For this case we have the following functions:
[tex]f (x) = 4x ^ 2 + 1\\g (x) = x ^ 2-5[/tex]
We must find[tex](f-g) (x):[/tex]
By definition of operations with functions we have:
[tex](f-g) (x) = f (x) -g (x)[/tex]
So:
[tex](f-g) (x) = f (x) -g (x) = 4x ^ 2 + 1- (x ^ 2-5) = 4x ^ 2 + 1-x ^ 2 + 5 = 3x ^ 2 + 6[/tex]
Answer:
Option A
[tex]3x ^ 2 + 6[/tex]
what is the multiplicitive inverse of 3?
Answer:
1/3
Step-by-step explanation:
Multiplicative inverse means we want to end up with 1
3 * what = 1
Divide each side by 3
3* what /3 = 1/3
what = 1/3
The multiplicative inverse of 3 is 1/3
Answer:
1/3
Step-by-step explanation:
The mult. inverse of 3 is 1/3.
I’m trying to round the divisor to the nearest whole number
198,200 divided by 4.033
The divisor is 4.033 because it divides 198,200. Rounded to the nearest whole number, it is 4 because 0 is less than 5, so the next highest (whole) place is unchanged.
For this case we have a division where:
198,200 is the dividend4,033 is the divisorIf we want to round the divisor to the nearest whole number we have:
4.033 is equivalent to 4, because:
3 is less than 5, then we have 4.03
3 is less than 5, so we have 4.0 equivalent to 4.
Answer:
The divisor remains as 4, rounded to the nearest whole number.
Irunt
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each
notebook costs $3. Which of the following graphs represents the possible
combinations of pens and notebooks that she may purchase?
To find the possible combinations of pens and notebooks Amanda can purchase, we need to consider her budget and the cost of each pen and notebook. The correct graph representing these combinations is Graph B.
Explanation:To find the possible combinations of pens and notebooks that Amanda can purchase, we need to consider her budget and the cost of each pen and notebook.
Each pen costs $2 and each notebook costs $3.
Let's assume Amanda buys x number of pens and y number of notebooks.
So, the total cost of pens would be 2x and the total cost of notebooks would be 3y.
Given that Amanda has $30 to spend, we can set up the equation: 2x + 3y = 30.
To graph this equation, we can plot different points that satisfy this equation.
The graph that represents the possible combinations of pens and notebooks Amanda can purchase would be a line passing through points where the x-coordinate represents the number of pens and the y-coordinate represents the number of notebooks.
Answer: The correct graph is Graph B.
Amanda allocates $30 for pens and notebooks. Each pen costs $2, and each notebook is $3. The inequality 2P + 3N ≤ 30 is solved algebraically (P ≤ 15, N ≤ 10) and graphically, considering whole numbers for precision.
Amanda is limited to spending $30 on pens and notebooks. With each pen costing $2 and each notebook priced at $3, the total cost equation is C = 2P + 3N. The corresponding inequality is 2P + 3N ≤ 30.
Algebraically, solving for P and N involves finding values when N = 0 and when P = 0.
When N = 0:
2P ≤ 30
P ≤ 15
When P = 0:
3N ≤ 30
N ≤ 10
So, the solution is P ≤ 15 and N ≤ 10.
For a graphical representation:
Draw a coordinate plane.
Plot the points (15, 0) and (0, 10).
Shade the region below and to the left of the line formed by connecting these points.
The question probable may be:
Amanda only has $30 to buy pens and notebooks. Each pen costs $2. Each notebook costs $3. write inequality showing the relationship and solve them also solve them graphically.
Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the points used to determine the slope and how the equation was determined.
Answer:
[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]
Step-by-step explanation:
You only need two points on a line to find the equation for that line.
We are going to use 2 points that cross that line or at least come close to. You don't have to use the green points... just any point on the line will work. You might have to approximate a little.
I see ~(67.5,67.5) and ~(64,65).
Now once you have your points, we need to find the slope.
You may use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] are points on the line.
Or you can line up the points vertically and subtract then put 2nd difference over 1st difference.
Like this:
( 64 , 65 )
-( 67.5, 67.5 )
--------------------
-3.5 -2.5
So the slope is -2.5/-3.5=2.5/3.5=25/35=5/7.
Now use point-slope form to find the equation:
[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line.
[tex]y-65=\frac{5}{7}(x-64)[/tex]
Distribute:
[tex]y-65=\frac{5}{7}x-\frac{5}{7}\cdot 64[/tex]
Simplify:
[tex]y-65=\frac{5}{7}x-\frac{320}{7}[/tex]
Add 65 on both sides:
[tex]y=\frac{5}{7}x-\frac{320}{7}+65[/tex]
Simplify:
[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]
CHECK ALL THAT APPLY
She did not find the correct vertex; it should be at (8, 5).
She used the wrong area formula; it should be A=1/2 b * h.
She used the wrong length for the base; it should be 7, like the given base.
She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3.
She should have found a segment for the top that was not parallel to the bottom.
Answer:
* The error she made:
# She did not find the correct vertex; it should be at (8, 5)
# She used the wrong length for the base; it should be 7, like the given base
# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3
Step-by-step explanation:
* Lets explain how to solve the problem
- She has three vertices of the parallelogram
- The vertices are (12 , 2) , (5 , 2) , (1 , 5)
∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates
∴ The length of the base of the parallelogram is 12 - 5 = 7 units
- In parallelogram each two opposite sides are equal and parallel
∴ The opposite side to the base is 7
∴ The x coordinate of the missing point equal the x-coordinate of the
point (1 , 5) + the length of the base
∴ The x coordinate of the missing vertex = 1 + 7 = 8
∵ The y-coordinate of the missing vertex is the same with the
y-coordinate of the point (1 , 5)
∴ The y-coordinate of the missing vertex is 5
∴ The missing vertex is (8 , 5)
- The area of the parallelogram is A = bh, where b is the base of it
and h is the height of this base
- Remember the height must be perpendicular on the base
∵ The perpendicular distance between the two parallel bases is the
difference between the y-coordinates of the two points each one
belong to one of the two parallel bases
∴ The height of the parallelogram = 5 - 2 = 3 units
∴ Its area = 7 + 3 = 21 units ²
* The error she made:
# She did not find the correct vertex; it should be at (8, 5)
# She used the wrong length for the base; it should be 7, like the
given base
# She used a side length of the parallelogram for the height instead
of a line segment perpendicular to the base; the height should be 3
Write the equation of a function whose parent function, f(x) = x + 6, is shifted 4 units to the right.
g(x) = x − 10
g(x) = x − 4
g(x) = x + 2
g(x) = x + 10
Answer:
g(x) = x + 2 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise the translation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
* Lets solve the problem
∵ The parent function f(x) = x + 6
∵ f(x) is shifted four units to the right
- The translation of a function by h units to the right change the x in
the function by subtracting h from it
∴ The x in f(x) will change to (x - 4)
∴ The new function = (x - 4) + 6
- Simplify the function
∴ The new function = x + 2
∵ The new function is g(x)
∴ g(x) = x + 2
Answer:
Step 3
Step-by-step explanation:
Which of the following are not affected by the others outcomes?
compound evention
independent events
overlapping events
dependent events
Answer:
The Answer is Indepentant.
Step-by-step explanation:
The reason that the answer is Indepentant is that you don't rely on the other thing. Like you have a bag of marbles. You pick one and you put it back. You haven't changed anything. You put the marble back and restored the marble.
Plz, pick me as Brainly!
Independent events are not afftected by the others outcomes.
What are independent events ?If outcomes of an event doesn't affect the outcomes of other event, the events are called independent events, i.e. they are independent to each other.
Example : "Rolling dice" and "getting good marks in exam" are independent events, because the outcomes of "rolling dice" doesn't affect the outcome of the event "getting good marks in exam".
What is the correct answer ?By seeing the definition & description of independent events given above, we can say that,
One of the independent events can not affected by the another one. Each independent event's outcomes are independent too.
So,the independent events are not affected by the others outcomes.
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If C(t) = 180 + 10t represents ISP A and C(t) =
25t represents ISP B, how long would the service
contracts need to be for the total costs to be the same?
Answer:
12
Step-by-step explanation:
You want the costs to be the same so set them equal.
180+10t=25t
Subtract 10t on both sides:
180. =15t
Divide both sides by 15:
180/15. =t
12. =t
So t=12 would give us the costs being the same.
Answer:
After 12 months, the service contracts will cost the same.Step-by-step explanation:
The given functions are
[tex]C(t)=180+10t\\C(t)=25t[/tex]
To answer the question, we just need to solve this system. We are gonna replace the second function into the first one,
[tex]C(t)=C(t)\\180+10t=25t\\15t=180\\t=\frac{180}{15}=12[/tex]
Therefore, after 12 months, the service contracts will cost the same.
The recipe for a batch of applesauce uses 2 1/2 pounds of apples. If Michael wants to make 3/4 of a batch of applesauce, how many pounds of applesauce will he need
Answer:
15/8
Step-by-step explanation:
for 1 batch=5/2 pounds
for 3/4 batch=[5/2]×(3/4)
Answer: Michael will need 15/8 pounds of apples.
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the amount of apples that a batch of applesauce needs (2 1/2) by the number of batches of applesauce that Michael wants to make (3/4).
Mathematically speaking;
2 1/2 x 3/4 = ([2x2+1] / 2 ) x 3/4 = 5/2 x 3/4 = (5x3) / (2x4) = 15/8
He will need 15/8 pounds of apples.
Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, −4b), and Z(−2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of WZ
Answer:
-a,2b
Step-by-step explanation:
here is your answer
Answer:
Option C
Step-by-step explanation:
In this question coordinates of rhombus WXYZ are given as W(0, 4b), X(2a, 0), Y(0, −4b), and Z(−2a, 0).
Now we have to find the coordinates of midpoint of WZ as part of the proof.
Since mid point of two points (x, y) and (x', y') is represented by
[tex](\frac{x+x'}{2}[/tex] [tex]\frac{y+y'}{2})[/tex]
For midpoint of WZ,
[tex](\frac{0-2a}{2}[/tex] [tex]\frac{4b+0}{2})[/tex]
= (-a, 2b)
Option C will be the answer.
A music teacher charged $80.25 for 2 1/2hours. What was the hourly fee to the nearest cent?
(SHOW WORK)
Answer:
The hourly fee charged by the teacher was $32.10.
Step-by-step explanation:
A music teacher charged for [tex]2\frac{1}{2}[/tex] hour = $80.25
To calculate the hourly fee of the teacher, we have to divide 80.25 by 2.5
Therefore, hourly fee of the teacher [tex]=\frac{80.25}{2.5}[/tex]
= $32.10
The hourly fee charged by the teacher was $32.10.
Let f(x)=x^2+3 and g(x)= x+2/x . Find(fog)(2).
[tex]\bf \begin{cases} f(x)=&x^2+3\\\\ g(x)=&\cfrac{x+2}{x}\\\\ (f\circ g)(x)=&f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(2)=\cfrac{(2)+2}{(2)}\implies g(2)=\cfrac{4}{2}\implies g(2)=\boxed{2} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{x=2}{f(~~g(2)~~)}=\left( \boxed{2} \right)^2+3\implies f(~~g(2)~~)=4+3\implies \stackrel{(f\circ g)(2)}{f(~~g(2)~~)}=7[/tex]
insert parentheses to make the equality a true statement.
12+3*8-8÷4=16
Answer:
12+[(3*8-8)÷4]=16
Step-by-step explanation:
The given expression is:
12+3*8-8÷4=16
Now to insert parenthesis in this statement to make it equality statement we will follow the rule of BODMAS:
BODMAS stands for Bracket, Of, Division,Multiplication,Addition, Subtraction.
It explains the order of expression to solve an expression. If an expression contains (), {}, [], we have to solve or simplify the brackets first and then division, multiplication,addition and subtraction from left to right.
Now take an example of the given statement and place parenthesis:
12+3*8-8÷4=16
12+[(3*8-8)÷4]=16
According to BODMAS rule simplify the terms inside () completely and then [ ].
12+[(24-8)÷4]=16
12+[16÷4]=16
When we divide 16 by 4, it gives the answer 4.
12+ 4 =16
16 = 16
Hence we have made the statement true by inserting parenthesis in order. 12+[(3*8-8)÷4]=16 ....
What is the solution to this equation?
X- 12 = 9
Answer:
X = 21
Step-by-step explanation:
X- 12 = 9
Add 12 to each side
X- 12+12 = 9+12
X = 21
What conic section is produced when both nappes of a right circular cone are
intersected by a plane that does not pass through the vertex of the cone?
A. Hyperbola
B. Parabola
C. Circle
D.Eclipse
Please help now !!!
Answer:
Option a) Hyperbola
Step-by-step explanation:
Conic sections are generated by intersection of plane with a cone.Various types of conic sections are obtained when a plane intersect with cone in different manners.Different possible conic sections are parabola, ellipse, hyperbola, circle.If a plane intersect cone in such a way that plane passes through both the nappes of the cone and does not pass through the vertex of the cone.If this plane is parallel to y-axis then, the resultant conic section is hyperbola.Thus, option a) is the correct answer.value of y when 10= 2y+4
Answer:
y=3
Step-by-step explanation:
Lets make y the subject of the equation by bringing the like terms together through mathematical operations.
10=2y+4
2y=10-4
2y=6
y=3
What is the slope of the line?
-2
-1/2
1/2
2
Answer:
[tex]\large\boxed{m=-\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph we have the points (2, 3) and (4, 2). Substitute:
[tex]m=\dfrac{2-3}{4-2}=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]
Other method.
Look at the picture.
[tex]m=\dfrac{\Delta y}{\Delta x}[/tex]
[tex]\Delta y=-1\\\\\Delta x=2[/tex]
Substitute:
[tex]m=\dfrac{-1}{2}=-\dfrac{1}{2}[/tex]
The coordinates of the preimage are: A(8,8) B(10,6) C(2,2) We want to reflect over y=−1 first. Our new coordinates are: A′(8, ) B′(10, ) C′(2, ) Now we will reflect over y=−7 and our new coordinates will be: A′′(8, ) B′′(10, ) C′′(2, ) We can also see that −7−(−1)=−6. We know that two reflections is the same as a translation of 2h units. So 2(−6) is a translation of −12 units down.
Answer:
1)A'(8,-10), B'(10,-8), C'(2,-4)
2)A''(8,-4), B''(10,-6), C''(2,-10
Step-by-step explanation:
Given:
Points A(8,8) B(10,6) C(2,2)
reflection over y=-1
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3
after reflections, the perpendicular distance will be 18,14,6 and the points will be at
A'(8,-10), B'(10,-8), C'(2,-4)
Now
Points A(8,-10), B(10,-8), C(2,-4)
reflection over y=−7
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3
after reflections, the perpendicular distance will be 6,2,6 and the points will be at
A''(8,-4), B''(10,-6), C''(2,-10) !
Evaluate 3(x-1)+1 when x=5
3(5-1)+1
(15-3)+1
12+1
13
[tex]\huge{\boxed{13}}[/tex]
Substitute. [tex]3(5-1)+1[/tex]
Subtract. [tex]3*4+1[/tex]
Multiply. [tex]12+1[/tex]
Add. [tex]\boxed{13}[/tex]
What are the solutions of 3x^2 - x+ 7 =0
[tex]3x^2 - x+ 7 =0\\\Delta=(-1)^2-4\cdot3\cdot7=1-84=-83\\x\in\emptyset[/tex]
no real solutions
The product of seven and a number is negative 21. Find the number
Answer:
-3
Step-by-step explanation:
Let n be the number
product of seven and a number
7n
is negative 21
7n = -21
Divide each side by 7
7n/7 = -21/7
n = -3
The number is -3
a cuboid with a volume of 924 cm3 has dimensions 4cm (x+1)cm and (x+11)cm. show clearly that x^2 +12x-220=0. show the equation by factorisation. State both values of x. and finally find the dimensions of the cubiod.
Answer:
4cm, 11cm, 21cm
Step-by-step explanation:
4(x + 1)(x + 11)
4(x ^ 2 + 12x + 44)
x ^ 2 + 12x + 11 = 231
x ^ 2 + 12x + 11 - 231 = 0
x ^ 2 + 12x - 220 = 0
(x - 10)(x + 22) = 0
x = 10 and x = - 22
4cm , 11cm , 21cm
Both values of x are 10 and -22
The dimension of the cuboid is 4cm by 11cm by 21cm
The formula for calculating the volume of a cuboid is expressed as:
Volume of a cuboid = Length * Width * Height
Given the following parameters
Length = 4 cm
Width = (x+1) cm
Height = (x+11) cm
Volume = 924cm³
Substitute into the formula as shown:
924 = 4(x+1)(x+11)
Factorize
924 = 4(x²+11x + x + 11)
924/4 = x²+12x+11
231 = x²+12x+11
Swap
x²+12x+11 = 231
x²+12x = 231 - 11
x²+12x = 220
x²+12x - 220 = 0 (Proved)
On factorizing
x²+12x - 220 = 0
x²+22x-10x - 220 = 0
x(x+22)-10(x+22) = 0
(x-10)(x+22) = 0
x = 10 and -22
Hence both values of x are 10 and -22
Get the dimensions
Length = 4cm
Width = x+ 1 = 10 + 1 = 11cm
Height = x+11 = 10 + 11 = 21cm
Hence the dimension of the cuboid is 4cm by 11cm by 21cm
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Which expression is equivalent to
(2^3)^-5
(2^3)^5
=2^(3*5)
= 2^15
hope it helps
Answer:
A
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] and
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex](2^3)^{-5}[/tex]
= [tex]2^{3(-5)}[/tex] = [tex]2^{-15}[/tex] = [tex]\frac{1}{2^{15} }[/tex]
A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of
a new solution that will contain 25% salt. How much of each of the original
solutions should the chemist use?
Let [tex]x[/tex] be the amount (in L) of the 40% solution to be used, and [tex]y[/tex] the amount (L) of the 20% solution. The chemist wants a new solution of 50 L, so that
[tex]x+y=50[/tex]
Each L of the 40% solution contributes 0.4 L of salt, while each L of the 20% solution contributes 0.2. The new solution should have a concentration of 25% salt, so that
[tex]0.4x+0.2y=0.25(x+y)=12.5[/tex]
Now
[tex]x+y=50\implies y=50-x[/tex]
[tex]0.4x+0.2y=12.5\implies0.4x+0.2(50-x)=12.5\implies0.2x=2.5[/tex]
[tex]\implies\boxed{x=12.5}\implies\boxed{y=37.5}[/tex]
To make a 50 L solution containing 25% salt, the chemist should use 25 L of the 40% salt solution and 0 L of the 20% salt solution.
Explanation:To solve this problem, we can use the method of mixing solutions. Let x represent the amount of the 40% salt solution used, and 50-x represent the amount of the 20% salt solution used. The amount of salt in the 40% solution is 0.4x, and the amount of salt in the 20% solution is 0.2(50-x). Since the new solution will contain 25% salt, the amount of salt in the new solution is 0.25(50). Setting up an equation, we have:
Simplifying the equation, we get:
The chemist should use 25 L of the 40% salt solution and 25 - 25 = 0 L of the 20% salt solution to make 50 L of the new solution containing 25% salt.
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please help asap !!!!find f(-2) for f(x)=2*3^x
Answer:
2/9
Step-by-step explanation:
f(x)=2*3^x
Let x=-2
f(-2) = 2 * 3^(-2)
When the exponent is negative, it flips from the numerator to the denominator
= 2 * 1/(3^2)
= 2 * 1/9
= 2/9
Answer:
It's 2/9.
Step-by-step explanation:
Replace to x by -2.
y = 2 * 3^(-2)
= 2 / 3^2
= 2/9.
Ari is designing a patio that will be 20 feet long and 16 feet wide. He makes a scale drawing of the patio using a scale of 1 inch to 4 feet.
The ratio of the area of the scaled drawing to the actual area of the patio is 1 square inch to
square feet.
Answer:
1 square inch to 16 square feet
Step-by-step explanation:
The real patio area is
[tex]20\cdot 16=320\ ft^2[/tex]
The dimensions of the scale drawing are
[tex]20:4=5\ in\text{ and }16:4=4\ in,[/tex]
so the area of the scale patio is
[tex]5\cdot 4=20\ in^2[/tex]
The ratio of the area of the scaled drawing to the actual area of the patio is
[tex]20:320=1:16[/tex]
or 1 square inch to 16 square feet.
Answer:
I hope this helps
Step-by-step explanation:
A certain field has 3 mice. in five months, you now have 18 mice. if the population grows exponentially, how many mice will be in the field after 1 year?
The number of mice in the field after 1 year is 221 mice.
Given data:
If the population of mice in the field grows exponentially, we can use the exponential growth formula to determine the future population.
The exponential growth formula is given by:
P(t) = P₀ * e^(kt)
Where:
P(t) is the population at time t,
P₀ is the initial population,
e is Euler's number (approximately 2.71828), and
k is the growth rate.
So, the initial population (P₀) is 3 mice, and after five months, the population (P(t)) is 18 mice.
18 = 3 * e^(5k)
Dividing both sides by 3, we get:
6 = e^(5k)
To solve for k, we can take the natural logarithm (ln) of both sides:
ln(6) = 5k
k = ln(6) / 5 ≈ 0.35835
So, the growth rate is k = 0.3583
Now that we have the growth rate, determine the population after 1 year (12 months).
Substituting the values into the formula:
P(12) = 3 * e^(0.35835 * 12)
Calculating this expression, we find:
P(12) ≈ 3 * e^(4.3) ≈ 3 * 73.699 ≈ 221.09
Hence, it is expected that there will be approximately 221 mice in the field after 1 year if the population grows exponentially.
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Final Answer:
After 1 year, the field is expected to have approximately 221 mice.
Explanation:
To solve this exponential growth problem, we'll use the exponential growth formula:
[tex]\[ P(t) = P_0 \times e^{rt} \][/tex]
where:
- [tex]\( P(t) \)[/tex] is the population at time t,
- [tex]\( P_0 \)[/tex] is the initial population size,
- r is the growth rate,
- e is Euler's number (approximately 2.71828),
- t is the time in consistent units.
We need to find the growth rate r using the information that we have (the initial population [tex]\( P_0 \)[/tex] is 3, and after 5 months,[tex]\( P(5) \)[/tex] is 18). Then, we'll calculate the population after 1 year (12 months).
Let's apply the given values to the formula at t = 5 months:
[tex]\[ 18 = 3 \times e^{5r} \][/tex]
Now we need to solve for r. We start by dividing both sides of the equation by 3:
[tex]\[ 6 = e^{5r} \][/tex]
Next, we take the natural logarithm (ln) of both sides to solve for r. The natural logarithm of [tex]\( e^{5r} \)[/tex] is equal to 5r:
[tex]\[ \ln(6) = 5r \][/tex]
Now we divide by 5:
[tex]\[ \frac{\ln(6)}{5} = r \][/tex]
We can use a calculator to find r. The natural logarithm of 6 is approximately 1.79176, so:
[tex]\[ r = \frac{1.79176}{5} \\\\\[ r \approx 0.358352 \][/tex]
Now that we have the monthly growth rate r, we can use it to find the population after 12 months. Plugging r, [tex]\( P_0 \)[/tex], and t = 12 months into the exponential growth formula, we get:
[tex]\[ P(12) = 3 \times e^{0.358352 \times 12} \][/tex]
Using a calculator, we compute the value of [tex]\( e^{0.358352 \times 12} \)[/tex], which is approximately [tex]\( e^{4.300224} \)[/tex].
[tex]\[ P(12) = 3 \times e^{4.300224} \][/tex]
Using a calculator to find [tex]\( e^{4.300224} \)[/tex], we get a value of approximately 73.699.
[tex]\[ P(12) = 3 \times 73.699 \\\\\[ P(12) \approx 221.097 \][/tex]
Since we can't have a fraction of a mouse, we would round to the nearest whole number.
Thus, after 1 year, the field is expected to have approximately 221 mice.
Natalia is writing a recursiye formula to represent the
sequence
8. 12, 18, 27,
What value should she use as the common ratio in the
formula? Write the answer as a decimal rounded to the
tenths place.
Mark this and return
Save and Exit
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11:13 PM
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Answer:
1.5
Step-by-step explanation:
As the common difference is not same for all terms, the given sequence is a geometric sequence
the standard formula for a geometric sequence is:
[tex]a_n=a_1r^{n-1}[/tex]
The formula to calculate common ratio is:
[tex]r = \frac{a_n}{a_{n-1}}[/tex]
Dividing the term by previous term
So,
r = 12/8 = 18/12 = 27/18 = 1.5
The value for common ratio will be:
1.5 ..
Answer:
3/2
Step-by-step explanation:
3/2 is the value
At a party, there are 8 small tables with 4 chairs at each table. Which expression can be used to find the number of chairs there are at the party?
8 + 4
8 – 4
8 × 4
8 ÷ 4
Using the piling method, which of the following can be constructed from polygons alone and discs alone
Check all that a
Options:
A-Cube
B-Cone (not including a vertex)
C-Pyramid(including a vertex)
D-Prism
E-Cone(including a vertex)
F-Cylinder
Answers: A: cube D: prism B: cone (not including the vertex) F : Cylinder
CORRECT ANSWER!!!!!!
Using the piling method, polygons alone can be used to construct a cube, pyramid, and prism. Discs alone can be used to construct a cylinder.
Explanation:The piling method involves stacking two-dimensional shapes to create three-dimensional solids. Using this method, the following can be constructed:
A-Cube: A cube can be constructed using polygons alone. It is made up of six equal square faces.C-Pyramid (including a vertex): A pyramid can be constructed using polygons alone. It has a polygonal base and triangular sides that converge to a common vertex.D-Prism: A prism can be constructed using polygons alone. It has two congruent polygonal bases and rectangular or parallelogram-shaped lateral faces.F-Cylinder: A cylinder can be constructed using discs alone. It has two congruent circular bases and a curved lateral surface.