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Complete Question
Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3.
a) How much of each juice is needed to make 25 liters of this punch?
b) How much punch can she make if she has only 6 cups of plum juice?
c) How many cups of pear juice should she use to make the quantity of punch from part (b)?
Answer:
a)For pear =
12.5 liters
For Pineapple
= 5 liters
For plum
= 7.5 liters
b) 20 cups of punch
c) 10 cups of pear juice
Step-by-step explanation:
Jane’s favorite fruit punch consists of pear, pineapple, and plum juices in the ratio 5:2:3.
The total proportion is :
5 + 2 + 3 = 10
a) How much of each juice is needed to make 25 liters of this punch?
For pear =
5/10 × 25 = 12.5 liters
For Pineapple
= 2/10 × 25 = 5 liters
For plum
= 3/10 × 25 = 7.5 liters
b) How much punch can she make if she has only 6 cups of plum juice?
The ratio of plum juice is 3
6 cups / 3 = 2 cups per portion
Since 2 equals 2/3 of 3,
The quantity of pineapple juice = 2/3 of the plum juice
2/3 x 6 cups = 4 cups
Since 5 equals 5/3 of 3, the amount of pear juice amount 5/3 of the plum juuce
5/3 x 6 cups = 10 cups
So, the number of cups are
Pear juice = 10 cups
Pineapple juice = 4 cups
Plum juice 6 cups
Total=( 10 + 4 + 6) = 20 cups of punch
c) How many cups of pear juice should she use to make the quantity of punch from part (b)?
10 cups of pear juice can be used to make the quantity of punch in part b
Answer:
10 cups of pear juice
Step-by-step explanation:
Find angles in isosceles triangles...
Answer:
68
Step-by-step explanation:
Given is an isosceles triangle, therefore measures angles opposite to equal sides would be equal.
Hence,
56° + 56° + x° = 180°
112° + x° = 180°
x° = 180° - 112°
x° = 68°
x = 68
Answer:
x = 68°Step-by-step explanation:
The triangle is isosceles as two sides have same length
Angles opposite to same sides have same value, therefore two of them equal to 56°
x = 180° - 2*56°x = 180° - 112°x = 68°Which algebraic expression represents “the class was divided into six equal groups”?
6 + w
6w
StartFraction 6 Over w EndFraction
StartFraction w Over 6 EndFraction
Answer:
Option D StartFraction w Over 6 EndFraction is correct option.
Step-by-step explanation:
We need to find algebraic expression that represents “the class was divided into six equal groups”
Let complete class strength is w
Dividing into six equal groups we get w/6
The algebraic expression that represents “the class was divided into six equal groups” is w/6
So, Option D StartFraction w Over 6 EndFraction is correct option.
Answer:
d
Step-by-step explanation:
i got it right
Simplify the given expression using only positive exponents. Then complete the statements that follow. [(X^2y^3)^-1/(x^-2y^2z)^2]^2
The exponent on x is___
The exponent on y is___
The exponent on a is____
Answer:
As
[tex]\:\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=x^4y^{-14}z^{-4}[/tex]
The exponent on x is 4The exponent on y is -14The exponent on z is -4Step-by-step explanation:
Given the expression
[tex]\left[\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right]^2[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}[/tex]
[tex]\left(\frac{\left(x^2y^3\right)^{-1}}{\left(x^{-2}y^2z\right)^2}\right)^2=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]
[tex]=\frac{\left(\left(x^2y^3\right)^{-1}\right)^2}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex]
as
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]
so the expression becomes
[tex]=\frac{\frac{1}{x^4y^6}}{\left(\left(x^{-2}y^2z\right)^2\right)^2}[/tex] ∵ [tex]\left(x^2y^3\right)^{-1}=\frac{1}{x^2y^3}[/tex]
as
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n[/tex]
so the expression becomes
[tex]=\frac{\frac{1}{x^4y^6}}{\frac{y^8z^4}{x^8}}[/tex] ∵ [tex]\left(x^{-2}y^2z\right)^2=\frac{y^4z^2}{x^4}[/tex]
as
[tex]\mathrm{Divide\:fractions}:\quad \frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot \:d}{b\cdot \:c}[/tex]
so the expression becomes
[tex]=\frac{1\cdot \:x^8}{x^4y^6y^8z^4}[/tex]
[tex]=\frac{x^8}{x^4y^6y^8z^4}[/tex]
as
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
so the expression becomes
[tex]=\frac{x^{8-4}}{y^8y^6z^4}[/tex]
[tex]=\frac{x^4}{y^8y^6z^4}[/tex]
[tex]=\frac{x^4}{y^{14}z^4}[/tex]
as
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-1}=\frac{1}{a}[/tex]
so the expression becomes
[tex]=x^4y^{-14}z^{-4}[/tex]
Therefore,
The exponent on x is 4The exponent on y is -14The exponent on z is -4Olivia went to buy shoes at the mall. The shoes cost $55. If tax was 8%, how much did Olivia pay in all? i don't understand it
Answer:
$59.40
Step-by-step explanation:
8% is equal to 0.08
since you are adding the tax to the original cost you will multiply 55 by 1.08 to get the cost of the shoes plus the tax.
Answer:
55 times .8 =44$
Step-by-step explanation:
Will mark BRAINLIEST!!
3=1/2(x+4)
3=1/2(x+4)
x+4= 3×2
x+4= 6
x=6-4
x=2
Can a right triangle have sides of 12, 16, and 20?
Determine if the statement is True or False:
The length of the shorter segment cut by the altitude from the obtuse angle to the longer base of an isosceles trapezoid is equal to the average of the bases.
2.1(0.2x−1.4)=1.3(0.4x−3.5)
Answer:
x=9.84375
Step-by-step explanation:
...
Answer:
16.1=x
Step-by-step explanation:
2.1(0.2x-1.4)=1.3(0.4x-3.5) Distribute
0.42x-2.94=0.52x-4.55 Combine like terms
+4.55 +4.55
0.42x+1.61=0.52x
-0.42x -0.42x
1.61=0.1x
0.1 0.1
16.1=x
what is 4.9x10^-3 in standard form
Answer:
0.0049
Step-by-step explanation:
Answer: 0.0049
There u go luv, have a nice day :)
A ship leaves port on a bearing of 20.2 degrees East of North and travels 6.5 miles. The ship then turns due East and travels 3.8 miles.
How far is the ship from the port, and what is its bearing?
Distance: 8.6 miles; Bearing: 20.2 degrees West of North.
Distance: 8.6 miles; Bearing: 20.2 degrees East of North.
Distance: 8.6 miles; Bearing: 44.7 degrees East of North.
Distance: 8.6 miles; Bearing: 44.7 degrees West of North.
Answer:
C
Step-by-step explanation:
Distance: 8.6 miles; Bearing: 44.7 degrees East of North.
The distance of the ship which leaves port on a bearing of 20.2 degrees East of North is 8.6 miles and its bearing is 44.7 degrees East of North.
What is cosine law?When the three sides of a triangle is known, then to find any angle, the law of cosine is used.
It can be given as,
[tex]c^2=a^2+b^2-2ab\cos C\\a^2=c^2+b^2-2ab\cos A\\b^2=a^2+c^2-2ab\cos B[/tex]
Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.
A ship leaves port on a bearing of 20.2 degrees East of North and travels 6.5 miles. The ship then turns due East and travels 3.8 miles.
This problem is shown in the image. The distance of ship from initial point is,
[tex]c=\sqrt{6.5^2+3.8^2-{2\times6.5\times3.8\times\cos (110.2)}}\\c\approx8.6\rm\; miles[/tex]
The measure of the angle x is,
[tex]\angle x=\cos^{-1}\dfrac{8.6^2+3.8^2-6.5^2}{2\times8.6\times3.8}\\\angle x=44.7^o[/tex]
Hence, the distance of the ship which leaves port on a bearing of 20.2 degrees East of North is 8.6 miles and its bearing is 44.7 degrees East of North.
Learn more about the law of cosine here;
https://brainly.com/question/4372174
PLEASE HELP ME! (It's not "B")
Answer:
b is the correct answer
7) How far away from a 340 foot redwood tree would you need to stand, if the angle of elevation to the top of the tree is 550? Round your answer to the nearest foot.
Answer:
The required distance away from the foot of the tree is 238.0 feet.
Step-by-step explanation:
The height of the redwood tree = 340 feet, and the angle of elevation to its top = [tex]55^{o}[/tex].
let the required distance be represented by x, applying the appropriate trigonometry function, we have;
Tan θ = [tex]\frac{opposite}{adjacent}[/tex]
Tan [tex]55^{o}[/tex] = [tex]\frac{340}{x}[/tex]
⇒ x = [tex]\frac{340}{Tan 55^{o} }[/tex]
= [tex]\frac{340}{1.4282}[/tex]
= 238.062
x = 238.0 feet
The required distance away from the foot of the tree is 238.0 feet.
Three Variables LINEAR EQUATION
Answer:
x= 1, y= -2, z= 5
Step-by-step explanation:
Please see the attached picture for the full solution.
Which answer choice shows 12.444 rounded to the nearest half?
A. 11
B. 11.5
C. 12
D. 12.5
Answer:
C. 12
Step-by-step explanation:
Remember 0 to 4 turn it back
5 or above give it a shove.
Since 12.444 is around 0 to 4.
We can round that to 12.
Answer:
C.12
Step-by-step explanation:
Rounding a number involves replacing the number with an approximation of the number that results in a shorter, simpler, or more explicit representation of said number based on specific rounding definitions. For example, if rounding the number 2.7 to the nearest integer, 2.7 would be rounded to 3.
There are screws, nuts and bolts in a tool box. The ratio of the number of
Screws to the number of nuts to the number of boits is 2:3:7. The
difference between the number of nuts and the number of bolts is 112.
Find the number of each item
Answer:
Step-by-step explanation:
56:84:196 would be the answer
1
2 3
4
5
6
7
8
7
During a basketball practice, Mai attempted 40 free throws and was successful on
25% of them.
How many successful free throws did she make?
The answer
Answer:
10Step-by-step explanation:
Total attempts = 40Successful attempts = 25%Number of successful free throws:
25% of 40 =0.25*40 = 10Question 121 pts
Daniel had $30 to spend at the fair. If the admission to the fair is $8 and the rides cost $1.25 each, what is the greatest number of rides Daniel can go on?
Answer:
17 rides
Step-by-step explanation:
30-8=22
22 divided by 1.25=17.6 and then you cant go on without 1.25 so 17
Valeria does not charge an initial fee for babysitting but charges $10 an hour. Daniel charges $8 per hour plus an initial fee of $10. How many hours does Valeria need to babysit in order to make more money than Daniel?
Answer:
it depends how many hours both of them make but here is what you can do:
Valeria needs to do 2 hours more than Daniel. This is because Daniel makes $18 and hour and Valeria makes only 10. If you do 10*2 or 10+10 you get 20 which is greater than 18. I hope this helps and good luck!
Plz help me with this question if you can explain plz do also thank you!!
Answer:
The answer is b because h = hours and 45 is the mph
Step-by-step explanation:
the diagram shows a right-angle triangle.
Answer:
Step-by-step explanation
The shortest length of the right-angled triangle is 4 cm.
What is a right-angle triangle?A right-angled triangle is a triangle, that has one of its interior angles equal to 90 degrees or anyone angles is a right angle.
Given is, the diagram shows a right-angle triangle.
We have area of the right-angle triangle = 18 cm²
We know that area of a right-angle triangle = 1/2(base)(height)
18 = 1/2(x - 1)(x + 4)
36 = (x - 1)(x + 4)
x² + 4x - x - 4 = 36
x² + 3x - 4 = 36
x² + 3x - 4 - 36 = 0
x² + 3x - 40 = 0
x² - 5x + 8x - 40 = 0
x(x - 5) + 8(x - 5) = 0
x + 8)(x - 5) = 0
x = -8 or 5
we can only use positive numbers because length can't be negative,
Thus, x = 5
The shortest side is definitely one of the 2 legs. The hypotenuse of a triangle is the longest side.
Therefore,
height = x - 1 = 5 - 1 = 4 cm
base = x + 4 = 5 + 4 = 9 cm
Hence, the shortest length of the right-angled triangle is 4 cm.
learn more on right-angled triangle here:
brainly.com/question/2292567
#SPJ2
Solveby factoring :
p2 + 8p + 12 = 0
(show steps please)
Answer:
(p + 6)(p + 2)
Step-by-step explanation:
I believe you meant p^2 + 8p + 12 = 0, in which " ^ " indicates exponentiation.
Note that 12 = 2*6, and that these two factors, 2 and 6, add up to 8. Thus,
p^2 + 8p + 12 = 0 = (p + 6)(p + 2)
The water level of a lake is at 35ft. It is rising at a rate of 3 inches per day. How many days will it take the lake to reach 40 ft?
hello! um what is the equivalent to 3/7?
Answer:
9 goes in the blank
Step-by-step explanation:
Since 21 divided by 7 is 3 then you would have to multiply 3 to the numerator to get the equivalent. Hope this helped :)
Answer:
9/21
Step-by-step explanation:
multiply the numerator and denominator by 3 and you will get 9/21
is y= 12 x a proportinal relationship
Answer: yes
Step-by-step explanation:
AWARDING MORE POINTS question in pic
Answer:
sad
Step-by-step explanation:
Given that 4x−5y=39
Find y when x=3
Give your answer as an improper fraction in its simplest form.
Answer:
- [tex]\frac{27}{25\\}[/tex]
Step-by-step explanation:
4x−5y=39
for x=3
12 - 5y = 39
-5y = 39 -12
-5y = [tex]\frac{27}{5\\}[/tex]
-y = [tex]\frac{27}{25\\}[/tex]
y = - [tex]\frac{27}{25\\}[/tex] = -1 [tex]\frac{2}{25\\}\\[/tex]
-27/5 or -5 2/5
Step-by-step explanation:
4x-5y=39 while x=3
4(3)-5y=39 add x into bracket
12-5y=39 result of 4*3
12-5y-12=12-39 substrate non variable number to each side
5y = -27 the result from upper substraction
y= -27/5 the result mixed fraction form -5 2/5
Which ratio is less than 15 Over 24
A. 1/2
B. 7/8
C. 19/24
D. 6/8
Answer:
A
Step-by-step explanation:
Pls, help Which of the following is true?
|−6| < 5
|−6| < |5|
|−5| < |−6|
|−5| < −6
Answer:
C
Step-by-step explanation:
Its not A because The left side 6 is not less than the right side 5, which means that the given statement is false.
Its not B because The left side 6 is not less than the right side 5, which means that the given statement is false.
Its C because The left side 5 is less than the right side 6, which means that the given statement is always true.
Its not D because The left side is 5 is not less than the right side 6, which means that the given statement is false.
A fair spinner has 9 equal sections: 3 red, 4 blue and 2 green. It is spun twice. What is the probability of getting not green then green?
Simplify the expression
Answer:
f(x) = x - 6 g(x) = x - 5Step-by-step explanation:
[tex]\dfrac{x^2-8x+12}{x^2-7x+10}\\\\x^2-7x+10\ne0\ \iff\ x=\frac{7\pm\sqrt{49-40}}{2}\ne0\ \iff\ x\ne5\ \wedge\ x\ne2\\\\\\\dfrac{x^2-8x+12}{x^2-7x+10}=\dfrac{x^2-2x-6x+12}{x^2-2x-5x+10}=\dfrac{x(x-2)-6(x-2)}{x(x-2)-5(x-2)}=\\\\\\ =\dfrac{(x-2)(x-6)}{(x-2)(x-5)}=\dfrac{x-6}{x-5}\\\\\\f(x)=x-6\\\\g(x)=x-5[/tex]
