Considering the given quadratic function, it is found that:
1. The rocket splashes down after 50.8 seconds.
2. The rocket peaks at 3365.3 meters above sea level.
When does the rocket splashes down?The height of the rocket after t seconds is given according to the following rule:
h(t) = -4.9t² + 241t + 402.
Which is a quadratic equation with coefficients given by:
a = -4.9, b = 241, c = 402.
It splashes down when it hits the ground, that is, when h(t) = 0, hence:
-4.9t² + 241t + 402 = 0.
Then:
[tex]\Delta = 241^2 - 4(-4.9)(402) = 65960.2[/tex][tex]x_1 = \frac{-241 + \sqrt{65960.2}}{-9.8} = -1.62[/tex][tex]x_2 = \frac{-241 - \sqrt{65960.2}}{-9.8} = 50.8[/tex]Time is a positive measure, hence it splashes down after 50.8 seconds.
What is the maximum height?The height of the rocket is a concave down quadratic equation, hence the maximum height is the y-coordinate of the vertex, given as follows:
[tex]h_{MAX} = -\frac{\Delta}{4a}[/tex]
Both these parameters have been found in the previous item, hence:
[tex]h_{MAX} = -\frac{65960.2}{4(-4.9)} = 3365.3[/tex]
3365.3 meters.
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if you need to install carpet in a room that is 80ft x 50ft how many 10ft x 50ft rolls of carpet do you need to cover the room
Given:
The dimensions of the room are,
[tex]\begin{gathered} l=80ft \\ b=50ft \end{gathered}[/tex]The dimensions of the carpet are,
[tex]\begin{gathered} l_1=10ft \\ b_1=50ft \end{gathered}[/tex]To find:
The number of rolls of carpet.
Explanation:
The number of rolls of carpet is calculated by,
[tex]\begin{gathered} \frac{Area\text{ of the room}}{Area\text{ of a carpet rool}}=\frac{l\times b}{l_1\times b_1} \\ =\frac{80\times50}{10\times50} \\ =8rolls\text{ of carpet} \end{gathered}[/tex]Therefore, the number of rolls of carpet is 8.
Final answer:
The number of rolls of carpet is 8.
which number is the closest approximation to the value of 3/94?
Answer:
[tex] \frac{1}{3} [/tex]
Step-by-step explanation:
[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]
On a particular production line the likelihood that a light bulb is defection is 5%. Ten light bulbs are randomly selected. What is the probability that at most 3 of the light bulbs will be defective
The probability that at most 3 of light bulbs will be defective will be 0.998.
Probability may be defined as an expression which may be used to determine the possibility of occurring of any event. The probability of happening an event surely is 1 and probability of not happening an event is zero. Since, 5 percent of bulbs are defective then
5% = 0.05 Now,
Non defective bulbs = 1 - 0.05 = 0.95
n = number of light bulbs = 7
We can calculate this using binomial distribution.
p(x) = ⁿCₓ × (pˣ)(1-p) ^n-x
Our question says at most 3 is defective, so it will be
(⁷C₀ × 0.05⁰ × 0.95⁷) + (⁷C₁ × 0.05¹ × 0.95⁶) + (⁷C₂ × 0.05² × 0.95⁵) + (⁷C₃ × 0.05³ × 0.95⁴)
= 0.698 + 0.257 + 0.040 + 0.003
= 0.998 which is the required probability.
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the table shows the workout results for for joggers complete the table to order the joggers from the slowest to the fastest rate
For Wesley:
distance = 7.7miles, time = 3.5h
[tex]\text{Rate (Wesley) = }\frac{7.7}{3.5}=2.2\text{ miles / hour}[/tex]For Xavier:
distance = 3.5 miles, time = 1.25h
[tex]\text{ Rate (}Xavier)\text{ = }\frac{3.5}{1.25}=2.8\text{ miles / hour}[/tex]For Yvette:
distance = 4.224 miles, time = 1.76h
[tex]\text{ Rate (}Yvette)\text{ = }\frac{4.224}{1.76}=2.4\text{ miles / hour}[/tex]For Zubin:
distance = 5.175 miles, time = 2.25h
[tex]\text{Rate (Zubin) = }\frac{5.175}{2.25}=2.3\text{ miles / hour}[/tex]Therefore, the complete table is as given below
The quadratic function G parentheses X parentheses is shown in the table below for the integer values on the interval negative one less than or equal to X less than or equal to four, two just
Since (2,1) is the turning point, let's write the function in its vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ so\colon \\ y=a(x-2)^2+1 \end{gathered}[/tex]Let's use one of the points:
[tex]\begin{gathered} (3,2) \\ 2=a(3-2)^2+1 \\ 2=a(1)^2+1 \\ so\colon \\ a=2-1 \\ a=1 \end{gathered}[/tex][tex]y=(x-2)^2+1[/tex]Therefore:
[tex]\begin{gathered} x=0 \\ y=(0-2)^2+1 \\ y=5 \end{gathered}[/tex]A profit of $1.45 was earned on each bag of oranges sold. (See 13 bags.) Find the profit if all the bags were sold.
Solution:
If a profit of $1.45 was earned on each bag of oranges sold, then the profit, if all 13 bags were sold, would be:
13 x $1.45 = $18.85
so that, the correct answer is:
$18.85
(x,2) is a solution to 7x-5>y
No, becuase not all the posible values of x make the inequality true.
For example, if x = 0
7(0) - 5 > 2
0 - 5 > 2
- 5 > 2 This is not true.
If you spend 1 hours a week studying for English and 3.5 hours studying for math what is the ratio of time spent studying in math to studying for English?
The ratio of time spent studying math to studying English is 7:2.
According to the question,
We have the following information:
One spends 1 hour a week to study English and 3.5 hours to study math.
Now, we know that the ratio can be simply understood as the division.
So, we will divide the number of hours devoted to math by the number of hours devoted to English.
Ratio of time spent studying math to studying English = 3.5/1
Ratio of time spent studying math to studying English = 35/10
(Now, we will convert this fraction into the simplest form by dividing both the numerator and denominator of the fraction by 5.)
Ratio of time spent studying math to studying English = 7/2
Ratio of time spent studying math to studying English = 7:2
Hence, the ratio of time spent studying math to studying English is 7:2.
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Given sin 60degrees √ 3/2 find cos 60°
cos 60°
Step-by-step explanation:
if I understand you correctly, then you got
sin(60°) = sqrt(3/2)
and now we have to find cos(60°) based on that.
but : sin(60°) = sqrt(3/4) = sqrt(3)/2
I will continue with that.
one major observation with the trigonometric functions in a norm circle (radius = 1) is that sine and cosine are the legs of a right-angled triangle.
the radius at the angle is the Hypotenuse.
and so, Pythagoras applies
c² = a² + b²
c is the Hypotenuse, a and b are the legs.
so,
radius² = sin²(x) + cos²(x)
and because radius = 1
1² = 1 = sin²(x) + cos²(x)
in our case
1 = sin²(60) + cos²(60)
1 = (sqrt(3)/2)² + cos²(60) = 3/4 + cos²(60)
cos²(60) = 1 - 3/4 = 1/4
cos(60) = sqrt(1/4) = 1/2
IXL Transversals of parallel lines: prove angle relationships 6QF for geometry, please help
4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)
5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)
6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)
7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)
8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)
9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)
10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)
Solve for x
12x-6 need answer please
Answer:
-72
Step-by-step explanation:
Answer:
Step-by-step explanation:
12x-6 = 90 because opposite angles are equal if intercepted in parallel lines
12x=96
x= 8
All eleven letters from the word MISSISSIPPI are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter P written on it?
Given:
There are 11 letters in the word 'MISSISSIPPI'
The number of P's are 2.
The probability that the randomly chosen slip of paper have the letter P written on it is,
[tex]\begin{gathered} P=\frac{Number\text{ of letter P}}{\text{Total letters}} \\ P=\frac{2}{11} \end{gathered}[/tex]The probability that the randomly chosen slip of paperdoes not have the letter P written on it is,
[tex]\begin{gathered} P^{\prime}=1-\frac{2}{11} \\ P^{\prime}=\frac{9}{11} \end{gathered}[/tex]The odd against event is calculated as,
[tex]\begin{gathered} Odd\text{ against=}\frac{P(not\text{ E)}}{P(E)} \\ Odd\text{ against}=\frac{P^{\prime}}{P}=\frac{\frac{9}{11}}{\frac{2}{11}}=\frac{9}{2} \end{gathered}[/tex]Answer: The odds against the paper having the letter P written on it is 9/2 (9:2)
Which algebraic expression shows the average function points of helium, hydrogen and neon if h represents the function point of hydrogen and represents the neon point
The answer is the option C. (h + j + k)/3
Because to find the average of 3 quantities, you have to add them all and then divide the result by 3
Help my hw is due by 12:00 am for final grade!!
Length has 5 cubes
width has 3 cubes
height has 7 cubes
Volume = length x width x height
5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of _____ makes this
argument true.
A premise or premiss is a true or false statement that helps form the body of an argument, By law of syllogism the statement is true. Your cat will chase mice.
What are premises?A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion.
If the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
If you have a cat, then it will chase mice.
is the given statement.
Let p is you have a cat
q is chase mice.
r is cat will chase mice.
iby the law of syllogism Your cat will chase mice. because (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .
Hence by law of syllogism the statement "if you have a cat, then it will chase mice" is true.
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Graph the following inequalities.4x + y ≥ 0I need TWO COORDINATES
We need to graph the following inequality:
[tex]4x+y\ge0[/tex]First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:
[tex]\begin{gathered} 4x+y-4x\ge0-4x \\ \\ y\ge-4x \end{gathered}[/tex]Now, notice that:
[tex]y=-4x[/tex]represents a line containing all points with coordinates (x,y) such that y=-4x.
The solution to the inequality includes those points, and also the points for which y is greater than -4x.
Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:
Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:
[tex]\begin{gathered} x=0\Rightarrow y=0\text{ point }(0,0) \\ \\ x=1\Rightarrow y=-4\text{ point }(1,-4) \end{gathered}[/tex]The number of hours it takes for ice to melt varies inversely with the air temperature. A block of ice melts in 2.5 hours whenthe temperature is 54 degrees.How long would it take for the same block of ice to melt if the temperature was 45 degrees?
Let t be the time in hours it takes a block of ice to melt at T degrees.
Since both variables have an inverse relation, we can say that:
[tex]t=\alpha\cdot\frac{1}{T}[/tex]Where alpha is a constant value.
Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:
[tex]\begin{gathered} 2.5=\alpha\cdot\frac{1}{54}\rightarrow2.5\cdot54=\alpha \\ \Rightarrow\alpha=135 \end{gathered}[/tex]Therefore, our expression would be:
[tex]t=\frac{135}{T}[/tex]For T = 45,
[tex]\begin{gathered} t=\frac{135}{45} \\ \\ \Rightarrow t=3 \end{gathered}[/tex]We can conclude that it would take 3 hours for the block of ice to melt.
vera wants to prove that any rectangle is also a parallelogram
We are given a rectangle ABCD
Recall that a rectangle is a quadrilateral in which all angles are right angles (90°)
Each pair of interior angles are supplementary. The two right angles add to a straight angle which means that the opposite sides of a rectangle are parallel.
In quadrilateral ABCD, if m∠A = m∠B = m∠C = m∠D = 90° then AB || DC and AD || BC
Hence, a rectangle is also a parallelogram.
Option B is the correct answer.
Helping my son with homework.. I have no clue what this is
Answer:
45 times
Step-by-step explanation:
it is 45 times because it can land on blue or green 5 out of 8 times so u do 72 divided by 8 and u get 9 so I do 9 times 5 and u get 45
The scatter plot shows the price of gas per gallon. Based on the trend line, which is closet to the expected price of 11 gallons of gas?A. $34B. $36C. $38D. $40
see the attached figure below to better understand the problem
Please give me a minute
The price is about $38
therefore
The answer is option C
what is 84i?I'm learning about imaginary numbers but I need extra help
The imaginary number 'i" can be written in another form below:
[tex]i=\sqrt[]{-1}[/tex]Whenever we have the root of a negative number, we use the imaginary number 'i' to write it in an easier form.
For example:
[tex]\begin{gathered} \sqrt[]{-4}=\sqrt[]{-1\times4} \\ =\sqrt[]{-1}\times\sqrt[]{4} \\ =2\times\sqrt[]{-1} \\ =2\times i \\ =2i \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} 84i=84\sqrt[]{-1} \\ =\sqrt[]{84^2\times-1} \\ =\sqrt[]{-7056} \end{gathered}[/tex]tommie works at a local store on the weekends. He earns $11.50 per hourr. tommie will get a 10% raise after working 4 weeks. How much will he make per hour after his raise?\
EXPLAIN YOUR ANSWER PLEASE asap!!!=)
Tommie will make $12.65 per hour after his raise.
We will perform addition of value equal to mentioned percentage. So, representing this as equation -
Amount of money earned after raise = 11.5 + 10%×11.5
Converting percentage to whole number
Amount of money earned after raise = 11.5 + (10/100×11.5)
Performing multiplication and division on Right Hand Side of the equation
Amount of money earned after raise = 11.5 + 1.15
Performing addition on Right Hand Side of the equation
Amount of money earned after his raise = $12.65
Therefore, after increase in 10% raise, Tommie will earn total $12.65.
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Find the indicated probability. Round to three decimal places.A machine has 6 identical components which function independently. The probability that a component will fail is 0.3. Themachine will stop working if more than two components fail. Find the probability that the machine will be working.
Answer: 74.43%
Let us first list down the probabilities of the machine working.
First is the probability that none of the components will fail. We can write this probability as:
[tex]P(0)=(1-0.3)^6[/tex]Next, the probability that one of the components will fail. This will give us:
[tex]P(1)=C^1_6(1-0.3)^5(0.3)[/tex]Then, the probability that 2 of the components will fail.
[tex]P(2)=C^2_6(1-0.3)^4(0.3)^2[/tex]Adding all of these probabilities and we will have:
[tex]P=(1-0.3)^6+C^1_6(1-0.3)^5(0.3)+C^2_6(1-0.3)^4(0.3)^2[/tex][tex]P=(0.7)^6+(6)(0.7)^5(0.3)+(15)(0.7)^4(0.3)^2[/tex][tex]P=0.74431\times100=74.43\%[/tex]Therefore, the probability that the machine will be working would be 74.43%.
If f (x) = x
2 − 2 x , g (x) = x − 2
1) prove that : f(2) = g(2)
2) If g (K) = 7 , find : the value of k
1. The value of f(2) = 0 and g(2) = 0
2. The value of k is 9
What is a function?A function can simply be described as a law, rule, theorem or expression that explains the relationship between two terms.
These terms are known as;
The dependent variableThe independent variableGiven the functions;
f(x) = x^2 - 2xg(x) = x - 21To prove that f(2) = g(2)
Substitute the value of x as 2 in the functions, we have;
f(2) = 2^2 - 2(2)
expand the bracket
f(2) = 4 - 4
f(2) = 0
Then for g(2), we have;
g(2) = 2 - 2
g(2) = 0
Then, f(2) = g(2) = 0
If g(k) = 7
Then, we have;
k - 2 = 7
collect like terms to determine the value of k
k = 7 + 2
k = 9
Hence, the value is 9
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the difference. Write your answer in simplest form.
The mixed fraction 11 [tex]\frac{7}{16}[/tex] - 4[tex]\frac{7}{12}[/tex] is equivalent to the fraction to 6 41/48
How to solve an equation?An equation shows the relationship between two or more numbers and variables.The mixed fraction 11 7/16 is equivalent to the fraction (11 * 16 + 7)/16 = 183/16
The mixed fraction 4 7/12 is equivalent to the fraction (4 * 12 + 7)/12 = 55/12
Substituting:= 18 [tex]\frac{3}{16}[/tex] - 5 [tex]\frac{5}{12}[/tex]
Simplifying:= 329/48
= 6 41/48
11 [tex]\frac{7}{16}[/tex] - 4 [tex]\frac{7}{12}[/tex] is equal to 6 [tex]\frac{41}{48}[/tex]
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Rewrite the expression with a rational exponent as a radical expression.
The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.
The given expression is [tex](3^{\frac{2}{3} } )^{\frac{1}{6} }[/tex].
What is a rational exponent?Rational exponents are exponents of numbers that are expressed as rational numbers, that is, in [tex]a^\frac{p}{q}[/tex], a is the base and p/q is the rational exponent where q ≠ 0.
Now, the given expression can be solved as follows:
Using power law [tex](a^m)^n=a^{m\times n}[/tex], we get
[tex](3^{\frac{2}{3} } )^{\frac{1}{6} }=3^{\frac{2}{3}\times \frac{1}{6}}[/tex]
[tex]=3^{\frac{1}{9} }[/tex]
The equivalent expression to [tex]=3^{\frac{1}{9} }[/tex] is [tex]\sqrt[9]{3}[/tex].
The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.
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HELP ASAP HELP ASAP PLEASEEEEE
The distance between the parallel lines measured in the y direction is 3 units.
How to find the distance between the two given linesgiven data
y = - 3x + 4
y = - 3x + 1
let line 1 be y = - 3x + 4 and line two be y = -3x + 1
Analyzing the two lines show that the slope is equal hence parallel
slope = -3
The y intercept of the line or just the intercept is what varied
line 1 = 4line 2 = 1The difference between these two pints represents the distance between them measured in the y direction.
The difference is solved as
4 - 1 = 3 units
The distance is 3 units
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Red Brass is an alloy made by combining copper with zinc in a ratio of 16 to 3. How much zinc should be combined with 40 kg of copper to make red brass?
To make red brass alloy ratio of copper : zinc is 16 :3 ,then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.
As given,
Ratio given to make red brass alloy using copper and zinc is:
Copper :Zinc=16 :3
Given quantity of copper to make red brass alloy=40 kg
Let y kg be the quantity required to make red brass alloy using 40 kg copper
Using ratio and proportion we get,
40 :y=16 :3
⇒y ×16=40×3
⇒y=120/16
⇒y=7.5 kg
Therefore, to make red brass alloy ratio of copper : zinc is 16 :3 , then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.
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I need questions 10 , 13 , 15 , and 16 solved with steps and graph
10. |x - 4| - 4 = 1/2x
⇒ Multiplying by 2,
2 |x - 4| - 8 = x
So, x - 4 = (x + 8)/2
= -(x + 8)/2
When,
x - 4 = (x + 8)/2
2x - 8 = x + 8 (Multiplying by 2)
2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)
x = 16
When,
x - 4 = - (x + 8)/2
2x - 8 = -x - 8 (Multiplying by 2)
2x + x = -8 + 8 (Adding 8 and x to both sides)
3x = 0
x = 0
Hence, the solution is x = 16 and x = 0.
13. (3/4)x = 2x - 10
⇒ Subtract 2x from both sides.
-5x/4 = -10
Multiply both sides by 4/(-5).
(-5x/4)×4/(-5) = -10 × 4/(-5).
x = 8 is the solution of the equation.
15. x² - 7x - 8 > 0
⇒ Solve the quadratic equation by splitting the middle term,
x² - 8x + x - 8 > 0
x(x - 8) + 1(x -8) > 0
(x + 1)(x- 8) > 0
-1 and 8 are the critical points of the inequality.
x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.
16. x - 5 > - 2x + 4
⇒ Adding 2x to both sides.
3x - 5 > 4
Adding 5 to both sides.
3x > 9
Divide both sides by 3.
x > 3 is the required solution represented by blue shade region in the graph.
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Which function has the greatest average rate of change over the given interval?
Answer: C(x) > a(x) , meaning c(X) has the greatest average rate of change over the given interval.
Explanations :
• The greatest average rate of change = slope
,• given by formula :
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex](a) For a(x),[tex]\begin{gathered} minitial\text{ = }\frac{-2+3\text{ }}{0+1\text{ }} \\ \text{ = 1/1} \\ \text{ = 1 } \end{gathered}[/tex][tex]\begin{gathered} m\text{ final = }\frac{13-6}{3-2} \\ \text{ = }7\text{ } \end{gathered}[/tex]• The average rate of change over the given interval = 7-1 = 6
(b) for b(x) , we have [tex]\begin{gathered} M\text{ initial = }\frac{3-1}{0+1} \\ \text{ = 2} \end{gathered}[/tex]and
[tex]\begin{gathered} m\text{ final = }\frac{9-7\text{ }}{3-2\text{ }} \\ \text{ = 2} \end{gathered}[/tex]• We can see that b(x) has constant average rate of change at 2 , therefore this will not be considered for this purpose of the exercise.
(c) for C(x) , we have [tex]\begin{gathered} M\text{ initial = }\frac{-1+2}{0+1} \\ \text{ = 1 } \end{gathered}[/tex]
and
[tex]\begin{gathered} m\text{ final = }\frac{13-5\text{ }}{3-2} \\ \text{ = }8\text{ } \end{gathered}[/tex]• The average rate of change over the given interval =, 8 -1 = 7
in conclusion , C(x) = 7 , whereas a(x) = 6 ,
Therfore C(x) > a(x)