Part 1: The function that models the height of the basketball is [tex]\( h(t) = -16t^2 + 15t + 6.5 \).[/tex]
Part 2: The basketball hits the ground after approximately 0.97 seconds.
Part 3: The basketball reaches its maximum height at approximately 0.47 seconds.
Part 4: The maximum height of the basketball is approximately 11.39 feet.
Part 1: To model the height of the basketball, we use the given function [tex]\( h(t) = -16t^2 + v0t + h0 \)[/tex] with the initial velocity [tex]\( v0 = 15 \)[/tex] ft/sec and the initial height [tex]\( h0 = 6.5 \)[/tex] feet. Plugging in these values, we get the function:
[tex]\[ h(t) = -16t^2 + 15t + 6.5 \][/tex]
Part 2: To find the time it takes for the basketball to hit the ground, we set the height function equal to zero and solve for [tex]\( t \)[/tex]:
[tex]\[ -16t^2 + 15t + 6.5 = 0 \][/tex]
Using the quadratic formula [tex]\( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \),[/tex]where [tex]\( a = -16 \), \( b = 15 \)[/tex], and [tex]\( c = 6.5 \)[/tex], we get two solutions. We discard the negative solution because time cannot be negative, and we round the positive solution to the nearest hundredth:
[tex]\[ t = \frac{-15 \pm \sqrt{15^2 - 4(-16)(6.5)}}{2(-16)} \] \[ t = \frac{-15 \pm \sqrt{225 + 416}}{-32} \] \[ t = \frac{-15 \pm \sqrt{641}}{-32} \] \[ t \approx \frac{-15 + 25.31}{-32} \] \[ t \approx 0.97 \text{ seconds} \][/tex]
Part 3: To find when the basketball reaches its maximum height, we need to find the vertex of the parabola. The time coordinate of the vertex of a parabola [tex]\( ax^2 + bx + c \)[/tex] is given by [tex]\( t = -\frac{b}{2a} \)[/tex]. For our function, [tex]\( a = -16 \)[/tex]and [tex]\( b = 15 \)[/tex], so:
[tex]\[ t = -\frac{15}{2(-16)} \] \[ t = \frac{15}{32} \] \[ t \approx 0.47 \text{ seconds} \][/tex]
Part 4: To find the maximum height, we substitute the time at which the maximum height is reached back into the height function:
[tex]\[ h(0.47) = -16(0.47)^2 + 15(0.47) + 6.5 \] \[ h(0.47) \approx -16(0.2209) + 7.05 + 6.5 \] \[ h(0.47) \approx -3.5344 + 7.05 + 6.5 \] \[ h(0.47) \approx 11.39 \text{ feet} \][/tex]
Therefore, the basketball reaches a maximum height of approximately 11.39 feet after approximately 0.47 seconds.
When algebraic, or numerical fractions are added or subtracted, the result is a single fraction. True False
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
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.
Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.
A) Are the first flight leaving on time and the luggage making the connection independent events? Explain.
B) What is the probability that her luggage arrives in Denver with her?
Answer:
(A) The two events are Not Independent.
(B) The probability that Leah's luggage arrives in Denver is 0.695.
Step-by-step explanation:
Let F = Leah's first flight leaves on time and C = Leah's luggage will make the connecting flight.
Given:
P (F) = 0.15, P (C|F) = 0.95 and P (C|F') = 0.65
Here F' represents the events that Leash's first flight was not on time.
(A)
The events F and C are not independent.
For the luggage to make the connecting flight Leah's first flight must be on time.
As it is provided that the probability that the the luggage will make the connecting flight provided that the first flight is delayed is 0.65, i.e. there 0.35 probability that the luggage will not make the connecting flight.
Thus, implying that the two events F and C are dependent.
(B)
Compute the probability that Leah's luggage arrives in Denver as follows:
P (D) = P (C|F) × P (F) + P (C|F') × P (F')
[tex]= (0.95\times0.15)+(0.65\times (1-0.15))\\=0.695[/tex]
Thus, the probability that Leah's luggage arrives in Denver is 0.695.
The first flight leaving on time and the luggage making the connection are dependent events. The probability that Leah's luggage arrives in Denver with her is 0.695.
Explanation:A) In order to determine whether the first flight leaving on time and the luggage making the connection are independent events, we need to compare the probability of the luggage making the connection when the first flight is on time (0.95) to the probability of the luggage making the connection when the first flight is delayed (0.65).
If these probabilities are the same, then the events are independent.
However, since the probabilities differ, the events are dependent.
B) To find the probability that Leah's luggage arrives in Denver with her, we need to consider two scenarios:
The first flight leaves on time and the luggage makes the connection (0.15 * 0.95)The first flight is delayed and the luggage makes the connection (0.85 * 0.65)We can then add these probabilities together to get the total probability: (0.15 * 0.95) + (0.85 * 0.65) = 0.1425 + 0.5525 = 0.695
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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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
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
Find an equation for the nth term of the arithmetic sequence. -15, -6, 3, 12, ...
an = -15 + 9(n + 1)
an = -15 x 9(n - 1)
an = -15 + 9(n + 2)
an = -15 + 9(n - 1)
Answer: [tex]t_{n}=-15+9(n-1)[/tex]
Step-by-step explanation:
The formula for finding the nth term of an arithmetic sequence is given as:
[tex]t_{n}=a+(n-1)d[/tex]
[tex]a =[/tex] first term = -15
[tex]d =[/tex] common difference = -6 - (-15) = 9
[tex]n =[/tex] number of terms
substituting into the formula , we have :
[tex]t_{n} = -15+(n-1)9[/tex]
[tex]t_{n}=-15+9(n-1)[/tex]
A local factory shut down in 1990 the population of 35,000 in 1991 the population was 24,500 In 1992 it was 17,150 what is expected population in 1999
Answer: the expected population in 1999 is 1412
Step-by-step explanation:
The population is decreasing in geometric progression. This is true because there is a common ratio between consecutive years.
Common ratio = 24500/35000 = 17150/24500 = 0.7
The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence.
r represents the common ratio.
n represents the number of terms.
From the information given,
a = 35000
r = 0.7
n = 10
The 9th term, T9 is
T9 = 35000 × 0.7^(10 - 1)
T9 = 35000 × 0.7^9
T9 = 1412
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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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
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
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%) .
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.
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:
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 height of a soccer ball that is kicked from the ground can be approximated by the function:
y = -18x^2 + 54
where y is the height of the soccer ball in feet x seconds after it is kicked.
Find the time it takes the soccer ball to reach its maximum height in seconds
Answer:
[tex]\displaystyle \sqrt{3}\:sec.[/tex]
Step-by-step explanation:
[tex]\displaystyle -54 = -18x^2 → \frac{-54}{-18} = \frac{-18x^2}{-18} \\ \\ 3 = x^2 → \sqrt{3} = x[/tex]
I am joyous to assist you anytime.
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
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:
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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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)
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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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
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.
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
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.
Laura bought 8 3/10 yard of ribbon. She used 1 2/5 yard to tie a package and 2 1/3 yard to make a bow. Joe later gave her 4 3/5 yard. How much ribbon does she now have?
Answer:
Amount of ribbon remaining with Lara is [tex]10\frac{1}{3}\ yard[/tex].
Step-by-step explanation:
Given:
Amount of ribbon Lara bought = [tex]8\frac{3}{10} \ yard[/tex]
[tex]8\frac{3}{10} \ yard[/tex] can be Rewritten as [tex]\frac{83}{10}\ yard[/tex]
Amount of ribbon Lara bought = [tex]\frac{83}{10}\ yard[/tex]
Amount of ribbon used to tie a package = [tex]1\frac{2}{5} \ yard[/tex]
[tex]1\frac{2}{5} \ yard[/tex] can be Rewritten as [tex]\frac{7}{5}\ yard[/tex]
Amount of ribbon used to tie a package = [tex]\frac{7}{5}\ yard[/tex]
Amount of ribbon used to make bow= [tex]2\frac{1}{3} \ yard[/tex]
[tex]2\frac{1}{3} \ yard[/tex] can be Rewritten as [tex]\frac{7}{6}\ yard[/tex]
Amount of ribbon used to make bow = [tex]\frac{7}{6}\ yard[/tex]
We need to find the amount of ribbon remaining with Lara.
Solution:
Now we can say that;
Amount of ribbon remaining with Lara can be find by subtracting Amount of ribbon used to tie a package and Amount of ribbon used to make bow from Amount of ribbon Lara bought.
framing in equation form we get;
Amount of ribbon remaining = [tex]\frac{83}{10}-\frac{7}{5}-\frac{7}{6}[/tex]
Now we will make the denominator common using LCM.
LCM of 5,6,10 is 30
So we get;
Amount of ribbon remaining = [tex]\frac{83\times3}{10\times 3}-\frac{7\times6}{5\times6}-\frac{7\times5}{6\times5}=\frac{249}{30}-\frac{42}{30}-\frac{35}{30}[/tex]
Now the denominator are common so we will solve the numerator we get;
Amount of ribbon remaining = [tex]\frac{249-42-35}{30}= \frac{172}{30}[/tex]
Now Given:
Amount of ribbon Joe gave = [tex]4\frac{3}{5}\ yard[/tex]
[tex]4\frac{3}{5}\ yard[/tex] can be rewritten as [tex]\frac{23}{5}\ yard[/tex]
Amount of ribbon Joe gave = [tex]\frac{23}{5}\ yard[/tex]
Now we can say that;
Amount of ribbon remaining with her = [tex]\frac{172}{30}+\frac{23}{5}[/tex]
Now again we will make the denominator common using LCM we get;
Amount of ribbon remaining with her = [tex]\frac{172\times1}{30\times1}+\frac{23\times6}{5\times6} = \frac{172}{30}+\frac{138}{30}[/tex]
Now denominators are common so we will solve the numerators we get;
Amount of ribbon remaining with her = [tex]\frac{172+138}{30}=\frac{310}{30}=\frac{31}{3}\ yard \ \ Or \ \ 10\frac{1}{3}\ yard[/tex]
Hence Amount of ribbon remaining with her is [tex]10\frac{1}{3}\ yard[/tex].
Final answer:
To find out how much ribbon Laura now has, we start with her initial amount, subtract the yardage used in two activities, and add the amount received from Joe, combining fractions and whole numbers to reach the final total yardage.
Explanation:
To calculate the amount of ribbon Laura has after her transactions, we need to perform a few steps involving addition and subtraction of mixed numbers, and then convert that number to a single unit if necessary. Here is how we solve this:
Start with the total ribbon Laura bought: 8 3/10 yards.
Subtract the ribbon used to tie a package: 1 2/5 yards.
Also, subtract the ribbon used to make a bow: 2 1/3 yards.
Add the ribbon given by Joe: 4 3/5 yards.
Combine the fractions and whole numbers separately for precision.
Finally, add or subtract the totals to find out how much ribbon Laura now has.
Let's do the math:
Laura's total ribbon after using some and receiving more from Joe is:
8 3/10 (initial amount) - 1 2/5 (package) - 2 1/3 (bow) + 4 3/5 (from Joe) = Laura's current ribbon amount.
Simplify the fractions and calculate:
Step by step:
Convert mixed numbers to improper fractions or work directly with mixed numbers.
Find common denominators for the fractions.
Add and subtract the fractions.
Add and subtract the whole numbers.
Combine the totals.
We'll end up with a total that represents the yardage of ribbon Laura has left.
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 $325. This means that
5x + 15y ≤ 325 - - - - - - - - -2
4x = 240 - 7y
x = (240 - 7y)/4
Substituting
5(240 - 7y)/4 + 15y ≤ 325
(1200 - 35y)/4 + 15y ≤ 325
1200 - 35y + 60y ≤ 1300
25y ≤ 1300 - 1200
25y ≤ 100
y ≤ 100/25
y ≤ 4
4x + 7 × 4 = 240
4x + 28 = 240
4x = 212
x = 212/4 = 53
Therefore, the solution (53, 4) means that she would make at most 53 batches of soap and at most 4 batches of lotion
What is the value of x?
Enter your answer, as a decimal, in the box. Do not round your answer.
x=
The value of x is [tex]5.625[/tex]
Explanation:
Since, from the figure we can see that, a ray bisects the angle of a triangle.
Then, the angle bisector theorem states that, "if a ray bisects an angle of a triangle, then it divides the opposite sides of the triangle into segments that are proportional to the other two sides".
Thus, we have,
[tex]$\frac{A C}{B C}=\frac{A D}{B D}$[/tex]
where [tex]AC=4, BC=7.5, AD=3[/tex] and [tex]DB=x[/tex]
Substituting the values, we get,
[tex]$\frac{4}{7.5}=\frac{3}{x}$[/tex]
Simplifying, we have,
[tex]4x=22.5[/tex]
Dividing both sides by 4,
[tex]x=5.625[/tex]
Thus, the value of x is [tex]5.625[/tex]