The amount of time it would take this object to hit the ground is 2.56 seconds.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable to an output variable.
What is the maximum value of a function?The maximum value of a function can be defined as a point on the graph where the function reaches its highest point. This ultimately implies that, the maximum value of a function simply refers to its vertex on a graph.
The height (h) in meters, of this falling object is related to the time by the following function:
h = -4.9t² + d
Substituting the given parameters into the formula, we have;
0 = -4.9t² + 32
4.9t² = 32
Time, t² = 32/4.9
Time, t² = 6.53
Time, t = √6.53
Time, t = 2.56 seconds.
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y is inversely proportional to x. when x=3 y=8. work out the value of y when x is 8
Answer:
y = 3
Step-by-step explanation:
given y is inversely proportional to x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion
to find k use the condition x = 3, y = 8
8 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )
24 = k
y = [tex]\frac{24}{x}[/tex] ← equation of proportion
when x = 8 , then
y = [tex]\frac{24}{8}[/tex] = 3
Answer
3
Step-by-step explanation:
when one is increasing the other one should decrease.since 3 has increased by 5 ,then y should decrease by 5.
suppose you have 3 possible mutually exclusive initiating events (causes) and 4 possible outcome events (consequences) that are not mutually exclusive. how many scenarios do you have?
The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. The two events are mutually exclusive if they cannot occur at the same time.
What pairs of occurrences can never coexist?
Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously.
A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.
What are some examples of mutually exclusive events?
Several instances of occurrences that can never occur simultaneously include:
The outcomes of receiving head or tail while flipping a coin are mutually exclusive.
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Two ships leave a port at the same time. the first ship sails on a bearing of 32 degrees at 16 knots and the second on a bearing of 122 degrees at 24 knots. how far apart are they after 2.5 hours?
The ships and the port form a right triangle and hence, their distance is 72.1 nautical miles
Knot is a velocity unit equals to nautical miles per hour.
The situation can be depicted in the attached picture.
The distance travelled by the 1st ship after 2.5 hours is:
s1 = 16 knots x 2.5 hours = 40 nautical miles.
The distance travelled by the 2nd ship id:
s2 = 24 knots x 2.5 hours = 60 nautical miles.
Since the angle difference between those 2 ships is 90⁰, the distance between the ships can be obtained using the Pythagorean Theorem.
Referring to the attached picture,
d² = 40² + 60²
d² = 1600 + 3600
d² = 40² + 60²
d² = 5200
d = 72.1 nautical miles
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John is putting 10 books in a row on his bookshelf. He will put one of the books, Pride and Prejudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf?
John is putting 10 books in a row on his bookshelf. he would arrange it in
40,320 ways.
What is permutation?Generally, A permutation is a rearrangement of a set of elements. In other words, it is a way to arrange a set of items in a specific order. For example, the permutations of the set {1, 2, 3} are {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}. The number of possible permutations of a set of n elements is n!.
John is placing 8 books on the shelf in between Pride and Prejudice and Little Women.
The number of ways to arrange these 8 books is 8! (8 factorial).
since the order of the books in the first and last spots is predetermined,
The final answer is 8! = 40320ways
= 40,320 ways.
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Can someone help me ASAP please!!!!
Answer:
18 ft
Step-by-step explanation:
a=wl (3)(4) = 12
1/2bh 1/2(3)(4) = 6
12+6 = 18
A store sells
79 virtual reality headsets. How much
money does the store collect?
Hint (headset cost $125)
Answer: 9,875
Step-by-step explanation: 125 x 79 = 9,875
You have a budget of $300 to order shirts for a math club. The equation. 10x + 12y = 300 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
a. Interpret the terms and coefficients in the equation.
b. Graph the equation. Interpret the intercepts.
c. Find three possible solutions in the context of the problem.
The x-intercept is at point (30,0) and the y-intercept is at point (0,25). The graph of the equation is attached below.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that Short-sleeved shirts cost $10 each.
The Long-sleeved shirts cost $12 each.
The total budget is $300.
The given equation is 10x + 12y = 300
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
We have, 10x + 12y = 300
Substitute the value x = 0
10(0) + 12y = 300
12y = 300
y = 25
So, the y-intercept will be at 0,25).
Substitute y = 0
10x + 12(0) = 300
10x = 300
x = 30
So, the x-intercept is at point (30,0).
The x-intercept is at point (30,0), that means the number of short-sleeved shirts is 30. The y-intercept is at point (0,25), that means the number of long-sleeved shirts is 25.
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What is the slope of the line represented by the equation 3x+4y= 12?
Answer:
A line parallel to 3x+4y=12 must have a slope of -34
Marisol is organizing a party for the student council with a $50 budget. the linear function 15x+2y=50 represents the number of pizzas x and the number of bottled drinks y she can buy. if marisol buys 2 pizzas, how many bottled drinks can she buy?
The number of bottled drinks bought by Marisol is 10 in the student council party.
What is defined as the liner equation in two variables?A linear equation in two variables is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero. For example, 12x+8y = 3 but also -x+8y = 2 are two-variable linear equations.For the given linear equation;
The total budget of the party is $50.
The linear function function which represents the number of pizzas x and the number of bottled drinks y is;
15x + 2y = 50
Now, the number of pizza bought = 2.
To find the value of bottled drinks, put x = 2 in the linear function.
15×2 + 2y = 50
Simplify the equation;
30 + 2y = 50
2y = 50 - 30
2y = 20
y = 10
Thus, the total number of bottled drink bought by the Marisol is 10.
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Seven friends use an online code to get a $30 discount on each world-series
baseball game ticket. They spent $840 for the seven tickets. Find the price of one
ticket without the discount.
The price of one ticket is $150 without the discount.
What is discount?Discounts are defined as lowered prices or the sale of an item for less than it would typically cost. A pocketbook offered at 50% off the regular price or a shop that specializes in selling designer goods at below-market pricing are two examples of things that might be considered discounts.
Given Data
$30 discount on each world-series baseball game ticket.
They spent $840 for the seven tickets.
7 tickets = $840
1 ticket = [tex]\frac{840}{7}[/tex]
1 ticket = $120
Price of 1 ticket = $120 + $30
Price of 1 ticket = $150
The price of one ticket is $150 without the discount.
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Which inequality is true when the value of z is -16
The temperature in a town is 36.6F during the day and -12.6F at night. What is the temperature change from day to night?
( if possible could it be step-by-step please? thank you :D )
Answer:
49.2F
Step-by-step explanation:
To find the difference you can see how far they both are from 0 and add them together. So for this, it would be 36.6+12.6=49.2
Write fraction as a decimal
3/8
7/5
21/7
5/3
All you do is divide:
3 ÷ 8 = 0.375 or 0.38 or 0.4
7 ÷ 5 = 1.4
21 ÷ 7 = 3
5 ÷ 3 = 1.66666666667 or 1.67 or 1.7
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Identify the area of the rhombus.
Answer:
2160ft²Step-by-step explanation:
rhombus formed by 4 right triangles, 51ft hypotenuse and 45ft cathetus (90: 2 = 45). we use pythagoras to find the missing side so that we can find the area of a triangle and multiply it by 4
c = √(51²-45²)
c = √(2601 - 2025)
c = √576
c = 24ft
Area triangle= (½)×b×h
(½)45 * 24 =
(½)1080=
540ft²
multiply by 4
540 * 4 =
2160ft² (Area of the rhombus)
or
Rhombus Area Using Diagonals:
A = ½ × d1 × d2
A = ½ * 90 * 48
A = 2160ft² (Area of the rhombus)
(1.1: modeling) matt is a software engineer writing a script involving 6 tasks. each must be done one after the other. let ti be the time needed to complete the ith task. these times have a certain structure: •the total time needed to complete any 3 adjacent tasks is half the total time required to complete the next two tasks. •the second task takes 1 second. •the fourth task takes 10 seconds.
(t₁......t₆) = (5, 1, 44, 10, 90, 20) is the solution of the given matrix.
(A) An augmented matrix for a system of equations is a matrix of numbers where each column represents all the coefficients for a single variable and each row represents the constants from one equation (both the coefficients and the constant on the other side of the equal sign).
The system's augmented matrix is shown here:
[tex]\left[\begin{array}{cccccc|c}1 & 1 & 1 & -\frac{1}{2} & -\frac{1}{2} & 0 & 0 \\0 & 1 & 1 & 1 & -\frac{1}{2} & -\frac{1}{2} & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & 0 & 0 & 10\end{array}\right][/tex]
(B) Use these row operations to convert this augmented matrix to a reduced echelon form.
Row 2 should be subtracted from row 1, row 2 from row 3, and row 3 should be added to row 2.Increase row 3 by 1.Subtract row 4 from row 3 and multiply row 4 by row 1.Here is the augmented matrix's reduced echelon form:
[tex]\left[\begin{array}{ccccccc}1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & -\frac{1}{2} & -\frac{1}{2} & -11 \\0 & 0 & 0 & 1 & 0 & 0 & 10\end{array}\right][/tex]
(C) There are more rows:
[tex]\begin{array}{lllllll}0 & 0 & 0 & 0 & 0 & 1 & 20\end{array},\\\begin{array}{lllllll}1 & 1 & 1 & 0 & 0 & 0 & 50\end{array}[/tex]
Augmented matrix:
[tex]\left[\begin{array}{ccccccc}1 & 0 & 0 & 0 & 0 & \frac{1}{2} & 15 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & -\frac{1}{2} & -\frac{1}{2} & -11 \\0 & 0 & 0 & 1 & 0 & 0 & 10 \\0 & 0 & 0 & 0 & 0 & 1 & 20 \\1 & 1 & 1 & 0 & 0 & 0 & 50\end{array}\right][/tex]
(D) You must employ these row operations in order to solve the system.
Subtract row 1 from row 6, row 2 from row 6, row 3 from row 6, swap rows 5 and 6, add row 5 to row 3, multiply row 5 by 2, subtract row 1 from row 6, and row 1 from row 6 multiplied by 1/2. Add row 6 multiplied by 1/2 to row 3.[tex]\left[\begin{array}{lllllll}1 & 0 & 0 & 0 & 0 & 0 & 5 \\0 & 1 & 0 & 0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 & 0 & 0 & 44 \\0 & 0 & 0 & 1 & 0 & 0 & 10 \\0 & 0 & 0 & 0 & 1 & 0 & 90 \\0 & 0 & 0 & 0 & 0 & 1 & 20\end{array}\right][/tex]
Therefore, (t₁......t₆) = (5, 1, 44, 10, 90, 20) is the solution of the given matrix.
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ANSWER ASAP PLEASE TEST ALMOST DUE
Your boss is still trying to save money on car rentals. You compare Alpha Car Rental, which charges $72.00 per day with unlimited free mileage, and Amazing Car Rental, which charges $22.90 plus 30 cents per mile.
a. Some days you drive many miles, and some days you drive fewer miles. Determine the range of daily mileage for which each company is the less expensive choice.
b. Write a report to your boss that includes your recommendations about which car-rental company to use depending on the number of miles you plan to drive. Explain how you arrived at your recommendation. Use computations/written work, graphs, or tables to provide support for your conclusions.
Answer:
A)
If you are driving many miles a day, Alpha Car Rental is cheaper. If you are driving fewer miles a day, then Amazing Car Rental is cheaper.
B)
You can find this out by graphing the 2.
Alpha: y = 0x + 72.
Amazing: y = 0.30x +22.9
Where y is cost, and x is miles.
When you graph the 2, Alpha is a straight line because it has no mileage charge. The 2 linear functions meet at point (163.6, 72). Meaning if you drive more than 163 miles, it is cheaper to use Alpha Car Rental over Amazing Car rental.
Hope that helps
Write a real-world problem
that is represented by the division problem 38 ÷ 5 = 7 R3 in which it makes sense to round the quotient up to 8.
Answer:
See below
Step-by-step explanation:
Comment
This is a good question. It makes you think about when you should round and maybe when you shouldn't.
You have a building side that is 38 square yards. You want to know how much paint to buy to cover the given side.
Let us say that each can of paint could cover 5 square yards. You cannot buy any can that might be smaller to take care of the 3 remaining square yards.
You have no choice. You have to round the answer from 7 R 3 to 8.
Expand the following
8(p+ 4)
Answer:
8p+32
Step-by-step explanation:
Suppose you have a population with mean 25 and standard deviation 20. You take samples of size 100 and consider the distribution of the means of those samples. What is the mean of the sample means?.
The mean of the sample means will be 25
As Sample mean is an estimate of the population mean. If we increment the number of observations the precision of the sample means will be improved to get closer to the population mean and according to Central Limit Theorem, The sampling distribution of the sample statistic can be considered roughly if any of the below-mentioned criteria is satisfied :
The sample measure is expansive or at the slightest 30. If the sample estimate is less than 30 at that point the distribution of the population from which the sample is chosen ought to be normal.We are provided with a sample size which is 100, a population mean which is 25, and a population standard deviation which is 20.
So , n =100
μ= 25
σ= 20
therefore, the mean of the sample means is
μₓ =μ
= 25
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molly and kali are selling fruit for a school fundraiser. customers can buy small boxes of grapefruit and large boxes of grapefruit. molly sold 12 small boxes of grapefruit and 5 large boxes of grapefruit for a total of $200. kali sold 4 small boxes of grapefruit and 10 large boxes of grapefruit for a total of $200. what is the cost of one small box of grapefruit and one large box of grapefruit?
The cost of one small box is $10 and the cost of one large box of grapefruit is equal to $16.
This type of problem can be solved using linear equations.
If we consider x to be the cost of one small box and y to be the cost of one large box of fruit, the linear equations can be given as;
12x + 5y = 200
4x + 10y = 200
Multiplying the second equation by 3
12x + 5y = 200
12x + 30y = 600
Now by subtracting both equations we get;
-25y = -400
y = -400 / -25
y = 16
Now adding this value of y = 16 in the first equation;
12x + 5y = 200
12x + 5(16) = 200
12x + 80 = 200
12x = 200 - 80
12x = 120
x = 120 / 12
x = 10
Therefore, $10 is the cost of one small box and $16 is the cost of one large box of grapefruit.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 80 pounds. There were twice as many large boxes shipped as small boxes shipped and the total weight of all boxes was 1435 pounds. Determine the number of small boxes shipped and the number of large boxes shipped.
Solving a system of equations we can see that:
7 small boxes were shipped.14 large boxes were shipped.How to determine the number of boxes?
Let's define the variables:
x = number of small boxes.y = number of large boxes.With the given information we can write the system of equations:
y = 2*x
x*45 + y*80 = 1435
To solve the system, we can replace the first equation into the second one.
x*45 + (2*x)*80 = 1435
x*45 + x*160 = 1435
x*205 = 1435
x = 1435/205 = 7
x = 7
So we conclude that 7 small boxes were shipped, and then:
y = 2*x = 2*7 = 14
14 large boxes were shipped.
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Select the correct rounding place. 438.612439,000
B. tens
C. hundreds
D. thousands
E ten thousands
The correct rounding place for 438.612439000 is thousands as there are 3 zeros at end of the decimals which has no value.
What is rounding?To estimate a specific number in a context, rounding is a process. Look at the next digit in the correct position to determine how to round a number; if it is less than5, round down, and if it is 5 or more, round up.
The term "rounding decimals" describes the accurate rounding of decimal numbers. To the nearest whole, tenth, or hundredth, we can round decimals.
To quickly and easily estimate an answer, rounding decimals is helpful. Finding out the approximate average score of the students in a class is also helpful.
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Please help me to wrap my head around #22please included the Subjects I need to work on for (HW).
chaperones/students; 1/7 = x/45
7x = 45
x = 6.43
the min amount would be 7, as there can not be .43 of a chaperone. It cannot also be 6 because 6 x 7 would be 42 < 45.
helpppppsjiwhanwkgeuehdb
Answer:
Sum of angles in a triangle add up to 180°.
x = 180 - 76 - 44 = 60°
Virginia got twice as much snow as Tennessee.
Together, both states got a total of 30 feet of snow.
How much snow did Virginia get? HELP!
Answer: 15
Step-by-step explanation:
For them to both get 30 you have to get 15 because 15+15 equals 30!
Sense Virginia got twice as much just times 15 by 2 to get 30
Very simple ! Hope this helped ! Have a great day ! :D
a restaurant offers 4 appetizers, 2 main courses, and 3 desserts. carlos wants to order 3 appetizers, 0 main courses, and 3 desserts. how many different meals could carlos order?
Here is the question but if you look at that questiion and you dont like it read
-t-h-e c-o-m-m-e-n-t-s :)
Based on the anchor points for the trend line, the equation of the line can be found to be y = 6x + (-2)
How to find the equation of the line?To find the equation of a trend line, you first need to find the difference between the anchor points:
= Change in y / Change in x
= (28 - (-38)) / (5 - (-6)
= (28 + 38) / (5 + 6)
= 66 / 11
= 6
The y intercept is:
y = mx + c
28 = 6(5) + c
c = 28 - 30
c = - 2
The equation of the line is:
y = 6x + (-2)
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During the msr activity for the month of april, the teacher announced that every student will be awarded 10 points for a good deed and (-5) for not attempting a good deed each day. a) if teena did good deed for all 17 days in april, find her score. b) if tia did not attempt any good deed for 5 days in the same month, find her score
If 10 points are awarded for a good deed and (-5) for not attempting a good deed each day then, a) The score of Teena is equal to 105 b) The score of Tia is equal to 225
a) As Teena did a good deed for 17 days, she would receive 10 points for 17 days, and for the rest of the days, she would be deducted 5 points for each day for not attempting a good deed.
Number of days she did not attempt a good deed = 30 - 17 = 13
Points she got = 17 × 10 = 170
Points for not attempting a good deed = 13(-5) = 65
The final score of Teena can be calculated using subtraction;
Teena score = 170 - 65 = 105
b) If Tia did not attempt any good deed for 5 days this means she did a good deed for 25 days (30 - 5 = 25)
Points she got = 25 × 10 = 250
Points for not attempting a good deed = 5(-5) = -25
Tia score = 250 - 25 = 225
Hence the score of Teena and Tia were calculated to be 105 and 225 respectively.
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An online streaming service that offers TV shows, documentaries, and movies charges an initial fee of $20.25 and an additional monthly membership fee of $3.75. The total cost, N(t), for a member after t months can be expressed with the function N(t) = 3.75t + 20.25. What is the range of the function in the context of the problem?
ℝ
[0, ∞)
[3.75, ∞)
[20.25, ∞)
The range of the function N(t) is [20.25, ∞). The correct option is D.
What is the range of the function?A function's range is the set of possible output values. For example, the range of the function f(x)=x² on the domain of all real numbers (xR) is the non-negative real numbers, which can be written as f(x)0 (or [0,] in interval notation).
In this question, we have been given that an online streaming service that offers TV shows, documentaries, and movies charges an initial fee of $ 20.25 and an additional monthly membership fee of $3.75.
The total cost, N(t), for a member after t months can be expressed with the function N(t) = 3.75t + 20.25
As t is the number of months, t can take values from 0 to infinity.
For t = 0 years,
N(0) = 3.75(0) + 17.25
N(0) = 0 + 17.25
N(0) = $17.25
For x tends to ∞, the value of function would be ∞. The range will be (20.25,∞).
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please i’m giving 50 pointssss
Answer:
Step-by-step explanation:
The ratio of flour to honey is always 10/8 because she uses a constant ratio.
1. The missing values in the table would be the value of honey (1, 16, 30, h) times 10/8.
2. The equation would be f = (10*h)/8
3. Plug 15 and 17 into the equation above.