Algebra help please.
Find the value of 21 + 4(3^2 - 5).
25
37
100
the answer would be 37
The table below represents the atmospheric temperature at a location as a function of the altitude:
Altitude
(in thousand feet)
x
Temperature
(in °C)
f (x)
15
4
20
−6
25
−16
30
−26
The average rate of change of the function between x = 15 to x = 25 is ___degrees Celsius per thousand feet and represents the rate of change of temperature per thousand feet
from x15 to x 25 is 4 - -16 = -20 degree change
25 -15 = 10000 feet
-20/10 = -2 degrees every 1000 feet
How many ways can you split 12 people into 3 groups?
Which value is needed to create a perfect square trinomial from the expression x2 + 8x + _____?
A bag contains 44 red balls and 55 blue balls. 22 balls are selected at random. find the probability of selecting 22 red balls.
The probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given,
A bag contains 44 red balls and 55 blue balls
The total number of balls=44+55=99
22 balls are selected at random from bag.
We need to find the probability of selecting 22 red balls.
The probability of selecting 22 red balls from 44 balls
[tex]^{44} C_{22}[/tex]
2,104,098,963,720
and [tex]^{99} C_{22}[/tex] is 5.7190121704386E+21
So probability of selecting 22 red balls is
[tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
Hence, the probability of selecting 22 red balls is [tex]\frac{^{44} C_{22} }{^{99} C_{22}}[/tex]
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how do u do that 2*2/2*2
Does negative fractions become positive when you reciprocal
please help
its really important
1/2 divided by 5=1 over blank I need to know the blank number
{12x + 4y = 15232x + 12y = 42012x + 4y = 15232x + 12y = 420 In the equations, xx represents the cost of a chicken lunch and yy represents the cost of a vegetarian lunch. Which is the cost of the vegetarian lunch?
Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled. How many hours did it take the first plane to travel to the destination? Enter an equation that can be used to solve this problem
Answer:
4.5 hours
[tex]496 x= 558 x-279[/tex]
Step-by-step explanation:
We are given that two airplanes left the same airport and arrives at the same destination at the same time.
We have to find the number of hours taken by first plane to travel to the destination and find the equation that can be used to solve this problem
We are given that the first airplane left at 8:00 a.m
Let y be the distance traveled by the first airplane
The average rate of first airplane =496 miles per hour
The average rate of second airplane =558 miles per hour
Let x represents the number of hours that the first airplane traveled.
The number of hours that the second plane traveled =x-0.5
Because the second airplane take half an hour less than the first airplane
We know that [tex] distance=speed\times time [/tex]
[tex]d=496 x[/tex]
[tex]d=558(x-0.5)[/tex]
[tex]496 x= 558 x-279[/tex]
[tex]279=558 x-496 x[/tex]
[tex]279=62 x[/tex]
[tex]x=\frac{279}{62}[/tex]
x=4.5 hours
Hence, the first airplane takes 4.5 hours to travel to the destination.
You have the answer?
t=d+pm for p
i dont understand what this is asking me to do
To solve for "p" in the equation "t = d + pm," isolate "p" by subtracting "d" from both sides: "t - d = pm." Then, divide both sides by "m" to find "p": "p = (t - d) / m." This formula allows you to calculate "p" based on given values of "t," "d," and "m."
To solve for "p" in the equation "t = d + pm," you need to isolate "p" on one side of the equation. Here's how you do it step by step:
Start with the Equation:
The equation is t = d + pm, where "t" represents a value, "d" represents another value, "p" is the variable we want to solve for, and "m" is yet another value.
Isolate the "pm" Term:
To get "pm" by itself, we need to eliminate the "d" term on the right side. We can do this by subtracting "d" from both sides of the equation:
t - d = pm
Solve for "p":
Now that "pm" is isolated on the right side, we can solve for "p" by dividing both sides by "m":
p = (t - d) / m
So, the solution for "p" in terms of "t," "d," and "m" is given by the formula p = (t - d) / m. This formula tells you how to calculate the value of "p" based on the values of "t," "d," and "m."
In practical terms, this equation might be used in various scenarios. For example, if "t" represents total distance, "d" represents a fixed distance, and "m" represents a constant speed, then "p" would represent the time it takes to cover the remaining distance to reach "t." This formula can be quite useful in solving real-world problems involving time, distance, and speed.
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Describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
Transformation #1
Transformation #2
Write an ordered-pair rule for each transformation in the sequence.
Transformation #1
Transformation #2
Answer: The required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
Step-by-step explanation: We are given to describe in words a sequence of transformations that maps ∆ABC to ∆A'B'C'.
From the figure, we note that
the co-ordinates of the vertices of triangle ABC are A(0, 4), B(0, 0) and C(2, 3).
And, the co-ordinates of the vertices of triangle A'B'C' are A'(-2, -3), B'(2, -3) and C'(-1, -1).
We see that if triangle ABC is rotated 90 degrees in anticlockwise direction about the origin, then its co-ordinates changes according to the following rule :
(x, y) ⇒ (-y, x).
That is
A(0, 4) ⇒ (-4, 0),
B(0, 0) ⇒ (0, 0),
C(2, 3) ⇒ (-3, 2).
Now, if the vertices of the rotated triangle are translated 2 units right and 3 units down, then
(x, y) ⇒ (x+2, y-3).
That is, the final co-ordinates after rotation and translation will be
(-4, 0) ⇒ (-4+2, 0-3) = (-2, -3),
(0, 0) ⇒ (0+2, 0-3) = (2, -3),
(-3, 2) ⇒ (-3+2, 2-3) = (-1, -1).
We see that the final co-ordinates are the co-ordinates of the vertices of triangle A'B'C'.
Thus, the required sequence of transformations is
Transformation 1 : a rotation by 90 degrees in the counterclockwise direction about the origin, (x, y) ⇒ (-y, x).
Transformation 2 : a translation by 2 units right and 3 units down, (x, y) ⇒ (x+2, y-3).
POINTS POINTS POINTS POINTS POINTS! harder question!
45(34- 2)
Answer:
answer is 1440,ok
Step-by-step explanation:
A pair of shoes usually sells for $55. If the shoes are 40% off, and sales tax is 7%, what is the total price of the shoes, including tax?
Simplify 12 to the sixteenth power over 12 to the fourth power
Given the number 2464829438 what is the next number?
A bag contains 10 green marbles and 4 yellow marbles. If two marbles are chosen at random, one at a time and without replacement, what is the probability of getting two green marbles?
Answer: The required probability of getting two green marbles is 49.45%.
Step-by-step explanation: Given that a bag contains 10 green marbles and 4 yellow marbles. Two marbles are chosen at random, one at a time and without replacement.
We are to find the probability of getting two green marbles.
Let S denote the sample space for the experiment of choosing a marble from the bag and A denote the event of getting a green marble.
The, n(S) = 10 + 4 = 14 and n(A) = 10.
So, the probability of event A will be
[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{10}{14}=\dfrac{5}{7}.[/tex]
After getting one green marble and not replacing, let S' denote the sample space for the experiment of choosing a marble from the bag
and
let B denote the event of getting another green marble.
Then, n(S') = 14 - 1 = 13 and n(B) = 10 - 1 = 9.
Then, the probability of getting two green marbles is given by
[tex]P\\\\=P(A)\times P(B)\\\\=\dfrac{5}{7}\times\dfrac{n(B)}{n(S')}\\\\\\=\dfrac{5}{7}\times\dfrac{9}{13}\\\\\\=\dfrac{45}{91}\times100\%\\\\=49.45\%.[/tex]
Thus, the required probability of getting two marbles is 49.45%.
Any number that is divisible by 2 is also divisible by 8. Find a counter example to show that the conjecture is false. 24 28 16 32
Write an inequality that represents the verbal expression. All real numbers greater than or equal to 74
What is the area of a triangle with vertices at (−2, 1) , (2, 1) , and (3, 4) ?
The area of the triangle is 6 square units.
Explanation:To find the area of a triangle with vertices at (-2, 1), (2, 1), and (3, 4), we can use the formula for the area of a triangle: Area = 1/2 × base × height.
First, we need to find the base and height of the triangle. The base is the distance between the points (-2, 1) and (2, 1), which is 4 units. The height is the distance between the point (3, 4) and the line formed by the base, which is the vertical distance from (3, 4) to the line y=1, which is 3 units.
Plugging these values into the formula, we get Area = 1/2 × 4 ×3 = 6 square units.
The length of the rectangle exceeds its breadth by 3 cm. if the length and breadth are each increased by 2 cm, then the area of new rectangle will be 70 sq. cm more than that of the given rectangle. find the length and breadth of the given rectangle.
Let's suppose the breadth of the rectangle be x cm
The length of the rectangle = x + 3 cm
It is assumed that the length and breadth of the rectangle is amplified by 2.
Now, the breadth of the rectangle = x + 2
The length of the rectangle = x + 3 + 2 = x + 5
It is also assumed that the area of the rectangle is 70 sq. cm
Hence, the area of the rectangle = length x breadth = (x + 2)(x + 5) = 70
= x2 + 5x + 2x + 10 = 70
= x2 + 7x = 70 - 10
= x2 + 7x = 60
= x2 + 7x - 60 = 0
= x2 + 12x - 5x - 60 = 0
= x( x + 12) -5(x + 12) = 0
= ( x + 12) (x - 5) = 0
=x + 12 = 10 or =x - 5 = 0
= x = 10 - 12 = -2 = x = 5
The breadth of a rectangle is never negative, so the value of x is 5 cm
Therefore, the breadth of the rectangle = 5 cm
The length of the rectangle = 5 + 3 = 8 cm
What is the equation of the parabola with a vertex of (0,7) and passing through (-1,10)?
Solve.
2x + 6 - 7x = 21
If a and b are positive numbers, find the maximum value of f(x) = xa(7 â x)b on the interval 0 ⤠x ⤠7.
Final Answer:
The maximum value of f(x) = xa(7 - x)b on the interval 0 ≤ x ≤ 7 occurs when x = 7/2 for a > 0 and b > 0.
Explanation:
To find the maximum value of f(x) on the interval 0 ≤ x ≤ 7, we'll use calculus. First, take the derivative of f(x) with respect to x.
f'(x) = a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a
Setting f'(x) = 0 to find critical points:
a * (7 - x)^b * x^(a-1) - b * a * (7 - x)^(b-1) * x^a = 0
Solving for x gives x = 7/2. To determine if this point is a maximum, minimum, or inflection point, we'll use the second derivative test.
f''(x) = a * (7 - x)^(b-1) * x^(a-2) * ((a - 1) * x - 7) - b * a * (7 - x)^(b-2) * x^(a-1) * ((b - 1) * x - 7)
When x = 7/2, f''(7/2) > 0, indicating a concave-up shape and confirming it as a local minimum. Therefore, the maximum value of f(x) occurs at the endpoints of the interval, x = 0 and x = 7, or potentially at x = 7/2 if it surpasses these values.
For a > 0 and b > 0, plugging in x = 7/2 into f(x) = xa(7 - x)b yields the maximum value of the function within the given interval.
Understanding the critical points through derivatives helps identify where the maximum or minimum points occur in the function. In this case, x = 7/2 stands as the point of maximum value within the interval 0 ≤ x ≤ 7 when a and b are both positive.
Karen Johnson rode her 27” bicycle to the store and back. The store is 1 mile from Johnson’s Home. Approximately how many rotations did Johnson’s bicycle wheels make in going to the store and back
Mario bought $5 worth of stamps at the post office. He bought ten more 6-cent stamps than 10-cent stamps. The number of 8-cent stamps was three times the number of 10-cent stamps. He also bought two 20-cent stamps. How many of each kind of stamp did he purchase?
Determine whether the given value is a statistic or a parameter. upper a sample of students is selected and it is found that 25 % own a computer.a sample of students is selected and it is found that 25% own a computer.
a) Simplify the expression and explain each step. (2 points)
4(3x + 2) – 2
b) Factor the expression completely. (1 point)
20b – 16
Answer:
a) [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) [tex]20b-16= 4\left(5b-4\right)[/tex]
Step-by-step explanation:
a) To simplify the expression you must:
Expand [tex]4(3x + 2)[/tex]:
Apply the distributive law: [tex]\:a\left(b+c\right)=ab+ac[/tex]
[tex]a=4,\:b=3x,\:c=2\\\\4\left(3x+2\right)=4\cdot \:3x+4\cdot \:2[/tex]
Simplify [tex]4\cdot \:3x+4\cdot \:2= 12x+8[/tex]
[tex]12x+8-2[/tex]
Subtract the numbers: [tex]4\left(3x+2\right)-2=12x+6[/tex]
b) To factor the expression [tex]20b - 16[/tex] you must:
Rewrite 16 as [tex]4\cdot 4[/tex] and 20 as [tex]4\cdot 5[/tex]
[tex]20b-16=4\cdot \:5b-4\cdot \:4[/tex]
Factor out common term 4
[tex]20b-16= 4\left(5b-4\right)[/tex]