Answer:
3 quarts
Step-by-step explanation:
The Figure below shows a rectangular prism and a cube:
How many such cubes are required to completely pack the prism without any gap or overlap?
A. 288
B. 576
C. 1,152
D. 1,636
A chemist is adding pure (100%) acid to a 12 liter solution that is 15% acid in order to increase it to 49% acid. How much pure acid must she add?
How many ounces of 35% ethanol must be added to a 23 ounce mixture that contains 26% ethanol in order to obtain a mixture of 30.86% ethanol?
How many liters of 30% acid must be added to 10 liters of 53.66% acid in order to obtain a mixture that is 43% acid?
Answer:
1) 8 liters of pure acid
2) 27 liters of 35% ethanol
3) 8.2 liters of 30% acid
Step-by-step explanation:
The inicial amount of acid is 15% of 12 L, and the inicial volume is 12L.
Adding 'x' L of 100% acid, we have the amount of acid equal to 12 * 0.15 + x * 1, and the volume of 12 + x. The concentration is the amount of acid over the volume, so we have that:
(12*0.15 + x) / (12 + x) = 49/100
(1.8 + x)*100 = (12 + x) * 49
180 + 100x = 588 + 49x
51x = 408
x = 8 liters of pure acid
Similar to the solution above, for the second question we have:
(23*0.26 + 0.35*x) / (23 + x) = 30.86/100
(5.98 + 0.35*x)*100 = (23 + x) * 30.86
598 + 35x = 709.78 + 30.86x
4.14x = 111.78
x = 27 liters of 35% ethanol
For the third question, we have:
(10*0.5366 + 0.3*x) / (10 + x) = 43/100
(5.366 + 0.3x)*100 = (10 + x)*43
536.6 + 30x = 430 + 43x
13x = 106.6
x = 8.2 liters of 30% acid
Solve the system of equations.
y= 3x
y= x2-10
Answer:
(-5, 2) and (2, 6)
Step-by-step explanation:
Use the substitution method. We know that y = 3x and y = x^2 - 10, so we can set them equal to one another.
3x = x^2 - 10
x^2 - 3x - 10 = 0
Use the quadratic equation to solve for x.
x = - 5, 2
Now solve for y using these two values of x by substituting it back into the equations.
y = - 15, 6
In coordinate form, (-5, 2) and (2, 6)
Solve for u: 75u+2=12 .
Answer:
2/15
Step-by-step explanation:
75u = 12 - 2
75u = 10
u = 10 / 75 = 2/15
Answer:
75u=12-2
75u=10
u=10/75
In the function y+3=(1/3x)^2+1 what effect does the number 1/3 have on the graph as compared to the graph of y=x^2
Answer:
I think the answer is
B. it stretches the graph horizontally by a factor of 3
Step-by-step explanation:
Answer:
It shrinks the graph vertically to 1/3 its original height
One of the skylights on the roof of Bianca’s building is in the shape of the solid below.
A rectangular pyramid has a base of 14 inches by 14 inches and a height of 9 inches. A rectangular prism has a length of 14 inches, width of 14 inches, and height of 2 inches.
What is the total volume of air inside the skylight?
392 inches cubed
588 inches cubed
870 inches cubed
980 inches cubed
Answer:
B. 588 inches cubed.
Step-by-step explanation:
the pyramid base with 2inch height = 392 - 14 x 14 = 196 = 392-196 = 196
the pyramid with 9 inch height = 588.25 = 14 x 14 = 196 the adjoined upper base.
= 588.25 - 196 = 392.25 + 196 = 588^3 (inches cubed ) we only needed one base structure
We check the slant = (1/2)base = 7 then divide 392.25/7 = 56.0357142857/4
Then divide by 4 = 56.0357142857/4 = 14 and we know the slant is also 14.
We can find the isosceles central height and know it will be the smaller measure as it always is, using 14^2 - 7^2 = a^2
= 196sr - 49sr = 47sr
a^2 = √47 = 6.8556546004
So we know the diagram isn't to scale.
The equation of a rectangle pyramid =
A=lw+√l (w2)
2+√ 2+w
(l2)2+√ h2
The base is l*w*h - l*l = 392-196
or l*w + 4* h*w =196
The total volume of air inside the skylight is 980 inches cubed. Option D is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
The volume of the rectangular pyramid is (1/3) × base area × height = (1/3) × 14² × 9 = 588 cubic inches.
The volume of the rectangular prism is length × width × height = 14 × 14 × 2 = 392 cubic inches.
The total volume of air inside the skylight is the sum of the volumes of the pyramid and prism, which is 588 + 392 = 980 cubic inches.
Therefore, the answer is (D) 588 inches cubed.
Learn more about Volume here:
https://brainly.com/question/1578538
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Factor: b2-3b-4
Multiplying Quadratics—Box Method
Hey there! :)
Answer:
(b - 4)(b + 1)
Step-by-step explanation:
b² - 3b - 4
Factor by determining which numbers add up to -3 and multiply to equal -4.
-4 + 1 = -3
-4 × 1 = -4
Therefore, in factored form, the equation would be:
(b -4)(b + 1)
Please hurry
What is the solution?
Answer:
no solution
Step-by-step explanation:
I tried to solve this by doing the square root of [tex]x^{2} +49[/tex], which is x+7. x+7≠x+5
(Will mark brainliest + 20 points :)) Gary randomly chose an item from the following lot. Use this lot to match the questions in the first column with their corresponding answer.
Answer:
1) Ice cream cone = 2/7
⇒ The number of ice cream cones in the lot = 4
The total number of items in the lot = 14
Probability = the number of that particular item in the lot ÷ the total number of items in the lot.
Probability = 4/14 = 2/7
2) Soccer Ball = 1/7
⇒ The number of soccer balls in the lot = 2
The total number of items in the lot = 14
Probability = the number of that particular item in the lot ÷ the total number of items in the lot.
Probability = 2/14 = 1/7
3) Books = 5/14
⇒The number of books in the lot = 5
The total number of items in the lot = 14
Probability = the number of that particular item in the lot ÷ the total number of items in the lot.
Probability = 5/14
4) Coins = 3/14
⇒ The number of coins in the lot = 3
The total number of items in the lot = 14
Probability = the number of that particular item in the lot ÷ the total number of items in the lot.
Probability = 3/14
PLS MARK ME AS BRAINLIEST!!
Ruth contributes 18% of the total cost of her individual health care. This is $67.50
deduction from each of her biweekly paychecks. What is the total value of her individual
coverage for the year?
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
To learn more about Total Coverage, refer https://brainly.com/question/17596754?referrer=searchResults
Answer:
Step-by-step explanation:
Total value of annual health coverage = $ 9000
Calculation of total annual health coverage
Let the total annual health care expenditure = x
Ruth pays 18% of total health care expenditure, which is $ 67.50 for two weeks (ie 15 days)
So, total paid for one month = 67.5 x 2 = 135
And, total paid for full year = 135 x 12 = 1620
As mentioned, she pays 18% of total annual health care expenditure
Hence, 18% x = 1620
18 x / 100 = 1620
x = (1620 x 100) / 18
= 9000
Rosalia went on a long bike ride. The table shows how long she biked and the distance she
traveled. Determine whether the relationship between hours biked and miles traveled is
proportional.
-91
O The relationship is not proportional.
O The relationship is proportional.
Answer:
The relationship is not proportional.
Step-by-step explanation:
To see if many ratios are (fair in amount, related to something else/properly sized compared to something else), you could write them as fractions, reduce them, and compare them. If the reduced fractions are all the same, then you have (fair in amount, related to something else/properly sized compared to something else) ratios.
y/x=c.o.p
c.o.p=constant of proportionality.
the rate of change also know as the constant of (fair in amount, related to something else/properly sized compared to something else)ity (k = y/x) which is the constant ratio between two (fair in amount, related to something else/properly sized compared to something else) amounts y/x represented by the symbol k which may be a positive clear and sensible number. The x value is related to the y value such as in the equation y = kx.
Guess the riddle!!!!
1 rabbit saw 9 elephants while going to the river. Every elephant saw 3 monkeys going to the river. Each monkey had 1 tortoise on each hand.
How many animals are going to the river ?
Answer: 10 animals would be going to the river
Step-by-step explanation:
Took the test
6x + 3y = 9
2x + 3y = 1
Solve the system of equations.
A)
x = 2, y = -1
B)
x = -1, y = 2
C)
x=1/2,y=3
D)
x=3,y=-1/2
Answer:
A
Step-by-step explanation:
Given the 2 equations
6x + 3y = 9 → (1)
2x + 3y = 1 → (2)
Subtracting the 2 equations term by term eliminates the y- term
Subtract (2) from (1) term by term, that is
(6x - 2x) + (3y - 3y) = 9 - 1
4x = 8 ( divide both sides by 4 )
x = 2
Substitute x = 2 into either of the 2 equations and evaluate for y
Substituting into (2)
2(2) + 3y = 1
4 + 3y = 1 ( subtract 4 from both sides )
3y = - 3 ( divide both sides by 3 )
y = - 1
The solution is x = 2, y = - 1 → A
Plz answer the following equation. Plz answer all the questions... !!! 20 pts !! With explanations of each and plz can you make e understand them.
Answer:
add the negative to the 0 that is left alone at the end then carry the x2 over to the side bringing it down with the x and cancel them taking away the 2. the answer is -1
Step-by-step explanation:
Answer:
2+√3
2-√3
Step-by-step explanation:
4x-1-x²=0x²-4x+1=0x²-4x+4-3=0(x-2)²=3x-2=√3 ⇒ x= 2+√3x-2= -√3 ⇒ x= 2-√3Roots are irrational
The point-slope form of the equation of the line that passes through points 8,4 and 0,2 is y-4=1/4 (x-8) what is the slope intercept form of the equation for this line
Answer:
Step-by-step explanation:
y - 4 = 1/4(x - 8)
y -4 = 1/4x - 2
y = 1/4x + 2
someone help please, summer school is annoying
Answer:
6
Step-by-step explanation:
2y/3 + 1/3 = y/2 + 1/6
We want to eliminate the fractions
The least common multiple of 3,2 and 6 is 6
Multiply each side by 6 to get rid of the fractions
6(2y/3 + 1/3) = 6(y/2 + 1/6)
4y +2 = 3y +1
$4.25 for 64 fluid ounces .
What is the unit rate
Answer: $0.07 per unit
Step-by-step explanation:
4.25/64
Answer:
0.07
Step-by-step explanation:
divide
A parking lot has four sides. One pair of opposite sides are 100 yards long. The other two sides are 60 yards long. The distance from one end of the longer side to the opposite end of the shorter side is 120 yards. Is the parking lot a rectangle? Answer the questions below to find out.
5. If the distances given form a right triangle, which number is the hypotenuse, and why?
6. Which numbers are the two sides?
Answer:
The parking lot does not form a rectangle.
Step-by-step explanation:
Given: One pair of opposite sides of parking lot are 100 yards long. The other two sides are 60 yards long.
The distance from one end of the longer side to the opposite end of the shorter side is 120 yards.
To find: If the distances given form a right triangle?
Also, to find the hypotenuse and the numbers which represent the two sides.
Solution:
In a triangle, if the square of the length of the longest side is equal to the sum of the squares of the other two sides, then the triangle is said to be a right angled triangle.
[tex](60)^2+(100)^2=3600+10000=13600\\(120)^2=14400\\\therefore (60)^2+(100)^2\neq (120)^2[/tex]
So, the triangle is not a right angled triangle.
So, none of the angles of the parking lot forming a quadrilateral is equal to [tex]90^{\circ}[/tex].
Hence, the parking lot is not a rectangle although the opposite sides are equal.
(A quadrilateral in which opposite sides are equal such each angle is [tex]90^{\circ}[/tex] is a rectangle )
The distances given do not form a right triangle.
The fuel efficiency of passenger cars has increased significantly since the 1970s. A linear model of this situation is given below, where x represents the number of years after 1970, and y represents the average miles per gallon. Interpret the slope.
A. For each year since 1970, passenger car fuel efficiency has increased by 0.29 gallons per mile.
B. For each year since 1970, passenger car fuel efficiency has increased by 13 gallons per mile.
C. For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
D. For each year since 1970, passenger car fuel efficiency has increased by 13 miles per gallon.
its C not A because
For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
Answer: The answer is C. For each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
Step-by-step explanation:
In a linear model of the form y = mx + b, m is the slope and b represents the y-intercept.
In this situation, 0.29 is the slope.
The slope is the ratio of the change in y to the change in x.
In context, the slope indicates an increase of 0.29 miles per gallon per year after 1970.
Therefore, the slope means that for each year since 1970, passenger car fuel efficiency has increased by 0.29 miles per gallon.
What is the answer to this 8-(-8)=
Answer:
16
Step-by-step explanation:
the two negatives cancel out so if you are subtracting -8 from 8 you would actually end up adding them.
hope it helps!
Answer:
16
Step-by-step explanation:
personally I learned that when I see " -(- " in a equation it just means addition.
Draw rectangles such as the ones shown to find fraction equivalent to 2/5 and 1/3 that have the same denominator
Answer:
2/5: 1/3:
6/15 5/15
Step-by-step explanation:
Sorry I couldn't upload a photo for some reason. If you multiply 2/5 by 3 you'll get 6/15, and if you multiply 1/3 by 5 you will get 5/15. I really hope this helps, and yes, I double-checked, it is correct. Have a great day!!!
The equation d = 3sin (16t) measures the displacement of a swinging object in simple harmonic motion.
t is measured in
seconds and d is measured in inches.
What is the displacement to the nearest inch, when t = 10? NOTE: The angle is in
radians.
Provide your answer:
d=
inches
Answer:thats hard
Step-by-step explanation:
Indicate the method you would use to prove the two triangles congruent. If no method applies, enter "none."
SSS
SAS
ASA
AAS
None
Answer:
SSS Theorem
Step-by-step explanation:
Answer:
SSS
Step-by-step explanation:
They share a side so that's the third side that's the same
A tree casts a 204 centimeter shadow. A person next to the tree casts a 85 centimeter shadow. If the person is 154 centimeters tall, how tall is the tree to the nearest centimeter?
Answer
would it be 135?
Step-by-step explanation:
Solve for x: x + 18 = -37 A. x = -55 B. x = -18 C. x = -19 D. x = 14
Answer:
A. x= -55
Step-by-step explanation:
got it
which is lighter 900000g or 9 tonnes
900000g coz 9 tonnes is like 9000000g
Answer:
900000gm is lighter than 9 tonnes
Step-by-step explanation:
907185 = 1 ton
907185 x 9 = 8164665
You underline how many digits = 7 and see that 900000gm has only 6 digits.
14 weeks is expressed as a percentage of 50 weeks is?
Answer:
28%
Step-by-step explanation:
Express 14 as a fraction of 50 and multiply by 100%, that is
[tex]\frac{14}{50}[/tex] × 100% ( cancel 50 and 100 by 50 )
= 14 × 2 %
= 28%
please help as quickly as possible
Answer:
54/125
Step-by-step explanation:
2/375, 2/125, 6/125, 18/125
It is obvious the common ratio = 3
The next term = 3*18/125= 54/125
Answer: 54/125
Step-by-step explanation:
Please answer!!! i’m trynna pass
Answer:
-6 ≤y≤9
Step-by-step explanation:
The range is the values for the outputs
The range is from -6 inclusive to 9 inclusive
-6 ≤y≤9
What is the area of the composite figure?
(6pi+4) cm
O(6pi+16) cm
0 (12pi +4) cm
0 (12pi+16) cm
2 cm
Answer: [tex]6\pi +4[/tex]
Step-by-step explanation:
The normal formula for area of a circle is [tex]\pi r^2[/tex] so remember it. Itll be important for the rest of your life. Now this isnt a normal circle, this is a semi circle. So, you should divide by 2.
Three Semi-Circles:
We are given the radius which is 2 cm. [tex]\frac{\pi2^2 }{2} =2\pi[/tex]
Now we gotta multiply that answer by 3 because there are three semi circles.
[tex](2\pi )(3)=6\pi[/tex]
Area of a Square:
This is simple, do [tex]s^2[/tex] to get 4