The given partial fraction divided by the fraction of sugar in a scoop is
equal to multiplying the partial fraction by the reciprocal of the fraction.
The number of scoops of sugar needed is 10 scoops.Reasons:
The amount of sugar the recipe Emma is making needs = 2 1/2 cups
Amount of sugar in each scoop of sugar = 1/4 cups
Required:
The amount of scoops Emma needs to add for the entire recipe
Solution:
The amount of sugar needed = 2 1/2 cups
Amount of sugar per scoop = 1/4 cups/scoop
Therefore;
[tex]\displaystyle Number \ of \ scoops = \mathbf{\frac{Cups \ of \ sugar \ needed}{Cups \ of \ of \ sugar \ per \ scoop}}[/tex]Which gives;
[tex]\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}}[/tex][tex]\displaystyle 2 \frac{1}{2} = \frac{5}{2}[/tex]
[tex]\displaystyle \frac{ \frac{5}{2}}{\frac{1}{4} } = \mathbf{ \frac{5}{2} \times \frac{4}{1} = \frac{20}{2 }} = 10[/tex]
Therefore;
[tex]\displaystyle Number \ of \ scoops \ needed = \mathbf{\frac{2 \frac{1}{2} \ cups \ of \ sugar }{\frac{1}{4} \ cups \ of \ sugar \ per \ scoop}} = 10 \, scoops[/tex]
The number of scoops she needs for the entire recipe is 10 scoops
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Joseph invests money in an account paying a simple interest of 2.9% per year. If he invests $60 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
Find a pair of positive integers for and b in these questions
18 + 65 = 1865
23 + 7 = 2314
Answer:
a=100
b=1
Step-by-step explanation:
18a+65b=1865
23a+7b=2314
We need to make one of the variables equal to the other
So...
The LCM for 65 and 7 is 455
So multiply 7 with 18a+65b=1865
and Multiply 65 with 23a+7b=2314
7 times 18a+65b=1865 is 126a+455b=13055
65 times 23a+7b=2314 is 1495a+455b=150410
So Subtract 126a+455b=13055 and 1495a+455b=150410
So 1369a=137355
Divide:
Which is about 100 (The actual value is 100.3323594)
Thus a=100
Substitute:
b=1
Hope this helps!
(The answer is rounded)
Will give brainly,5 stars,and thanks
Answer:
Give the person above me brainliest
Step-by-step explanation:
If the purchase price for a house is $218,500, what is the monthly payment if you put 3. 5% down for a 30 year loan with a fixed rate of 6. 5%? a. $1,332. 73 b. $1,378. 19 c. $1,247. 54 d. $646. 40.
Answer: A $1,332.73
Step-by-step explanation:
The monthly payment if you put 3. 5% down is a. $1,332. 73.
Down payment=218,500 - (218.500×3.5%)
Down payment=218.500-7,647.5
Down payment=210,852.50
Time = 12×30=360 months
rate=6.5/1,200 = 0.005416667
Using the loan payment formula
Monthly payment = (Rate + [Rate / (((1 + rate)^months) -1)] × Principal
Let plug in the formula
Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] × principal
Monthly payment = (0.005416667 + [0.005416667 / (((1.005416667)^360)-1)] ×principal
Monthly payment = 0.005416667 + [(0.005416667 / 6.9917988084 -1)] ×210,852.50
Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50
Monthly payment = 0.005416667 + [(0.005416667 / 5.9917988084)] × 210,852.50
Monthly payment = (0.005416667 + 0.0009040135) × 210,852.50
Monthly payment = 0.0063206805× 210,852.50
Monthly payment = 1,332.73
Inconclusion the monthly payment if you put 3. 5% down is a. $1,332. 73.
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List all congruent angles and write a proportion that relates the corresponding side
Proportion of corresponding side is FH/JH = HG/HK = FG/JK.
What are congruent triangles?Congruent triangles are triangles that are the same size and shape in every way. The sign for congruent is ≅ . Two triangles are considered to be congruent if the measurements of one triangle's three sides and three angles are the same as those of another triangle's sides and three angles.
Given triangles are similar ΔFGH ∼ ΔJKH
We can make the angles of this statement that correspond to each other congruent. We can then write a proportion that relates the corresponding sides to one another because the sides of similar triangles are proportional to one another.
so angles ∠GFH ≅ KJH; ∠GHF ≅ ∠KHJ; ∠HFG ≅ ∠HJK
and proportion of corresponding side is FH/JH = HG/HK = FG/JK.
Hence the proportion that relates the corresponding side are FH/JH = HG/HK = FG/JK.
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Lizzy wants to solve the equation 6(2x + 1) = 4x – 5. Which step would be an appropriate first step for Lizzy to take to solve for x?
Answer:
distribute parenthesis
Step-by-step explanation:
6(2x + 1) = 4x - 5 ← distribute parenthesis on left side
12x + 6 = 4x - 5 ( subtract 4x from both sides )
8x + 6 = - 5 ( subtract 6 from both sides )
8x = - 11 ( divide both sides by 8 )
x = - [tex]\frac{11}{8}[/tex]
(7g+2)(5g+4)=
help please !
Answer:
35g^2+38g+8
Step-by-step explanation:
(7g+2)(5g+4)
35g^2+10g+28g+8
35g^2+38g+8
Points A, B and C lie on a circle, centre O.
Angle AOC = 142°.
Find the value of y.
The value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
Let suppose that quadrilateral [tex]OABC[/tex] is a parallelogram. Then, the following conditions must be fulfilled:
[tex]\overline {OA} \cong \overline {BC}[/tex] [tex]\overline{AB} \cong \overline{OC}[/tex] [tex]\angle AOC \cong \angle ABC[/tex]In addition, if we have a rhombus we have the additional condition as A, B and C lie on the circle:
[tex]\overline{OA} \cong \overline {AB} \cong \overline {BC} \cong \overline{OC}[/tex] (4)
If we know that [tex]\angle AOC = 142^{\circ}[/tex], then the value of [tex]\angle ABC = y = 142^{\circ}[/tex].
Based on all these finding, we conclude that the value of the angle [tex]y[/tex] within the quadrilateral [tex]OABC[/tex] inscribed the circle is 142°.
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Evaluate the expression if a = 4, b = 9, and c = 1.
3b÷c1−a
–27
–9
9
27
Answer:
I used the discriminant which is √-4ac
Then I filled the numbers in, and found that 9 gets plug in for b and this becomes 9 squared, and that becomes 81. 4 is multiplied to 4 and 1 and becomes 16. Then 81 and 16 are subtracted and we get 65. We then find the square root, and will find that the answer is C.
Step-by-step explanation:
Answer:
3b÷c1−a
=3×9÷1×1-4
=27÷1-4
=27-4
=23
Please show any steps you used to solve the equation!
Solve the equation [tex]sec(theta)=2 \\0\leq theta\ \textless \ 2\pi[/tex]
I'll mark brainliest if correct!
sec(θ) = 2
By definition of secant,
cos(θ) = 1/2
Solve for θ :
θ = arccos(1/2) + 2nπ or θ = -arccos(1/2) + 2nπ
(where n is any integer)
θ = π/3 + 2nπ or θ = -π/3 + 2nπ
We get two solutions in the interval 0 ≤ θ < 2π :
θ = π/3 or θ = 5π/3
Write an equation of the line that passes through the point (3,-5) and has the slope of 2
Answer:
Y-Y1=M(x-x1)
that's the formula then fixing in your values we have
y + 5 =2(x-3)
y+5 =2x-6
Crossing over we have
y-2x=-6-5
equation of the line equals
y-2x-11 =0
Answer this .i will make you brainliest
[tex]\huge{\underline{\underline{\boxed{\sf{\purple{ǫᴜᴇsᴛɪᴏɴ}}}}}}[/tex]
(8) An aeroplane takes off from Dubai located in the +4 time zone at 13:00. It arrives in Manila in Philippines, located in the +8 time zone at 20:00.(1) Find the time in Manila when the aeroplane departsfrom Dubai.(ii) Find the time duration of the flight.(iii) What is the time in Dubai when the aeroplane arrives in Manila?[tex]\huge{\underline{\underline{\boxed{\sf{\ref{Answer}}}}}}[/tex]
(i)17.00(ii)3 hours(iii) 16.00[tex]\large\huge\green{\sf{♥ Explanation♥}}[/tex]
Dubai located +4 zone, takes off at 13.00,∴Hence, at standard it is 13.00-4 =99.00 STD talk
off reached at Manila +8 Zone at 20.00
∴Hence at standard & 2000 -8
reached.⇒ 12.00 STD
Hence time of flight was = 3 hours.(i) Time at Manila, whicle Plane de parts
12-3+8 ⇒9+8 → 17.00
(ii) duration = 3 hours.
(iii) in dubai 13.00 + 3 = 16,00
_____________________
Ans
i)17.0.0 (ii) 3 hours (iii) 16.00
________________________
♕ hence we done:) xD
Find the volume of the figure below.
Answer:
0.6
Step-by-step explanation:
10ft of object and 6ft of ground side
Josue broke a cell sample into 12 batches, each weighing 6.9 x 10 ^-10
grams. How much did the original sample weigh? Use scientific notation to express your answer.
Using proportions, it is found that the original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
This question is solved by proportions, using a rule of three.The weight of 1 batch, in grams, is of [tex]6.9 \times 10^{-10}[/tex]. How much do the sample of 12 batches weigh?The rule of three is:
1 batch - [tex]6.9 \times 10^{-10}[/tex] grams.
12 batches - x grams
Applying cross multiplication:
[tex]x = 12 \times 6.9 \times 10^{-10} = 82.8 \times 10^{-10}[/tex]
Applying scientific notation:
[tex]8.28 \times 10^{-9}[/tex]
The original sample weighed [tex]8.28 \times 10^{-9}[/tex] grams.
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Which of the following is in the range of the function based on the input-output table below?
Answer:
A.
Step-by-step explanation:
The answer is A because first:
1. we are looking for y so B and D are off the table
2. It goes from least to greatest so C is also gone
3. You are left with A
Answer:
A
Step-by-step explanation:
The range is the y value.
In this table the y value is pay per month.
What are the outliers for 7,1,9,9,12,25,9,7,7,
What is the volume of a pencil
solve the equations 3/4x = 21
Therefore, the answer is 28.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
a point f(–3, 1) is translated along the vector ⟨5, –1⟩.what are the coordinates of the image f′ ?
What is 100 plus 300??????
Answer:
The answer is 400
Step-by-step explanation:
...........
Answer:
the answer is 400 darlin
Step-by-step explanation:
Each big square below represents one whole.
What percent is represented by the shaded area?
Answer:
the frist one
Step-by-step explanation:
hope it helps
using the letters from the word equation, how many 5-letter patterns can be formed in which q isfollowed immediately by u?
Using the arrangements formula, it is found that there are 720 words that can be formed.
The number of possible arrangements of n elements is the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem:
The non-qu letters of the word equation will be arranged in 5 positions.The "qu" can be positioned in 6 ways(letters 1-2 to letters 6-7), hence:[tex]T = 6 \times 5! = 6! = 720[/tex]
There are 720 words that can be formed.
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Fred is 5 inches shorter than the quotient of Rick’s height and 4. let r represent Rick’s height. Write an expression that represents Fred’s height
Answer:
[tex] \frac{r}{4} - 5[/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
The expression till now
[tex]\\ \sf{:}\Rrightarrow \dfrac{r}{4}[/tex]
But we need the expression for five less than the quotient
[tex]\\ \sf{:}\Rrightarrow \dfrac{r}{4}-5[/tex]
You use a juice mix to make orange juice.
You combine 12 ounces of the mix with 36 ounces of water.
What is a unit rate that describes your juice?
Mr. and Mrs. Ozawa are driving their family to a vacation spot 496 miles away. They want to get there in 8 hours. What is the average speed they need to drive?
Answer:
1. Ounces
2. 62 miles per hour
Step-by-step explanation:
1. 12 OUNCES and 36 OUNCES
2. 496/8 = 62 (check 62x8 = 496)
Can i get some help ?:
Answer:
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
Step-by-step explanation:
7 + 3² - 2.5 / 4 - 1.2 = 4.82142857
( 3/4 + 1/8 ) ÷ 1/8 - 2² = 3
Which means :
7 + 3² - 2.5 / 4 - 1.2 > ( 3/4 + 1/8 ) ÷ 1/8 - 2²
There are 12 students with brown hair and 45 students with black hair in a math class. What is the ratio of students with brown hair to students with black hair?
Answer:
57 Students........................
31. One serving of party drink is comprised of 3oz of syrup, 4oz of water, and 3oz of apple juice. If a large bowl of the drink contains 237oz of apple juice, how much of the total drink is in the bowl
Answer:
790 oz
Step-by-step explanation:
Ratio:
3oz syrup : 4oz water : 3oz apple juice: 1 serving: 10oz total mixture
We know there is 10oz total mixture because 3oz of syrup + 4oz of water + 3oz of apple juice = 10oz total mixture
We want to find
237oz apple juice: ?oz total mixture
To do this, we can multiply the ratio
3oz apple juice: 10oz total mixture by 237/3, because 237/3 * 3 = 237, getting us to 237oz apple juice on one side and maintaining the ratio so that we can find the total mixture amount, so we have
237oz apple juice: 10*237/3 oz total mixture = 10*79 = 790 oz
HURRY PLS
What is the equation of this line?
y=2x-3
y= -1/2x-3
y= -2x-3
y=1/2x-3
Simplify: 1/6x + 42 + 2/5x - 8/3 -19
A: 97/30x + 23
B: 21/10x - 23
C: -21/10x + 23
D: 97/30x - 23
Answer:
A: 97/30x + 23
8-kg lead brick falls from a height of 1.6 m.
(a) Find its momentum as it reaches the ground.
Ikg-m/s
(b) What Impulse is needed to bring the brick to rest?
N-s
(c) The brick falls onto a carpet, 2.0 cm thick. Assuming the force stopping it is constant, find the average force the carpet exerts on the brick
N
(d) If the brick falls onto a 6,0 cm foam rubber pad, what constant force is needed to bring it to rest?
The magnitude of the impulse needed to bring the brick to rest is given by the initial momentum of the brick.
The correct responses are;
(a) 44.8 kg·m/s(b) 44.8 N·s(c) 6,278.4 N(d) 2,092.8 NReasons:
The velocity of the brick as it reaches the ground is given by the formula;
v² = 2·g·h
v = √(2·g·h)
Where;
h = The height of the brick, h = 1.6 m
g = The acceleration due to gravity ≈ 9.81 m/s²
Therefore;
v ≈ √(2 × 9.81 m/s² × 1.6 m) ≈ 5.6 m/s
(a) Momentum = Mass × Velocity
The momentum of the brick = 5.6 m/s × 8 kg = 44.8 kg·m/s
(b) Impulse = Force × Δt = Mass × Δv
Mass × Δv = 8 kg × (5.6 m/s - 0) = 44.8 kg·m/s = 44.8 N·s
Therefore, the impulse = 44.8 N·s
(c) The distance over which the carpet stops the brick = 2.0 cm = 0.02 m
Initial energy in the brick, E = m·g·h
Which gives;
E = 8 kg × 9.81 m/s² × 1.6 m = 125.568 J
Energy = Force × Distance
[tex]\displaystyle Force \ carpet \ exerts \ on \ brick, \ F = \frac{125.568 \, J}{0.02 \, m} = \mathbf{ 6,278.4 \, N}[/tex]
The average force the carpet exerts, F = 6,278.4 N
(d) If the brick falls on a foam which is 6.0 cm (thickness), we have;
Distance = 6.0 cm = 0.06 m
Therefore;
[tex]\displaystyle Force, \, F = \frac{125.568 \, J}{0.06 \, m} = \mathbf{2,092.8 \, N}[/tex]
The constant force needed to bring the brick to rest is, F ≈ 2,092.8 N
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