To ensure safe chlorine levels in the pool, the inequality |Cl - 3.25| ≤ 1.75 must be met, representing levels between 1.50 ppm and 5.00 ppm. The lifeguard found the level at 1.0 ppm, which is below the safe range, so more chlorine needs to be added.
Explanation:Absolute Value Inequality for Chlorine Levels:
The county government specifies that a safe level of chlorine is within 1.75 ppm of 3.25 ppm. We can express this using an absolute value inequality to represent the acceptable range for the chlorine levels: |Cl - 3.25| ≤ 1.75. This represents that the chlorine level (Cl) can be at most 1.75 ppm above or below 3.25 ppm.
To solve this inequality, we consider both the upper and lower bounds:
Therefore, the chlorine level must be between 1.50 ppm and 5.00 ppm.
Analysis of the Chlorine Level Measurement:
As the lifeguard measures the chlorine level in the pool at 1.0 ppm, it falls below the acceptable range established by the inequality. Consequently, the lifeguard should add more chlorine to bring the concentration up to within the safe range, specifically, at least to the minimum safe level of 1.50 ppm.
Mary just got a new job at Justice. She makes $10 an hour plus 4% commission on her sales. If she worked 6 hours
on Saturday and did $350 in sales how much did she make for the day?
Answer: $74
Step-by-step explanation:
cost for an hour = $10
since she worked for 6 hours , this means that she made $(6x10) = $60
Also , she made 4% commission on her sale and she sold $350 , this means that she made 4% of 350 =$14
Therefore: she made $ 60 + $14 for the day. Thai is , she made $74 for the day
What is are if a rectangle of length of 5 and width of 3x-5y+6What is the area of a rectangle with a length of 5 and a width of 3x-5y+6
The area of rectangle is 15x - 25y + 30 sqaure units
Solution:
Given that, a rectangle with a length of 5 and a width of 3x - 5y + 6
To find: Area of rectangle
The area of rectangle is given by formula:
[tex]Area = length \times width[/tex]
From given,
Length = 5
Width = 3x - 5y + 6
Substituting the values in formula, we get,
[tex]Area = 5 \times (3x - 5y + 6)\\\\\text{Multiply 5 with each term inside the bracket }\\\\Area = 5(3x) -(5)(5y) +5(6)\\\\\text{Simplify the above expression }\\\\Area = 15x -25y + 30[/tex]
Thus area of rectangle is 15x - 25y + 30 sqaure units
The width of a photograph is 4 centimeters more than three tenths of the length. If the width is 13 centimeters, what’s the length?
Answer:
30 centimeters
Step-by-step explanation:
since the width is 4 centimeters more than 3/10 of the length, then 13 is 4 centimeters more than 3/10 of the length. 4 less than 13 is 9, so nine is 3/10 of the length. if 9 is 3/10, then 3 is 1/10 because 3/10 is three times 1/10. If 3 is 1/10, that means that 30 is the length because 1/10 multiplied by 10 is 10 tenths, or 1.
219 divided by 4 equals what
Answer:
54.75
Step-by-step explanation:
219 divided by 4. Just plug it into a calculator
Answer:
54¾
Step-by-step explanation:
To start
4 goes in 219 = 54 times
remaining 3
so, writing as mixed fraction we have
219/4 = 54¾
The top of a ladder is 4m up a vertical wall.The bottom is 2m from the wall.The coordinate axes are the wall and the horizontal ground.
a)Find the equation representing the ladder.
b)A square box just fits under the ladder.Find the coordinates of the point where the box touches the ladder.
Answer:
Part a) [tex]y=-2x+4[/tex]
Part b) The coordinates of the point are [tex](\frac{4}{3},\frac{4}{3})[/tex]
Step-by-step explanation:
Part a) Find the equation representing the ladder
we have the ordered pairs
(0,4) and (2,0)
Find the slope
[tex]m=(0-4)/(2-0)=-2[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-2\\b=4[/tex]
substitute
[tex]y=-2x+4[/tex]
Part b) A square box just fits under the ladder.Find the coordinates of the point where the box touches the ladder.
If the box is a square
the x-coordinate of the point where the box touches the ladder must be equal to the y-coordinate
x=y
[tex]y=-2x+4[/tex]
substitute
[tex]x=-2x+4\\3x=4\\x=\frac{4}{3}[/tex]
[tex]y=x=\frac{4}{3}[/tex]
therefore
The coordinates of the point are [tex](\frac{4}{3},\frac{4}{3})[/tex]
what fractions are less than and greater than 1/2
Answer:
Less than: 1/4, 1/8, 1/16,...
Greater than: 5/8, 3/4, 1,...
Hope this helps :)
What is 321 in standard and expanded form
Answer:
321 300 20 1
Step-by-step explanation:
In written for: Three hundred twenty-one
Expanded form: 300 + 20 + 1
Standard form: 321
Fraction form: 321/1
Decimal form: 321.00
A submarine hovers at 66 and two-thirds yards below sea level. If it ascends 24 and StartFraction 1 over 8 EndFraction yards and then descends 78 and three-fourths yards, what is the submarine’s new position, in yards, with respect to sea level? Negative 169 and StartFraction 13 over 24 EndFraction Negative 121 and StartFraction 7 over 24 EndFraction Negative 12 and StartFraction 1 over 24 EndFraction 12 and StartFraction 1 over 24 EndFraction
A submarine hovers at 66 and 2/3 yards below sea level. If it ascends 24 and 1/8 yards and then descends again 78 and 3/4 yards, what is the submarine’s new position, in yards, below sea level?
Answer:
The submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Solution:
Given that a submarine hovers at [tex]66\frac{2}{3}[/tex] yards below sea level. This means that the position of submarine is negative
Therefore, we get [tex]-66\frac{2}{3}[/tex]
Also given that it ascend [tex]24\frac{1}{8}[/tex] yards
So we have to add [tex]-66\frac{2}{3}[/tex] and [tex]24\frac{1}{8}[/tex]
[tex]\rightarrow -66\frac{2}{3} + 24\frac{1}{8}\\\\\text{Convert mixed fractions to improper fractions }\\\\\rightarrow -\frac{66 \times 3+2}{3} + \frac{24 \times 8+1}{8} = \frac{-200}{3} + \frac{193}{8}\\\\\rightarrow \frac{-200 \times 8}{3 \times 8} + \frac{193 \times 3}{8 \times 3}\\\\\text{Simplify the above expression }\\\\\rightarrow \frac{-1600}{24} + \frac{579}{24} = \frac{-1021}{24}[/tex]
The submarine descends again 78 and 3/4 yards
This means we need to subtract [tex]-78\frac{3}{4}\text{ yards from } -\frac{1021}{24}\text{ yards}[/tex]
[tex]\rightarrow \frac{-1021}{24} -(78\frac{3}{4})\\\\\rightarrow \frac{-1021}{24} - \frac{78 \times 4 + 3}{4}\\\\\rightarrow \frac{-1021}{24} - \frac{315}{4} = \frac{-1021}{24} - \frac{315 \times 6}{4 \times 6}\\\\\rightarrow \frac{-1021 -1890}{24} = \frac{-2911}{24}\\\\\text{Simplify the expression }\\\\\rightarrow \frac{-2911}{24} = -121\frac{7}{24}[/tex]
Therefore, the submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.
Answer:
The answer-121 and 7/24
Hope this helps
:D
If I'm wrong sorry
And sorry that I'm super late
m=0 passing through p(-2,-2)
Answer:
The equation of line is y+2=0
Step-by-step explanation:
The equation of line passing through the point [tex](x_{1},y_{1} )[/tex]and having slope m is
[tex]y-y_{1} = m (x-x_{1}[/tex]
Given slope m=0 and given point is is (-2,-2)
[tex]y-(-2)=0(x-(-2))[/tex]
[tex]y+2=0[/tex]
therefore equation of the straight line is [tex]y+2=0[/tex]
Therefore the straight is parallel to negative x-axis(y=-2)
Write 6,219 in expanded
form.
Answer: 6000+200+10+9
Step-by-step explanation:
The ones place multiplies by 1 so 9*1=9
The tens place multiplies by 10 so 10*1=10
The hundreds place multiply by 100 so 100+2=100
The thousands place multiply by 1000 so 1000*6=6000
Hope This Helps!!!
A saleswoman earns 20% commission on all the merchandise that she sells . Last month she sold $800 worth of merchandise . How much commission (in dollars) did she earn last month ?
Answer:
160
Step-by-step explanation:
20 percent of 800 is 160
The saleswoman earned a commission of $160 last month from selling $800 worth of merchandise, given that her commission rate was 20%.
Explanation:The subject of your question lies in the domain of Mathematics, specifically, a concept taught in Middle School known as percentages. In this case, we're tasked with finding out how much commission a saleswoman earned by selling $800 worth of merchandise, given that she earns a 20% commission on all items sold.
The process for calculating this is straightforward. You multiply the total amount of the sold merchandise by the percentage commission to find out the amount earned. In mathematical form:
Total commission earned = Total amount of items sold * Commission Rate
Substitute the given values into this equation:
Total commission earned = $800 * 20%
To convert the percentage to a decimal, you divide by 100, thus, 20% = 20/100 = 0.2
Hence, Total commission earned = $800 * 0.2 = $160
Therefore, the saleswoman earned a commission of $160 last month from selling the merchandise.
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Stefan sells Jin a bicycle for $140 and a helmet for $16. The total cost for Jin is 130% of what Stefan spent originally to buy the bike and helmet. How much did Stefan spend originally? How much money did he make by selling the bicycle and helmet to Jin?
Final answer:
Stefan spent $120 originally to buy the bike and helmet and made $36 by selling them to Jin.
Explanation:
To find out how much Stefan spent originally, we need to divide the total cost for Jin by 130%.
Let's call the original amount x.
Jin's total cost is 130% of x, which can be expressed as 1.3x.
We know that the total cost for Jin is $140 for the bike + $16 for the helmet = $156.
So we have the equation 1.3x = $156. To solve for x, divide both sides of the equation by 1.3. x = $156 / 1.3 = $120.
Therefore, Stefan spent $120 originally to buy the bike and helmet.
To find out how much money Stefan made by selling the bike and helmet, we subtract the original amount spent from the total cost for Jin.
Money made = $156 - $120 = $36.
If Damian is able to read 80 pages in 2 hours how long does it take for him to reach each page
Answer:
Step-by-step explanation:
If he reads 80 pages in 2 hours, that means he reads 80 pages in 120 minutes. 80 pages/120 minutes simplifies to 2 pages/3 minutes. It also means it takes him 1 and a half minutes to read each page.
sharon rives 30 mi at 60 mi/h and 60 mi at 30 m/h. what is sharons average speed, in miles per hour, for the whole trip ?
Answer: 45mph
Step-by-step explanation: to solve this, all you have to do is add all of your data, and divide it by the number amount of data you have
Answer:
36 miles per hour
90miles/2.5hr = 36
Brian borrowed a 20 foot extension ladder to use when he paints hes house. If he sets the base of the ladder 6 feet from the house, as shown below, how far up will the top of the ladder reach?round to one decimal place.
Answer:
It is 20.9feet
Step-by-step explanation:
Answer:19.1
Step-by-step explanation:
what is -2x + 8 = -6
Answer:
The solution is x=7
Step-by-step explanation:
We want to solve for x in the equation
[tex] - 2x + 8 = - 6[/tex]
Subtract 8 from both sides of the equation:
[tex] - 2x + 8 - 8 = - 6 - 8[/tex]
Simplify to get:
[tex] - 2x + 0 = - 14[/tex]
This implies that:
[tex] - 2x = - 14[/tex]
[tex]x = \frac{ - 14}{ - 2} [/tex]
[tex]x = 7[/tex]
Are 8÷2 and 2÷8 equivalent
Answer:
No, 8 / 2 and 2 / 8 are not equivalent.
Step-by-step explanation:
2 Numbers switched makes a different result.
For example, switching numbers in 82.
As we switch the 8 and the 2, we get 28.
28 is not equivalent to 82.
As we do 8 / 2, when we switch the numbers, we get 2 / 8.
2 / 8 is not equivalent to 8 / 2.
As we solve both equations, 8 / 2 = 4, 2 / 8 = 0.25.
0.25 is not equivalent to 4.
Therefore, 8 / 2 and 2 / 8 are not equivalent.
Hope this helps!
[tex]\text{Hey there!}[/tex]
[tex]\bf{Are\ 8\div2\ and\ 2\div8\ equivalent?}[/tex]
[tex]\text{The answer to this question is \bf{\underline{NO}}}[/tex] [tex]\checkmark[/tex]
[tex]\bf{Reason: because \ 8\div2=4 \ and\ 2\div8 = 0.25. \ So, both\ gives\ you}\\\bf{different\ answers\ and \ NOT\ the\ same\ answers}[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
Use the bank of numbers below,
Which number makes each equation below true?
72 6n + 8 = (n + 2)(n + )
- 160 - 63 = (n - 7)(n + 0)
om - 17 n + 14 = (2n + 7)(-3n+2)
13 - 39 - 18 = (0 - 600 + D)
202 * 100 * 12 = 0(+ 2)(v + 3)
143? * 172.45 = (ex - 5)(2x + 1)
522-4-4(5x + 4)(x + C)
Answer:
Look at the photo below for the answer.
:)
Answer: 4
Step-by-step explanation:
how do you convert decimals into fractions?
Simplify: 18³×18²×18³
Answer:
18 to the 8th power
Step-by-step explanation:
18 + 2 + 3 + 3round 7,834 to the nearest hundred
Answer:
7,800
Step-by-step explanation:
Because the 3 goes down.
What is 2,731 divided by 31 with a remainder
Answer:?
Step-by-step explanation:
not sure..
Write 2.346 as a percent to the nearest tenth of a percent
Answer:
[tex]234.6\%[/tex]
Step-by-step explanation:
we know that
To convert decimal number as a percent, multiply the number by 100 (just move the decimal point two places to the right)
we have
[tex]2.346[/tex]
Convert as a percent
Multiply by 100
[tex]2.346(100)=234.6\%[/tex]
The left and right page numbers on an
open book add to 333. What are the
page numbers?
and
The student's question is a math problem involving consecutive numbers and a basic linear equation. The page numbers of an open book are consecutive, implying the left page is x and the right is x+1. Solving the equation x+(x+1)=333 results in the left page being 166 and the right page 167.
Explanation:The problem can be approached using the basic concept of consecutive integers in Mathematics. If the total sum of the two page numbers is 333, this means we are dealing with two consecutive numbers (since the left and right page numbers of an open book are always consecutive). Let's represent the left page number as x (unknown at this point). So, the right page number would be x+1 setting up our equation as x+(x+1)=333. Solving this equation will help us find the actual page numbers.
First combine like terms in your equation: 2x+1=333. Subtract 1 from both sides to isolate the term with x: 2x = 332 Divide both sides by 2 to solve for x: x = 166. This is our left page number. Substitute x in to x+1 to find the right page number: x+1 = 167. This is our right page number.
So, the left and right page numbers are 166 and 167 respectively.
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Please help! Also, show work, please!
if each person had to run 1/25 of a mile then you would need to have 5 people per team. it takes 5/25 to equal 1/5. So your answer is 5!!
Hope this helps! :)
What is (x+7)3y equal to
Answer:
(x + 7)3y = 3xy + 21y
Step-by-step explanation:
Expand the expression in the question by using the distributive property. This means you multiply the term (number) outside the bracket with each of the terms (numbers) inside the bracket.
(x + 7)3y Expand this
= (x)(3y) + (7)(3y) Multiply 3y with x and 7
= 3xy + 21y Simplified, final answer
The green goober a wildly unpopular hero mixes 3 L of yellow paint was 5 L of blue plate to make a leader is a special green paint for his costume right in equation that relate to why the amount of yellow paint and leaders and be the amount of blue paint in liters needed to make the green goobers special green paint
Answer:
The equation can be y = 3b/5 or b = 5y/3
Correct statement and question:
The Green Goober, a wildly unpopular superhero, mixes 3 liters of yellow paint with 5 liters of blue paint to make 8 liters of special green paint for his costume.
Write an equation that relates the amounts (in liters) of yellow paint (y) and blue paint (b) needed to make the Green Goober's special green paint.
Source:
Previous question that can be found at brainly
Step-by-step explanation:
Let y to be the amount of liters of yellow paint needed to make the Green Goober's special green paint.
Let b to be the amount of liters of blue paint needed to make the Green Goober's special green paint.
We know that:
y:b = 3:5
Therefore,
5y = 3b, dividing by 5 at both sides we have:
y = 3b/5
And also dividing by 3 at both sides we have:
b = 5y/3
Both equations relate the amounts (in liters) of yellow paint and blue paint needed to make the Green Goober's special green paint.
factorise the following question2xsaquare-8x
Answer:
2x(x - 4)
Step-by-step explanation:
Given
2x² - 8x ← factor out 2x from each term
= 2x(x - 4) ← in factored form
Line XY bisects and is perpendicular to AB and CD. CD = 10 and XY = 24. What is the length of AP?
Answer:
AP = 13
Step-by-step explanation:
See the attached figure.
CD = 10 and XY = 24
Line XY bisects and is perpendicular to AB and CD
∴ XY bisects at Y
∴ CY = 0.5 CD = 0.5 * 10 = 5
And from the geometry of the shape
P is the midpoint of XY
∴ XP = YP = 0.5 XY = 0.5 * 24 = 12
XY is perpendicular to CD
∴ ΔPYC is a right triangle at Y
∴ PC (hypotenuse) = [tex]\sqrt{PY^2+YC^2} =\sqrt{12^2+5^2}=\sqrt{144+25} =\sqrt{169} =13[/tex]
From the figure AP = PC = 13
what is the equation of the line that passes through (1,5) and (-2,14) in slope intercept form
Answer: y = -3x + 8
Step-by-step explanation:
The formula for finding equation of line when two points are given is :
[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]x_{1}[/tex] = 1
[tex]x_{2}[/tex] = -2
[tex]y_{1}[/tex] = 5
[tex]y_{2}[/tex] = 14
Substituting the values , we have
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{14-5}{-2-1}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{9}{-3}[/tex]
[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{-3}{1}[/tex]
y-5 = -3(x-1)
y -5 = -3x + 3
writing the equation in slope - intercept form , we will make y the subject of the formula:
y = -3x + 3 + 5
y = -3x + 8