A colony of bacteria that starts with 1 bacterium and doubles in number every half hour will contain approximately 281,474,976,710,656 bacteria at the end of 24 hours.
Explanation:The number of bacteria in a colony that starts with 1 bacterium and doubles in number every half hour can be calculated using the formula 2ⁿ, where n is the number of generations. Since each generation is half an hour, there are 48 generations in 24 hours. Plugging in n=48 into the formula, we get 2⁴⁸, which is approximately 281,474,976,710,656 bacteria.
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A) side-side-side triangle similarity postulate
B) angle-angle triangle similarity postulate
C) angle-side-angle triangle similarity postulate
D) hypotenuse-lag triangle similarity postulate
let n be the first 3 of consecutive even integers. what is the sum of those integers?
traveling at 65 miles per hour how many minutes rounded to the nearest whole number does it takes to drive 125 miles from san digit to malibu
divide total miles by speed
125/65 = 1.923 hours
there are 60 minutes per hour
multiply 1.923*60 = 115.384 minutes
rounded off to nearest whole number = 115 minutes
Given the following triangle side lengths, identify the triangle as acute, right or obtuse. Show your work.
a. 3in, 4in, 5 in
b. 5in, 6in, 7in
c. 8in, 9in, 12in
From the information, A is a right angle, B is an acute triangle and C is an acute angle.
How to solve the triangleIt will be a right triangle if a² + b² = c². It will be аcute if a² + b² > c² and it'll be obtuse if a² + b² < c².
For the first one,
a² + b² = 3² + 4² = 9 + 16 = 25 and c² = 5² = 25
25 = 25
This is a right triangle.
For the second one,
a² + b² = 5² + 6²
= 25 + 36 = 61
c² = 7² = 49
61 > 49 = аcute triangle.
For the third one,
a² + b² = 8² + 9²
= 64 + 81 = 145
c² = 12² = 144
145 > 144 = аcute triangle.
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(07.05 MC)
An equation is shown below:
4x + 2(x – 3) = 4x + 2x – 11
Part A: Solve the equation and write the number of solutions. Show all the steps. (6 points)
Part B: Name one property you used to solve this equation. (4 points
Answer:
-6 = -11
Distributive Property
Step-by-step explanation:
A.
4x + 2(x – 3) = 4x + 2x – 11
4x + 2x - 6 = 4x + 2x - 11
6x - 6 = 6x - 11
-6 = -11
since -6 is not equal to -11, so there's no solution
B. Distributive property
SOMEBODY HELP ME WITH THESE PLEASE! I really need the help like NOW PLS!
Answer:
97.
For finding f(g(x)) we will plugin value of g(x) in place of x in f(x).
99.
Step-by-step explanation:
this the picture for my question
The sum of four consecutive whole numbers is 54, what are the four numbers
what is the period of the sinusoid given by y=-4sin( [tex] \frac{2π}{3} [/tex] x) ?
Answer:
The answer is 3 for A P E X
Step-by-step explanation:
What are the roots of the function y = 4x2 + 2x – 30? To find the roots of the function, set y = 0. The equation is 0 = 4x2 + 2x – 30.
Factor out the GCF of .
Next, factor the trinomial completely. The equation becomes .
Use the zero product property and set each factor equal to zero and solve. The roots of the function are .
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
Roots of a quadratic equationThe given quadratic equation is:
[tex]y=4x^2+2x-30[/tex]
Set y = 0
[tex]4x^2+2x-30=0[/tex]
Factor the trinomial completely
[tex]4x^2-10x+12x-30=0\\\\2x(2x-5)+6(2x-5)=0\\\\(2x-5)(2x+6)=0[/tex]
Set each factor to zero and solve
2x - 5 = 0
2x = 5
x = 5/2
2x + 6 = 0
2x = -6
x = -6/2
x = -3
The roots of the equation [tex]y=4x^2+2x-30[/tex] are x = -3 and x = 5/2
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(Solve for r) 0.5r − 3.8 = 5.66
I don't get it I got a different answer then these
Can you square both sides of an inequality
Squaring both sides of an inequality can be valid if you know both sides are non-negative, but it can introduce extraneous solutions. Therefore, it's important to check any solutions against the original inequality to ensure their validity, especially in cases involving negative numbers or functions with restricted domains.
When you're working with inequalities, you have to be careful when performing operations like squaring both sides. Unlike equalities, where multiplication or division by the same number on both sides does not change equality, with inequalities, the effect can be more complex due to the direction of the inequality sign and the possibility of dealing with negative numbers.
For instance, squaring both sides of an inequality is not always a valid operation because if one or both sides of the inequality are negative, squaring could lead to incorrect results. When you square a negative number, it becomes positive, which could potentially reverse the inequality's direction. However, if you know that both sides of the inequality are non-negative, then squaring both sides is permissible. This concept is similar to solving quadratic constraints without introducing square roots, using identities like |(1 + ix)²|² = ([1 + ix|²)².
To avoid introducing solutions that were not there originally (extraneous solutions), it is important to check the solutions obtained after squaring against the original inequality. An example where squaring both sides might be questioned is when solving trigonometric inequalities, where a common mistake is to square both sides without considering the domain of the original function.
Line BC has an equation of a line y = 2x + 3, and line EF has an equation of a line y = negative one over 2 x + 4. These two equations represent
Answer:
Perpendicular lines.
Step-by-step explanation:
We have been given that line BC has an equation of a line [tex]y=2x+3[/tex] and line EF has an equation of a line [tex]y=-\frac{1}{2}x+4[/tex]. We are asked to determine what these both equations represent.
We know that slope of two perpendicular lines is negative reciprocal of each other. This means the product of slope of both lines is equal to [tex]-1[/tex].
Let us find the product of slopes of both lines.
[tex]2\times \frac{-1}{2}[/tex]
Upon cancelling 2 with 2 we will get,
[tex]=-1[/tex]
Therefore, the given two equations represent equations of two perpendicular lines.
The sum of two rational numbers will always be
How could the relationship of the data be classified?
scatter plot with points loosely scattered going down to the right
A positive correlation
A causation
A negative correlation
No correlation
Answer: A negative correlation
Step-by-step explanation:
If the points in the scatter plot scattered going down to the right, it shows that there are inverse relationship between the quantities.
With the increase of one quantity or variable there is decrease in the other quantity or variable.
Therefore, if in the scatter plot with points loosely scattered going down to the right , then the relationship of the data be classified as a negative correlation.
Use the given graph to determine the limit, if it exists. A
Find limit as x approaches three from the left of f of x..
A giraffe can run 40 meters per second what is its speed in miles per hour
Use complete sentences to describe the range of the sine function.
system of equations with different slopes and different y-intercepts have one solution.
A. Always
B. Sometimes
C. Never
I think it is A but I am not sure and it is impossible for system of equations with different slopes and different y-intercepts to be parallel or infinite.
(25 Points)Enter numbers to write 4.23×10^3 in standard notation.
Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.
Part A: Find (f + g)(x). Show your work. (3 points)
Part B: Find (f ⋅ g)(x). Show your work. (3 points)
Part C: Find f[g(x)]. Show your work. (4 points)
A line passes through (2, –1) and (8, 4).Write an equation for the line in point-slope form.
Rewrite the equation in standard form using integers.
Hello : let
A(2,-1) B(8,4)
the slope is : (YB - YA)/(XB -XA)
(4+1)/(8-2) = 5/6
Answer: Equation of line in point slope form,
[tex]y + 1 = 5 ( x - 2 )[/tex]
And, Equation of line in standard form,
[tex]5 x - 6 y = 16[/tex]
Step-by-step explanation:
Since, If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] ,
Then the equation of line,
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Here [tex]x_1 = 2[/tex], [tex]y_1=-1[/tex], [tex]x_2=8[/tex] and [tex]y_2=4[/tex]
Thus, the equation of the given line,
[tex]y-(-1)=\frac{4-(-1)}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{4+1}{8-2} (x-2)[/tex]
⇒ [tex]y+1=\frac{5}{6} (x-2)[/tex] -----(1)
⇒ [tex]6(y+1)= 5(x-2)[/tex]
⇒ 6 y + 6 = 5 x - 10
⇒ 6 = 5x - 6y - 10 ( By subtracting by on both sides )
⇒ 6 + 10 = 5x - 6y ( By adding 10 on both sides )
⇒ 16 = 5x - 6y
⇒ 5 x - 6 y = 16 ------(2)
Since, in slope for of a line is, [tex]y-y_1= m (x-x_1)[/tex]
Thus, equation (1) shows the in slope form of the line.
And, standard form of the line is ax + by = c where a, b and c are the integers.
Thus, equation (2) shows the standard form of the given line.
Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.
A video game club charges a fixed annual membership fee of $18 and $3 per video game rented. Let f(n) represent the total annual cost of renting n video games. Which of the following functions best represents the relationship between f(n) and n if the membership was increased by $20 the next year?
Answer:
The correct answer is f(n)=3n+38
Step-by-step explanation:
Put in y=mx+b form, so y= f(n), $3 is fee per video game rented and n is the number of video games rented, b is ($18 fixed fee for this year +$20 fee for next year). So, f(n)=3n+38.
Two 6-sided dice are rolled. what is the probability the sum of the two numbers on the die will be 4?
Answer:
[tex]\frac{1}{12}[/tex].
Step-by-step explanation:
Given : Two 6-sided dice are rolled.
To find : what is the probability the sum of the two numbers on the die will be 4.
Solution : We have given
Two 6-sided dice are rolled.
Dice have number { 1,2,3,4,5,6} { 1,2,3,4,5,6} .
[tex]Probability =\frac{outcome\ happn}{total\ outcome}[/tex].
sum of the two numbers on the die will be 4.
Case (1) : first dice rolled 3 and second dice rolled 1.
{3,1}
3 +1 = 4 .
Case (2) : first dice rolled 1 and second dice rolled 3 .
{1,3}
1 + 3 = 4 .
Case (3) : first dice rolled 2 and second dice rolled 2.
{2,2}
2 + 2 = 4.
Then there are 3 possible outcomes where the sum of the two dice is equal to 4.
The number of total possible outcomes = 36.
[tex]Probability =\frac{3}{36}[/tex].
[tex]Probability =\frac{1}{12}[/tex].
Probability of getting sum of two dice is [tex]\frac{1}{12}[/tex].
Therefore, [tex]\frac{1}{12}[/tex].
Write an equation for the line that is parallel to the given line and that passes through the given point.
y = 1/2 – 8; (–6, –17)
A.) y = 2x – 14
B.) y = 1/5x + 5/2
C.) y = -2x + 14
D.) y = 1/2x – 14
Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption, the volume of the flask is ____ cubic inches. If both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be _____ times the original volume.
options for the first blank are: 20.22, 35.08, 50.07, or 100.11
options for the second blank are: 2, 4, 6 or 8
The total volume of the flask will be 50.06 [tex]\rm inches ^3[/tex] and if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
Given :
Flask can be modeled as a combination of a sphere and a cylinder.
The volume of Sphere is given by the:
[tex]V_s = \dfrac{4}{3}\pi r^3[/tex]
Given - diameter of sphere = 4.5 inches. Therefore, radius is 2.25 inches.
Now, the volume of sphere of radius 2.25 inches will be:
[tex]V_s = \dfrac{4}{3}\times \pi\times (2.25)^3[/tex]
[tex]\rm V_s = 47.71\; inches^3[/tex]
The volume of Cylinder is given by the:
[tex]V_c = \pi r^2h[/tex]
Given - diameter of cylinder = 1 inches then radius is 0.5 inches and height is 3 inches.
Now, the volume of cylinder of radius 0.5 inches and height 3 inches will be:
[tex]V_c = \pi\times (0.5)^2 \times 3[/tex]
[tex]\rm V_c = 2.35\; inches^3[/tex]
Therefore the total volume of the flask will be = 47.71 + 2.35 = 50.06 [tex]\rm inches ^3[/tex].
Now, if both the sphere and the cylinder are dilated by a scale factor of 2 than:
Radius of sphere = [tex]2.25\times 2[/tex] = 4.5 inches
Radius of cylinder = [tex]0.5\times 2[/tex] = 1 inch
Height of cylinder = [tex]3\times 2[/tex] = 6 inches
Now, the volume of sphere when radius is 4.5 inches will be:
[tex]V_s' = \dfrac{4}{3}\times \pi \times (4.5)^3[/tex]
[tex]\rm V_s' = 381.70\; inches ^3[/tex]
And the volume of cylinder when radius is 1 inch and height is 6 inches will be:
[tex]V_c' = \pi \times (1)^2\times 6[/tex]
[tex]\rm V_c'=18.85\;inches^3[/tex]
Therefore the total volume of the flask after dilation by a scale factor of 2 will be = 381.70 + 18.85 = 400.55 [tex]\rm inches ^3[/tex].
Now, divide volume with dilation by theorginal volume of the flask.
[tex]\dfrac{400.55}{50.06}=8[/tex]
Therefore, if both the sphere and the cylinder are dilated by a scale factor of 2, the resulting volume would be '8' times the original volume.
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A rectangular garden has length twice as great as its width. A second rectangular garden has the same width as the first garden and length that is 4 meters greater than the length of the first garden. The second garden has area of 70 square meters. What is the width of the two gardens?
What is the equation of the line that passes through the point of intersection of the lines y = 2x − 5 and y = −x + 1, and is also parallel to the line y=1/2x+4?