For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.
Let us consider 'x' be the rate at which Rick paddles in still water
'y' be the rate of the current
Distance covered while going in upstream = 20 miles
Time taken while going 20 miles upstream = 4 hours
Rate of upstream = 20 / 4
⇒ x - y = 5 miles /hours ___(1)
Distance covered while going in downstream = 20 miles
Time taken while going 20 miles downstream = 2.5hours
Rate of downstream = 20 / 2.5
⇒ x + y = 8 miles /hours ___(2)
Solve (1) and (2) we get,
x - y = 5
x + y = 8
2x = 13
⇒ x = 6.5miles per hour
y = x - 5
⇒ y = 1.5 miles per hour
Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.
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OK I need this answer quick A model of Seattle, Washington space Needle is 20 inches tall The actual Space Needle is approximately 600 feet tall
a: what does the 1 inch represent in the model? what is the scale?
b: what is the scale factor model ?
it would mean a lot if someone could answer this!!
a. The representation of 1 inch in the model is 30 feet.
ii. The scale is 1:30.
b. The scale factor of the model is 1:360.
What is a scale factor?A scale factor is also referred to as a representation fraction which is the rate of length on drawing to that of the original length.
i.e. scale factor = length on drawing/ original length
Given that Washington space Needle is 20 inches tall. And the actual space Needle is approximately 600 feet tall, then;
a. 1 inch in the model = 600 feet/ 20 inch
= 30 feet / inch
i. The representation of 1 inch in the model is 30 feet.
ii. The scale is 1:30 i.e. 1 inch on the drawing is equal to 30 feet on the actual model.
b. The scale factor of the model is;
1 feet = 12 inches
600 feet = x
x = 7200 inches
scale factor = 20 / 7200
= 1/ 360
The scale factor is 1:360. i.e. 1 inch on the drawing is equivalent to 360 inches on the actual model.
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a positive integer with exactly eight positive divisors, two of
which are 21 and 33
21 = 3 · 7
33 = 3 · 11
If 21 and 33 are two divisors, then so are 3, 7, 11, and 77. And 1 and the number itself are always divisors.
So, we have 1, 3, 7, 11, 21, 33, 77, and the number. That's eight divisors.
So the number is 3·7·11 = 231, the product of only the prime divisors of the number.
A recipe for sparkling grape juice calls for 1 quarts of sparkling water and
quart of grape juice.
a. How much sparkling water would you need to mix with 9 quarts of grape juice?
18
b. How much grape juice would you need to mix with quarts of sparkling water?
c. How much of each ingredient would you need to make 100 quarts of sparkling
grape juice?
Please answer all no need for a step by step I just need the answers thanks :)
a. 9 quarts of sparkling water
b. 1 quart of grape juice
c. 50 quarts of sparkling water and 50 quarts of grape juice
What is the rational behind these values?The rationale behind the values above are as explained below:
a. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 9 quarts of grape juice, you would need 9 quarts of sparkling water.
b. If the recipe calls for 1 quart of sparkling water to be mixed with 1 quart of grape juice, then to mix with 1 quart of sparkling water, you would need 1 quart of grape juice.
c. To make 100 quarts of sparkling grape juice, using the 1:1 ratio in the recipe, you would need 50 quarts of sparkling water and 50 quarts of grape juice.
Therefore, the correct answers are as given above
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it takes country a 30 minutes to produce a car and 20 minutes to produce a tank. it takes country b 12 minutes to produce a car and 10 min to produce a tank. it is true that
Country B is more efficient than Country A when it comes to producing cars and tanks.
Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.
We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:
Cars per hour = (60 minutes/minutes to produce car)
Tanks per hour = (60 minutes/minutes to produce tank)
For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.
For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.
Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.
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Use the equation to answer the question.
12a+9b=k(2a+32b)
Which value of k makes the equation true?
a. 6
b. 2
c. 4
d. 3
The value of k that makes the equation true is given as follows:
a. 6.
How to obtain the value of k?The equation for this problem is defined as follows:
12a + 9b = k(2a + 3/2b).
The equation will be true is both sides are equal.
Applying the distributive property to the right side, we have that:
12a + 9b = 2ak + 3kb/2.
Taking one of the terms, the value of k is obtained as follows:
2ak = 12a
k = 12a/2a
k = 6.
Meaning that the correct option is given by option A.
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please help me with this geometry question
Answer:
Step-by-step explanation:
a)
Because if you visualize the formation of it size x will fit perfectly on the 6cm side therefore x = 6cm
b)
6 x 9 = 54cm
Each of the s swimmers on the relay team swam an equal number of the 8 laps in a race. Write an expression that shows how many laps each swimmer swam.
Answer: If each of the s swimmers on the relay team swam an equal number of the 8 laps in a race, the expression that shows how many laps each swimmer swam would be 8/s.
This expression shows that each swimmer swam 8 laps, divided by the total number of swimmers on the team, s.
So, if there are 's' swimmers on the relay team, each swimmer swam 8/s laps.
Step-by-step explanation:
A shop assistant sells goods to the value of $3400 during a certain week. If she is
paid 7.5% commission on these sales, calculate the amount of commission earned.
If she is paid a basic wage of $450, calculate her total wage for that week.
Answer:
$705
Step-by-step explanation:
($3400)(0.075) = $255 commission earned
Total wage for that week = $450 + $255 = $705
note: this answer assumes that $450 is the weekly basic wage, not daily
Sarah took the advertising department from her company on a round trip to meet with a potential client. Incluc trip. She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total bud $11,720. How many first class tickets did she buy? How many coach tickets did she buy?n took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 15 people took the She was able to purchase coach tickets for $200 and first class tickets for $1290. She used her total budget for airfare for the trip, which was $11,720. How many first class tickets did she buy? How many coach tickets did she buy?
6 coach tickets and 9 first-class tickets were bought, totaling the number of tickets purchased.
Explain about the expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
A mix of operators, constants, and variables make up an expression. An expression can yield a value by using one or more operands and one or more operators.
An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You can think of expressions as being comparable to phrases.
The algebraic expression that results from multiplying two variables, x and y, is xy.
Let's say that x coach tickets were purchased.
And y is the total number of first-class tickets bought.
Now,
15 people in total, including Sarah, made the journey.
Thus,
x + y = 15(1)
Coach and first-class tickets are priced at $200 and $1290, respectively.
The trip's total spending for air travel is $11,720.
Therefore,
200x + 1290y = 11720
20x + 129y = 1172
We obtain by resolving both equations.
x = 6
y = 9
Consequently, 6 coach tickets and 9 first-class tickets were acquired, making up the total number of tickets.
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How do I do it? I’m unsure and would like to achieve the answer
The equivalent ratio where the amount of stock is 100 mL is 80 mL
How to an equivalent ratio?
An equivalent ratio is a ratio that is equal to another ratio, but with the terms in a different order or with different values.
Since the recipe calls for 350 mL of Dashi in order to make a smaller batch using 280 mL of Dashi. Thus, we can say:
equivalent ratio = 280/350
Thus, an equivalent ratio where the amount of stock is 100 mL will be:
280/350 = x/100
0.8 = x/100
x = 0.8 × 100
x = 80 mL
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The classic 60° triangle has a hypotenuse of length 2. An opposite side of length v3 and an adjacent
side of length 1:
60°
V3 - 1732
What is the value of costo
A 0. 5
B 0. 572
C 0. 866
ОА
The value of cosθ = 0.5
The correct option is (A).
Now, According to the question:
Basic Trigonometric Function Formulas:
By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.
Remember that in a right triangle, we have that:
cos(θ) = (adjacent cathetus)/(hypotenuse)
Here we have:
θ = 60°adjacent cathetus = 1hypotenuse = 2Replacing all that in the equation we get:
cos(60°) = 1/2 = 0.5
Hence, the value of cosθ = 0.5
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let the sum of a set of numbers be the sum of its elements. let $s$ be a set of positive integers, none greater than 15. suppose no two disjoint subsets of $s$ have the same sum. what is the largest sum a set $s$ with these properties can have?
No S with sum greater than 61 is possible and 61 is indeed the maximum.
By using the greedy algorithm, we obtain 61, with S={15,14,13,11,8}.
We must now prove that no such set has sum greater than 61. Suppose such a set [tex]$S$[/tex] existed. Then [tex]$S$[/tex] must have more than 4 elements, otherwise its sum would be at most 15+14+13+12=54.
S can't have more than 5 elements. To see why, note that at least.
[tex]$\left(\begin{array}{l}6 \\ 0\end{array}\right)+\left(\begin{array}{l}6 \\ 1\end{array}\right)+\left(\begin{array}{l}6 \\ 2\end{array}\right)+\left(\begin{array}{l}6 \\ 3\end{array}\right)+\left(\begin{array}{l}6 \\ 4\end{array}\right)=57$[/tex] of its subsets have at most four elements (the number of subsets with no elements plus the number of subsets with one element and so on), and each of them have sum at most 54. By the Pigeonhole Principle, two of these subsets would have the same sum. If those subsets were disjoint, we would directly arrive at a contradiction; if not, we could remove the common elements to get two disjoint subsets.
Thus, [tex]$S$[/tex] would have to have 5 elements. [tex]$S$[/tex] contains both 15 and 14 (otherwise its sum is at most 10+11+12+13+15=61.
It follows that [tex]$S[/tex] cannot contain both a and a-1 for any [tex]$a \leq 13$[/tex], or the subsets {a,14} and {a-1, 15} would have the same sum. So now [tex]$S$[/tex] must contain 13 (otherwise its sum is at most 15+14+12+10+8=59, and S cannot contain 12, or the subsets, {12,15} and {13,14} would have the same sum.
Now the only way [tex]$S$[/tex] could have sum at least 62=15+14+13+11+9
would be if S={15,14.13,11.9}. But the subsets {9,15} and {11,13} have the same sum, so this set does not work.
Therefore, no S with sum greater than 61 is possible and 61 is indeed the maximum.
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Your height i 3 1/2 in and you ue a cale of 1 inch on the portrait repreent 20 inche on the decal what i the height of the decal if your actual height i 55 inche
The height of the wall decal when my actual height is 5.5 inches, is equals to the 110 inches.
We have, My height in the portrait measures = 3 1/2 inches = 7/2 = 3.5 inches
According to the scale used by company,
one inch measurement on portrait = 20 inches on the wall decal. That is portrait measurement / wall decal = 1/20 ( in inches) . We have to determine the height on the wall decal if my actual height is 5.5 inches. Let the height of wall decal be "h inches" when my actual height is 5.5 inches. Write the proportion like this to calculate the value of h , 1/20 = 5.5/ h
Cross multiply we get,
=> 1× h = 5.5 × 20
=> h = 110.0
Hence, the required height of the decal is 110 inches.
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Complete question:
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?
When compared to my actual height of 5.5 inches, the wall decal's height is 110 inches.
We've got My height in the image is 3 1/2 inches plus 7/2, which is 3.5 inches.
On the basis of the scale:
20 inches are equal to one inch in a portrait on the wall decal. That is a portrait measurement divided by a 20-inch wall decal. If my real height is 5.5 inches, we must determine the height on the wall decal. Let the wall decal's height be "h inches" even though my height is 5.5 inches. To compute the value of h, write the ratio as 1/20 = 5.5/h.
When we cross multiply,
1× h = 5.5 × 20
h = 110.0
Therefore, 110 inches is the minimum height for the decal.
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Note: The complete question would be as bellow,
Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?
A. The ratio of triangles to squares is 2 to 4.
B. The ratio of squares to smiley faces is 6 : 4.
C. The ratio of smiley faces to triangles is 6 to 4.
D. There are two squares for every triangle.
E. There are two triangles for every smiley face.
F. There are three smiley faces for every triangle.
Find x and y.
65°
40°
to
Answer:
x 23 y 60
Step-by-step explanation:
Statistics Help! Will give Brainliest!
The probability that a teenage boy has a cholesterol level greater than 200 is 0.33: Option D
What is probability?It is the chance of occurrence of an event E
To solve this problem you must first find the z-score associated with a cholesterol level greater than 200.
The general formula for a z score is:
z = (x-µ)/σ
Where z is the z score, x is the data point, µ is the mean, and σ is the standard deviation. With your numbers that would become:
z = (200-170)/30
z = 1.833
If you are using a graphing calculator, such as the TI-83 Plus, you can then go to 2nd vars, and the second option is normalcdf
To use normalalcdf enter normalcdf (lower z score, upper z score) in your case normalcdf (1.833, 1E99) to get the probability that a teenage boy has a cholesterol level greater than 200 Which will give you .0337.
If you are using a z table, find the probability associated with your z score of 1.83, and subtract that from 1. You subtract from 1 because a z table gives you the probability of a score being below the one you obtained.
This implies therefore that the probability is 0.337
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If the number of tickets sold is 125, what will be the total sales?
Answer:
I don't know????????....................
Plane A is flying according to the relation = − 2 + 10 and plane B is flying
according to the relation 2 − 3 = − 6 . They are both heading towards the airport and
will meet there. Determine the position of the airport on the grid.
Show your method of graphing by writing down the information you used to graph each line
in the space provided. Plane A: Plane B:
Answer: plane a is faster than plane b because it has more speed than plane b
Step-by-step explanation:
rewrite in simplest form
put -x+3y<6 into cordinates
The inequality -x+3y < 6 passes through the points (-6, 0) and (0, 2).
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
We have an inequality,
-x+3y < 6.
The graph of the inequality is given in the attached image.
And inequality passes through the points (-6, 0) and (0, 2).
Therefore, the graph of the inequality is given in the attached image.
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Modeling Real Life A train ride from Chicago to Emeryville, California, is 2,438 miles. It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan. About how long is the train ride from Chicago to Port Huron?
As per the given ratio between distance, The Train ride from Chicago to Port Huron is 304.375 miles.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, A train ride from Chicago to Emeryville, California, is 2,438 miles.
Since It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan.
Thus,
The train ride from Chicago to Port Huron = 2438/8
The Train ride from Chicago to Port Huron = 304.375 miles
Therefore, The Train ride from Chicago to Port Huron is 304.375 miles.
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A string is placed on the outside of a clock going clockwise from 12to 9. The clock has a radius of 6 inches. What is the length of the string
Answer:
9π inches
Step-by-step explanation:
we know clock start from 12 o'clock to 9 o'clock, it will be 270 degree. Then we convert it to radian is 3π/2. We get the radian and the radius. So we can apply the formula of the lenghth of an arc.
l = rθ
l=6*3π/2=9π inches
given f(x)=x^2+2x-5 and the values of the linear function g(x) in the table, what is the range of (f+g)(x)
x: -6 -3 -1 4
g(x): 16 10 6 -4
Answers:
(infinity,1]
[-1,1]
R
The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.
What are a domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function.
The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.
x -6 -3 -1 4
g(x) 16 10 6 -4
The function g(x) will be:-
g(x) = mx + c
m = ( 10 - 16 ) / ( -3 + 6 )
m = -6 / 3
m = -2
c = y - mx
c = 10 - 6
c = 4
g(x) = -2x + 4
The function ( f + g)(x) will be:-
( f + g)(x) = f(x) + g(x)
( f + g)(x) = x²+ 2x - 5 - 2x + 4
( f + g)(x) = x² - 1
At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).
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Hank bought a four family residence for a rental property he put 20% down on 300,000 rental unit how much will he be able to depreciate using the class recovery period for residential rental. Properties each year
The amount he will be able to depreciate using the class recovery period for a residential rental property each year is D. $10,909.09.
The term depreciation defines as an accounting method used to allocate the cost of a tangible or physical asset over its useful life.
It also represents how much of an asset's value has been used, and allows companies to earn revenue from the assets they own by paying for them over a certain period of time.
Using this formula:
Depreciation=Rental unit amount/ MACRS residential rental property recovery period
Where:
Rental unit amount=$300,000
MACRS Residential rental property recovery period=27.5 years
Let's plug in the formula
Depreciation=$300,000/27.5
Depreciation=$10,909.09
In conclusion, the amount he will be able to depreciate using the class recovery period for a residential rental property each year is: D. $10,909.09
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Simplify the rational expression. x2 – 5 x + 5 –x – 5
The answer is -1(x - 5)(x + 1)
To simplify the rational expression x^2 - 5x + 5 - x - 5, we can combine like terms and factor out the greatest common factor of the numerator and denominator.
Step 1: First, we can combine like terms in the numerator to get x^2 - x - 5
Step 2: Next, we can factor out the greatest common factor of -1 from the numerator to get -1(x^2 - x - 5)
Step 3: Now we can factor the expression in the parenthesis:
-1(x - 5)(x + 1)
So the simplified form of the given rational expression is: -1(x - 5)(x + 1)
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Answer:
-6x+x^2
Step-by-step explanation:
To start off the equation you want to make everything have the same symbol:
x^2+-5x+5+-x+-5
next, you can rearrange the symbols to combine terms:
5+-5+-x+-5x+x^2
Now we combine:
-6x+x^2
the 5 cancels out. The -x plus the -5x gets you -6x. and the x^2 can not be combined.
Your answer:
-6x+x^2
Before the baseball season begins, a field manager outlines the "on-deck" circle with chalk and covers the area with dirt.
If the "on-deck" circle has a diameter of 6 feet, about how long is the chalk outline?
The length of the chalk outline is 19 feet.
The field is circular and the line drawn by chalk is the length of the rim of the circular field and is called the circumference. It can be calculated from the radius(or diameter) of the circle.
The formula of the circumference of a circle:
Circumference of circle [tex]= 2 * \pi * r = \pi * d[/tex]
where r means the radius of the circle and d means the diameter of the circle.
The diameter d = 2 times of radius
Thus, we have:
Length of a chalk outline [tex]= \pi * d = \pi * 6 = 3.14 * 6 = 18.84 = 19 feet[/tex]
So, the length of the chalk outline is 19 feet.
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if there are 240 boys in a school with a total of 960 students, then what percent of the students are girls?
Answer
60%
Step-by-step explanation:
Answer: 75% of students are girls.
Step-by-step explanation: First, you divide 960 by 100 to get 9.6. Then you do 960-240 to get the amount of girls (720), then you divide 720 by 9.6 to get 75.
per's debate team at thunderbird high sclusel, 20% of the members are sophomores, 39% arts and the closing argent, the team has a probability of 0 253 of winning the debute. if a junior gives that closing argument, the probabilay of if or cloons, the probability of winning is 083 (4) find the probability that the tests wins the debate (b) describe the design of a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debutes explain clearly how you would use a table of random digits to carry out the simulation (e) the dotplot below shows the number of sophomores chosen in 50 simulated sets of 5 debates in which 20% of the time a sophomore is selected and 80% of the time a junior or senice is selected to give the closing argument for the team in the next 5 debates, a sophomore was never chosen to give the closing argument. the sophomores on the team claim that they were purposely ignored. use the results of the simulation to determine if there is convincing evidence that the sophomores were purposely ignored.
Here to solve the probability of this sum, it is difficult to say that the probability without no information.
(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.
(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.
A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.
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Find the value of x, y, and z in the rhombus below.
104°
(10y+6)°
(z+7)
(-x-10)°
The value of x, y, and z in the rhombus are -114, 7 and 59 respectively
How to find the value of x, y, and z in the rhombus?Since the opposite angles of a rhombus are equal to each other. We can write:
(-x-10)° = 104°
-x-10 = 104
-x = 104 + 10
x = -114
Since the adjacent angles in rhombus are supplementary. We have:
114 + (z + 7) = 180
121 + z = 180
z = 180 -121
z = 59
104 + (10y + 6) = 180
110 + 10y = 180
10y = 180 - 110
10y = 70
y = 70/10
y = 7
Thus, the value of x, y, and z are -114, 7 and 59
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Hector spent $26.75 for 2 DVDs that cost the same amount. The sales tax on his purchase was $4.15. Hector also used a coupon for $1.00 off his purchase.
The cost of one DVD to Hector is $11.8.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
Hector spent $26.75 for 2 DVDs that cost the same amount.
The sales tax on his purchase was $4.15.
That means,
the cost of 2 DVDs = 26.75 - 4.15 = $22.6
Hector also used a coupon for $1.00 off his purchase.
That means,
the cost of 2 DVDs = $23.6
The cost of one DVD = 23.6 /2 = $11.8
Therefore, the cost of one DVD is $11.8.
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