After removing 600 litres from a tank that was half full, it became one-third full. By setting up an equation, we determine that every 600 litres represents one-sixth of the tank's full capacity. Multiplying 600 litres by 6, we find the tank's full capacity is 3600 litres.
The question involves determining the total capacity of a tank based on information given about volume reductions and proportions of fullness. Initially, the tank is half full, but after removing 600 litres, it becomes one-third full. We can set up an equation to find out the total capacity of the tank (T).
Since removing 600 litres takes the tank from being half full to one-third full, that means 600 litres correspond to one-sixth of the tank's capacity because one half minus one-third equals one-sixth.
Now we set up our equation: 600 litres = T/6. To solve for T, we multiply both sides of the equation by 6:
(600 litres)Therefore, the full capacity of the tank is 3600 litres.
Which description can be written as the expression 6b+5?
a) the difference of six times a number and five
b) the sum of six times a number and five
c) quotient of six times a number and five
d) the product of six times a number and five
Answer: b) the sum of six times a number and five
Step-by-step explanation:
The given expression is [tex]6b+5[/tex], where b represents any number.
The above expression has two terms combined by addition operation.
In the first term there is one variable b and 6 as coefficient of b and the second term is a constant term of 5.
Therefore, the correct description of the given expression [tex]6b+5[/tex] is " the sum of six times a number and five".
Option: b is the correct answer.
b) the sum of six times a number and five.
Step-by-step explanation:We are given an algebraic expression in term of a variable 'b' as:
6b+5
As we could see that here there are two terms in an expression one is: 6b and the other is 5 which is separated by a summation sign.
Hence, when 6 times of a number 'b' is added to 5 we get the given expression(i.e. 6b+5)
Hence, the answer is: Option: b
What is 0.43 as a fraction in simplest form?
is 3/4 equivalent to 12/15
Simplify (6 +i)(8 – 3i)
51 – 10i
48 – 32i
45 – 10i
48 – 10i – 3i^2 ...?
Holly records the temperature, in degrees fahrenheit, for two different cities. ln one of the cities, the temperature is 15 degrees above zero. holly records this as 15. ln the other city, the temperature is 15 degrees below zero.
Solve for n.
-7/2n = 49
n =
in uniform circular motion, the speed v of point on the edge of a spinning disk is v=2π/T times r. where r is the radius of the disk and T is the time it takes the point to travel once around the circle. Solve the formula for r.
Round 89,891 to the nearest ten-thousands place.
Angela and Neil are going to the movies. They each bought a medium popcorn, and Neil got a small soft drink. Angela had a $5 gift certificate to put toward the cost, and Neil paid the rest, which came to $27.90. A movie ticket costs $10.00, and a medium popcorn costs $5.50. How much does a soft drink cost at the theater?
$1.90
$7.40
$2.90
$17.40
Answer:
$1.90
Step-by-step explanation:
Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate?
Answer
Triangle ABD and Triangle ECD
Triangle ABD and Triangle ADC
Triangle ADC and Triangle ABC
Triangle ABC and Triangle ECD
Answer: Triangle ABC and Triangle ECD
Step-by-step explanation:
In Triangle ABC and Triangle ECD
BD=CD and AD=ED [given in the figure]
∠BDA=∠EDC [Vertically opposite angles are equal]
⇒ΔABC ≅ ΔECD [By SAS postulate]
SAS postulate or Side Angle Side postulate tells that if two sides and their included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Which set of side lengths represents a triangle with 3 lines of reflectional symmetry?
Answer:
The answer is 5,5,5.
Step-by-step explanation:
Reflection mean same like a mirror, it says reflectional symmetry. So the sides are the same.
The marginal cost function of producing q mountain bikes is 600/0.3q+5.
If the fixed cost in producing the bicycles is 2200 , find the total cost to produce 30 bicycles.
If the bikes are sold for 205 each, what is the profit (or loss) on the first 30 bicycles?
Find the marginal profit on the 31st bicycle. ...?
The total cost to produce 30 bicycles is $5599.89. The profit from first 30 bikes is $550.11. The marginal profit on the 31st bike is $126.57.
Explanation:The marginal cost function given is 600/(0.3q+5). To find the total cost to produce 30 bicycles, we need to integrate the marginal cost from 0 to 30 and add the fixed cost of 2200.
The result of the integration is 2000*(ln|1+0.3q|). Calculating from 0 to 30 gives us 3599.89. Thus, the total cost to produce 30 bicycles considering the fixed cost is 5599.89.
The revenue of each bike sold is $205. So, the total revenue generated from selling 30 bikes is 30*$205 = $6150. The profit is then the difference between the revenue and the total cost, giving us $6150-$5599.89 = $550.11.
To find the marginal profit on the 31st bike, subtract the marginal cost at 31 bikes from the selling price. The marginal cost at 31 bikes is the marginal cost function evaluated at q=31, which is approximately $78.43, and hence, the marginal profit on the 31st bike is $205 - $78.43 = $126.57.
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To find the total cost, multiply the quantity by the marginal cost function and add the fixed cost. To find the profit or loss, subtract the total cost from the revenue. The marginal profit can be found by subtracting the marginal cost from the selling price.
Explanation:To find the total cost to produce 30 bicycles, you need to calculate the variable cost and add it to the fixed cost. The variable cost can be found by multiplying the marginal cost function by the quantity of bikes. So, the variable cost is (600/0.3*30 + 5) = 6105. Adding the fixed cost of 2200 gives us a total cost of 8305.
To find the profit or loss on the first 30 bicycles, we need to subtract the total cost from the revenue, which is the selling price multiplied by the quantity. So, the revenue is 205 * 30 = 6150. The profit or loss is then 6150 - 8305 = -2155, indicating a loss of $2155.
The marginal profit on the 31st bicycle can be found by subtracting the marginal cost from the selling price. So, the marginal profit is 205 - (600/0.3*31 + 5) = -55, indicating a loss on the 31st bicycle.
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What is eight times four?
What is the square root of 1.395?
Evaluate 5x3 + 2 for x = -1.
-7
-3
4
6
Answer:
The correct option is B) -3
Step-by-step explanation:
Consider the provided expression.
[tex]5x^3 + 2[/tex]
We need to solve the expression when x=-1.
Substitute the values of x in the provided expression.
[tex]5(-1)^3 + 2[/tex]
Simplify the expression.
[tex]5\times -1+ 2[/tex]
[tex]-5+ 2[/tex]
[tex]-3[/tex]
Hence, the value of the provided expression when x=-1 is -3.
Therefore, the correct option is B) -3
Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30. What is the greatest age Brooke could be?
a.)7
b.)8
c.) 9
d.)10 ...?
The correct answer is b. 8. 8 is the greatest age Brooke could be.
Let's denote Brooke's age as B and Mia's age as M. According to the information given:
M = 2B + 3 (since Mia is three years older than twice Brooke's age).
We also know that the sum of their ages is less than 30:
M + B < 30.
Substituting the expression for M into the inequality, we get:
2B + 3 + B < 30,
3B + 3 < 30,
3B < 27,
B < 9.
Since Brooke's age must be a whole number, the greatest integer less than 9 is 8. Therefore, the greatest age Brooke could be is 8 years old.
Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?
Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.
(−5, 1)
(5, −1)
(−5, −1)
(5, 1)
Answer:
First option is correct. The location of point A after the transformations is (-5,1).
Step-by-step explanation:
It is given that the coordinates of point A are (-5,1).
Rectangle ABCD is reflected over the x-axis. then x-coordinate remains the same but the sign of y-coordinate is changed.
[tex](x,y)\rightarrow (x,-y)[/tex]
Coordinates of point A are
[tex](-5,1)\rightarrow (-5,-1)[/tex]
After that ABCD is reflected over the y-axis, then y-coordinate remains the same but the sign of x-coordinate is changed.
[tex](x,y)\rightarrow (-x,y)[/tex]
Coordinates of point A are
[tex](-5,-1)\rightarrow (5,-1)[/tex]
After that ABCD rotated 180 degrees about the origin, then the sign of both coordinates are changed.
[tex](x,y)\rightarrow (-x,-y)[/tex]
[tex](5,-1)\rightarrow (-5,1)[/tex]
Therefore option 1 is correct.
How many feet are in 120 inches?
__ ft
what is a mathematical statement that two expressions are equal
A spruce tree is approximately the shape of a cone with a slant height of 20 ft. The angle formed by the tree with the ground measures 72 degrees. Estimate the height of the tree. Round to the nearest foot.
(picture below)
It’s C on Ed It is C It is C
Planning for the possibility that your home might get struck by lightning and catch on fire is part of a plan for
Answer:
Th answer is - protecting assets
Step-by-step explanation:
Planning for the possibility that your home might get struck by lightning and catch on fire is part of a plan for protecting assets.
The protection of assets is a module of financial planning where one is needed to protect his assets against anything like - natural disaster or creditor's claims etc.
About 11% of the population is math phobic. If two people are randomly selected, what is the probability that both are math phobic? What is the probability that at least one is math phobic? ...?
Answer:
P(at least one phobic)
= 1 - P(none phobic)
= 1 - 0.89^2
= 1-0.7921
= 0.2079
Step-by-step explanation:
Ryan bought a calculator for $200 he resold it and made a profit of 25% how much did he sell the calculator for?
At a candy store, Jenny bought 1 pound of jelly beans and 5 pounds of gummy worms for $41. Meanwhile, Ozzie bought 6 pounds of jelly beans and 2 pounds of gummy worms for $50. How much does the candy cost?
when translating English sentences into math equations, the word is usually translates to which math symbol?
How do i write 7.6% as a fraction in simplest form and as a decimal?
A cylinder has a volume of 320 pi cu. in. and a height of 5". Find the radius of the cylinder. ...?
Answer:
radius of the cylinder is, 8 inches
Step-by-step explanation:
Volume of cylinder(V) is given by:
[tex]V = \pi r^2h[/tex] .....[1]
where,
r is the radius of the cylinder and
h is the height of the cylinder.
As per the statement:
A cylinder has a volume of 320 pi cu. in. and a height of 5"
⇒[tex]V = 320 \pi[/tex] cubic inches and h = 5 inches
Substitute these values in [1] we have
[tex]320 \pi = \pi r^2 \cdot 5[/tex]
Simplify:
[tex]320 = r^2 \cdot 5[/tex]
Divide both sides by 5 we have;
[tex]64=r^2[/tex]
or
[tex]r^2 = 64[/tex]
⇒[tex]r = \sqrt{64} = 8 in[/tex]
Therefore, the radius of the cylinder is, 8 inches
Final answer:
To find the radius of the cylinder, use the formula for the volume of a cylinder, V = πr²h. Rearrange the formula to solve for the radius, and solve the equation to find the value of r.So,radius of cylinder r=8inches.
Explanation:
To find the radius of the cylinder, we can use the formula for the volume of a cylinder, which is V = πr²h. In this case, we need to solve for the radius, so we rearrange the formula as follows:
320π = πr²(5)
We can cancel out the π's on both sides of the equation:
320 = r²(5)
Divide both sides of the equation by 5:
64 = r²
Take the square root of both sides to solve for r:
r = √64
r = 8
Therefore, the radius of the cylinder is 8 inches.
A code is formed using four of these letters: A, B, I, K, N, O, and T. (Note that the order of the letters in the code matters; for example, ABIK is a different code from BAIK.) The size of the sample space is___ . The probability that the first three letters of the four-letter code are vowels is___ .
Answer:
[tex]7^4[/tex][tex]\dfrac{27}{343}[/tex]Step-by-step explanation:
we are given 7 alphabets out of which we need to choose 4 alphabets in order to make a code of 4 letters.Hence the size of the sample space is: [tex]7^4[/tex]
since we have to fill in 4 places with the help of these 7 letters.
so in first place we can select one out of any 7 letters, similarly for the second place as it is not mentioned that repetition is not allowed and the same can be done for third and fourth place.
Hence size of sample space is: [tex]7\times7\times7\times7=7^4[/tex]
Now the probability of an event is given by:Probability=(Number of favourable outcomes)/(Total number of outcomes)
Hence here the total number of outcomes=[tex]7^4[/tex]
Total number of favourable outcomes=outcomes that the first three letters are vowels=[tex]3\times3\times3\times7[/tex] (since in the first place we have three choices for a vowel{A,I,0} similarly for second and third place and in the fourth place any one of the 7 letters could come)
Hence the probability(P) that the first three letters of the four-letter code are vowels is given by:
[tex]P=\dfrac{3\times3\times3\times7}{7\times7\times7\times7}=\dfrac{3\times3\times3}{7\times7\times7}=\dfrac{27}{343}[/tex]
Hence, the Probability is: [tex]\dfrac{27}{343}[/tex]
What is 4/3 divided by 6?
A fox, a coyote, and a wolf weigh a total of 120 pounds. The ratio of the weight of the fox to the weight of the coyote is 3:8. The weight of the coyote is 32 pounds. What is the weight of the wolf?
Answer:
the wolf is 76 lbs.
Step-by-step explanation:
first you have to divide 32 by 8, which is 4. Then you know that 4 is the divider to the simplified ratio, 3:8. So you multiply 3 and 4 which is 12. so you add 32 and 12 which is 44. then you subtract 44 by 120 which is 76. So The weight of the wolf is 76 lbs.