4.7.4 Modeling Pumpkin launch, we were covering graphs of quadratic functions please help! Thank you
Answers
Using a quadratic function, it is found that:
a) The coordinates of the second x-intercept are: (50,0).
b) The vertex shows the maximum flight of the projectile.
c) The coordinates of the vertex are (25, 62).
3) The graph of the equation y = -0.0992(x² - 50x) is given at the end of the answer.
Quadratic functionA quadratic function has two x-intercepts, x' and x'', and is defined as follows:
y = a(x - x')(x - x'').
The intercepts are given as follows:
First x-intercept: coordinates (0,0), as the fruit is thrown from the ground.Second x-intercept: coordinates (50,0), as the fruit travels a distance of 50 feet to hit the ground.The vertex is found as follows:
x-coordinate of 25, which is the mean of the two intercepts.y-coordinate of 62, which is the maximum height.Hence the coordinates are: (25, 62).
The equation can be defined as follows:
y = ax(x - 50)
y = a(x² - 50x).
When x = 25, y = 62, hence the leading coefficient is found as follows:
62 = a(25² - 50(25))
-625a = 62
a = -62/625
a = -0.0992.
Hence the equation is:
y = -0.0992(x² - 50x).
The domain of the function is between the roots, hence 0 ≤ x ≤ 50, and the graph is sketched at the end of the answer.
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Related Questions
Why are there two possible solutions to the equation, X2 = 100?
Answers
Answer:
100 is perfect square
Step-by-step explanation:
in x² =100, we have x×x=100 and x could be ±10 since both 10² and (-10)² is equal to 100
A wholesaler sells a guitar for $1,396.20. What is the percent markup based on cost if the wholesaler paid $780 for the guitar?
Answers
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
Given,
The cost price of the guitar = $780
The selling price of the guitar = $1396.20
We have to find the markup percent based on the cost;
Markup percentage;
The gross profit of a unit, which is its sales price less its cost to produce or acquire for resale, is divided by the unit's cost to determine the markup %.
Markup percent = (Selling price - cost price) / cost price x 100
= (1396.20 - 780) / 780 x 100
= 616.20 / 780 x 100
= 0.79 x 100
= 79%
That is,
The Markup percentage based on cost if the wholesaler paid $780 for the guitar is 79%
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write the equation of a line through ( -3, 5), parallel to y = -x.
y= ___ x + ___
Answers
Answer:
We took it at grade 7 oh god
Kadeesha invested
$
900
$900 in an account that pays 1.5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Kadeesha would have in the account 11 years after her initial investment. Round to the nearest tenth (if necessary).
Answers
The amount of money Kadeesha have in her account after 11 years is $1059.3.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex]
Given that, principal=$900, rate of interest=1.5% and time period =11 years.
Now, amount =900(1+1.5/100)¹¹
= 900(1+0.015)¹¹
= 900(1.015)¹¹
= 900×1.177
= $1059.3
Therefore, the amount of money Kadeesha have in her account after 11 years is $1059.3.
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The bar graph shows the percentage of college freshmen in a certain country with an average grade of Ain high school.The data displayed by the bar graph can be described by the mathematical model p =4x- + 25 where xis the number of years after 1980 and p is the percentage of college freshmen who had an average
Answers
Okay, here we have this:
Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:
So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:
p=4x/5+25
Replacing:
p=4(30)/5+25
p=120/5+25
p=24+25
p=49
So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.
the weights of items produced by a certain company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. the manager of the production line wants to discard any item whose weight is in the lower 2.5%. what is the maximum possible weight for the items discarded?
Answers
Using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
What is meant by standard deviation?The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values. A low standard deviation means that the values tend to be close to the established mean, whereas a large standard deviation suggests that the values exist distributed throughout a greater range.A measure of a data set's variance from the mean is referred to as "standard deviation." While a high standard deviation indicates that the data are more spread, a low standard deviation suggests that the data are clustered around the mean.So,
Mean = 4.5Standard deviation = 0.3(A) P(x > 4.14)
z = (4.14 - 4.5) / 0.3= -1.20P(z > -1.20) = P(z < 1.20)= 0.8849(B) P(4.8 < x < 5.04)
= P (4.8 - 4.5/0.3 < x - μ/σ < 5.04 - 4.5/0.3)= P(1 < z < 1.80)= P(z < 1.80) - P(z < 1)= 0.9641 - 0.8413= 0.1228 or 12.28 %(C) P(x > x) = 0.05
z value will be, 1.6451.645 = (x - 4.5) / 0.3x = 4.9935(D) P(x < 5.01)
= (z = x - μ/σ)= (5.01 - 4.5) / 0.3 = 1.7P(z < 1.70) = 0.9554n = 27875/0.9954= 28004Therefore, using standard deviation, the maximum possible weight for the items discarded is 28004 ounces.
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Correct question:
The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces. a. What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces? b. What percentage of the items weighs between 4.8 and 5.04 ounces? c. Determine the minimum weight of the heaviest 5% of all items produced. d. If 27,875 items of the entire production weigh at least 5.01 ounces, how many items have been produced?
A bag contains twelve balls labeled 1 through 12. One ball will be randomly picked.
What is the probability of picking an even number?
Write your answer as a fraction in simplest form
Answers
Hello there!
If a bag has 12 balls labelled 1 through 12, that means that the balls inside the bag includes:
1 2 3 4 5 6 7 8 9 10 11 12
When creating a fraction for a probability, the numerator usually consists of a specific probability you are trying to find; the denominator usually consists of the total amount of samples in the bag.
In this example: What is the probability of picking an even number?
Ask yourself: What are we trying to find?
We are trying to find the probability of even numbers.
Then ask yourself: What is the amount of possibilities that we can get an even number from the bag?
The bag consists of: 1 2 3 4 5 6 7 8 9 10 11 12
Even numbers are divisible by 2 and has a remainder of 0 ; which means in this bag, the bolded numbers are even.
Then we can conclude that in this bag, counting all of the bolded numbers, we have 6 possibilities of choosing an even number.
Finally, think about: What is the total amount of samples in this bag?
We know that there are 12 balls, so 12 would be the total amount.
To conclude, we can find 6 even numbers in a bag of 12 balls;
Therefore, the chances you can pick an even number is [tex]\frac{6}{12} ,[/tex] or [tex]\frac{1}{2}[/tex].
please help thank you
Answers
Answer:
%25 of customers ordered ice tea.
Step-by-step explanation:
To find percentage = Part/Whole x 100
35/140 x 100 = 0.25 x 100 = %25
35 of 140 can be written as:
35/140
To find percentage, we need to find an equivalent fraction with denominator 100. Multiply both numerator & denominator by 100
Therefore, the answer is 25%
If you are using a calculator, simply enter 35÷140×100 which will give you 25 as the answer.
Robert has 3 black marbles in a bag, along with 5
marbles of other colours. Robert picks a marble from the bag without looking. What is the probability that Robert picks a black marble?
Answers
The probability that Robert picks a black marble is 3/8. The result is obtained from the ratio of the number of black marble to all marbles.
What is probability?Probability is a numerical description of how possible an event to happen. Tha value of probability is between 0 to 1. Zero probability means something is impossible to happen. Probability 1 shows certainty.
Probability of an event can be expressed as
P(A) = n(A) / n(S)
Where
P(A) is the probability of an event An(A) is the number of favorable outcomesn(S) is the total number of events in the sample spaceIn case Robert has 3 black marbles and 5 marbles of other colors, then he picks a marble randomly, what is the probability of picking black marble?
Total number of marbles is 3 + 5 = 8.
n(S) = 8
Number of black marble is 3.
n(A) = 3
The probability of picking black marble is
P(A) = n(A) / n(S)
P(A) = 3/8
Hence, the probability that Robert picks a black marble is 3/8.
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in 1982, the us mint changed the composition of pennies from all copper to zinc with copper coating. pennies made prior to 1982 weigh 3.1 grams. pennies made since 1982 weight 2.5 grams. if you have a bag of 1267 pennies, and the bag weighs 3541.9 grams, how many pennies from each time period are there in the bag?
Answers
Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams. 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
Given that,
The 1982 change in pennies composition from all copper to zinc with copper coating was made by the US Mint. Prior to 1982, pennies weighed 3.1 grams. Coins produced after 1982 weigh 2.5 grams.
We have to find how many coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
An issue of quantity and amount. In this context, the term "amount" refers to weight. The variables should be identified with letters that will make them easy to distinguish: Z for largely zinc and C for all copper. Create weight and quantity equations:
C + Z = 1287
3.1 C + 2.5 Z = 3601.5
By multiplying all three components of the first equation by -2.5 and placing them under the second equation, drawing a line, and then subtracting, you can eliminate the Z using this method.
3.1 C + 2.5 Z = 3601.5
-2.5 C - 2.5 Z = -3217.5
--------------------------------
0.6 C = 384
Divide both sides by .6.
C = 640
Subtract 640 from 1287.
Z = 647
Therefore, 647 coins from each period are there in the bag if it contains 1267 pennies and weighs 3541.9 grams.
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write equations for the horizontal and vertical lines passing through the point (-7,7)
Answers
The vertical line's equation is x = -7, and the horizontal line's equation Is y = 7.
Where the given coordinate is (--7, 7).
What do the vertical and horizontal lines represent?A vertical line is a straight, up and down line in a coordinate plane that is parallel to the y-axis. The horizontal line, on the other hand, is parallel to the x-axis and goes straight, left, and right.Here,
The value of x, is -7, will never change for a vertical line. This holds true for any y value. As a result, x = -7 is the equation for a vertical line passing through this point.
Similarly, the value of y, is 7, will never change for a horizontal line. This holds true for any x value. As a result, the equation for a horizontal line passing through this point is as follows: y =7
As a result, the vertical line's equation is x = -7 and the horizontal line's equation is y = 7.
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If you write every whole number from I to
100. how many times will you write the digit
"2"?
Answers
Answer:
20 times
Step-by-step explanation:
Digit 2 appears 20 times in first 100 natural numbers
solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter “n.a” for the second solution. (picture of equation listed below)
Answers
Answer
x = 1 or x = n.a.
Step-by-step explanation
[tex]\frac{1}{x}+\frac{1}{x-10}=\frac{x-9}{x-10}[/tex]Multiplying by (x - 10) at both sides of the equation:
[tex]\begin{gathered} (x-10)(\frac{1}{x}+\frac{1}{x-10})=\frac{x-9}{x-10}(x-10) \\ \text{ Distributing and simplifying:} \\ \frac{x-10}{x}+\frac{x-10}{x-10}=x-9 \\ \frac{x-10}{x}+1=x-9 \end{gathered}[/tex]Multiplying by x at both sides of the equation:
[tex]\begin{gathered} x(\frac{x-10}{x}+1)=x(x-9) \\ \text{ Distributing and simplifying:} \\ \frac{x(x-10)}{x}+x=x^2-9x \\ x-10+x=x^2-9x \\ 2x-10=x^2-9x \end{gathered}[/tex]Subtracting 2x and adding 10 at both sides of the equation:
[tex]\begin{gathered} 2x-10-2x+10=x^2-9x-2x+10 \\ 0=x^2-11x+10 \end{gathered}[/tex]We can solve this equation with the help of the quadratic formula with the coefficients a = 1, b = -11, and c = 10, as follows:
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm{}\sqrt{b^2-4ac}}{2a} \\ x_{1,2}=\frac{11\pm\sqrt{(-11)^2-4\cdot1\operatorname{\cdot}10}}{2\operatorname{\cdot}1} \\ x_{1,2}=\frac{11\pm\sqrt{81}}{2} \\ x_1=\frac{11+9}{2}=10 \\ x_2=\frac{11-9}{2}=1 \end{gathered}[/tex]The solution x = 10 is not possible because it makes zero the denominator in 2 of the rational expressions of the original equation. In consequence, it must be discarded.
write an equation of the line below.
Answers
Answer:
y = 2x + 3
Step-by-step explanation:
The y-intercept is where x = 0. Therefore, the y-intercept would be 3. To find the slope, you do Δy/Δx (Δ = Change In). To find that, you go up 4 times, then move to the right 2 times to reach the second dot. Now, you do 4 / 2, which equals 2. Your final equation will be y = 2x + 3.
you are given the set of letters {a, b, c, d, e}. what is the probability that in a random five-letter string (in which each letter appears exactly once, and with all such strings equally likely) the letters a and b are next to each other?
Answers
The probability in a random 5-letter string that the letters A and B will be next to each other is 0.4
For A and B to be next to each other in the string of letters, consider the AB combination as a single letter. Then there are 4 letters AB, C, D, E.
There are 4! number of ways to arrange these 4 letters.
4!= 24 ways
We know AB can be arranged in 2 ways ( AB or BA)
Thus there are 2*4! = 2 * 24 = 48 ways of arranging the letters such that AB are next to each other in the random Five-letter string
The total number of letters in the set is 5 and hence the total number of ways the letters can be arranged without A and B necessarily being next to each other is 5!= 120
The probability that in the random five-letter string( in which each letter appears only once with all such strings equally likely) the letters A and B are next to each other= 48/120 = 0.4
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WXYZ is a kite. Angle WXY has a measure of 133 degrees and angle ZYX has a measure of 34 degrees. Find the measure of angle ZWY.
Angle ZWY has a measure of what
degrees.
Answers
Angle ZWY has a measure of 13 degrees.
Define angles.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle. a geometric shape made up of two lines that meet at the same point or two planes that meet at the same line. the distance in degrees between such lines or planes.
Given,
Angle WXY has a measure of 133 degrees
Angle ZYX has a measure of 34 degrees
Angle ZWY:
= 180 - 133 -34
= 13
Angle ZWY has a measure of 13 degrees.
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HELP ME PLSS OMLLL IMA CRY
Answers
Answer:
1. 15 pieces of candy
2. 48 cows
3. 81 ham subs
4. 24 boys
Step-by-step explanation:
Assuming you just want answers, but lmk
1 (Express 360° into centesimal system.)
Answers
Answer: 400 gradians
Reason:
100 gradians = 90 degrees
4*100 gradians = 4*90 degrees
400 gradians = 360 degrees
Find the slope between these two points:
(9,3),(19,-17)
Answers
Answer:
Slope = -2
Step-by-step explanation:
(9, 3), (19, -17)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -17 - 3 -20
m = ------------ = ------------ = -------- = -2
x₂ - x₁ 19 - 9 10
y - y₁ = m(x - x₁)
y - 3 = -2(x - 9)
y - 3 = -2x + 18
+3 +3
-----------------------
y = -2x + 21
I hope this helps!
a candy manufacturer produces bags of jelly beans. the weight of a bag of jelly beans is normally distributed with a mean of 12 ounces and a standard deviation of 0.4 ounces. if a random sample of 4 bags of jelly beans is selected what is the probability that the sample average will be greater than 11.6?
Answers
Answer:
2%
Step-by-step explanation:
Find where the graphs intersect; f(x)=2x+3 and g(x)=-0.5x+7
Answers
Step 1
Given
[tex]\begin{gathered} f(x)=\text{ 2x+3} \\ g(x)\text{ = -0.5x+7} \end{gathered}[/tex]Required: To find where the graph of both functions intersect. In other words the find the value of x and hence f(x) and g(x).
Step 2
Solve both equations simultaneously.
[tex]\begin{gathered} we\text{ will take f(x) and g(x) = y, so that} \\ y=2x+3\text{ -----(1)} \\ y=-0.5x+7----(2) \\ \end{gathered}[/tex]Subtract equation 2 from 1
Hence,
[tex]\begin{gathered} 4=\text{ 2.5x} \\ \frac{4}{2.5}=\frac{2.5x}{2.5} \\ x\text{ = 1.6} \end{gathered}[/tex]Step 3
Check
[tex]\begin{gathered} f(x)\text{ = 2x+3} \\ f(1.6)=\text{ 2(1.6) + 3 = 6.2} \\ g(x)=\text{ -0.5x+7} \\ g(1.6)=\text{ -0.5(1.6) +7 = 6.2} \\ \text{since the check gave us the same values, x = 1.6} \\ \text{And the coordinate point of the solution will be ( 1.6, 6.2)} \end{gathered}[/tex]Hence the graph intersects at the point where x = 1.6 and y =6.2. Remember y = f(x) and g(x)
The radioactive substance cesium-137 has a half-life of 30 years. The amount A(t) (in grams) of a sample of cesium -137 remaining after t years is given by the following exponential function.A (t) = 523 (1/2)^t/30Find the initial amount in the sample and the amount remaining after 100 years.Round your answers to the nearest gram as necessary.Initial amount:Amount after 100 years:
Answers
After 100 years:
Replace t by 100:
A (t) = 523 (1/2)^t/30
A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams
The initial amount of the sample is 523
Please answer only if you know the answer.
Answers
Step-by-step explanation:
The slope-intercept form of the equation of a line that passes through (5, -4) and has a slope of 3/4 is y = (3/4)x - 31/4.
What is the slope-intercept form?
The slope-intercept form of a line is y=mx + c.
Where, x and y are coordinates. m = slope and c = y intercept.
Given, slope (m) = 3/4
Substituting the values of (x, y) as (5, -4) and m = 3/4, we get:
-4 = (3/4) × 5 + c
⇒ c = -4 - (3/4) × 5 = -4 - 15/4 = -31/4
Now, putting the value of c in the standard equation:
y = (3/4)x - 31/4
⇒ 4y = 3x - 31
⇒ 3x - 4y = 31
Answer is Option C
a ball dropped from rest and falls for 8 seconds
whats the final velocity
and whats te average velocity
how far did it fall
Answers
If y varies directly with x, write an equation for the direct variation. Then find each value.1. If x= -12 when y= -3 find x when y= -6
Answers
Since y varies directly with x then
[tex]\begin{gathered} \frac{y}{x}=k \\ \text{Where k }is\text{ the constant of proportionality} \end{gathered}[/tex]So,
[tex]\frac{y}{x}=\frac{-3}{-12}=\frac{3}{12}=\frac{1\cdot3}{4\cdot3}=\frac{1}{4}[/tex]Then, 1/4 is the constant of proportionality. So that,
[tex]\begin{gathered} \frac{y}{x}=\frac{1}{4} \\ \frac{-6}{x}=\frac{1}{4} \\ -\frac{6}{x}\cdot x=\frac{1}{4}\cdot x \\ -6=\frac{x}{4} \\ 4\cdot-6=\frac{x}{4}\cdot4 \\ -24=x \end{gathered}[/tex]H=4(x+3y)+2 make x the subject
Answers
When the formula is changed to x, the equation is x = 1/4(H - 2) - 3y
How to change the subject of formula to x?From the question, the equation is given as
H=4(x+3y)+2
Subtract 2 from both sides of the equation
So, we have the following equation
H - 2 =4(x+3y)+2 -2
Evaluate
So, we have the following equation
H - 2 =4(x+3y)
Divide by 4
So, we have the following equation
1/4(H - 2) = x +3y
Subtract 3y from both sides
x = 1/4(H - 2) - 3y
Hence, the solution for x is x = 1/4(H - 2) - 3y
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The simplified solution for the x is given as x = [H - 2]/4 - 3y.
As mentioned in the question, for an equation H=4(x+3y)+2, we have to transform the equation in the subject of x.
The operational processes in mathematics for the functions to make the function or expression.
Here,
Simplification of the given function in a manner to the transposition of the variables from left to right,
H=4(x+3y)+2
H - 2 = 4(x+3y)
{H - 2}/4 = (x + 3y)
x = [H - 2]/4 - 3y
Thus, the simplified solution for the x is given as x = [H - 2]/4 - 3y.
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A magical basket of pennies doubles every day. If the basket if full on the 15th day, on what day was the basket one-quarter full?
Answers
The basket of pennies will be 1/4 full on the 13th day
How to determine the day?From the question, the given parameters are:
Rate of change, r = 2 i.e. doubleFull basket, = 15th dayThe above parameters illustrate an exponential function
An exponential function is represented as
A(n) = A * (r)ⁿ⁻¹
Where
A represents the initial value
It is full on the 15th day
So, we have
1 = A *(2)¹⁵⁻¹
Evaluate
1 = A *(2)¹⁴
Divide by (2)¹⁴
A = (2)⁻¹⁴
Substitute A = (2)⁻¹⁴ in A(n) = A * (r)ⁿ⁻¹
A(n) = (2)⁻¹⁴ * (2)ⁿ⁻¹
When it is one-quarter full, we have
1/4 = (2)⁻¹⁴ * (2)ⁿ⁻¹
Multiply by (2)¹⁴
(2)¹² = (2)ⁿ⁻¹
By comparison, we have
n - 1 = 12
Add 1 to both sides
n = 13
Hence, the basket will be one-quarter full on the 13th day
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When Madison left her house this morning, her cell phone was 80% charged and itthen started to lose 8% charge for each hour thereafter. Write an equation for B, interms of t, representing the charge remaining in Madison's battery, as a percentage, thours after Madison left her house.
Answers
Given:
Initially, the cell phone was 80% charged.
Then started to lose 8% charge for each hour thereafter.
To find:
The equation for B in terms t
Write the equation of the line in y=mx+b form using the following two points:
(-2,-1) and (-1,-2)
Enter you equation here: type your answer....
10 points
Answers
Answer: The slope-intercept form for a line with the coordinates of (-2,-1) and (-1,-2) is:
y= -1.00x + -3.00
(results are in decimal form, rounded to the nearest 100th)
i hope i helped it is for if it was for like slope intercept form
Step-by-step explanation:
Two numbers have a sum of 35 and a product of 250. what are the numbers
Answers
Answer:
25 and 10
Step-by-step explanation:
because 25+10=35 and 25*10=250