After calculating the initial velocity with which the ball was thrown upwards, the time taken for the ball to reach its peak and fall back to earth was calculated to be approximately 38 seconds.
Explanation:In order to find out how long the ball will be in the air, we are essentially dealing with an example of free fall in Physics. When the ball reaches its maximum height, its velocity will be zero and it will have spent a certain amount of time t to reach there. But the total time it will be in the air is twice this amount, as it will take the same amount of time to go up and come back down.
Using the second equation of motion, v = u + gt (where v = final velocity, u = initial velocity, g = acceleration due to gravity and t = time), when the ball reaches maximum height, its final velocity (v) is zero. If we rearrange this equation, we get t = (v - u) / -g.
As the problem doesn't state the initial velocity with which the ball is thrown upward, we need to find it first. We can do this by applying the equation of motion: v² = u² + 2gs, where s = displacement. If we set v = 0 at maximum height, the equation becomes u = √(2gs). Given s = 178 m and g = 9.8 m/s², we find u ≈ 186.26 m/s. Substituting these values into our time equation, we get t ≈ 19 seconds for the time to reach maximum height. As mentioned, the ball will take the same time to fall back, hence the total time in air will be around 38 seconds.
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Rectangle ABCD has vertices A(3,5),B(5,5),C(5,1), and D(3,1). Drag and drop the coordinates of each vertex when rectangle ABCD is rotated 90 degrees counter clockwise around origin
Answer:
A'(-5,3), B'(-5,5), C'(-1,5) and D'(-1,3).
Step-by-step explanation:
If a point P(h,k) is rotated counterclockwise by 90° about the origin then the image point P' will become with coordinates (-k,h).
Now, the rectangle ABCD with vertices A(3,5), B(5,5), C(5,1) and D(3,1) is rotated 90 degrees counter-clockwise around the origin and the image rectangle will be A'B'C'D' with coordinates A'(-5,3), B'(-5,5), C'(-1,5) and D'(-1,3). (Answer)
An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30o angle. To the nearest foot, how far does a person travel from the bottom to the top of the escalator?
a) 50 ft
b) 43 ft
c) 87 ft
d) 25 ft
Answer:
a person travel 50 ft from the bottom to the top of the escalator
Step-by-step explanation:
An escalator lifts people to the second floor of a building, 25 ft above the first floor. The escalator rises at a 30 degree angle
The escalator forms a right angle triangle
opposite to 30 degree angle is 25 feet. to find the distance from the bottom to the top of the escalator we find the hypotenuse
let x be the hypotenuse
[tex]sin(theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]sin(30)=\frac{25}{x}\\x sin(30)= 25\\x=\frac{25}{sin(30)} \\x=50\\[/tex]
a person travel 50 ft from the bottom to the top of the escalator
Using trigonometry, the person travels approximately 50 ft from bottom to top. So, the answer is (a) 50 ft.
To find the distance a person travels from the bottom to the top of the escalator, we can use trigonometric functions. Since the escalator rises at a 30° angle, we can use the sine function to find the vertical component of the distance traveled.
Let's denote the distance traveled from the bottom to the top of the escalator as ( d ).
We know that the vertical component of the distance traveled is [tex]\( d \cdot \sin(30°) \).[/tex]
Given that the height of the second floor is 25 ft, we have:
[tex]\[ d \cdot \sin(30°) = 25 \][/tex]
To find ( d ), divide both sides by ( sin(30°) ):
[tex]\[ d = \frac{25}{\sin(30°)} \][/tex]
Now, let's calculate:
[tex]\[ \sin(30°) \approx 0.5 \][/tex]
So:
[tex]\[ d = \frac{25}{0.5} = 50 \][/tex]
Therefore, the person travels approximately 50 ft from the bottom to the top of the escalator.
So, the correct answer is:
a) 50 ft
All per-unit concepts rely on ratios,meaning,to provide a type of measurement
Answer:
It is True that all concepts rely on ratios meaning to provide a type of measurement because ratio compares one quantity to another
Step-by-step explanation:
Ratio shows how many times one quantity is to another
Answer:
it's division.
Step-by-step explanation:
If the last digit of weight measurement is equally likely to be any of the digits 0 through 9. Round your answers to one decimal place (e.g. 98.7). What is the probability that the last digit is 0?
Answer:Probability that the last digit is 0=0.1
Step-by-step explanation:
The likely digits for the last digits runs from 0 through 9 giving a total of 10 digits
The fore P(last digit to be 0) = 1/10 = 0.1
If the last digit of a weight measurement rounded to the nearest tenth place is equally likely to be any of the digits from 0 through 9, then the probability that the last digit is 0 is 0.1 or 10%.
Explanation:The question is asking about the probability that the last digit in a weight measurement, rounded to one decimal place, is 0. Given that the last digit is equally likely to be any digits from 0 through 9, this is a basic probability problem with each outcome being equally likely.
Since there are 10 possible results (the digits 0 through 9), and we are interested in only 1 of these results (the digit 0), the probability can be calculated as 1 divided by 10. Therefore, the probability that the last digit is 0 is 0.1 or 10%.
This is a standard concept in an introductory probability course and is a fundamental idea that will be used in more complex probability problems.
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is 2 - 2 + 5x; 5x equivalent
Answer:
Yes
Step-by-step explanation:
The First section of the equation (2-2) cancel each other out and you are left with 5x=5x
Answer:
Yes
Step-by-step explanation:
Because In the equation we have 2-2+5x
2-2=0
So, 0+5x = 5x
Jill found a new fruit punch recipe that calls for orange juice and lemon-lime soda. If orange juice costs $3.60 per bottle and lemon-lime soda costs $1.80 per bottle and the recipe calls for 3 times as many bottles of lemon-lime soda as orange juice, at most how many bottles of orange juice can she buy if she only has $54.00?
Answer:
She can buy at most 6 bottles of orange juice.
Step-by-step explanation:
Consider the provided information.
The recipe calls for 3 times as many bottles of lemon-lime soda as orange juice,
Let she buy x bottles of orange juice.
According to question: Lemon lime soda = 3x
Orange juice costs $3.60 per bottle and lemon-lime soda costs $1.80 per bottle. She only has $54.00
[tex]3.60x+1.80(3x)=54[/tex]
[tex]3.60x+5.4x=54[/tex]
[tex]9x=54[/tex]
[tex]x=6[/tex]
Hence, she can buy at most 6 bottles of orange juice.
Jill can buy at most 6 bottles of orange juice.
Explanation:To find out how many bottles of orange juice Jill can buy, we need to determine the cost of the orange juice and the cost of the lemon-lime soda based on the given prices. Let's assume she can buy 'x' bottles of orange juice. Since the recipe calls for 3 times as many bottles of lemon-lime soda, she can buy 3x bottles of lemon-lime soda. The total cost of the orange juice and the lemon-lime soda must not exceed $54.00.
The cost of the orange juice is $3.60 per bottle, so the cost of 'x' bottles of orange juice is 3.60x dollars. The cost of the lemon-lime soda is $1.80 per bottle, so the cost of 3x bottles of lemon-lime soda is 1.80 * 3x = 5.40x dollars.
To find the maximum number of bottles of orange juice she can buy, we need to solve the inequality:
3.60x + 5.40x ≤ 54.00
Combining like terms, we have:
9.00x ≤ 54.00
Dividing both sides of the inequality by 9.00, we get:
x ≤ 6
Jill can buy at most 6 bottles of orange juice.
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Rita bought a pair of jeans for $89. The sales-tax rate is 11 percent. What is the total amount she paid for the jeans?
Total amount paid by Rita is $98.79
Step-by-step explanation:
Step 1: Given sales tax = 11% and cost of jeans = $89Step 2: Calculate amount of sales tax = 11% of 89 = 11/100 × 89 = $9.79Step 3: Calculate the total amountTotal Amount = 89 + 9.79 = $98.79
in the figure, p║ q find m∠1
1. m∠1 = 69
2. m∠1= 50
3. m∠1= 61
4. m∠1 = 40
Answer:
Hope this helps you.
The answer is 61, x+40+5x+14=180, so x equals 21. 5(21)+14 ends up equaling 119, so 180-119 equals 1
A concrete mixer is in volume proportions of 1 part cement, 2 parts water, 2 parts aggregate, and 3 parts sand. How many cubic feet of each ingredient are needed to make 54cu ft of concrete?
Answer:
Step-by-step explanation:
The total volume of cement in cubic feet to be made is 54 cu ft.
A concrete mixer is in volume proportions of 1 part cement, 2 parts water, 2 parts aggregate, and 3 parts sand. This means that the ratio of the ingredients is
1 : 2 : 2 : 3
Total ratio = 1 + 2 + 2 + 3 = 8
Therefore,
Volume of cement needed would be
1/8 × 54 = 6.75 cubic feet
Volume of water needed would be
2/8 × 54 = 13.5 cubic feet
Volume of aggregate needed would be
2/8 × 54 = 13.5 cubic feet
Volume of sand needed would be
3/8 × 54 = 20.25 cubic feet
As a secondary mathematics teacher, Hernandez conducted a study that explored whether giving children recess prior to testing helped their test performance. For one of the semesters, he sends half of his classes out for 10 minutes of recess prior to testing for the other half, he provides 10 minutes of free time after the test. Which of the following best represents the design of Hernandez's study?
Full Question
As a secondary mathematics teacher, Hernandez conducted a study that explored whether giving children recess prior to testing helped their test performance. For one of the semesters, he sends half of his classes out for 10 minutes of recess prior to testing for the other half, he provides 10 minutes of free time after the test. Which of the following best represents the design of Hernandez's study?
a. One-shot case study
b. Post-test only control group
c. Solomon four group
d. Static-group comparison
Answer:
Static-Group Comparison
Explanation:
A Static-Group Comparison describes a study that involves two non-randomly selected groups, where one groups receive the treatment, and the other does not before the test. Afterwards, a post-test examination of the score is then carried out to examine the different in performance between both groups.
You are certain to get 3 jacks when selecting 51 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive? The probability is nothing
Answer:
1
Step-by-step explanation:
The probability of selecting (at least)3 jacks out of a shuffled deck of 51 cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1
Answer:
1
Step-by-step explanation:
The probability of selecting (at least)3 jacks out of a shuffled deck of 51 cards is 1. This is because in every shuffled deck of 51 cards, we are certain to find at least 3 jacks and this is 100% certain. So, the probability of selecting (at least) 3 jacks P(J)= 100% = 100/100 = 1
A reduction in inventory will improve return of equity by: Group of answer choices A. Increasing cash, which will increase asset turnover B. reducing cost of goods sold, which will increase asset turnover C.Increase assets, which will increase asset turnover and profit margin D. Reducing cost of goods sold, which will increase the profit margin
Answer:
A. Increasing cash, which will increase asset turnover
C.Increase assets, which will increase asset turnover and profit margin
Step-by-step explanation:
A reduction in inventory will improve business performance by increasing the efficiency of the company..
return of equity (ROE) can be calculated by: net profit/shareholder equity.
where share holder equity can be calculated by company assets minus debts.
Therefore ROE = Net profit/ (Assets - debts)
With, this formula, it can be deduced mathematically that, increasing ROE will Increase profit gain and increase asset turnover.
ROE help company to estimate how management is using company assets to actualize profit. Reducing inventory is a reduction in the cost of procurement of goods needed by the company. this eventually increase the cash income of the company.
Also, a reduction in company debts can drastically improve the ROE.
A French restaurant used 92,870 ounces of cream last year. This year, due to a menu update, it used 100% less. How much cream did the restaurant use this year?
Answer:
The French restaurant did not use cream this year, due to a menu update.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Amount of cream used by a French restaurant last year = 92.870 ounces
Amount of cream used by the French restaurant this year = 100% less
2. How much cream did the restaurant use this year?
The answer is zero and we calculated it this way:
92,870 - 100% (92,870) = 92,870 - 92,870 * 1 = 92,870 - 92,870 = 0
The French restaurant did not use cream this year, due to a menu update.
Answer:60%
Step-by-step explanation: i know its correct bc i got it wrong and it told me the answer
Which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cone with a radius of 1 unit
a cylinder with a radius of 1 unit
a cylinder with a radius of 2 units
a rectangular prism with a base length of 1 unit
Yo sup??
This question can be solved by just imagining the object formed or practically trying it out.
Therefore the correct answer to this question is option 2 ie
a cylinder with a radius of 1 unit.
Hope this helps.
Answer:
a cylinder with a radius of 1 unit
Step-by-step explanation:
Two hikers are 33 miles apart and walking towards each other. They meet in 10 hours. Find the rate of each Hiker if one joker walks 1.1 mph fast than the other
Answer:
Step-by-step explanation:
Let x represent the rate of the first hiker.
if one hiker walks 1.1 mph fast than the other, it means that the rate of the second hiker would be x + 1.1
Two hikers are 33 miles apart and walking towards each other. They meet in 10 hours. This means that in 10 hours, both hikers travelled a total distance of 33 miles.
Distance = speed × time
Distance covered by the first hiker in 10 hours would be
x × 10 = 10x
Distance covered by the second hiker in 10 hours would be
10(x + 1.1) = 10x + 11
Since the total distance covered by both hikers is 33 miles, then
10x + 10x + 11 = 33
20x + 11 = 33
20x = 33 - 11 = 22
x = 22/20 = 1.1 miles per hour
The rate of the second hiker would be
1.1 + 1.1 = 2.2 miles per hour.
A box of donuts has 12 total. One-fourth of the donuts have sprinkles. Of the remaining donuts, one-third have cherry filling. The rest are plain. How many plain donuts are in the box?
Answer:
13
Step-by-step explanation:
Trust me
The number of plain donuts in the box will be 6.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a box of donuts has 12 total. One-fourth of the donuts have sprinkles. Of the remaining donuts, one-third have a cherry filling. The rest are plain.
The number of plain donuts will be calculated as below:-
Number = 12 - ( 12 /4) - ( 9 / 3 )
Number = 12 - 3- 3
Number = 12 - 6
Number = 6 plain donuts
Therefore, the number of plain donuts in the box will be 6.
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A theatre sold a total of 98 adult and senior tickets. Adult tickets sold for 12$ each and senior tickets sold for 8$ each bringing in a total of 1,072$. How many adult tickets were sold
Answer: 72 adult tickets were sold.
Step-by-step explanation:
Let x represent the number of adult tickets that were sold.
Let y represent the number of senior tickets that were sold.
A theatre sold a total of 98 adult and senior tickets. It means that
x + y = 98
x = 98 - y - - - - - - - - - - - - -1
Adult tickets sold for 12$ each and senior tickets sold for 8$ each bringing in a total of 1,072$. This means that
12x + 8y = 1072 - - - - - - - - - - - 2
Substituting equation 1 into equation 2, it becomes
12(98 - y) + 8y = 1072
1176 - 12y + 8y = 1072
- 12y + 8y = 1072 - 1176
- 4y = - 104
y = - 104/ - 4
y = 26
Substituting y = 26 into equation 1, it becomes
x = 98 - 26 = 72
Kwan wants to place a fence around a circular flower garden in his yard. If the radius of the garden is 4 yards, what is minimum amount of fencing that Kwan needs, to the nearest tenth of a yard A. 8.0 B. 12.6 C. 25.1 D. 50.2
Answer:
cccccccccccccccc
Step-by-step explanation:
A carpenter has at most $250 to spend on lumber the inequality 8x+12y<250 represents the numbers x of 2 by 8 boards and the numbers y 4 by 4 boards the carpenter can buy can the carpenter buy twelve 2 by 8 boards and fourteen 4 by 4 boards?
Answer:
The carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Step-by-step explanation:
Given:
Amount a carpenter can spend at most = $250
The inequality to represent the amount he can spend on each type of board is given as:
[tex]8x+12y<250[/tex]
where [tex]x[/tex] represents '2 by 8 boards' and [tex]y[/tex] represents '4 by 4 boards'.
To determine whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Solution :
In order to check whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards' , we need to plugin the [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.
Plugging in [tex]x=12[/tex] and [tex]y=14[/tex] in the given inequality
[tex]8(12)+12(14)<250[/tex]
[tex]96+168<250[/tex]
[tex]264<250[/tex]
The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
Given that,
A carpenter has at most $250 to spend on lumber,
The inequality 8x + 12y < 250 represents,
The numbers x of 2 by 8 boards,
And the numbers y 4 by 4 boards.
We have to find,
The carpenter can buy can the carpenter buy twelve 2 by 8 boards and fourteen 4 by 4 boards.
According to the question,
The numbers x of 2 by 8 boards,
And the numbers y 4 by 4 boards.
Inequality [tex]8x + 12y < 250[/tex]
This means that a 2-by-8 board cost $8 each, while a 4-by-4 board cost $12 each.
x = 12 2-by-8 boards
y = 14 4-by-4 boards
In order to check whether the carpenter can buy 12 '2 by 8 boards' and 14 '4 by 4 boards' .
Plugin the and in the given inequality and see if it satisfies the condition or not or in other words (12,14) must be a solution for the inequality.
Putting x=12 and y=14 in the inequality,
[tex]8(12) + 12(14) <250\\96+168<250\\264<250[/tex]
Hence, The above statement can never be true and hence the carpenter will not be able to buy 12 '2 by 8 boards' and 14 '4 by 4 boards'.
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Ucon Inc., a manufacturing company, handles all the supply chain functions on its own. This has resulted in an inefficient use of resources and delays in production. To resolve these issues, the management decides to hire external agencies to perform some operations. In this scenario, Ucon Inc. is most likely to adopt the strategy of _____.
Answer: Outsourcing Processes
Step-by-step explanation:
The inefficient use of resources and delays in production in Ucon Inc. that needs to be resolved by hiring external agencies to perform some operations would be resolved by the adoption of outsourcing processes strategy.
It's most likely the strategy employed here because external agencies performing certain operations in a company means they are outsourced to help the company overcome certain challenges.
Julia is making pasta necklaces and wreaths. She uses n noodles in a necklace and 3/5 that number of noodles in wreaths. Which expression shows the number of noodles Julia uses if she makes 9 necklaces and 20 wreaths?
Answer:
the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths
= (9 [tex]\times[/tex] n ) + (20 [tex]\times[/tex] (3/5)n) = 9n + 12n = 21n
Step-by-step explanation:
i) there are n noodles in a necklace
ii) there are 9 necklaces
iii) therefore the number of noodles used to make the nine necklaces = 9 [tex]\times[/tex] n = 9n
iv) there are 3/5 noodles in a wreath
v) there are 20 wreaths
vi) therefore the number of noodles used to make the nine necklaces
= 20 [tex]\times[/tex] (3/5)n = 12n
vii) the expression that shows the number of noodles Julia uses to make 9 necklaces and 20 wreaths
= (9 [tex]\times[/tex] n ) + (20 [tex]\times[/tex] (3/5)n) = 9n + 12n = 21n
The expression 0.07x+(x−300) models the final price of a television set with an instant rebate in a state that charges a sales tax. The sales tax is on the original price.
Which expression represents the price of the television set after the instant rebate is applied but before the tax is applied?
Answer:
(x-300)
Step-by-step explanation:
Function Analysis
The model provided can be broken down into three parts: x is the original price of the television set before any changes were made on it. (x-300) is the price after the instant rebate was applied, and 0.07x is the sales tax (7%) charged by the state. Note this charge is applied on the original price.
Answer: (x-300) is price of the television set after the instant rebate is applied but before the tax is applied.
In a sample of 258 individuals selected randomly from a city of 750,339 people, 165 were found to be supportive of a new public works project. Find the 99.9% confidence interval for the support level percentage in the entire city
Answer: (54.13%, 53.83%)
Step-by-step explanation:
Confidence interval for population proportion is given by :-
[tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]\hat{p}[/tex] = sample proportion
n= sample size.
z* = critical z-value.
Let p be the proportion of individuals supportive of a new public works project.
As per given , we have
n= 258
[tex]\hat{p}=\dfrac{165}{258}\approx0.64[/tex]
For 99.9% confidence , significance level α= 0.001
Critical z-value for 99.9% confidence interval =[tex]z_{\alpha/2}=z_{0.001/2}=z_{0.0005}=3.29[/tex] [By z-table]
Then, the 99.9% confidence interval for the support level percentage in the entire city will be :
[tex]0.64\pm (3.29)\sqrt{\dfrac{0.64(1-0.64)}{258}}\\\\\approx 0.64\pm0.0983\\\\=(0.64-0.0983,\ 0.64+0.0983) = (0.5417,\ 0.7383= (54.13\%,\ 53.83\%)[/tex]
Hence, the 99.9% confidence interval for the support level percentage in the entire city is (54.13%, 53.83%) .
Zaire is making sand art her mom. She bought a rectangular vase that is 2.5 inches long, 3 inches wide, and 6 inches tall. Colored sand is sold for $0.50 per square inch. How much will she spend on sand to fill the jar
Answer:
$22.50
Step-by-step explanation:
I think the unit of the sand sold is actually in cubic inches and not square inches.
V = L*B*H
V = 2.5 * 3 * 6
V = 45 in³
If 1 in³ = $0.50
45 = x
x = 45 * $0.50
x = $22.50
The perimeter of a triangular garden is 66 feet. Find the length of the three sides if the middle length side is 5 feet greater than twice the length of the smallest side, and the longest side is 5 feet less than 3 times the length of the smallest side.
Answer: the length of the smallest side is 11 feet.
the length of the medium side is 27 feet.
the length of the longest side is 28 feet.
Step-by-step explanation:
Let x represent the length of the smallest side.
Let y represent the length of the middle side.
Let z represent the length of the longest side.
The perimeter of a triangular garden is 66 feet. This means that
x + y + z = 66 - - - - - - - - - -1
if the middle length side is 5 feet greater than twice the length of the smallest side, it means that
y = 2x + 5
The longest side is 5 feet less than 3 times the length of the smallest side. It means that
z = 3x - 5
Substituting y = 2x + 5 and z = 3x - 5 into equation 1, it becomes
x + 2x + 5 + 3x - 5 = 66
6x = 66
x = 66/6 = 11
y = 2x + 5 = 2 × 11 + 5
y = 27
z = 3x - 5 = 3 × 11 - 5
z = 28
The length of the three sides of the triangular garden is 11 feet, 27 feet, and 28 feet.
Explanation:The perimeter of a triangle is the sum of the lengths of its three sides. Let's assume the length of the smallest side is x. According to the given information, the middle length side is 5 feet greater than twice the length of the smallest side, so it can be expressed as 2x + 5. The longest side is 5 feet less than 3 times the length of the smallest side, so it can be expressed as 3x - 5.
Now, since the perimeter of the triangle is 66 feet, we can set up the equation:
x + (2x + 5) + (3x - 5) = 66
Simplifying this equation, we get:
6x = 66
Dividing both sides by 6, we get:
x = 11
So the length of the smallest side is 11 feet. The middle length side is 2x + 5 = 2(11) + 5 = 27 feet. The longest side is 3x - 5 = 3(11) - 5 = 28 feet.
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Jorie normally leaves work at 5:00 pm, but she is leaving work 30 minutes late today. She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road. Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late. Let x represent the number of minutes her normal commute takes when she leaves on time. Y equals one fourth times x minus thirty y = 4x − 30 y equals one fourth times x plus thirty y = 4x + 30
Answer:
[tex]y=x/4+30[/tex]
Step-by-step explanation:
Let x be the normal time it takes for her to commute. We know that if she was 30min late, this would had 30 min to the journey. She takes a different route, she can travel four times faster than the normal route.
Therefore the normal time of commute will be 4 times less:
[tex]y=x/4+30[/tex]
This equation states that the commute time will be four times faster and adding the 30min that she is late.
Y is equals to one fourth times x plus thirty, y = 4x + 30.
Given that,
Jorie normally leaves work at 5:00 pm, but she is leaving work 30 minutes late today.
She decides to make up time by taking the toll road instead of side streets. She can travel four times faster by taking the toll road.
We have to determine,
Create an equation in terms of x to represent the number of minutes after 5:00 pm she arrives home from work if she leaves late.
According to the question,
Let x represent the number of minutes her normal commute takes when she leaves on time.
She was 30min late, this would had 30 min to the journey. She takes a different route, she can travel four times faster than the normal route.
Therefore,
The normal time of commute will be 4 times less,
[tex]y = 4x +30\\\\[/tex]
Hence, The commute time will be four times faster and adding the 30min that she is late.
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Barry has 4 wooden identically shaped and sized blocks. 2 are blue, 1 is red and 1 is green. How many distinct ways can barry arrange the 4 blocks in a row? Barry's friend Billie is colour-blind and cannot distinguish between red and green. How many of Barry's distinct arrangements would Billie see different?
Answer:
Step-by-step explanation:
Distinct ways in which Barry can arrange the wooden shaped blocks is calculated from the permutation expression
4 permutation 3 =
P(n,r)=P(4,3) =4! ÷ (4−3)! = 24
Billie's distinct ways of seeing the arrangement would be 4 permutation 2
P(n,r)=P(4,2) =4! ÷ (4−2)! = 12
Answer:
The distinct arrangement Billie would see is P(n,r)=P(4,2) =4! ÷ (4−2)! = 12
Step-by-step explanation:
From the question, we recall the following:
Blue = 2, red =1 green =1
The way this can be solved for which Barry can arrange the wooden shaped blocks is applying the method called permutation
So,
4 permutation 3 = P(n,r)=P(4,3) =4! ÷ (4−3)! = 24
The ways Billie's would see the permutation arrangement is 4 permutation 2
With the expression given as
P(n,r)=P(4,2) =4! ÷ (4−2)! = 12
Will Give brainlist, Please Help, Show work, SEE ATTACHED PICTURES FOR QUESTIONS 4 TOTAL
Answer:
Step-by-step explanation:
1) the figure has 2 hemispheres and 1 cylinder.
2) The formula determining the volume of a hemisphere is expressed as
Volume = 4/3πr³
Where
r represents radius of the hemisphere.
π is a constant whose value is 3.14
The formula determining the volume of a cylinder is expressed as
Volume = 4/3πr³
Where
r represents radius of the cylinder
h represents the height of the cyinder.
3) volume of hemisphere = 4/3 × 3.14 × 2³ = 33.49mm³
Height of cylinder = 10 - (2+2) =6mm
Volume of cylinder = 3.14 × 2²× 6 = 75.36mm³
4) the composite volume is
2 × 33.49 + 75.36 = 142.34mm³
Renting a car cost 30dollars a day, or 600 per month. Renting daily is cheaper for a few days, but after how many days are the two options equal. (After which renting is cheaper)
Answer: The two options are equal after 20days of daily pay.
Step-by-step explanation:
If it cost $30 to rent a car for a day and $600 to rent the same car for a month(approximately 30days), renting daily is equal to the monthly rentage after 20 days ($30 for 20days which is $30×20 i.e $600)
According to the deduction above, the renting is cheaper daily only for the first 20 days after which the amount equals to the monthly rentage of the same car.
Answer:
20 days.
Step-by-step explanation:
Assume, 1 month = 30 days.
Options:
i. $600 per month
$600/month * 1 month/30 day
= $20 per day.
ii. $30/day.
Renting daily is equal to the monthly rent after 20 days ($30 for 20days which is $30×20 i.e $600)
That is, the renting is cheaper daily only for the first 20 days after which it is equal to the monthly rent.
Lilth makes soap and lotion. It takes her 20 minutes to make a batch of soap and 35 minutes to make a batch of lotion. The cost of producing each batch are $5 for the soap and $15 for the lotion. Lilth has 20 hours available to make soap and lotion. The materials to make the soap and lotion must cost at most $325. The systems of linear inequalities represent this situation. 5x+15y is less than or equal to 325 20x+35y is less than or equal to 1200 what does the solution (53, 4) represent?
Answer:
Step-by-step explanation:
Let x represent the number of batches of soap that Lilth makes.
Let y represent the number of batches of lotion that Lilth makes.
It takes her 20 minutes(20/60 = 1/3 hours) to make a batch of soap and 35 minutes(35/60 = 7/12 hours) to make a batch of lotion. Lilth has 20 hours available to make soap and lotion. This means that
x/3 + 7y/12 = 20
4x + 7y = 240- - - - - - - - - - -1
The cost of producing each batch are $5 for the soap and $15 for the lotion. The materials to make the soap and lotion must cost at most $325. This means that
5x + 15y ≤ 325 - - - - - - - - -2
4x = 240 - 7y
x = (240 - 7y)/4
Substituting
5(240 - 7y)/4 + 15y ≤ 325
(1200 - 35y)/4 + 15y ≤ 325
1200 - 35y + 60y ≤ 1300
25y ≤ 1300 - 1200
25y ≤ 100
y ≤ 100/25
y ≤ 4
4x + 7 × 4 = 240
4x + 28 = 240
4x = 212
x = 212/4 = 53
Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion