Answers
Answer:
[tex]9\frac{57}{63}[/tex]
Step-by-step explanation:
First, we need to turn them into improper fractions:
[tex]2\frac{4}{7}[/tex] + [tex]7\frac{3}{9}[/tex]
7 x 2 + 4
7 x 9 + 3
[tex]\frac{18}{7}[/tex] + [tex]\frac{66}{9}[/tex]
Next, we need to find a common multiple of both 7 and 9
7, 14, 21, 28, 35, 42, 49, 56, 63
9, 18, 27, 36, 45, 54, 63
So the denomonator turns into 63.
We've multiplied the denomonater 9 times for the first fraction and 7 times for the second fraction, we therefore have to do the same to the numerator.
18 x 9 = 162
66 x 7 = 462
[tex]\frac{162}{63}[/tex] + [tex]\frac{462}{63}[/tex] = [tex]\frac{624}{63}[/tex]
Next, we have to turn it back into a mixed number.
To work it out: 624 / 63 = 9 (1 s.f) <--- Mixed number.
9 x 63 = 567
624 - 567 = 57 (Working out the remainder.)
Combining them, the answer is therefore [tex]9\frac{57}{63}[/tex]
Hope this helps and have a good day!
Related Questions
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
Answers
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
https://brainly.com/question/4609414
Slope= -1/2 Y-intercept =4
Answers
Answer:
no I'm pretty sure it's wrong
Step-by-step explanation:
the y intercept for that to right us -4
Kyle was playing archery and shot 20 arrows. 30% of them hit the bullseye. how many of the arrows hit the bullseye?
Answers
0.2 = 1%
6 = 30%
6 arrows hit the bullseye
please help meeee, thank youuuu
Answers
Answer:
45
Step-by-step explanation:
I think so i dont know
Answer:
45
Step-by-step explanation:
Just do the regular number sequence (1-44) but add 1 since this specific sequence starts with 2.
Hope this helped! ^^how do i tell if an angel is comolentery, supplmentsry, or neither? I was not at school the day they showed me this?
Answers
Answer:
supplementary angles - two angles are supplementary when they add up to 180 degrees (a straight line)
complementary angles - two angles are complementary when they add up to 90 degrees (a right angle)
hopefully this helps! :)
Answer:
1. complementary
2. neither
3. supplementary
4. complementary (x = 6)
10x + 30 = 90 x + 3 = 9 x = 6
5. supplementary (x = 20)
4x + 40 + 3x = 180 7x = 140 x = 20
6. x = 50.5
2x + 79 = 180 2x = 101 x = 50.5
Step-by-step explanation:
When the measurement of the angles adds up to 90 degrees, the angles are complementary. When the sum of the angles is 180 degrees, then they are supplementary.
Solve the inequality f – 4 ≤ 9 for f
help me.
Answers
Answer:
13
Step-by-step explanation:
Have a great day!! :)
AMIGOS AND AMIGAS PLS HELP MY POOR BRAIN ILY FAM:
1) 8+ 9p = 9p - 7
2) 2(3x + 6) = 3(2x - 6)
Answers
1. 9p - 9p = -8 - 7
0 = - 15
2. 6x + 12 = 6x - 18
6x - 6x = - 18 - 12
0 = - 30
That's what I got
on a map where each unit represent one kilometer, two marainas are located at p(4,2) and Q(8,12). if a boat travels in a straight line from one marina to the other, how far does the boat travel?
Answers
Answer: 5 kilometers.
Step-by-step explanation:
simplify an expression for the perimeter of the rectangle
Answers
6w+10w-4
16w-4
16w-4
Hope this helps!!
The expression for the Perimeter of rectangle is 16w-4.
What is perimeter of rectangle?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Perimeter of the rectangle = 2(length+width)
Given the paramters are;
length = 5w-2
width = 3w
Perimeter of the rectangle = 2(length+width)
Perimeter = 3w+3w+(5w-2)+(5w-2)
= 6w+10w-4
= 16w-4
To know more about perimeter of rectangle refer to :
brainly.com/question/10452031
#SPJ2
this question is hard
Answers
A) Total number of old plans = 3500 + 4700 = 8200
In the new month, the unlimited plans increased by 55%, which adds
0.55 • 3500 = 1925
unlimited plans, while the limited plans decreased by 25%, which subtracts
0.25 • 4700 = 1175
limited plans. Then
Total number of new plans = (3500 + 1925) + (4700 - 1175) = 8950
which corresponds to a percent change of
(8950 - 8200)/8200 ≈ 0.0915 = 9.15%
That is, percent change is given by
(new value - old value) / (old value)
B) The percent change is positive, so it's a percent increase.
Find the slope of the line segment shown.
A) -1/2
B -1
C 1/3
D 1
Answers
Answer:
D)
Step-by-step explanation:
The answer would be D. The slope of a line is how fast it climbs. Height divided by base. Up divided by over. Thus, if it goes across 3 and up 1, its slope would be 1/3. If it goes across 1 and up 2, the slope is 2. If it goes across 1 and up -1, the slope is -1.
HOPE THAT HELP YOU MARK ME BRINILYLIST
After the first four games of a professional football season, three players scored a total of 80 touchdowns.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns.
Andre Roberts scored the remaining touchdowns.
How many touchdowns did Andre Roberts score?
A.20 touchdowns
B.28 touchdowns
C.32 touchdowns
D.52 touchdowns
Answers
Answer:
b
Step-by-step explanation:
Andre Roberts scored a total of 34 touchdowns
An equation is an expression that shows the relationship between two or more variables and numbers.
The total touchdowns is 80.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns. = 40% of 80 = 0.4 * 80 = 32
Let x represent the number of touchdowns scored by Andre Roberts, hence:
x + 14 + 32 = 80
x + 46 = 80
x = 34
Andre Roberts scored a total of 34 touchdowns
Find more about equation at: https://brainly.com/question/2972832
The minute hand of a clock has a length of 12 cm, and the hour hand has a length of 8 cm
a) How far does the tip of the minute hand travel in one hour?
b) How far does the tip of the hour hand travel in 12 hours?
c) How far does the tip of each hand travel in one week?
Answers
Answer:
I have no any ideas
Step-by-step explanation:
sorry
PLEASE SHOW YOUR WORK !!! I REALLY NEED HELP
Answers
I did the math in the link below
Can someone help me please?
Answers
Answer: a=(3,-4)
B=(3,-1)
C=(5,-2)
Step-by-step explanation:
What is the approximate value of t?
Answers
Answer:
8.48
Step-by-step explanation:
36 + 36 = 72
t^2 = 72
t = 6[tex]\sqrt{2}[/tex] = 8.48
Answer: 6
Step-by-step explanation:
HELLPPPP MEEEEE ASAPPPPPPP PLEASEEEEEEEEEEEEWEEEEEEEE
Answers
Answer:SORRY CANT HELP U THERE
Step-by-step explanation:
IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.
Answers
Answer:
I would say not valid
Step-by-step explanation:
well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject
Calculate the area of trapezium CDEF.
Answers
Answer:
i think 24 cm² is answer good luck
Translate and solve. The quotient of m and 6/7 is 5/6
Answers
Answer:
m / 6/7 = 5/6
m = 35
Step-by-step explanation:
Answer:
m = 5/7Step-by-step explanation:
The quotient of m and 6/7 is 5/6:
m ÷ 6/7 = 5/6m = 5/6 × 6/7m = 5/7Cans of peas are on sale at 2 for $1.19 how much would 12 cans cost
Answers
Answer:uh 2 divide 1.19 and add 12 i think
Step-by-step explanation:
what percent of 81 is 51
Answers
Answer:
62.96%
Step-by-step explanation:
do this
51/81 ×100%
Answer:62.953%
Step-by-step explanation:
81 * (%) = 51
% = 51 / 81
% = 62.953
(a) The area of a rectangular garden is 5658 m?.
If the width of the garden is 69 m, what is its length?
(b) The perimeter of a rectangular window is 262 cm.
If the length of the window is 73 cm, what is its width?
Answers
A) Length is 82 m
B) Width is 58 cm
Hope this is helpful!
What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!
Answers
Answer: A. they will have too much butter
Step-by-step explanation: to much
a cylinder has a radius of 3 feet and a height of 2.1 feet. what is the approximate volume of the cylinder? use 3.14 for pi. 12.6 ftł 59.3 ftł 237.5 ftł 8550.2 ftł
Answers
Answer:
59.3ft³
Step-by-step explanation:
The formula for the volume of a cylinder is V= πr²h, where r is radius and h height.
So in our case, we have r= 3ft and h=2.1 ft and π≅3.14
So from the formula for the volume of a cylinder, we get 3.14*3²*2.1 = 59.3 ft³
The volume of the cylinder is about 59.3 ft³
What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.
Answers
Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Did not get into their first-choice college.Event B: Took AP chemistry.According to the chain given, the percentages associated with not getting into their first-choice college are:
0.1375(chemistry).0.1575(physics).0.24(Env Sci).0.07(Biology).Hence:
[tex]P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605[/tex]
The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence [tex]P(A \cap B) = 0.1375[/tex]
Then, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273[/tex]
0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287
Answer: 0.2273
Step-by-step explanation: because it says so <3
Someone please help meh
Answers
Answer:
1100
Step-by-step explanation:
Answer:
A = 55.15
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos A = adj side / hypotenuse
cos A = 4/7
Taking the inverse cos of each side
cos ^-1 ( cos A) = cos ^-1( 4/7)
A =55.15009542
To the nearest hundredth
A = 55.15
What is the common denominator of StartFraction 1 Over a EndFraction StartFraction 1 Over b EndFraction in the complex fraction StartFraction 1 Over a EndFraction minus StartFraction 1 Over b EndFraction divided by StartFraction 1 Over a EndFraction 1 Over b EndFraction?.
Answers
The common denominator is 1
Given the expression:
[tex]\frac{1/a-1/b}{1/a1/b}[/tex]Find the LCM of the numerator to have:
[tex]\dfrac{\frac{b-a}{ab} }{\frac{1}{a} \frac{1}{b} }[/tex]Simplify both the numerator and the denominator to have:
[tex]= \dfrac{\frac{b-a}{ab} }{\frac{1}{ab} }\\= \frac{b-a}{ab} \times ab\\=\frac{b-a}{1} \times 1 \\=\frac{b-a}{1}[/tex]
From the result, we can see that the common denominator is 1
Learn more about fractions here: https://brainly.com/question/17743912
Answer:
here is the correct answer for edge2022
Step-by-step explanation:
3,408 divided by 41
Explanation in traditional method
52 POINTS PLS HELP
Answers
Answer:
83.1219512195
Step-by-step explanation:
Hope this helps!
83.12195
traditional method is either long division or short division