The object hits the ground after 17.5 seconds.
f(x) = ax2 + bx + c, where a, b, and c are integers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they always have the same fundamental "U" form.
The height of an object modeled by the function:
h(t) = −16t^2 + 4900
The object hits the ground when h(t) = 0
The equation becomes:
0 = −16t^2 + 4900
-16t² = -4900
t² = 4900/16
t² = 306.25
t = √306.25
t = 17.5 secs
Thus, the object hits the ground after 17.5 seconds.
Complete question: An object is 4900 ft above the ground. The object falls, and its height is given by the quadratic function: h(t) = −16t 2 + 4900. The height of the object above the ground is in feet and the time, t, is in seconds. Determine when the object hits the ground.
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in a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). the probability of rolling doubles with one roll of two fair six-sided dice is 16 . what is the probability that it takes three rolls until the player rolls doubles?
The probability of rolling doubles with three rolls of two fair six-sided dice is 0.512.
How do you calculate probability?
Probability is the likelihood that something will happen. Probability is calculated by dividing the number of ways the event can occur by the total number of outcomes.
The probability of rolling doubles with one roll of two fair six-sided dice is 16/36, or 1/6. This means that the probability of not rolling doubles with a single roll is 5/6.
The probability of not rolling doubles with two rolls is (5/6)^2, or 25/36.
The probability of not rolling doubles with three rolls is (5/6)^3, or 125/216.
Therefore, the probability of rolling doubles with three rolls of two fair six-sided dice is (216-125)/216, or 91/216, or 0.512.
P(doubles on 1 roll) = 1/6
P(not doubles on 2 rolls) = (5/6)^2 = 25/36
P(not doubles on 3 rolls) = (5/6)^3 = 125/216
P(doubles on 3 rolls) = 1 - (125/216) = 91/216 = 0.512
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Which value could be substituted for the variable to make the equation
TRUE? w-11 =15
Answer:
26 - 11 = 15
Step-by-step explanation:
jessie uses a graph to record deposits into her savings account. her account starts with $80 deposits. she adds $25 per week to the account
Camera search
Answer: y=25x+80
Step-by-step explanation:
from an ordinary deck of 52 cards, five cards are drawn randomly. what is the probability of drawing
The probability of drawing exactly three face cards is given as follows:
0.0660 = 6.60%.
What is the hypergeometric distribution formula?The mass probability formula is presented as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.N is the size of the population.n is the size of the sample.k is the total number of desired outcomes.Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:
N = 52, k = 12, n = 5.
The probability of drawing exactly three face cards is P(X = 3), obtained as follows:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660[/tex]
Missing InformationThe problem asks for the probability of drawing exactly three face cards.
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Find the equation of the median from vertex A if the coordinates are A(-3,-1), B(3,5) and C(7,-3)
Answer: [tex]y-1=\frac{1}{4}(x-5)[/tex]
Step-by-step explanation:
The median from vertex [tex]A[/tex] passes through [tex]A[/tex] and the midpoint of [tex]\overline{BC}[/tex].
Using the midpoint formula, the midpoint of [tex]\overline{BC}[/tex] has coordinates [tex]\left(\frac{3+7}{2}, \frac{5-3}{2} \right)=(5, 1)[/tex].
Therefore, we need the equation of the line passing through [tex](-3,-1)[/tex] and [tex](5,1)[/tex].
The slope of this line is [tex]\frac{-1-1}{-3-5}=\frac{1}{4}[/tex].
Using point-slope form, the equation is y[tex]y-1=\frac{1}{4}(x-5)[/tex].
mary needs to make a total of 40 deliveries this week she so far has made 38 oif them what percentage of her total deliveries has mary completed
The percentage of the total deliveries made by the Mary is equal to 95%.
As given in the question,
Total number of deliveries need to be delivered by the Mary this week = 40
Total number of deliveries completed by Mary is equal to 38
Percentage formula = [( Number obtained ) / (Total number ) ] × 100
Substitute the value in the formula we get,
The percentage of the completed deliveries made by Mary is
= ( 38 / 40 ) × 100
= 3800 / 40
= 95%
Therefore, the total percentage of the completed delivery made by Mary is equal to 95%.
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help me pls thank you!
Answer: Information given below…
Step-by-step explanation:
Answer:
QR =40
Step-by-step explanation:
25÷5=5
35÷7=5
They are similar so we can conclude that QPR is 5 times bigger than ABC
Therefore
8^5= 40
And that's the answer
17. Wekhomba bought a laptop in Uganda for Ush.1, 050,000. He then paid 60 US dollars as transportation charges to Kenya. On arrival in Kenya he paid duty and sales tax amounting to 55% of the cost in Uganda. He then gave it to a friend in Tanzania tax free. If the exchange rates were I US dollar = Ush 1016, 1Ksh Ush 24.83 and Tsh 1 = Ksh 0.0714 i. ii. iii. iv. Calculate the total expenses in Kenya shillings incurred by Wekhomba. Find the expenditure on transportation and taxes as a percentage of the total expenditure. What is the total value of the laptop in Tanzanian shillings? Find the overall increase in value of the laptop as percentage of the buying price.
Answer:
i. To calculate the total expenses in Kenya shillings incurred by Wekhomba, we need to first convert the cost of the laptop in Uganda shillings to Kenya shillings using the exchange rate of 1 US dollar = Ush 1016. The cost of the laptop in Kenya shillings is (1,050,000/1016) = 1,032,474.40
We then need to add the transportation cost of 60 US dollars which is (60 * 1016) = 61,596 Kenya shillings.
Taxes in Kenya amounting to 55% of the cost in Uganda is (1,050,000 * 55/100) = 577,500 Uganda shillings which is (577,500/1016) = 567,715.20 in Kenya shillings.
The total expenses in Kenya shillings incurred by Wekhomba is 1,032,474.40 + 61,596 + 567,715.20 = 1,661,785.60
ii. To find the expenditure on transportation and taxes as a percentage of the total expenditure, we need to divide the sum of transportation costs and taxes by the total expenses and multiply by 100.
Expenditure on transportation and taxes is 61,596 + 567,715.20 = 629,311.20.
Expenditure on transportation and taxes as a percentage of the total expenditure = (629,311.20/1,661,785.60) * 100 = 37.9%
iii. To find the total value of the laptop in Tanzanian shillings, we first need to convert Kenya shillings to Tanzanian shillings using the exchange rate of 1Ksh = Ush 24.83 and Tsh 1 = Ksh 0.0714,
1,661,785.60 Kenya shillings is (1,661,785.60/24.83) = 668,817.51 Uganda shillings which is (668,817.51 / 0.0714) = 93,622,817.16 Tanzanian shillings
iv. To find the overall increase in value of the laptop as a percentage of the buying price, we need to divide the increase in value (total value in Tanzanian shillings - buying price) by the buying price and multiply by 100.
Overall increase in value = 93,622,817.16 - 1,050,000 = 92,572,817.16
The overall increase in value as a percentage of the buying price = (92,572,817.16/1,050,000) * 100 = 88.1%
Step-by-step explanation:
you have some quarters and pennies worth $3.75 and 39 coins altogether. how many of each coin do you have?
There are 14 quarters and 25 number of pennies
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that some quarters and pennies worth $3.75
0.25x+0.01y=3.75
There are 39 coins altogether
x+y=39
x=39-y
Now plug in x value in 0.25x+0.01y=3.75
0.25(39-y)+0.01y=3.75
9.75-0.25y+0.01y=3.75
9.75-0.24y=3.75
9.75-3.75=0.24y
6=0.24y
Divide both sides by 0.24
25=y
x+y=39
x=14
Hence, there are 14 quarters and 25 number of pennies
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
In a paint factory, an old conveyer line has filled 22 barrels of paint and is filling more at a rate of 1 barrel per minute. A worker just switched on a newer line that can fill 12 barrels per minute. In a little while, the two lines will have filled an equal number of barrels. How many barrels will each line have filled? How long will that take?
It takes 10 minutes for the two lines to have filled an equal number of barrels
How many barrels will each line have filled?Each line will have filled 90 barrels
Let “x” be the number of minutes
The old conveyer line has filled 20 barrels of paint, and is filling more at a rate of 7 barrels per minute
Thus, a equation is framed as follows:
Old conveyor: 20 + 7(number of minutes)
Old conveyor: 20 + 7x ------- eqn 1
A worker just switched on a newer line that can fill 9 barrels per minute
Thus, a equation is framed as follows:
New conveyor: 9(number of minutes)
New conveyor: 9x -------- eqn 2
In a little while, the two lines will have filled an equal number of barrels.
Thus, eqn 1 must be equal to eqn 2
Thus it takes 10 minutes for the two lines to have filled an equal number of barrels
Substitute x = 10 in any one of equations
Substitute in eqn 2
9x = 9(10) = 90
Thus each line will have filled 90 barrels
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Artaud noticed that if he takes the opposite of his age and adds 43 he gets the number 27. How old is Artaud?
Step-by-step explanation:
Suppose that his age is x.
then the opposite of his age is -x.
from the question above, the equation can be written as
[tex] - x + 43 = 27[/tex]
[tex]then \: \\ x = 16[/tex]
Find the equation of the tangent line to the curve f(x) = 4x^3 - 2x^2 + 3x - 10 when x=4
Answer:
Is your question complete? there's no y term
Answer:
Refer to the image attached.
Step-by-step explanation:
what is the correct answer
By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given,
table shows the relation y = kx .
so the given x values = 2,3,5,8 .
and the y values = 5,7.5,12.5,20
From the relation y = kx .
By substituting the given values
we get,
y = kx
y=5 x = 2
5 = k * 2
k = 2.5
y=7.5 x = 3
7.5 = k*3
k = 7.5/3
k = 2.5
y = 12.5 x = 5
12.5 = 5*k
k= 12.5 / 5
k = 2.5
y=20 x = 8
20 = k*8
k = 20/8
k = 5/2
k = 2.5
Hence, By using the given relationship the values of k are 2.5 , 2.5,2.5,2.5 respectively.
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Find 2u, -3v, u + v, and 3u 4v for the given vectors u and v. u = (-2,9), = (6, -2) V 2u = -3v = u + V = 3u - 4y =
According to the vector rule, the values of the 2u, -3v, u + v, and 3u + 4v are (-4, 18), (-18, 6), (4, 7) and (18, 19) respectively.
Here we have given the following two vector such as
u = (-2, 9)
v = (6, -2)
Then as per the following vector rule, t
=> ku = (ka , kb)
where k refers the constant in vector.
Then the value of 2u is calculated as,
=> 2u = ((-2 x 2), (9 x 2)) = (-4, 18)
And the value of -3v is calculated as ,
=> -3v = ((-3 x 6), (-3 x- 2)) = (-18, 6)
Here we have to use the following rule, that is written as,
=> (u ± v) = (a ± c, b ± d)
Then the value of u + v is calculated as,
=> (u + v) = ((-2 + 6), (9 + (-2)) = (4, 7)
Then the value of 3u + 4v is calculated as,
=> 3u = ((3 x -2), (3 x 9)) = (-6, 27)
And the value of
=> 4v = ((4 x 6), (4 x- 2)) = (24, -8)
Then the value of
=> 3u + 4v = (-6, 27) + (24, -8)
=> 3u + 4v = ((-6+24) , (27 + (-8))
Therefore, the resulting value is (18, 19).
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The dimensions for a rectangular prism are x+5 for the length, x+1 for the width, and x for the height. What is the volume of the prism?
The volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.
Rectangular Prism:
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here.
The Volume of a Rectangular Prism Formula is,
The volume of a Rectangular Prism (V) = l × b × h
Where,
“b” is the base length of the rectangular prism
“l” is the base width of the rectangular prism
“h” is the height of the rectangular prism
The formula for the volume of a rectangular prism is length x width x height. So, the volume of this rectangular prism is (x+5) * (x+1) * x = x^3 + 6x^2 + 6x + 5.
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a triangle has dimensions 5, 8, and 10. a similar triangle is drawn with a scale factor of 0.5. what are the dimensions of the new triangle?
a. 10, 16, 20
b. 5.5, 8.5, 10.5
c. 2.5, 4, 5
d. 5, 8, 10
Answer is c. 2.5, 4, 5
Step-by-step explanation:
To find the dimensions of the new triangle,
we need to apply the scale factor of 0.5 to the original triangle's dimensions.
This means we need to multiply each dimension by 0.5.
Original Dimensions: 5, 8, 10
New Dimensions:
5 x 0.5 = 2.5,
8 x 0.5 = 4
10 x 0.5 = 5
Therefore, the dimensions of the new triangle are 2.5, 4, 5.
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Calculate the length of edge AD in the triangle-based pyramid below.
Give your answer to 2 d.p.
The length of AD is 70.26.
What is a pyramid?A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
We have,
ΔBCD
Tan 33 = BC/BD
0.65 = 37/BD
BD = 37/0.65
BD = 56.92
Now,
ΔABD
Sin 54 = BD/AD
0.81 = 56.92/AD
AD = 56.91/0.81
AD = 70.26
Thus,
The length of AD is 70.26.
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write the probability statement. (let k represent the score that corresponds to the 80th percentile.)
So, on solving the provided question we can say that by probability we have [tex]256.014[/tex]= sample mean for 80th percentile
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
[tex]P(x < 240)[/tex]
Transform to z score = (sample mean - population mean)/(standard deviation(std)[tex]/sample size^0.5)[/tex]
[tex]P(z < (240-250)/(50/49^0.5)[/tex]
[tex]P(z < -1.4) = 0.0808[/tex]
z-score corresponding to 80th percentile is 0.842
0.842 = (sample mean -[tex]250)/(50/49^0.5)[/tex]
[tex]6.014[/tex] = sample mean - [tex]250[/tex]
[tex]256.014[/tex]= sample mean for 80th percentile
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Mrs. mccall is renting a truck for one day. the two choices she had are company a and company b. what is the minimum number of miles that mrs.mccall would need to drive in order to make renting from campany b a better deal?
On solving the provide question, we can say that by unitary method McCall would need to drive 126 miles in order to make renting from Company B a better deal
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
so, we have -
Company A charges = $35 per day
plus = $0.45 per mile.
Company B charges = $60 per day
plus = $0.25 per mile.
McCall would need to drive 126 miles in order to make renting from Company B a better deal
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Which is the biggest difference between an installment loan and revolving credit?
a. Installment loans can be either unsecured or secured.
b. Installment loans have a fixed term and monthly payment, revolving credit is a credit line that is paid off and used again.
c. Qualification for revolving credit does not require credit scores and credit reports.
d. Revolving credit is always unsecured.
The biggest difference between an installment loan and revolving credit is that Installment loans have a fixed term and monthly payment, revolving credit is a credit line that is paid off and used again. That is option B.
What is an installment loan?An installment loan is defined as the type of loan an individual obtains from the bank which can be paid back in installments.
Revolving credit is defined as the type of loan that allows the borrower to spend the money they have borrowed, repay it, and borrow again as needed.
Therefore, the difference between an installment loan and revolving credit is that Installment loans have a fixed term and monthly payment, revolving credit is a credit line that is paid off and used again.
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I WILL MARK BRAINLIEST IMMEDIATELY PLSS
Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.
What is a system of equations?A system of equations refers to simultaneous equations.
Simultaneous equations are two or more equations solved concurrently.
Total investment in two accounts = $20,000
The simple interest rate for account one, x = 8%
The simple interest rate for account two, y = 10%
Total interest for a year = $1,920
Let account one = x and account two = y
Equations:x + y = 20,000 ... Equation 1
0.08x + 0.1y = 1,920 ... Equation 2
Multiply Equation 1 by 0.08
0.08x + 0.08y = 1,600 ... Equation 3
Subtract Equation 3 from Equation 2:
0.08x + 0.1y = 1,920
-
0.08x + 0.08y = 1,600
0.02y = 320
y = 16,000
= $16,000
In Equation 1, x + y = 20,000, Substitute y = 16,000:
x + 16,000 = 20,000
x = 4,000
= $4,000
Check:
From Equation 2:
0.08x + 0.1y = 1,920
0.08(4,000) + 0.1(16,000) = 1,920
320 + 1,600 = 1,920
Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.
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Complete Question:Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?
First account:
Second account:
Tabitha’s account balance is $3,800. Of this, $750 is for rent. Tabitha wants to keep a balance greater than $500. Write an inequality describing how much she can withdraw and still meet these conditions
The inequality describing how much she can withdraw is x < 3550
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
Inequalities are used in expression for non equal comparison of variables.
Let x represent the amount of money that can be withdrawn.
Tabitha’s account balance is $3,800. Of this, $750 is for rent. Hence:
Money remaining = 3800 - 750 = 3050
Tabitha wants to keep a balance greater than $500. Hence:
3050 - x > 500
x < 3550
The inequality is x < 3550
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Is Edgar or Ernesto correct?
Answer:
Edgar
Step-by-step explanation:
The domain of people would be the natural numbers 20 -25.
Ernesto domain would allow for 1/2 people and .75 if people. Willa only wants to invite whole people.
2 multiples of eight that are squared in numbers
Which figure shows an example of symmetry?
O A.
OB.
C.
D.
J Z
← PREVIOUS
Answer:
D
Step-by-step explanation:
If you folded the figure on the line of symmetry. The right side would fit perfectly over the left side.
Rick bought a photo printer and supplies for $186.90, which will allow him to print photos for $0.29 each. a photo store charges $0.55 to print each photo. how many photos must rick print before his total cost is less than getting prints made at the photo store? more than 718 photos. less than 718 photos. more than 900 photos. not enough information to solve.
The 718.85 < x inequality says that : He must print 719 photos or more.
Inequality:
In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are several notations used to represent various types of inequalities.
The notation a < b means a is less than b.The notation a > b means that a is greater than b.Given,
In the question:
Rick bought a photo printer and supplies for $186. 90, which will allow him to print photos for $0. 29 each.
and, A photo store charges $0. 55 to print each photo.
To find the how many photos must Rick print before his total cost is less than getting prints made at the photo store?
Now,
According to the question:
Let the photos be x
Rick bought a photo printer be $186.90
A photo store charges $0. 55 to print each photo.
The question is based on inequality:
Photo Printer < photo store
1.86.90 + 0.29x < 0.55x
- 0.29x - 0.29x
______________________
1.86.90 < 0.26x
Divide by 0.26x on both sides = 718.85 < x
Hence, The 718.85 < x inequality says that : He must print 719 photos or more.
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Elise tosses a fair coin three times in a row. What is the probability that she gets two heads in a row?
Answer:
[tex]\textrm{P(2 heads in a row) } =\boxed{\dfrac{3}{8}}[/tex]
Step-by-step explanation:
Let H represent the event that the coin turns up heads and T the event that coin turns up tails
So we can get H on the first toss, then 2 T's on the next two tosses, a T on the first toss and 2 H on the next two tosses, two T on the first two tosses and a H on the third toss etc.
The sample space for 3 tosses of a coin consists of 2³ elements since there are two possible outcomes for each of 3 events
The sample space is enumerated below
1 H H H
2 T H H
3 H T H
4 T T H
5 H H T
6 H T T
7 T H T
8 T T T
There are 3 possibilities where 2 H appear in a row
These are the ones in bold in the table above
Since only 3 outcomes out of a total of 8 possible outcomes can result in 2 heads in a row,
[tex]\textrm{P(2 heads in a row) } =\dfrac{3}{8}[/tex]
drag the labels to the correct locations on the image. each label can be used more than once, but not all labels will be used. consider function m. a line graph depicts x on the horizontal axis versus m of x on the vertical axis. a curve declines from (negative 4, 8) through (negative 2, 0), passes through (0, 0) and (4, negative 8), and rises through (6, 8). what is the domain of function m?
The function's approximate range will be specified by -∞<y≤12.
What is a function?The exact same number of elements from Y are assigned to each element of X via a mathematical function from a set X to a set Y.
The function's domain and codomain are respectively referred to as the sets X and Y as a whole.
Functions were first used to describe the idealized relationship between two varying quantities.
Now, drag as follows:
The collection of output values determines a function's range.
The function's indicated range will be -∞ < y ≤ 12.
From the linked graph,
The function's output values (values on the y-axis) range from zero to f(x)=12.
Therefore, the function's approximate range will be specified by -∞<y≤12.
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What index of x will equal to 1/x^x
Answer:
The index of x should be 0 so that its value will be equal to 1.
negative 3 plus negative 5
Answer: -8
Hope this helps :)
Step-by-step explanation:
Adding two negative integers is just like adding two regular numbers
Answer:
negative 8
Step-by-step explanation:
calculator
