x = number of hours after 9 am (eg: x = 1 means 1 hr after 9 am, so 10 am)
f(x) = population count x hours after 9 am
f(1) = population count at 10 am (1 hour later)
f(2) = population count at 11 am (2 hrs after 9 am)
f(2) - f(1) represents the difference in population counts from 10 am to 11 am, or put another way, how much the population increased during that time interval.
f(2)-f(1) represents the change in the population of bacteria from the first to the second hour after 9 a.m., giving us the rate of population growth over that one-hour period.
Explanation:The expression f(2)-f(1) in the function f(x), where x represents the hours after 9 a.m., illustrates the change in the population of the bacteria between the first and second hour after 9 a.m. Population growth in bacteria usually follows a logarithmic scale where it doubles every given time period, typically every hour. Thus, by calculating the difference between the population at the second hour (f(2)) and the first hour (f(1)), we can get the increase in the population of bacteria over that one-hour period.
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1 kilogram= 2.2 pounds, 1 stone= 14 pounds change 42 kilograms into stones
Answer:
6.6 stone
Step-by-step explanation:
We will use conversions to change kilograms to stones
1 kilogram= 2.2 pounds,
1 stone= 14 pounds
42 kilogram 2.2 lbs 1 stone
--------------- * ------------- * ---------------
1 kg 14 lbs
All the units cancel except stone
(42*2.2)/14 stone
6.6 stone
Answer:
42 kilograms is equal to 6.6 stones.
Step-by-step explanation:
Using the given conversion factors:
1 kilogram = 2.2 pounds
1 stone = 14 pounds
To Find: 42 kilograms into stones = ? stones
Solution:
42 kilograms = [tex]42\times 2.2 pounds=92.4 pounds[/tex]
Another conversion factor used:
1 stone = 14 pounds
[tex]1 pound = \frac{1}{14} stones[/tex]
[tex]92.4 pounds=92.4\times \frac{1}{14} stones=6.6 stones[/tex]
So, 42 kilograms is equal to 6.6 stones.
Which expression is equivalent to 100 in exponential form? A) 102 B) 210 C) 10 × 10 D) 4 × 25
Answer:
A) 10^2
Step-by-step explanation:
100 is 10 times 10 or 10 to the second power
100 = 10 * 10 = 10 ^2
Select the correct answer. x Probability 0 0.2 1 0.1 2 0.4 3 0.2 4 0.1 The probability distribution of x, a discrete random variable, is given in the table. What is the expected value of x? A. 0.8 B. 1.9 C. 2 D. 5
Answer: The option B. 1.9 is correct
Explanation:
We are given the below information:
x Probability P(x)
0 0.2
1 0.1
2 0.4
3 0.2
4 0.1
The expected value of x is given below:
[tex]E(x)=\sum x P(x)[/tex]
[tex]=(0 \times 0.2)+(1 \times 0.1)+(2 \times 0.4)+(3 \times 0.2)+(4 \times 0.1)[/tex]
[tex]=0+0.1+0.8+0.6+0.4[/tex]
[tex]=1.9[/tex]
Therefore, the expected value of x is 1.9
Which figures are quadrilaterals with at least one pair of parallel sides? Check all that apply. trapezoid rhombus parallelogram rectangle triangle square
Answer:
trapezoid rhombus parallelogram rectangle square
Step-by-step explanation:
It is easier to say that the triangle is the only one that does not apply. It only has 3 sides. The rest all have at least 1 set of parallel lines (trapezoid). The others have 2 sets of parallel lines.
Wrong !
The right response is :
All of the following except a trapezoid
An airplane climbs at an angle of 11 degrees with the ground. Find the distance it has traveled when it has attained an altitude of 400 feet. Using sin, cos, and tan.
The distance traveled by the airplane to attain an altitude of 400 feet is approximately 2164.8 feet.
Explanation:To find the distance traveled by the airplane, we can use trigonometric functions.
Let's use the side opposite the angle as the altitude (400 feet) and the hypotenuse as the distance traveled.
Using the sine function, we can solve for the distance:
sin(angle) = Opposite / Hypotenuse
sin(11 degrees) = 400 feet / x
x = 400 feet / sin(11 degrees)
Using a calculator, we find that x ≈ 2164.8 feet.
Therefore, the distance traveled by the airplane to attain an altitude of 400 feet is approximately 2164.8 feet.
The distance it has traveled when it has attained an altitude of 400 feet is 2096.34 feet.
Given, Climbing angle [tex](\(\theta\))[/tex] = 11°
Altitude (opposite side) = 400 feet
sin(angle)= opposite/hypotenuse
sin(11°)= 400/d
d=400/ sin(11°)= 0.1908/400 ≈ 2096.34
The airplane has traveled approximately 2096.34 feet when it has attained an altitude of 400 feet at an angle of 11° with the ground.
What is the value of arccos (-1/2)
Answer:
120° & 240° (given the angles are between 0° and 360°)
Step-by-step explanation:
We want to find [tex]arccos(-\frac{1}{2})[/tex].
This means we want to know the angle(s) for which cosine has a value of [tex]-\frac{1}{2}[/tex].
The basic acute angle that has a cosine of [tex]\frac{1}{2}[/tex] is 60°. But we want to know NEGATIVE [tex]\frac{1}{2}[/tex]. So in which quadrants is cosine negative? Second and Third
The rule to find 2nd quadrant angle with known acute angle is: 180 - αThe rule to find 3rd quadrant angle with known acute angle is: 180 + αWhere α is the basic acute angle (in our case it is 60°)
So 2nd quadrant angle is 180 - 60 = 120°
and 3rd quadrant angle is 180 + 60 = 240°
Answer:
120°
Step-by-step explanation:
arccos means the inverse of cosine.
arccos (-1/2) ⇒ We can rewrite this equation as;
cosФ = 1/2 Find the value of Ф.
Ф = arccos (-1/2) ⇒ This can be calculated directly from the calculator.
arccos (-1/2) = 120°
or arccos (-1/2) = (180 + 60)
= 240°
You can have more than one value of arccos (-1/2) since the cosine is negative in the second and third quadrant.
In the figure below, OMPN is a square. If the area of the circle O is 4π then what is the area of the shaded region?
Answer:
4 - π
Step-by-step explanation:
(a) Radius of circle
A = πr² Substitute value of A
4π = πr² Divide each side by π
r² = 4 Take the square root of each side
r = 2
(b) Area of MON
A = ¼ × area of circle
A = ¼ × 4π
A = π
(c) Area of MONP
l = r Substitute the value of r
l = 2
A = l² Substitute the value of l
A = 2²
A = 4
(d) Area of MPN
A(MPN) = A(MONP) – A(MON)
Area(MPN) = 4 - π
Please help with this question.
Answer:
Coordinate of Q (3,4)
Step-by-step explanation:
Let to points S(-2,-6) and T(5,8)
Le Q(x,y) be the point in which it divide the ST in the ratio 5:2
If a point (x,y)cut the line in the ratio a : b where the end coordinate are( x1,y1) and (x2,y2)
x = x1 + p/w(x2 - x1) and y = y1 + p/w(y2 - y1)
where p = a and w = a+b
To find the coordinate of Q
x = x1 + p/w(x2 - x1 )
x = -2 + 5/7(5 - -2) = -2 + 5=3
y = y1 + p/w(y2 - y1)
y = -6 + 5/7(8 - -6) = -6 + 10 = 4
Therefore the coordinate of Q is (3,4)
x ÷ 0.4 = 2 1/9 ÷ 3 1/6
x = __
Please Help!
X/0.4 = 10x/4
21/9÷31/6 = 21•6/31•9
so solving the equation gives
X=84/465
Answer:
Step-by-step explanation:
19/9÷19/6=2/3
then we have:
x÷0.4=2/3
×0.4. ×0.4
x=4/15
Boom shaka laka
What is COEFFICIENT of 12c
Inga divided two identical rectangles into equal parts. She colored one part of each rectangle.
What is true about the areas of the colored parts?
Clear Check
The areas are equal.
The area of the red part is greater than the area of the blue part.
The area of the blue part is greater than the area of the red part.
Answer:
The areas are equal.
Step-by-step explanation:
Let the first rectangle be R and
the second rectangle be R'.
Sine R and R' are identical, their lengths are equal and their breadths are equal.
So, if Inga divided each into equal parts, then each part of both rectangles are equal.
Hence, the colored parts of both rectangles are equal.
Marcus has $28 to spend. He spent $3.75 to buy a notebook. He needs to save $11.25 but he wants to buy a snack. Chips cost $1.30 per package. Tax has already been included in the price. What is the maximum number of packages that Marcus can buy? Write an inequality that represents the situation. Then solve your inequality by showing your work and steps.
Total money Marcus has = $28
Money spent to buy a notebook = $3.75
Money left now = [tex]28-3.75=24.25[/tex]
Money needed to be saved = $11.25
So, the amount of money Marcus can spend = [tex]24.25-11.25=13[/tex]
Cost of a packet of chips = $1.30
The inequality to determine the maximum number of chips he can buy is:
Let the number of chips Marcus can buy = x
As he cannot spend more than $13 to buy chips so equation becomes:
[tex]1.30x\leq 13[/tex]
Solving this we get
[tex]x\leq 10[/tex]
Hence, Marcus can buy a maximum of 10 packs of chips and save $11.25
What is the nth term of the sequence -5,5,-5,5,-5...
Answer:
-5Step-by-step explanation:
-5,5,-5,5,-5,5,-5,5,-5
Find the distance between points P and Q represented on the coordinate plane. If P=2,2 and Q= 6,8
A. √ 145 B. √ 65 C. √ 97 D. √ 113
Answer:
sqrt(52)
Step-by-step explanation:
Given points P(2,2) and Q(6,8)
To find distance between points we apply distance formula
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
(x1,y1) is (2,2) and (x2,y2) is (6,8)
Plug in the values in the formula
[tex]D = \sqrt{(6-2)^2+(8-2)^2}[/tex]
[tex]D = \sqrt{16+36}[/tex]
[tex]D = \sqrt{52}[/tex]
Answer:
answer is B sqrt65
Step-by-step explanation:
Please help me! Thank you.
Answer:
J=PM/300
Step-by-step explanation:
300J/P=M
*p *P
300J=PM
300J/300=PM/300
J=PM/300
Answer:
J=MP/300
Step-by-step explanation:
M=300J/P
now take p to the left hand side of the equation
MP= 300J
MP/300 = J
J= PM/300
Which equation has the least steep graph? A. y = x + 6 B. y = -x - 9 C. y = 2x + 1 D. y = -7x - 2
Answer:
A and B.
Step-by-step explanation:
To get to know the graph with least slope, we have to write all equations in the form y=mx + c.
where m is the slope and c is the the y-intercept.
A. y = x + 6
For this equation m = 1
B. y = -x - 9
For equation B, m = -1
C. y = 2x + 1
In this equation, m = 2
D. y = -7x - 2
In equation D, m = -7
The equation with the highest slope is D while the one with the least slope/steep is A and B.
The cost of admission to the State Fair changed from $8.50 last year to $10.00 this year. Round to the nearest tenth. Show your work. (3 points)
a.) What is the percent of change from last year to this year?
b.) Is this a percent of increase or decrease?
c.) If you have a 25% off coupon to use on the $10.00 ticket, what is the cost of your ticket?
Answer:
Percent increase is 17.6%
We still have to pay 7.50 with the coupon
Step-by-step explanation:
Percent increase = (new- original)/original *100%
= (10-8.5)/8.5 * 100%
= 1.5/8.5 * 100%
= 17.6470588%
Round to the nearest tenth
17.6%
This is an increase since the cost went up.
If we have 25% off, we still have to pay (100%-25%) = 75%
10 *.75 = 7.50
We still have to pay 7.50 with the coupon
26=−8/5y What is y? HELP ME PLZ
Answer:
exact form=-65/4
decimal form=-16.25
Step-by-step explanation: solve for y by simplifying both sides of the equation, then isolating the variable
The solution of expression is,
⇒ y = - 16.25
We have to give that,
An expression to simplify is,
⇒ 26 = - 8/5y
Now, We can simplify the expression as,
⇒ 26 = - 8/5y
Multiply by 5 on both sides,
⇒ 26 × 5 = - 8y
⇒ 130 = - 8y
⇒ - 8y = 130
Divide both sides by - 8,
⇒ y = - 130/8
⇒ y = - 16.25
Hence, the Solution is, y = - 16.25
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the bike is on sale for $130. if the original price of the bike $200, what is the percent discount ?
I definitely need a little help with this.
Answer:
It is given that,
there are 8 balls in the bag numbered 1 to 8
Only one ball color is gray and all others are white
P(X) = probability of getting white ball
P(not X) = Probability of getting gray ball
a) To find Probabilities P(X) and P(not X)
For event X, 1,3,4,5,6,7,8 are checked and P(X) = 7/8
for event 'not X' only 2 is checked and P(not X ) = 1/8
b) To find 1 - P(X)
1 - P(X) = 1 - 7/8 = (8 - 7)/8 = 1/8
c)1 - P(X) is same as P(not X)
On the first day 60% of the 300 tickets were sold how many tickets were sold the day
Answer:
180
Step-by-step explanation:
60% of 300 tickets equals?
(60/100) * 300 = x
0,6 * 300 = x
180 = x
Answer:
180 tickets
Step-by-step explanation:
We want to find 60 percent of 300
Change 60 percent to a decimal
60% = .6
.6 * 300 = 180
Draw an array to represent the problem 3x9
Answer:
27
Step-by-step explanation:
draw 3 groups of 9 somethings or 9 groups of 3 somethings
In the 3x9 array representation there are 3 rows and 9 columns, each initialized with the value 0
Since we know that,
A set of components of the same data type are stored collectively in contiguous memory regions in an array, which is a form of data structure. To organise data sets in a way that is simple to sort and search, computer programmers employ arrays in their programmes. They can make a programme operate more quickly and are more effective at storing data than individual variables.
Sure, here's a simple array that represents a 3x9 grid:
[tex]\left[\begin{array}{ccccccccc}0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\\0&0&0&0&0&0&0&0&0\end{array}\right][/tex]
In this array, there are 3 rows and 9 columns, each initialized with the value 0.
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84% of Astrid's books are fiction. What fraction of Astrid's books are fiction?
Answer:
[tex]\frac{21}{25}[/tex]
Step-by-step explanation:
If 84% are fiction, then the fraction of these are simply the percentage over 100:
[tex]\frac{84}{100}[/tex]
Simplified down by dividing by 4:
[tex]\frac{21}{25}[/tex]
Final answer:
To convert 84% to a fraction, divide 84 and 100 by their greatest common divisor, which is 4, resulting in the simplified fraction 21/25 representing the part of Astrid's books that are fiction.
Explanation:
To convert the percentage of Astrid's books that are fiction into a fraction, we simply write the percentage as a ratio out of 100 and then simplify it. Since 84% of her books are fiction, we start with the fraction 84/100. This fraction can be simplified by dividing both the numerator and the denominator by the greatest common divisor, which is 4 in this case.
84 ÷4 = 21
100 ÷ 4 = 25
Therefore, the simplified fraction of Astrid's books that are fiction is 21/25.
Write 2x^2+12x+3=0 in vertex form?
Answer:
y = 2x^2+12x+3 = 2(x + 3)^2 - 15
Step-by-step explanation:
Take 2 as a common factor out of the first 2 terms2(x^2 + 6x) + 3 = 0Add half 6 squared inside the brackets. Subtract the same number outside the brackets when multiplied by 22(x^2 + 6x + 3^2) + 3 - 2*3^2 = 0Combine the two terms on the end.2(x^2 + 6x + 9) + 3 - 2*9 = 02(x^2 + 6x + 9) + 3 - 18 = 02(x^2 + 6x + 9) - 15 = 0Express the terms inside the brackets as a perfect square2(x + 3)^2 - 15 = 0Discussion Graph
Technically, the vertex form would y = 2(x + 3)^2 - 15. It needs to be more general than equated to zero. I have solved it the way you presented it and graphed it by definition.
The red graph is y = 2x^2 + 12x + 3The blue graph is y = 2(x + 3)^2 - 15Notice they have the same critical point which means they are equivalent
simplify the expression:
(-2-2i)(-4+6i)
Answer: (-2-2i)(-4+6i) = 20 - 4i
Step-by-step explanation:
We have the expression:
(-2 - 2i)*(-4 + 6i)
the rule we need to know here is that i*i = -1
now, the first step is distribute the parentheses.
(-2 - 2i)*(-4 + 6i) = -2*-4 -2*6i - 2i*-4 - 2i*6i = 8 -12i + 8i -12*(i*i)
= 8 + (8 - 12)i +12 = 20 - 4i
least common multiple 84 , 36, and 15
Answer:
1260
Step-by-step explanation:
The least common multiple is the smallest positive number which is a multiple of the two. This means 84, 36, and 15 divide into it evenly. To find the multiple:
We list the prime factors of each number.We note how many times each occurs.We multiply each factor the greatest number of times it occurs in a number.84: 2*2*3*7
36: 2*2*3*3
15: 3*5
LCM: 2*2*3*3*5*7= 1260
in one u.s. city, the taxi cost is $3 plus $0.50 per mile. if you are traveling from the airport, there is an additional charge of $4.00 for tolls. how far can you travel from the airport by taxi for $19.50?
Answer:
You can travel 25 miles
Step-by-step explanation:
19.50-4.00=15.5
15.5-3=12.5
12.5÷0.5=25
Someone who can help would be great.
Answer:
x=5
Step-by-step explanation:
In a square, the diagonals are equal.
4x+17 = 12x-23
Subtract 4x from each side.
4x-4x+17 = 12x-4x-23
17 = 8x-23
Add 23 to each side
17+23 = 8x-23+23
40 = 8x
Divide each side by 8
40/8 = 8x/8
5 =x
What is the equation of the line in this graph?
The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the y-intercept (0, -3) → b = -3
Chose two points: (6, 1) and (0, -3). Substitute:
[tex]m=\dfrac{-3-1}{0-6}=\dfrac{-4}{-6}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]
Answer: [tex]\boxed{y=\dfrac{2}{3}x-3}[/tex]
Why is the converse of the Pythagorean Theorem equally as important as the Pythagorean Theorem?
Answer:
They're equally as important because they are the same thing, but just meant for finding different sides.
Step-by-step explanation: