Answer:
Step-by-step explanation:
8weeeks bc 22.50*8=180
A fish can swim at 14m/s with the current and at 6m/s against it. Find the speed
of the current and the speed of the fish in still water.
Answer:
10 m/s
Step-by-step explanation:
Let x = speed of fish and y = speed of current. When swimming with current, the fish's speed is x + y. When swimming against it, the speed is x - y. Therefore, we can set up a system of linear equations to solve for x, the speed of fish.
x + y = 14
x - y = 6
2y = 8
y = 4
x - 4 = 6
x = 10
The speed of fish in still water is 10 m/s, and the speed of current is 4 m/s.
Answer:
Speed of fish in still water = 10 m/s
Speed of current = 4 m/s
Step-by-step explanation:
Let the speed of the fish in still water = x m\s
Let the speed of the current = y m/s
Speed of the fish with the current = x + y
x +y = 14 m/s ------------------(I)
Speed of the fish against current = x -y
x - y = 6 m/s ----(II) &
Add the equations (I) & (II) and 'y' will be eliminated and we can find the value of 'x'.
x + y = 14
x - y = 6 {Now, add)
2x = 20
x = 20/2
x = 10
[tex]\sf \boxed{\text{\bf Speed of fish in still water = 10 \ m / s}}[/tex]
Plugin x = 10 in equation (I)
10 + y = 14
y = 14 - 10
y = 4
[tex]\sf \boxed{\text{\bf Speed of the current = 4 \ m/s}}[/tex]
Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
Solve this system. Write your answer as an ordered pair.
-5x + y = -3
3x - 8y = 24
[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]
Answer:
( 0, -3 )
Step-by-step explanation:
-5x + y = -3 ⇒ ( 1 )
3x - 8y = 24 ⇒ ( 2 )
We can make y the subject of equation 1.
y = 5x - 3 ⇒ ( 3 )
Now let us take equation 2.
Here we can replace y with ( 5x - 3 ) to find the value of x.
Value of x.
3x - 8y = 24
3x - 8 (5x - 3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
Now let us take equation 3 to find the value of y.
Here we can replace x with 0.
Let us find it now.
y = 5x - 3
y = 5 × 0 - 3
y = 0 - 3
y = -3
Now, let us write the answer as an ordered pair.
( x, y )
( 0, -3 )
1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find number of students that applied at most two universities.
The number of students who applied at most two universities is 26 students.
How is the calculation for the number done?The population of students in a class = 60 students
Number of students who applied for Addis Ababa University = 30 students
Number of students who applied for Bahir Dar University = 25 students
Number of students who applied for Wachemo University = 24 students
Number of students who applied for Addis and Bahir = 11 students
Number of students who applied for Addis and Wachemo = 6 students
Number of students who applied for Wachemo and Bahir = 9 students
The number of students who applied at most two universities is 26 (11+ 6 + 9).
Thus, the number of students who applied at most two universities is 26.
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m∠1 =
✔ 131
degrees
m∠2 =
✔ 49
degrees
m∠3 =
✔ 112
degrees
Answer:
what is the question show the pic
can someone provide me with step by step solution of this question
Answer:
the answer is 100,008.
Step-by-step explanation:
To convert temperatures in degrees Fahrenheit to Celsius, subtract 32 and multiply by 5556
Answer: 50° F = 10° C
Step-by-step explanation:
Given information
Convert 50° Fahrenheit to Celcius
Given formula
[tex]C~=~\frac{5}{9}~ (F-32)[/tex]
Substitute values into the formula
[tex]C~=~\frac{5}{9}~ (F-32)[/tex]
[tex]C~=~\frac{5}{9}~ ((50)-32)[/tex]
Simplify values in the parenthesis
[tex]C~=~\frac{5}{9}~ (18)[/tex]
Simplify the multiplication
[tex]\Large\boxed{C=10^\circ C}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Need help please thank you
Answer:
D. x = -7/3
Step-by-step explanation:
A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.
F(x) = 0The desired form can be found by subtracting 16 from both sides of the equation:
[tex]\left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16[/tex]
A graph is attached, showing x=-7/3 is the solution.
Algebraic solutionUsing powers of 4, the equation can be rewritten ...
[tex]\left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}[/tex]
Write the following number in scientific notation. 788,000
Answer:
7.88 x 10^5 is 788,000 is scientific notation
The perimeter is 54 m. The apothem is \root(3)(3) . To the nearest tenth, what is the area of this regular polygon?
The area of this regular polygon is 46.8 square units
How to determine the area of this regular polygon?The given parameters are:
Perimeter, p = 54 m
Apothem, a = √3
The area of this regular polygon is then calculated as:
Area = 0.5 * Apothem * Perimeter
Substitute the known values in the above equation
Area = 0.5 * √3 * 54
Evaluate the product
Area = 46.8
Hence, the area of this regular polygon is 46.8 square units
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A certain brand of coffee comes in two sizes. A 12.3-ounce package costs $2.99 . A 33.9-ounce package costs $8.74 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]
Find the critical value. Assume that the test is two -tailed and that n denotes the number of pairs of data. n =
20, α = 0.01
A) -0.570
B) 0.570
C) +0.447
D) +0.570
Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.
How to find the critical value of the t-distribution?It is found using a calculator, with three inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.The tail.In this problem, the inputs are given as follows:
Confidence level of 99%, as 1 - 0.01 = 0.99 = 99%.19 df, as 20 - 1 = 19.Two-tailed test, as stated in this problem.Hence, using a calculator, the critical value is of is of Tc = 2.8609.
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Simplify 4/16 to lowest terms and find an equivalent fraction that has a denominator of 32
A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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rearrange the equation a = 1/2 b to make b the formula
Answer:
b = 2a
Step-by-step explanation:
a = [tex]\frac{1}{2}[/tex] b ( multiply both sides by 2 to clear the fraction )
2a = b
Answer: b = 2a
Step-by-step explanation:
Original equation
a = (1/2) b
Multiply 2 on both sides
a * 2 = (1/2) b * 2
[tex]\Large\boxed{b=2a}[/tex]
Hope this helps!! :)
Please let me know if you have any quesitons
A survey was conducted among the students at Elmwood High School. What are the individuals in this study?
the types of sports
the music groups
the clubs
the students
Based on the information provided, the individuals in this study are: D. the students.
What is a study?A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.
What is a variable?In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.
Based on the information provided, the individuals in this study are the students and these include the following subclasses:
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The students are the individuals in this study and is therefore denoted as option D.
What is a Sample?This refers to a group of people which are chosen or taken from a large population for measurement or surveys.
In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.
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A large bakery buys flour in 20-pound bags. The bakery uses an average of 1050 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $15 per order. Annual Carrying costs are $ 55 per bag. a) Determine the economic order quantity? b) What is the average number of bags on-hand? c) How many orders per year will there be? d) Compute the total cost of ordering and carrying flour? e) If holding costs were to increase by $5 per year, how much would the minimum total annual cost?
Given the following:
Demand = 1050Ordering cost = 15Holding cost = 55The economic order quantity is 24.
What is the economic order Quantity?Eoq = √2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 55)
EOQ = 24
What is the average number of bags on-hand?The Average inventory = EOQ / 2
= 24 / 2
= 12
How many orders per year will there be?Expected number of orders = demand / EOQ
= 1050 / 24
= 44
What is the total cost of ordering and carrying flour?Annual holding cost (AHC) = (EOQ / 2) * Holding cost
= (24 / 2) * 55
= 660
Annual ordering cost (AOC) = (demand / EOQ) * ordering cost
= (1050 / 24) * 15
= 656
Thus,
Total cost of managing = AHC + AOC
= 660 + 656
TCM = 1,316
If holding costs were to increase by $5 per year, how much would the minimum total annual cost?5. For holding cost of 60
EOQ= √(2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 60)
= 23
Annual holding cost = (EOQ / 2) * holding cost
this gives us
= (23 / 2) * 60
= 690
Annual ordering cost = (demand / EOQ) * ordering cost
= (1050 / 23) * 15
= 685
Total cost of managing = AHC+ AOC
= 690 + 685
= 1375
Change in total annual cost = new - old
= 1375 - 1316
= 59
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Rhombus BCDE is shown below. Give the coordinates of C and D.
The coordinates of C - (2n, 0) and the coordinates of D - (n, -p). The diagonals of a rhombus are perpendicular and bisect each other.
What are the properties of a rhombus?The properties of a rhombus are:
All the sides of a rhombus are congruent and equalOpposite sides are parallelOpposite angles are equalThe adjacent angles add up to 180°Diagonals perpendicularly bisect each otherDiagonals bisect opposite anglesCalculation:The given rhombus BCDE has B(n, p) and E(0, 0).
Since the diagonals of a rhombus are perpendicular bisectors,
EO = OC or BO = OD
Where O is the midpoint of EC and BD.
In the given diagram, points B and D are opposite each other. They are reflecting each other over the x-axis.
So, if B has coordinates (n, p) then its reflection over the x-axis is (x, -y) i.e., (n, -p).
Thus, we have B(n, p), D(n, -p), and E(0, 0)
Consider the coordinates of C as (x, y).
The midpoint of BD = ([tex]\frac{n+n}{2}[/tex], [tex]\frac{p-p}{2}[/tex])
⇒ coordinates of O = (n, 0)
So,
The midpoint of EC = ([tex]\frac{0+x}{2}[/tex], [tex]\frac{0+y}{2}[/tex])
⇒ coordinates of O = (x/2, y/2)
⇒ (n, 0) = (x/2, y/2)
∴ x = 2n and y = 0
Then, the coordinates of C are (2n, o)
Therefore, the required coordinates of the given rhombus are C(2n, 0) and D(n, -p).
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Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number
The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.
What is a 2-digit number?A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.
A 2-digit number is any number between 10 and 99.
According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.
1001 - 994 = 7 (1 digit)1002 - 994 = 8 (1 digit)1004 - 994 = 10 (2 digit)Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.
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A triangle with a base of 16 cm and a height of 9 cm.
Answer: 288
Step-by-step explanation:
(16x9)x2
X
Erica works 30 hours/week for
$10/hour, but she must pay $30 in
taxes. What is her take-home income?
Answer:
$270
Step-by-step explanation:
Find her gross income....then subtract taxes:
30 hr/week * $10/hr - $ 30 = $270
y = x^3 - 52x^2 + 15x^4 + 16 + 20x
The factors of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
Given equation is [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex],
By performing L-division method, we get
[tex]y = (x-1)(15x^{3} +16x^{2} -36x-16)[/tex]
Then again doing the same L-division method to the cubic equation [tex]15x^{3} +16x^{2} -36x-16[/tex], we get
[tex]15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)[/tex]
Therefore, [tex]y = (x-1)(x+2)(15x^{2}-14x-8)[/tex]
Then finally the roots of the quadratic equation [tex]15x^{2}-14x-8[/tex] are (x-(4/3)) and (x+(2/5))
Hence, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )[/tex]
Therefore, the roots of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
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what is the length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm?
If the formula r=1/n-1 .....following data, what would be the value of x?
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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Can someone explain the steps I’m confused
Answer:
x = 8 ± [tex]\sqrt{10}[/tex]
Step-by-step explanation:
x² - 16x + 54 = 0 ( subtract 54 from both sides )
x² - 16x = - 54
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 54 + 64
(x - 8)² = 10 ( take the square root of both sides )
x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )
x = 8 ± [tex]\sqrt{10}[/tex]
then
x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]
Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 29 years and anticipate they will need funding for an additional 20 years. They determined that they would have a retirement income of $54,000 in today's dollars, but they would actually need $75,017 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 2 percent inflation rate and a return of 6
Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.
What amount do Peter and Blair need to save?First, find the income shortfall:
= 75,017 - 54,000
= $21,017
The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:
= 6% - 2% inflation
= 4%
The future value is:
= Income shortfall x future value interest factor, 4%, 29 years
= 21,017 x 3.1187
= $65,545.72
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If 2/3x − 1 = 4, then x=
Answer: 15/2 or 7.5
Step-by-step explanation:
2/3x = 5
5 divided by 2/3 or 5 x 3/2
= 15/2 or 7.5
Answer: 15/2
Step-by-step explanation:
[tex]\frac{2}{3} x-1=4\\\\\frac{2}{3}x=5\\ \\x=5(\frac{3}{2})\\\\x=\frac{15}{2}[/tex]
Sue has sourced four wholesalers from where she will buy most of her stock, including arrangements with two suppliers for 30 days credit, while the others are Cash on Delivery (COD).
She has purchased her store fittings and has $15000 of stock (Stock at Valuation - or SAV), with a further $10000 on 30-day credit). The business has an operating cash reserve of $20000.
How many wholesalers require terms of cash on delivery?
The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2
How can the question be analyzed to find the required number of wholesalers?The number of wholesalers Sue has sourced = 4
Terms of two suppliers = 30 days credit
Amount of stock Sue has = $15000
Amount of stock on credit = $10000
Operating cash reserve of the business = $20000
Required:
The number of wholesalers that require terms of cash on delivery
Solution:
Given that the number of wholesalers = 4
The number number of suppliers (wholesalers) that supply on 30-day credit = 2
Therefore;
The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2
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A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use. What is the area of the tarp?
Trapezoid ABCD with base side AD labeled 15 feet, top side BC labeled 10 feet, and right side CD labeled 5 feet. Angle C measures 120 degrees.
To find the height, first find that is
. This means the height of the trapezoid is approximately
feet. So, the area of the tarp is approximately
square feet.
The area of the tarp is 54.125 square feet
How to determine the measure of D?From the figure in the question, we have the following angle measure:
DCE= 120
This means that:
<C = DCE - 90
Substitute the known values in the above equation
<C = 120 - 90
Evaluate the difference
<C = 30
The measure of D is then calculated as
<D = 90 - <C
This gives
<C = 90 - 30
Evaluate the difference
<C = 60
How to determine the height of the trapezoid?Represent the height with h.
This is then calculated as:
sin(D) = h/5
This gives
sin(60) = h/5
Multiply both sides by h
h = 5 * sin(60)
Evaluate
h = 4.33
How to determine the area of the tarp?This is calculated as:
A = 0.5 * (10 + 15) * 4.33
Evaluate
A = 54.125
Hence, the area of the tarp is 54.125 square feet
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Answer:
In the image
Hope this helps!
Step-by-step explanation:
To find the height, first find that ∠D is 60°. This means the height of the trapezoid is approximately 4.3 feet. So, the area of the tarp is approximately 53.7 square feet.
Whats the increace if you go from $90 to $108
Answer:
The increase is $18.
(In case you are asked about the percent increase,
percent increase = 20%)
Step-by-step explanation:
To find an increase, subtract.
$108 - $90 = $18
The increase is $18.
Answer: The increase is $18.
If you are asked about the percent increase, then use this formula:
percent change = (new number - old number)/(old number) × 100%
Here, the new number is $108. The old number is $90.
percent change = ($108 - $90)/($90) × 100%
percent change = $18/$90 × 100%
percent change = 0.2 × 100%
percent change = 20%
Since the percent change is a positive number, it is a percent increase.
Answer: percent increase = 20%
A string of 254cm from a ball of string measuring 4m.Calculate the string left on the ball
Answer:
1.46m or 14600cm are left over
Step-by-step explanation:
Assuming you mean that there were 4m of string and 254cm were used/removed.
