Problem Safety standards require a pool to add 3 chlorine tablets to every 2,000 gallons of water. Today, the lifeguards at Park Pool added 8 chlorine tablets to their pool's 10,000 gallons of water. How does Park Pool's chlorine compare to the safety standards?
Answer:
In the park's pool there are 7 less chlorine tablets as compared to safety standards.
Step-by-step explanation:
Number of chlorine tablets in 2,000 gallons water = 3 tablets
Number of tablets in 1 gallon of water = [tex]\frac{3}{2,000} tablets[/tex]
Number of tablet to be added in 10,000 gallons of water :
[tex]\frac{3}{2,000}\times 10,000 tablets=15 tablets[/tex]
Number of chlorine tablets added by lifeguard in 10,000 gallon water=8 tablets
Tablets of chlorine to be more added =
=15 tablets - 8 tablets = 7 tablets
In the park's pool there are 7 less chlorine tablets as compared to safety standards.
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Triangle ABC has vertices A(1,4), B(−2,4) , and C(−1,−1) . A dilation with a scale factor of 0.25 and center at the origin is applied to the triangle.
What are the coordinates of B' in the dilated image?
Enter your answer in the boxes.
B' has a coordinate pair of (
,
)
The graph below shows the numbers of cups of mango juice that are mixed with different numbers of cups of lemon-lime soda to make servings of mango soda:
What is the ratio of the number of cups of mango juice to the number of cups of lemon-lime soda?
A.1:40
B.10:1
C.40:1
D.1:10
Answer:
(B)
Step-by-step explanation:
In the given graph, it is shown the number of cups of mango juice are mixed with different numbers o cups of lemon juice.
Then, From the graph, at Point(10,1),
Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{10}{1}[/tex]
=10:1
At point (20,2)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{20}{2}=\frac{10}{1}[/tex]
=10:1
At point (30,3)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{30}{3}=\frac{10}{1}[/tex]
=10:1
At point (40,4)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=[tex]\frac{40}{4}=\frac{10}{1}[/tex]
=10:1
Thus, Option B is correct.
Answer:
B
Step-by-step explanation:
In the given graph, it is shown the number of cups of mango juice are mixed with different numbers o cups of lemon juice.
Then, From the graph, at Point(10,1),
Ratio of the cups of mango juice to the number of cups of lemon juice soda=
=10:1
At point (20,2)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=
=10:1
At point (30,3)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=
=10:1
At point (40,4)
Ratio of the cups of mango juice to the number of cups of lemon juice soda=
=10:1
Thus, Option B is correct.
Liam’s football team scored a total of 43 separate times this season, with a mix of touchdowns and field goals. Each touchdown is worth 7 points, and each field goal is worth 3 points. If the team scored a total of 301 points this season, how many touchdowns and field goals did they score?
The football team scored 43 times this season, comprising solely of touchdowns worth 7 points each, totalling to 301 points. The team did not score any field goals worth 3 points.
Explanation:This problem can be solved using systems of linear equations. We have two equations here: 1. The total number of times the team scored, which is touchdowns(T) plus field goals(F) equals 43 (T+F=43). 2. The total points the team made, each touchdown being 7 points and each field goal being 3 points, equals 301 (7T + 3F = 301). By solving this system of equations, we can find the number of touchdowns and field goals.
From the first equation (T + F = 43), we can express T as (43 - F). Substitute T in the second equation: 7(43 - F) + 3F = 301, which simplifies to 301 = 301 - 4F. By rearranging, we get 4F = 0. Hence, F = 0. Returning to the first equation, T = 43 - F. As F=0, T = 43.
Thus, the team scored 43 touchdowns and 0 field goals.
Learn more about Systems of Linear Equations here:https://brainly.com/question/33609849
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How many numbers are written from n to k, including n and k?
Answer:
k-n
Step-by-step explanation:
Answer:
k-n-1
Step-by-step explanation:
This is what I think based on other formulas
2times 2 1/3 as a mixed number
If the quadratic formula is used to solve 2x(x + 5) = 4, what are the solutions? {-1/2, -9/2}
The solutions are:
[tex]x=-5.372\ and\ x=0.372[/tex]
Step-by-step explanation:The equation is given by:
[tex]2x(x+5)=4[/tex]
on using the distributive property of multiplication in the left hand side of the equation we have:
[tex]2x\times x+2x\times 5=4\\\\i.e.\\\\2x^2+10x=4\\\\i.e.\\\\2x^2+10x-4=0\\\\i.e.\\\\2(x^2+5x-2)=0\\\\i.e.\\\\x^2+5x-2=0[/tex]
Now, we know that the solution of the quadratic equation:
[tex]ax^2+bx+c=0[/tex] is given by:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here we have:
[tex]a=1,\ b=5\ and\ c=-2[/tex]
Hence, the solution is:
[tex]x=\dfrac{-5\pm \sqrt{5^2-4\times 1\times (-2)}}{2\times 1}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{25+8}}{2}\\\\i.e.\\\\x=\dfrac{-5\pm \sqrt{33}}{2}\\\\x=\dfrac{-5+\sqrt{33}}{2},\ x=\dfrac{-5-\sqrt{33}}{2}[/tex]
Hence, in decimal for the solution is:
[tex]x=-5.372\ and\ x=0.372[/tex]
pete spends 3/5 of his monthy pay on rent, 1/8 on bills and then spends half of what is left on food. if his monthly pay is $820, how much does he have left at the end of the month?
please help fast i will mark brainliest
A factory employs skilled laborers at$25 per hour and unskilled laborers at $12 per hour. The total hourly cost of the factory’s 24 workers is $405. How many of each type of laborer works at the factory.
Find an ordered pair (x,y) that satisfies both of the equations below:
2x - 3y = -5
5x - 2y = 4
Answer:
(2,3)
Step-by-step explanation:
Multiplying the first equation by 5 and the second equation by $-2$ gives
\begin{align*}
10x-15y&=-25,\\
-10x + 4y &=-8.\\
\end{align*}Adding the two equations gives $-11y = -33$, so $y=3$. Substituting $y=3$ in the first original equation gives $2x - 9 = -5$, so $2x = 4$ and $x = 2$. Therefore, the solution is $(x,y) = \boxed{(2,3)}$
write the equation of the line with x-intercept 3 and passing through the point (5,4).
A. y-2=1/2(x-4)
B. y+2=2(x+4)
C. y-2=2(x-4)
D. y-2=1/2(x-4)
Answer:
C. y-2=2(x-4)
Step-by-step explanation:
A bike wheel is 26 inches it in diameter what is the bikes with your diameter in millimeters
To convert the bike wheel diameter from inches to millimeters, multiply 26 inches by the conversion factor of 25.4 mm/inch, resulting in a diameter of 660.4 mm.
Explanation:To convert the diameter of a bike wheel from inches to millimeters, we use the conversion factor that 1 inch is equal to 25.4 millimeters. Hence, we multiply the diameter in inches by this conversion factor.
The calculation will be:
Multiply the diameter in inches (26 inches) by the conversion factor (25.4 mm/inch).The diameter in millimeters is 660.4 mm (26 inches × 25.4 mm/inch).Therefore, the diameter of the bike wheel is 660.4 millimeters.
the function f(x)=40x-80 models the number of visitors a website received x days after it was created. Which is the most appropriate domain for function?
The most appropriate domain for the given function is x ≥ 0.
Explanation:The domain of a function represents the set of all possible input values, or x-values, for which the function is defined. In this case, the function f(x) = 40x - 80 represents the number of visitors a website received x days after it was created. Since time cannot be negative and the website exists only after it was created, the most appropriate domain for the function would be x ≥ 0. This ensures that the function is defined for all non-negative values of x, which aligns with the context of the problem.
What’s the difference between an inscribed and circumscribed circle
HELP ANSWER FAST WILL PUT BRAINLIEST AND RATE IF CORRECT
A parallelogram has a height of 5 units. One side of the parallelogram is AB. The parallelogram has no right angles.
Draw the parallelogram using the Polygon tool.
Each segment of the grid represents 1 unit.
j is 25 more than 3
solve for j
Answer:
25+3=28 - 28=j or j=28
Step-by-step explanation:
just add 25 and 3 and you will get 28.
Jimmy invest $16,000 in an account that pays 7.03% compounded quarterly. How long (in years and months) will it take for his investment to reach $23,000?
A, B and C are integers. If B is greater than A, then the sum of A and B will always produce a solution C with the same sign as B. True or false?
Daniel wants to simplify this expression. Which like terms can he combine? 12ab - 8a + 3ab
what is 2 3/4 in simplest form
The length of rectangle ABCD is 4 in. The length of similar rectangle DEFG is 6 in. How many times greater than the area of ABCD is the area of DEFG?
The area of rectangle DEFG is 9/4 times greater than that of rectangle ABCD. This is determined by squaring the scale factor that relates their lengths, since the rectangles are similar.
The area of rectangle DEFG is how many times greater than the area of rectangle ABCD can be found by comparing the squares of their corresponding lengths, since they are similar rectangles. The length of rectangle ABCD is 4 inches, while the length of rectangle DEFG is 6 inches. To determine the area comparison, we square the scale factor, which is the ratio of the lengths of the two rectangles. This means the scale factor is 6/4, which simplifies to 3/2. Squaring this gives us (3/2)² = 9/4. Therefore, the area of DEFG is 9/4 times greater than the area of ABCD.
In the case of the squares Marta has, if one square has side lengths twice that of the other, the larger square will have an area that is 2² = 4 times larger than the smaller square. Applying this concept of squaring the scale factor to rectangles, as in the original question, gives us our ratio of areas between similar figures.
What is the exact volume of the cone?
80π ft³
4003π ft³
400π ft³
418710π ft³
The lengthy of a rectangle is 2 times its width. The area of the rectangle is 72 square inches. Find the dimensions of the rectangle
The width of the rectangle is 6 inches and the length is 12 inches.
Explanation:To find the dimensions of the rectangle, we can use the fact that the length is 2 times the width. Let's define the width as 'w' inches. According to the problem, the length is 2 times the width, so the length would be '2w' inches. The area of a rectangle is calculated by multiplying the length and the width, so we can set up the equation: 'w * 2w = 72'. Solving this equation, we find that 'w' equals 6 inches. Therefore, the width of the rectangle is 6 inches and the length is 2 times that, which is 12 inches.
Factor y3−9y2+y−9 by grouping.
Final answer:
To factor the expression y^3 - 9y^2 + y - 9 by grouping, divide it into two groups, factor out common factors, and note that (y - 9) is common to both, yielding the final factored form (y^2 + 1)(y - 9).
Explanation:
To factor by grouping the expression y3 − 9y2 + y − 9, we first split it into two parts where common factors are apparent:
(y3 − 9y2) and (y − 9)
Next, we factor out the common factors from each group:
y2(y − 9) + 1(y − 9)
Now, we notice that (y − 9) is a common factor in both terms. So, we factor (y − 9) out of the entire expression:
(y2 + 1)(y − 9)
This gives us the final factored form of y3 − 9y2 + y − 9, which is (y2 + 1)(y − 9).
The length of a rectangle is 6 feet longer than its width. If the perimeter of the rectangle is 56 feet, find its length and width.
Final answer:
The width is 11 feet and the length is 17 feet.
Explanation:
The question asks us to find the length and width of a rectangle where the length is 6 feet longer than the width and the perimeter is 56 feet. To solve this, let's denote the width of the rectangle as w feet.
Since the length is 6 feet longer, the length will be w + 6 feet.
The formula for the perimeter (P) of a rectangle is P = 2(length + width). We can plug in our expressions for length and width into this formula:
P = 2(w + 6 + w)
Given that the perimeter is 56 feet, we have:
56 = 2(2w + 6)
Dividing both sides by 2, we get:
28 = 2w + 6
Subtract 6 from both sides:
22 = 2w
Divide both sides by 2:
11 = w
Therefore, the width of the rectangle is 11 feet and the length is w + 6 = 11 + 6 = 17 feet.
**PLEASE HELP** Suppose your class is raising money for the Red Cross. You make $5 on each basket of fruit and $3 in each box of cheese that you sell. How many items of each type must you sell to raise more than $150?
a. Write a linear inequality that describes the situation.
b. write two possible solutions to the problem
chris are 1/8 of a banana cream pie with a 1/4 diameter. what is the area of the remaining portion of the pie
plz show work
Answer:153.9
Step-by-step explanations equation A=pi×r^2
A=pi×7^2
A=pi×79
A=153.9 i round
A model rocket is launched from the ground with an initial velocity of 160 ft/sec. how long will it take the rocket to reach its maximum height? Show all work in the space provided. Assume the model rocket’s parachute failed to deploy and the rocket fell back to the ground. How long would it take the rocket to return to Earth from the time it was launched? Show all work in the space provided.