Answer:
X= -3
Step-by-step explanation:
(4+5)-1/3(40-4)=X
X=9- 1/3(36)
X=9-12
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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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
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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2x + 4y = 15
6x +12y = 45
What would the solution to the system of equations be?
Answer:
They both have an infinite number of solutions.
Step-by-step explanation:
Given system of equations:
a) 2x + 4y = 15
b) 6x + 12y = 45
Slope-intercept form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Rewrite both equations into slope-intercept form:
a) 2x + 4y = 15
⇒ 2x + 4y = 15 [subtract 2x from both sides]
⇒ 2x - 2x + 4y = 15 - 2x
⇒ 4y = - 2x + 15 [divide both sides by 4]
⇒ 4y ÷ 4 = (-2x ÷ 4) + (15 ÷ 4)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
b) 6x + 12y = 45
⇒ 6x + 12y = 45 [subtract 6x from both sides]
⇒ 6x - 6x + 12y = 45 - 6x
⇒ 12y = - 6x + 45 [divide both sides by 12]
⇒ 12y ÷ 12 = (-6x ÷ 12) + (45 ÷ 12)
[tex]\sf \implies y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
New equations:
[tex]\sf a)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75\\\\\sf b)\ y = -\dfrac{1}{2}x\ + \dfrac{15}{4} \ or \ y=-0.5x\ + 3.75[/tex]
Both equations have the same slope (-½), and y-intercept (3.75). Therefore, they both have an infinite number of solutions.
System of equations can have the following:
No Solution: the same slope (both lines will be parallel)
One Solution: different slopes and different y-intercepts
Infinitely Many Solutions: the same slope and y-intercept
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Looking at the given expression, they do not seem to be in the slope-intercept form which is the most common form used for linear expression. Let us convert the equations that were given in the problem statement to follow the slope-intercept form.
Slope-Intercept Form ⇒ [tex]y = mx + b[/tex]m = slopeb = y-interceptEquation #1
Subtract 2x from both sides
[tex]2x + 4y = 15[/tex][tex]2x - 2x + 4y = 15 - 2x[/tex][tex]4y = -2x + 15[/tex]Divide both sides by 4
[tex]\frac{4y}{4} = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = \frac{-2}{4}x + \frac{15}{4}[/tex][tex]y = -0.5x + 3.75[/tex]Equation #2
Subtract 6x from both sides
[tex]6x + 12y = 45[/tex][tex]6x - 6x + 12y = 45 - 6x[/tex][tex]12y = -6x + 45[/tex]Divide both sides by 12
[tex]\frac{12y}{12} = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = \frac{-6}{12}x + \frac{45}{12}[/tex][tex]y = -0.5x + 3.75[/tex]Since both the first and second equation have the same exact number which means that they will fall exactly on top of each other. Therefore, there are infinite solutions as they will always continue on top of each other.
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]
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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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
Which smallest number is subtracted from the number 12675 to make it a perfect square?
6-2 6 grade home work
Answer:
list five solution to the energy crisis of nepal
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!
A card is picked from a standard deck of 52 cards. Determine the odds against and the odds in favor of selecting a jack .
Answer:
2/52 so the chance is unlikely.
Step-by-step explanation:
well I think I’m right because sometimes when my family has time we play blackjack in my house for fun or another card game so I should be right.
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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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]
6 kids play a tennis game. Each play each other once. How many games did they play altogether
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
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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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.
(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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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
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) ↑
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:
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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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!
Find the equation of the exponential function represented by the table below:
Y
8
0
1
2
3
3
12
48
192
no I dont feel like it is the answer
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
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:
.
If 8x + y = -1 is a true equation, what would be the value of y + 8x
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