angles are 15° , 45° , 120°
Evaluate 1/3b+7/12 when b= 1/4 .
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Since we know that [tex]b=\frac{1}{4}[/tex], we can simply substitute [tex]\frac{1}{4}[/tex] for [tex]b[/tex] in the equation:
[tex]\frac{1}{3}b+\frac{7}{12}\\\frac{1}{3}(\frac{1}{4})+\frac{7}{12}\\[/tex]
To multiply fractions, simply multiply the numerators of the multipliers to find the numerator of the resultant, and multiply the denominators of the multipliers to find the denominator of the resultant. Therefore, we multiply 1 x 1, which is 1, and 3 x 4, which is 12. The resultant fraction for the operation of [tex]\frac{1}{3}(\frac{1}{4})[/tex] is [tex]\frac{1}{12}[/tex].
Now, we just need to add the remaining fractions:
[tex]\frac{1}{12}+\frac{7}{12}[/tex]
When adding fractions with the sane denominator, we simply add the numerators. The addition of the numerators in this case is 8, so:
[tex]\frac{1}{12}+\frac{7}{12}=\frac{8}{12}[/tex]
We can still simplify the fraction of [tex]\frac{8}{12}[/tex]. Both the numerator and the denominator are divisible by four, so divide them both by four to get the final, simplified fraction:
[tex]\frac{8}{12}=\frac{2}{3}[/tex]
Answer:
[tex]\frac{23}{12}[/tex]
Alternative forms:
[tex]1.916, 1\frac{11}{12}[/tex]
Step-by-step explanation:
Substitute b = 1/4 into 1/3b + 7/12 :
[tex]\begin{matrix}\underline{1}\\\underline{3}\\4\\\end{matrix}+\frac{7}{12}[/tex]
Calculate
[tex]\begin{matrix}\underline{1}\\\underline{3}\\4\\\end{matrix}+\frac{7}{12}[/tex]
Divide a fraction by multiplying its reciprocal
[tex]\frac{4}{3}+\frac{7}{12}[/tex]
Find common denominator and write the numerators above common denominator
[tex]\frac{4\times4}{3\times4}+\frac{7}{12}[/tex]
Calculate the product or quotient
[tex]\frac{16}{3\times4}+\frac{7}{12}[/tex]
[tex]\frac{16+7}{12}[/tex]
Calculate the sum or difference
[tex]\frac{23}{12}[/tex]
I hope this helps you
:)
Help me please ASAP !!!!!!!
Answer:
its A
PLS MARK AS BRAINLESS I MEAN BRAINLIEST :)
Step-by-step explanation:
BD is the perpendicular bisector of AC. What is the perimeter of AABC?
A. 5 cm
B. 9 cm
D 4 cm
C. 14 cm
D, 18 cm
I WILL GIVE BRAINLEST
[tex] \huge{ \rm{Question:}}[/tex]
7. If a figure measures 7 centimeters high, 3 centimeters wide and 2 centimeters deep, what is the volume of the figure?
[tex] \huge{ \rm{Answer:}}[/tex]
The volume of the figure is 42.
Step-by-step explanation:
= 2 x 7 x 3
= 14 x 3
= 42
HOPE THIS HELPS^^
If a book and a pen together cost $11 and the book is $10 more than the pen, how much does the pen cost? Show solution please
Answer:
50 cents
Step-by-step explanation:
Since 1 dollar is too much, then try 50 cents. Then it worked.
what is the value of F
Answer:
-15
Step-by-step explanation:
Every property of a square is also a property of a rectangle. Is this true or false?
Answer:
False, every property of a square is not a property of a rectangle. Most of the properties of a square are also a property of a rectangle. If you square root the area of a square, you will get the side length of that square. If you square root the area of a rectangle, assuming the 4 sides of the rectangle are different, you will not get any of the correct dimensions.
If you have any questions, please let me know in the comments section of this answer! If you could mark this answer as the brainliest, I would greatly appreciate it! :D
3. Find the slope of the line that goes through the following points: (6.-1) and (-3, 11)
Answer:
1.33
Step-by-step explanation:
y2-y1/x2-x1
=11+1/-3-6
=12/-9
=-4/3
=1.33
Please help we are so confused
Answer:
160 dollars
Step-by-step explanation:
if its 10 less you just have to umm think its just adding (sorry i dont know how to explain)
HELP ME I WILL GIVE BRINLEST
Answer:
9 and 1 fourths
Step-by-step explanation:
Answer:
10 9/16
Step-by-step explanation:
For this equation, we are going to need to multiply these mixed numbers to get our answer. The quickest and easiest way to solve this would be to turn these mixed numbers into improper fractions.
(Important:) To make an improper fraction, multiply the denominator by the whole number, then add the numerator. This becomes your new numerator for your improper fraction.
With that said, we can now turn these into improper fractions. So:
3 1/4 = 13/4 and 13/4.
To find area, we need to multiply L x W (length x width) to get our answer. So:
13/4 x 13/4 = 169/16 = 10 9/16.
I hope that this helps.
it is good for getting answers
Answer:yes!!
Step-by-step explanation:suprisingly this website gives you the tools to get an answer for anything. People will find ur stuff and give an answer, or sometimes multiple people.
A common design requirement is that an environment must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. In designing an assembly work table, the sitting knee height must be considered, which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normally distributed with a mean of 21.8 in. and a standard deviation of 1.1 in. Females have sitting knee heights that are normally distributed with a mean of 19.3 in. and a standard deviation of 1.0 in. Use this information to answer the following questions.
What is the minimum table clearance required to satisfy the requirements of fitting 95% of men?
Using the normal distribution, it is found that the minimum table clearance required to satisfy the requirements of fitting 95% of men is of 23.6 in.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem, for men's knee heights, we have that:
The mean is of [tex]\mu = 21.8[/tex].The standard deviation is of [tex]\sigma = 1.1[/tex].The 95th percentile is X when Z has a p-value of 0.95, so X when Z = 1.645, then:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 21.8}{1.1}[/tex]
[tex]X - 21.8 = 1.1(1.645)[/tex]
[tex]X = 23.6[/tex]
The minimum table clearance required to satisfy the requirements of fitting 95% of men is of 23.6 in.
More can be learned about the normal distribution at https://brainly.com/question/24663213
If A+B+C = then prove that: n sin A cos A + sin B cos B + sin C cos C=2 sin A sin B sin C
Answer:
Let a, b, c be the sides that oppose angles A, B, C, respectively. By the Law of Sines,
asinA=bsinB=csinC=d
where d is the circumdiameter of the triangle. If we conveniently scale the triangle so that d=1, then we can say simply that
a=sinAb=sinBc=sinC
This is a common simplification technique, as it nicely blurs the distinction between edges and angles, giving us things like this wonderfully-symmetric area formula:
Area=12abc(=12absinC=12acsinB=12bcsinA)
(When you have this mindset, you can't look at the expression "sinA+sinB+sinC" and not think, "That's perimeter!" ... and then you find yourself pursuing proof approaches like this one.) In what follows, I'll continue to use "a", "b", "c", because they're more compact than "sinA", etc, but you should read them as "sinA", etc.
Gwen is building a fence around a square play area for her puppy. She wants the play area to be 256 feet squared. How many feet long should she build the play area
Answer:
64 feet of fencing needed
Step-by-step explanation:
sqrt(256)=16
16*4=64
Gwen need to build 64 feet of fencing around the square play ground.
What is a quadrilateral?
quadrilateral is a plane mathematical closed figure consist of four side and four edges. There are 7 types of quadrilateral.
Trapezium, Parallelogram, Rectangle, Rhombus, Square, Kite.
Here, it is given that Gwen wants a play ground squared shaped of 256 feet.
Firstly, Now let us find out the side of square a play ground to be fenced which will be :
a² = 256 feet²
a = √256
a = 16 feet
Now lets find the fencing length around a square play area for her puppy that will be equals to the 4 times of side of square that is :
perimeter of square fence = 4a
= 4x16
= 64 feet.
Therefore, Gwen need to build 64 feet of fencing around the square play ground.
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