Answer:
The airplane reaches its maximum height of 74 feet in 14 seconds.
Step-by-step explanation:
The easiest thing to do here is to plug in the two numbers given in the answer choices. Finding the height at 14 seconds and the height after 74 seconds is straightforward from here.
h (14) = -(14-14)²+ 74
h (14) = 0 + 74
h (14) = 74
h (74) = -(74-14)² + 74
h (74) = -(60)² + 74
h (74) = -3600 + 74
h (74) = -3,526
Now, we know that a height of an airplane won't be negative, as the height below the ground cannot be reached.
because our equation includes -(t-14)², any number greater than 14 will be a larger negative than 0--setting the height to an impossible number.
{However, we add +74 feet, so our t-14 could be any number that is less than 74 when squared (after first subtracting 14 from the number). Numbers like 15, (resulting in subtracting 1 from 74), 16 (resulting in -4 from 74), 17 (74-9), 18 (74-16), 19 (74-25), 20 (74-36), 21 (74-49), 22 (74-64) are still above the minimum input}
{So, our t could be up to 22, and any number above this maximum limit, such as 23, result in a height of 0}
for example: -(23-14)² + 74
-(9)² = -81
-81 + 74 = -7
All numbers below 14, which would end in an eventual negative outcome [ -(x)² = negative if x < 0 ]
are greater than a t of 14.
-(13-14)² = -1
; showing that t = 14 is our maximum height
(remember that if you have -(x)² you get the negative version of x² [pemdas. the negative outside of the parenthesis is equivalent to multiplying the parenthesis by -1. (E)xponents comes before (M)ultiplication].)
2 x 3 4/5 as a mixed number.
Answer:
7 3/5
Step-by-step explanation:
2 x 3 4/5
2 x 19/5
2x19/1x5 = 38/5 = 7 3/5
A particle is moving along the curve y= 4sqrt(5x+11) . As the particle passes through the point (5,24) , its -coordinate increases at a rate of 2 units per second. Find the rate of change of the distance from the particle to the origin at this instant
The rate of change of the distance from the particle to the origin at this instant is 3 units per second.
What is the rate of change?The instantaneous rate of change is the rate of change at a particular instant.
A particle is moving along the curve
[tex]y= 4\sqrt{5x+11} .[/tex]
The rate of change of y is given as:
dy / dx = 2
by differentiating both sides,
[tex]\dfrac{dy}{dx} = 4\dfrac{1}{2\sqrt{5x+11} } 5\dfrac{dx}{dt} \\\\\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\[/tex]
From the question, we have:
(x, y) = (5,24)
Substitute 5 for x and dy / dx = 2
[tex]\dfrac{dy}{dx} = \dfrac{10}{\sqrt{5x+11} }\dfrac{dx}{dt}\\\\\\5= \dfrac{10}{\sqrt{5(5)+11} }\dfrac{dx}{dt}\\\\\\\sqrt{5(5)+11} = 2\dfrac{dx}{dt}\\\\\\\dfrac{dx}{dt} = 6/ 2 = 3[/tex]
Hence, the rate of change of the distance from the particle to the origin at this instant is 3 units per second.
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A board game uses a deck of cards that players draw from to move tokens around the board. The probability of selecting a card that moves a player's token forward is 32%. Over the course of a game, the deck is shuffled and reused as necessary. Approximately how many cards must be drawn from the deck before players' tokens move forward 50 times?
Using the binomial distribution, it is found that approximately 156 cards must be drawn from the deck before players' tokens move forward 50 times.
What is the binomial probability distribution?It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
The expected number of trials until q successes is:
[tex]E_s(X) = \frac{q}{p}[/tex]
In this problem, the parameters are given as follows:
q = 50, p = 0.32.
Hence:
[tex]E_s(X) = \frac{50}{0.32} = 156[/tex]
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Line segment JM has endpoints with coordinates -2 and 14 on a number line. Points K and L are on segment JM. K has a coordinate of 2 and point L has a coordinate of 8. Find the probability that a point on JM is placed first on JL and a second point is not placed on KL.
5/8
25/64
15/64
8/15
Answer:
25/64Step-by-step explanation:
consider the events F and S :
F : «the first point is placed on JL»
S : «the second point is not placed on KL»
F∩S : «a point on JM is placed first on JL and a second point is not placed on KL»
[tex]p\left( F\right) =\frac{JL}{JM} =\frac{10}{16} =\frac{5}{8}[/tex]
[tex]p\left( \overline{S} \right) =\frac{KL}{JM} =\frac{6}{16} =\frac{3}{8}[/tex]
[tex]\Longrightarrow p\left( S\right) =1-p\left( \overline{S} \right) =1-\frac{3}{8} =\frac{5}{8}[/tex]
[tex]p\left( F\cap S\right) =p\left( F\right) \times p\left( S\right) =\frac{5}{8} \times \frac{5}{8} =\frac{25}{64}[/tex]
A box has candies in it: are taffy, are peppermint, and are caramel. (Each candy falls into only one of these categories.) Brian wants to select two candies to eat for dessert. The first candy will be selected at random, and then the second candy will be selected at random from the remaining candies. What is the probability that the first candy selected is taffy and the second candy is caramel?
Do not round your intermediate computations. Round your final answer to three decimal places.
Probability that the first candy selected is taffy and the second candy is caramel is 0.144.
The data missing in the question is
A box has 18 candies in it: 3 are peppermint, 4 are caramel, and 11 are taffy.
What is Probability ?Probability can be defined as the study of likelihood of an event to happen.
It has a range of 0 to 1.
Probability is the ratio of the expected outcomes / total coutcome.
Total outcomes = 18
The probability that the first candy is taffy is 11/18
Now as there is no replacement , the total outcomes can be 17
The probability that the second candy is caramel is 4/17
Probability that the first candy selected is taffy and the second candy is caramel = (11/18)(4/17)
= 0.144
Therefore the Probability is 0.144
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a quadrilateral is inscirbed in circle o. the angle measures the quadrilateral in degrees are given by the expressions shown in the figure.
what is the measure of angle c?
(will mark branliest + 20points)
Answer:
A. 65 degrees
Step-by-step explanation:
The required measure of the angle c in the quadrilateral is given as 65°.
As mentioned in the question,
A quadrilateral is inscribed in a circle o. the angle measures the quadrilateral in degrees is given by the expressions shown in the figure.
Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
In a quadrilateral, the sum of the composite angle is equal to 180°,
∠A + ∠C = 180
130 -x + 95 -2x = 180
-3x = 180 - 225
x = 15
Now,
∠c = 95 - 2x
∠c = 95 - 2×15
∠c = 65
Thus, the required measure of the angle c in the quadrilateral is given as 65°.
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L=24 B=12 area=______
Perimeter=_______
Answer:
Area= 288
Perimeter= 72
Step-by-step explanation:
In order to get the area of a rectangle, you multiply the length by the width, 24x12=288.
In order to find the perimeter just add all of the sides, there are 2 sides with a length of 24, and two sides with a width of 12.
24+24+12+12=72
pls help, thank you!!
Answer: 1, 3
For a cubic polynomial, there are either 3 real roots or 1 real root nad 2 complex roots in a conjugate pair.
The ratio of boys to girls is 3:2. f the class has 27 boys. How many pupils are in the class?
Answer:
the answer is 45
see the attachment photo!
Which smallest number is subtracted from the number 12675 to make it a perfect square?
The table gives information about the speeds, in kilometres per hour, of 80 motorbikes as each pass under a bridge.
Speed
(s kilometres per hour) Frequency
40 < s 50 10
50 < s 60 16
60 < s 70 19
70 < s 80 23
80 < s 90 12
(a) Write down the modal class
(b) Work out an estimate for the mean speed of the motorbikes as they pass under the bridge.
Give your answer correct to 3 significant figures.
The modal class is 70 - 80 and the mean speed is 66.4
How to determine the modal class?The table of values is given as:
Speed Frequency
40 - 50 10
50 - 60 16
60 - 70 19
70 - 80 23
80 - 90 12
The modal class is the class with the highest frequency
The class 70 - 80 has the highest frequency of 23
Hence, the modal class is 70 - 80
How to determine the mean?Rewrite the frequency table to include the class midpoints
x f
45 10
55 16
65 19
75 23
85 12
The estimate of the mean speed is then calculated as:
[tex]\bar x =\frac{\sum fx}{\sum f}[/tex]
So, we have:
[tex]\bar x = \frac{45* 10 + 55 * 16 + 65 * 19 + 75 * 23 + 85 * 12}{80}[/tex]
Evaluate
[tex]\bar x = 66.4[/tex]
Hence, the mean speed is 66.4
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Umberto plants a garden with an area of 16 square feet. What is the area of the garden in square inches
Answer:
2,304 inches
Step-by-step explanation:
1 square foot = 144 square inches
16 x 144 = 2,304 square inches
If 8x + y = -1 is a true equation, what would be the value of y + 8x
what is 0.02 to the power of 4? HELP NEEDED SOON
Answer:
1.6e-7, or .00000016
Step-by-step explanation:
Please solve the whole page please please
1d) ↑ (Do the same but turned if that's easier)
1a) 199
1b) 193
1c) 217
1e) Based on the box plot, we can for example, find the lowest and greatest values, the range (largest - smallest), the mean (all values / # values), and the median middle value or q2 given by the second line in the box.
2b) 7
2c) 9.5
2d) ↑
2e) because the data is not ordered, it is difficult to determine the quartile data. Once it is ordered like 6, 7, 7, 7, 8, 8, 9, 10, 10. The data can be visualized alot easier. With the box plot we can determine q3 of the data by looking at the 3rd line, using the whiskers of the box to find the minimum and maximum values.
3)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be: 4,6,8,8,9,11,12,14,14,16.
[4, 6, 8, 8, 9] [] [11, 12, 14, 14, 16]
4 is the minimum, 16 is the maximum, q1 is 8, q3 is 14, and median is 10.
4) ↑
5)
You need to find the minimum, maximum, the quartile data obtained by having an even amount of data on both sides, order it so that values can be grouped. this includes q1, q2 (or median), and q3.
In this case the ordered data would be:
45, 45, 50, 55, 60, 70, 70, 75, 80, 85
[45, 45, 50, 55, 60] [] [70, 70, 75, 80, 85]
45 is the minimum, 85 is the maximum, q1 is 50, q3 is 75, and median is 65.
6) ↑
help?
what fraction of a dollar is 236 cents?
236/100, 59/25, or 2 9/25
Step-by-step explanation:
There are 100 cents in a dollar, so 236/100 is your starting fraction. The simplest improper fraction would be 59/25. But if you're looking for a mixed number, you get 2 9/25.
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
To solve this problem,
We need to convert 236 cents into dollars.
Since there are 100 cents in one dollar,
we can divide 236 by 100 to get the equivalent dollar value.
⇒ 236 cents ÷ 100 cents per dollar = 2.36 dollars
Now that we know that 236 cents is equivalent to 2.36 dollars,
we can express it as a fraction of a dollar.
To do this, we'll use the fact that one dollar is equivalent to 100 cents, which means that one dollar can be expressed as the fraction 100/100.
To find the fraction of a dollar that 2.36 dollars represents,
we'll divide 2.36 by 1.
⇒ 2.36 ÷ 1 = 2.36/1
To express this as a fraction of a dollar,
Multiply both the numerator and denominator by 100 to get,
⇒ (2.36 x 100) / (1 x 100) = 236/100
Simplifying this fraction, we get,
⇒ 236/100 = 118/50
Therefore,
236 cents is equivalent to 118/50 or 2.36 dollars as a fraction of a dollar.
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6 kids play a tennis game. Each play each other once. How many games did they play altogether
Solve for D: 70D + 2 - 14D = 79 + 12D - 20
70d+2-14d= 79+12d-20
70d-14d-12d= 79-20-2
44d= 57
d= 57/44
what is the decimal equivalent for 15 1/4
Answer:
15.25
Step-by-step explanation:
1/4 is also 0.25 in decimals so add that to your 15 and you get 15.25.
Step-by-step explanation:
the fraction 1/4 is also equivalent to the decimal for of .25 + 15 equals 15.25
what is the range of exponential function f(x)=9*2^x
Answer:
uhm smhtn
Step-by-step explanation:
i really just want points.
Answer:
(0,infinity)
Step-by-step explanation:
.
(OAU
29 Mike knows that (3,6.5) and (4,17.55) are points on the graph of an exponential function, g(x), and
he wants to find another point on the graph of this function.
First, he subtracts 6.5 from 17.55 to get 11.05.
Next, he adds 11.05 and 17.55 to get 28.6.
He states that (5,28.6) is a point on g(x).
Is he correct? Explain your reasoning.
Mike's claim that (5,28.6) is a point on the exponential function g(x) is incorrect
How to determine if he is correct?The points are given as:
(3,6.5) and (4,17.55)
An exponential equation is represented as:
[tex]y = ab^x[/tex]
Using the given points, we have the following equations:
[tex]ab^3 = 6.5[/tex]
[tex]ab^4 = 17.55[/tex]
Divide both equations:
[tex]ab^4 \div ab^3 = 17.55 \div 6.5[/tex]
Evaluate
b = 2.7
Substitute b = 2.7 in [tex]ab^3 = 6.5[/tex]
[tex]a * 2.7^3 = 6.5[/tex]
Solve for a
[tex]a = \frac{6.5}{2.7^3}[/tex]
Substitute [tex]a = \frac{6.5}{2.7^3}[/tex] and b = 2.7 in [tex]y = ab^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
His point (5,28.6) means that:
x = 5 when y = 28.6
Substitute x = 5 in [tex]y = \frac{6.5}{2.7^3} * 2.7^x[/tex]
[tex]y = \frac{6.5}{2.7^3} * 2.7^5[/tex]
Evaluate
y = 47.385
y = 47.385 and y = 28.6 are not the same
Hence, Mike's claim is incorrect
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What is the value of F(x)=-x+9 if x=-7
Answer: F = - 2/7
Step-by-step explanation:
[tex]f(x) = x + 9\\f(-7) = -7 + 9\\f(-7) = 2\\f = -\frac{2}{7}[/tex]
Can someone please explain how the answer to this is, "19 and 3", "1 and 12"
Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18, 19.
What are Alternate Exterior Angles?These are known to be the Alternate exterior angles that are regarded as the pair of angles found on the outer side of the two parallel lines but they are seen on the opposite side of the transversal.
Note that in the image given, there are two parallel lines and two transversal lines.
Note also that to get the Alternate exterior angles, it has to be the angles seen on the seen on the opposite side of the transversal that has crossed the parallels lines and from the image given, only angle 1, 2, 3, 4,13,14, 18, 19 fit into the description.
Therefore, Using the image given, the angles that are Alternate Exterior Angles are: 1, 2, 3, 4,13,14, 18 19.
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f(x)=√x +3. Find the inverse of f(x) and its domain.
Answer:
f(x) = √x + 3
y = √x + 3
√x = y - 3
x = (y - 3)²
Hence inverse of f(x) = (x - 3)² and its domain is x >= 3.
Step-by-step explanation:
hope this helps
Solve the equation for x.
√x+5 -1 = 2
Answer:
Step-by-step explanation:
Equation
√(x + 5) - 1 = 2 I take it that you want the 5 to be with the x.
Solution
√(x + 5) - 1 = 2 Add 1 to both sides
√(x + 5) - 1 +1 = 2 + 1 Combine
√(x + 5) = 3 Square both sides
√(x + 5)² = 3² Combine
x + 5 = 9 Subtract 5 from both sides
x + 5- 5 = 9- 5
x = 4
Answer x = 4
there are 20 students 15 men and 5 women in a maths class,in how many different ways can a committee of 3 men and 2 women be choosen
[tex]\displaystyle\\\binom{15}{3}\cdot\binom{5}{2}=\dfrac{15!}{3!12!}\cdot\dfrac{5!}{2!3!}=\dfrac{13\cdot14\cdot15}{2\cdot3}\cdot\dfrac{4\cdot5}{2}=13\cdot7\cdot5\cdot2\cdot5=4550[/tex]
8 3/8 + 3 3/8 + 2 3/8 + 3/8
what is the answer of this ?
The simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have an expression:
[tex]= 8 \dfrac{3}{8} + 3 \dfrac{3}{8} + 2 \dfrac{3}{8} + \dfrac{3}{8}[/tex]
After simplification:
[tex]= \dfrac{67}{8} + \dfrac{27}{8} + \dfrac{19}{8} + \dfrac{3}{8}[/tex]
[tex]= \dfrac{67+27+19+3}{8}[/tex]
= 116/8
= 29/2
[tex]= 14\dfrac{1}{2}[/tex]
Thus, the simplification form of the expression 8 3/8 + 3 3/8 + 2 3/8 + 3/8 is 14 whole 1/2 or 14 1/2 after adding all the terms.
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Answer:
i dont understand your question
Step-by-step explanation:
2. A function fis given by f: x→ 5x-8, where x € R. Find
a. f(-4)
b. the value of x whose image is 12
Answer:
a. -28b. 4Step-by-step explanation:
f: x→ 5x-8
a. f(-4) = 5(-4) - 8 = -20 - 8. = -28
b. the value of x whose image is 12
To find the value of x ,we have to solve f(x) = 12
f(x) = 12
⇔ 5x-8 = 12
⇔ 5x = 12 + 8
⇔ 5x = 20
⇔ x = 20 ÷ 5 = 4
A bag contains 15 red candies, 15 yellow candies, and 15 blue candies. What is the probability of randomly
choosing two candies of the same color, without replacement?
[tex]|\Omega|=45\cdot44=1980\\|A|=15\cdot14\cdot3=630\\\\P(A)=\dfrac{630}{1980}=\dfrac{7}{22}\approx31.8\%[/tex]
Find the missing side of this right
triangle.
30
X
[?]
X = 1
Enter the number that belongs in the green box.
Answer:
see the attachment photo!