Swimming, Manufacturing, and Painting
Problem
Variables to use
Equation
Tyler swims at a constant speed, 5 meters every 4 seconds.
A factory produces 3 bottles of sparkling water for every 8 bottles of plain water.
A certain shade of light blue paint is made by mixing 1 ½ quarts of blue paint with 5 quarts of white paint.
For each of the previous three situations, write an equation to represent the proportional relationship.
The equations that represent the proportional relationships between the variables are as follows:
Problem Variables to use Equation
1. Tyler swimming Time / Distance D = 1.25t
2. Factory production Total quantity, Q, Q = 3s + 8p
and Sparkling / Plain
3. Paint mixture Blue / White Paints 6q = 1.5b + 5w
What is an equation?An equation models a mathematical statement in which two or more expressions (involving numbers, variables, and operands combined) are equated using the equation symbol (=).
Tyler:Speed = 5 m/4s
= 1.25 m/s (5/4)
Swimming equation: D = 1.25t
Where D = distance and t = time spent.
Given the speed and time, we can find the swimming distance covered by Tyler.
Factory:
Bottles of sparkling water = 3
Bottles of plain water = 8
Ratio = 3:8
Production equation, Q = 3s + 8p
Where Q = total quantity, s = sparkling water, and p = plain water
Paint:Blue paint = 1 ½ quarts
White paint = 5 quarts
Ratio = 1.5:5
Production equation, 6q = 1.5b + 5w
Where 6q = 6 quarts, b = blue paint, and w = white paint
Thus, using the equations, we can use the known variables to find the unknown variables.
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FIRST ANSWER GETS FIVE STARS AND BRAINLIEST!
Pine Street, Rector Street, and Taylor Street intersect to form a triangular-shaped park as shown.
(picture below)
What is the correct order of the lengths of the streets from longest to shortest?
Answer:
Rector, Pine, Taylor
Step-by-step explanation:
The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!
Can someone please help me thank you
The answers to the worksheet are in the included picture! :p
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This is just an example on how to simplify fractions: Write the simplified form of the fraction 12/24.
The given fraction is 12/24.
Step 1: Let us write the factors of 12 and 24.
Factors of 12 are: 1, 2, 3, 4, 6, 12
Factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Let us identify the common factors of 12 and 24.
Common factors are: 1, 2, 3, 4, 6, 12
Step 3: Keep dividing the numerator and denominator by the common factors.
(12 ÷ 2)/(24 ÷ 2) = 6/12
And
(6 ÷ 2)/(12 ÷ 2) = 3/6
Now divide by 3,
(3 ÷ 3)/(6 ÷ 3) = 1/2
Thus, 1/2 is the simplified fraction of 12/24.
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Have a great day and God bless! :D
1/3 divide by 4 3/4 simplest form
Step-by-step explanation:
first put 4 3/4 into a improper fraction ---> 19/4
you get 19/4 because 4 is equal to 16/3 plus the 3/4
then you will do keep, flip change so it becomes multiplication
so instead of 1/3 divided by 19/4 it will be 1/3 x 4/19 then
multiply it out to get 19/12
ASAP HELP
Please
Please
Given polynomial with descending degrees of x would be,
x^4z^4 + x^3 - x^2z + z^3
In this question we have been given a polynomial x^3 + z^3 - x^2z + x^4z^4
We need to write given polynomial by descending degrees of x.
The highest degree of x in above polynomial is 4
x^3 + z^3 - x^2z + x^4z^4
then the second term would be x with degree 3.
x^3 + z^3 - x^2z + x^4z^4
the third term would be x with degree 2
x^3 + z^3 - x^2z + x^4z^4
and the last term is the term x with degree 0:
x^3 + z^3 - x^2z + x^4z^4
Therefore, given polynomial with descending degrees of x would be, x^4z^4 + x^3 - x^2z + z^3
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Write an algebraic expression that represents each purchase.
a. Dr. Lin bought x number of soccer balls and 4 baseballs.
b. Nestor, Felix, Peter, and Hao are on a baseball team. They each bought a baseball and x pairs of sweat socks.
26. Suppose x has the same value in both of the expressions you wrote for 25. Are the two expressions you wrote for 25 equivalent? Explain.
27. Sophia says that the algebraic expression 4
4
5x, where x represents the cost of a baseball, describes the cost of a soccer ball. Do you agree? Explain.
1. An algebraic expression that represents each purchase is as follows:
a) 15x + 24b) 5x + 24.2. Supposing that x has the same value in both expressions written above, the two algebraic expressions are not equivalent because the slope of expression A is greater than the slope of expression B.
3. The cost of a soccer ball in relation to the cost of a baseball cannot be represented by the algebraic expression 4 + 5x because it is given that the cost of a soccer ball is $15, and no number can substitute the x variable to equate the two.
What is an algebraic expression?An algebraic expression is a combination of terms (variables and constants) using the mathematical operations of addition, subtraction, multiplication, division, etc.
a) 15x + 4(6) = 15x + 24
b) 4(6) + 5x = 24 + 5x or 5x + 24
c) Cost of a soccer ball = $15
Cost of a baseball = $6
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Question Completion:Soccer balls = $15 each
Baseballs=$6 each
Sweat socks =$5 per pair
1) Use the scale factor to
determine the new area of each
scale drawing.
Scale factor = 3
2 meters
4.5 meters
Solve the equation n x 5 = 5000 explain you solution
Answer:
1000
Step-by-step explanation:
n x 5 = 5000
n = 5000/5
n = 1000
A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.” If a simple random sample of 50 adult Americans is collected, what is the probability that more than one-fourth of them will have low levels of literacy as described above?
The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.
What is probability?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
Given: A study conducted by the Institute of Education Sciences from 1992 to 2003 found that about 22% of adult Americans had low levels of literacy and were “not able to locate information in text,” could not “make low-level inferences using printed materials” and were unable to “integrate easily identifiable pieces of information.”
A simple random sample of 50 adult Americans is collected.
n(p) = 50(0.22)
n(1 - p) = 50(1 - 0.22)
The CLT would hold here.
n = 50
p = 0.22
p cap = 0.25
The test statistic, z = (p cap - p) / (√p (1 - p) / n)
z = (0.25 - 0.22)/(√0.22(1-0.22)/50)
z = 0.51
The p-value is 0.3043.
Hence, The probability that more than one-fourth of them will have low levels of literacy as described above is 0.3043.
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The doubling period of a bacterial population is 20 minutes. At time t=120 minutes, the bacterial population was 90000.
What was the initial population at time t=0?
Find the size of the bacterial population after 3 hours.
The initial population of the bacterial population at time t = 0, can be found to be 1,406.25.
The size of the bacterial population after 3 hours is 720,000.
How to find the bacterial population?The doubling period of the bacterial population is said to be 20 minutes. The number of doubling periods in 120 minutes is:
= 120 / 20
= 6 doubling periods
The initial population is:
= Population at 120 minutes / 2 ^ number of doubling periods
= 90,000 / 2⁶
= 1,406.25
The bacterial population at 3 hours is:
= Bacterial population at t = 0 x 2 ^ number of doubling periods in 3 hours
= 1,406.25 x 2 ^ (180 minutes in 3 hours / 20)
= 1,406.25 x 2⁹
= 720,000
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Chelsea was reading at steady pace.By the time she stopped reading for the night she had 64 pages in 20 minutes.What is Chelsea's unit rate
Answer:
3.2 pages per minute
Step-by-step explanation:
Unit Rate: 64 / 20 = 3.2 pages per minute
A unit rate is just a measure of either how fast you can do one of something, or how fast you can do something in one unit of time :)
Answer:
Step-by-step explanation
64 pages ÷ 20 =
20 minutes ÷ 20 =
3.2 pages
1 minute
so she read 3.2 pages per minute
Jamar has invested $300 in an annuity each month, earning 5.5% interest for 30 years.
Beth has invested $600 in an annuity each month, earning 5.5% interest for 15 years.
Which of the following must be true?
Select the correct answer below:
Answer:
(d) Jamar's ending account balance is higher than Beth's ending balance.
Step-by-step explanation:
You want to know the best description of the relationship between final balances of two ordinary annuities:
300 per month for 30 years at 5.5%600 per month for 15 years at 5.5%Future valueThe attached calculator display shows the ending balance for Jamar's annuity and for Beth's annuity. We assume the final balance is the balance after the final payment. That is, Beth's balance will be known 15 years before Jamar's balance is known.
Jamar's balance: $274,083.57
Beth's balance: $167,247.33
The best description is ...
Jamar's ending account balance is higher than Beth's ending balance.
__
Additional comment
Jamar makes twice as many payments of half the amount each, so his total contribution is the same as Beth's. His early payments are earning interest for twice as long as Beth's, so his account earns more interest.
The continent of Australia is 8,508,238 sq. km while it's largest island, New
Guinea, is 787,878 sq. km.
How much larger is Australia?
OA) 9,296,116 sq. km
O B)
7,720,360 sq. km
OC) 7,720,260 sq. km
OD) 7,719,360 sq. km
Answer:
B) 7,720,360 sq. km
Step-by-step explanation:
8,508,238 - 787,878 = 7,720,360 sq. km
Hope this helped :)
Which two operations are needed to write the expression that represents "five less than the quotient of a number and
three"?
The two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.
What is the quotient?
A result is obtained by dividing two amounts.
The quotient is the result of a division.
The term "less than" represents subtraction.
So, the two operations that are needed to write the expression that represents "five less than the quotient of a number and three" are Division and subtraction.
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A director of reservations believes that 9% of the ticketed passengers are no-shows. If the director is right, what is the probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3%? Round your answer to four decimal places.
The probability that the proportion of no-shows in a sample of 789 ticketed passengers would differ from the population proportion by less than 3% is 0.9968
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 9% = 0.09
sample size, n = 789
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.09(1 - 0.09)) / 789}
= √{(0.09 * 0.91) / 789}
= 0.0102
The probability
differ from the population proportion by less than 3%
|X - 0.09| < 0.03
X < 0.12 OR X > 0.06
0.06 < X < 0.12
P(z < 0.12) - P(z < 0.06 )
z score for z < 0.06
z = (0.06 - 0.09) / 0.0102
= -2.9412
p value for z < -2.9412 = 0.0016
z score for z < 0.12
z = (0.12 - 0.09) / 0.0102
= 2.9412
p value for z < 2.9412 = 0.9984
The probability required = 0.9984 - 0.0016 = 0.9968
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Maria deposits $1,400 into the Park Avenue Bank. The account pays 2.5% annual interest compounded semi-annually. What is her ending balance after 3
years? Round to the nearest cent (2 digits after the decimal point).
The ending balance is
The ending balance after 3 years is $1508.34
What is compound interest?
The interest that is paid on both the initial principal and the accumulated past interest is known as compound interest.
The compound amount and compound interest are calculated by:
Compound amount, [tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
Compound interest, [tex]I = A - P[/tex]
where, P is the principal amount
r is the rate of interest(in decimal)
n is the number of times the interest is compounded annually
t is the time.
Given, Principal amount, P = $1400
rate of interest, r = 2.5% = 0.025
n = 2 (compounded semi-annually)
t = 3 years
Then, the compound amount is calculated by:
[tex]A=1400(1+\frac{0.025}{2} )^{2*3}\\[/tex]
or, [tex]A=1400(1+0.0125 )^{6}\\[/tex]
or, [tex]A=1400(1.0125 )^{6}\\[/tex]
or, [tex]A=1508.34[/tex]
Therefore, the ending balance is $1508.34
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what is 5\sqrt(3ft *3\sqrt(12))
The solution of 5√3 × 3√12 = 30√3.
What is square root?Square root of a number is defined as the number in which the multiplication by itself gives the original number. That is the square root of 9 would be = 3 in which when multiplied by itself gives the original number being 9.
Other examples include √ 4 = 2, √ 25 = 5, √100 = 10.
To simplify the give expression;
5√3 × 3√12= 5√3 × 3√4×3
= 5√3 × 3×2√3
= 5√3 × 6 √3
= 30√3.
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What is the equation of the line that passes through the point (6, 4) and has a slope 2/3
The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x
Given,
The points which the line passes through = (6, 4)
Slope = 2/3
We have to find the equation of line;
Linear equation;
Y = mx + b is one way to represent a linear equation.
A point's coordinates are x and y.The slope is m.The position of the point where the line crosses the y axis is represented by the integer b, which is the ordinate to the origin.Here,
x is 6 and y is 4
Slope, m is 2/3
Then,
Substitute the values in y = mx + b
Here,
y = mx + b
4 = 2/3 (6) + b
4 = 12/3 + b
4 = 4 + b
b = 4 -4
b = 0
Then,
The equation of line is, y = 2/3x + 0
That is,
The equation of line passes through the point (6, 4) with a slope 2/3 is, y = 2/3x
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Rebecca wants to buy a new phone. She has already saved $110 and received a gift of $50 from her grandmother that she added to her savings. She plans to earn the rest by selling necklaces for $5 each. The phone she wants to purchase costs $485. Write an equation that represents how many necklaces Rebecca will need to sell in order to have enough money to get her phone.
Answer:
5x=325+160
Step-by-step explanation:
this was very easy but i guess with so many words it could confuse people
What line is perpendicular to the line y= -1/2x + 8
Answer: y=2x+8
Step-by-step explanation:
you take the reverse of the slope being 2 including the negative.
57) A roundabout consists of a carriageway with a width of 4.5 meters and a circular inner area with a diameter of 16 meters.
a) There is a fence around the inner area. How many meters is the length of the fence? Round to two decimal places.
b) The inner area is sown with grass. 25 grams of grass seed is needed per m². Calculate how many kg of grass seed is needed for the indoor area. Round to one decimal place.
c) Calculate the area of the carriageway on the roundabout in m². Round to one decimal place.
d) In the case of road works, a white line will be placed in the middle of the carriageway of the roundabout. The striping car travels at a speed of 25 cm per second. How many minutes does it take to apply the line? Round to wholes.
a) Length of Fence = 50 meters
b) Weight of Grass Seeds = 20 kg
c) Area of Carriageway = 516 sq. meters
d) Time taken by the Striping Car = 7.6 minutes
What is a Circle?
A circular plane figure with a circumference made up of points equidistant from a given point (the center).
Solution:
a) To calculate the length of fence we need to find the circumference of the inner circle
Circumference of Circle = 2*22/7 *Radius
Circumference of Circle = 2 * 22/7 * (16)/2
Circumference of Circle = 50.24
So, the length of fence is 50 meters approx
b) To calculate the the total weight of grass we need to first find the area of the inner circle
Area of Circle = 22/7 * (Radius)^2
Area of Circle = 22/7 * (16)^2
Area of Circle = 22/7 * 256
Area of Circle = 803.84 meter sq.
For 1 meter sq. = 25 grms of grass seeeds are required
So, for 804 meters = 25*804 = 20100 grams
20100 grams = 20.1 kg = 20 kg (approx)
c) The are of Inner Carriageway will be calculated by substracting the area of inner circle from outer circle
Area of Outer Circle = 3.14 * (16+4.5)^2
Area of Outer Circle = 1320 sq. meters (approx)
Area of Inner Circle = 804 sq. meters (approx) #we have calculated it above
Area of Carriageway = 1320 - 804 = 516 sq. meters (approx)
d) Speed of Stripping Car = 25 cm/sec
Circumference of the part to be stripped = 2*3.14*(16+2.25)
Circumference = 115 meters approx. = 11500 cm
Time = Distance / Speed
Time = 11500/25 = 460 seconds
460 seconds in minutes = 7.6 minutes
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12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G
By using linear pair, we have found that the value of x is 3.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
Given that Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.
Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.
Thus, by linear pair
Angle ROG + Angle QGP = 180
80° + 32x + 4 = 180
32x = 100 - 4
x = 96/32
x = 3
Hence, the value of x is 3.
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1/3a^2+a=0
It's rather urgent, please or else I will fail my semester...
The solution of the equation given as 1/3a² + a=0 is a = 3
How to determine the solution to the equation?From the question, we have the following equation that can be used in our computation:
1/3a^2+a=0
Rewrite the equation properly
So, we have
1/3a² + a=0
Multiply through the above equation by 3
So, we have the following equation
3 * (1/3a² + a) =0 * 3
Evaluate the products
So, the equation becomes
a² + 3a = 0
Next, we divide through the equation by the variable a
This gives
a + 3 = 0
Subtract 3 from both sides of the equation
i.e. Add -3 to both sides of the equation
a = -3
The above equation cannot be solved further.
So, we leave it like that and stop solving
Hence, the solution to the equation is a = -3
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attachment above please
Elijah read his book from 4:30pm until 6:00pm. He read 1 chapter every 10 minutes.
How many chapters total did Elijah read?
Answer:
he read 9 chapters
Step-by-step explanation:
4:30 pm to 6:00 pm is 1:30 hours, which is 90 minutes
90/10=9
Maya bought a new pack
of trading cards. The cards
originally cost $5.00. She had a
coupon for 20% off. How much
did Maya have to pay for the
trading cards after the coupon?
here are the first 5 terms of an arithmetic sequence, 2,6,10,14,18... is 86 a term in this sequence, you must give a reason for your answer
Answer: Yes
Step-by-step explanation:
Because if you keep going it will reach 86, since it's added by 4, so 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86.
5x + y = 8
2x + y = 5
Answer:
x=1 y=3
Step-by-step explanation:
By looking at the equations, you can use substitution
Set the equation equal to y
y=-5x+8
y=-2x+5
Then put equation together
-5x+8=-2x+5
Move numbers over
3x=3
x=1
Put x back into equation
5+y=8
2+y=5
y=3
Which of the following equations does the graph below represent?
A. 3x + 7y = 21
B. -3x + 7y = 21
C. x + 7y = 21
D. -3x + y = 21
Answer:
B
Step-by-step explanation:
if x = 0 ; y = 3
if x = -7 ; y = 0
A 0 + 7(3) = 21
0 + 21 = 21
21 = 21 (ok)
3(-7) + 0 = 21
-21 = 21 (false)
B
0 + 21 = 21
21 = 21 (ok)
(-3)(-7) + 0 = 21
21 = 21 (ok)
10. Chelsea had completed 2/3 ofa 5-mile race when
her shoelace came untied. How many miles had
Chelsea completed at that point?
Answer:
3.3 miles with a bar notation on decimal 3
Step-by-step explanation:
convert 2/3 to decimal (2 divided by 3)
multiply 5 by decimal of 2/3
add bar notation on repeating decimal