Answer:
(a) The relative rate of growth is 0.2
(b) The initial population is 985
(c) The amount of bacteria at time t = 5 is 2677.5
Explanation:
An exponential equation to model exponential growth is:
[tex]G(t)=Ie^{rt}[/tex]Where:
• I is the initial population
,• r is the rate of relative growth
,• t is the time
We have in this problem:
[tex]n(t)=985e^{0.2t}[/tex]Then:
(a) The relative rate is 0.2
(b) The initial population is 985
(c) To find the population at t = 5, we evaluate the equation:
[tex]n(5)=985e^{0.2\cdot5}=985e^1=985e\approx2677.5[/tex]
Can you help me with this test I got I can give you all the info you need.
Given data:
The given radius is JK=JM=3.
The given length is LM=2.
The tangent is always perpendicular to the radius, the expression for the Pythagoras theorem is,
[tex]\begin{gathered} (JK)^2+(KL)^2=(JL)^2 \\ (JK)^2+(KL)^2=(JM++ML)^2 \end{gathered}[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} (3)^2+(KL)^2=(3+2)^2 \\ 9+(KL)^2=25 \\ (KL)^2=16 \\ KL=4 \end{gathered}[/tex]Thus, the first option is correct.
+3Which of the following is the function f(x) if f'(x) =
f(x) = 8(x -3) (option C)
Explanation:
[tex]f^{-1}(x)\text{ = }\frac{x}{8}+3[/tex]let y = inverse of f(x)
[tex]y\text{ = }\frac{x}{8}+\text{ 3}[/tex]Interchange x and y:
[tex]\begin{gathered} x=\text{ }\frac{y}{8}+\text{ 3} \\ mu\text{ltiply through by 8:} \\ 8(x)\text{ = 8}(\frac{y}{8})+\text{ 3(8)} \\ 8x\text{ = y + 24} \end{gathered}[/tex][tex]\begin{gathered} \text{make y the suject of by subtracting 24 to both sides} \\ 8x\text{ - 24 = y} \\ y\text{ = 8(x - 3) (option C)} \\ f(x)\text{ = 8(x - 3) (option C)} \end{gathered}[/tex]Question 1 of 5
Drag each tile to the correct location on the table. Not all tiles will be used.
Match each quadratic function with the attributes of its graph.
A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the points A, B, C, D, and E in the aforementioned figures are vertices.
Vertex form the equation again.Fill in the square for 2 x ² + 8 x + 7.
To continue, tap...
2 ( x + 2 ) 2 − 1 Set y to the newly created right side.
y = 2 ( x + 2 ) 2 − 1
Find the values of a, h, and k using the vertex form, y = a (x h ) 2 + k. a = 2 h = 2 k = 1
Find the (h,k) vertex. ( 2, 1 ) .
2 x ² + 8 x - 7
Discover the initial derivative.
4 x + 8
Solve the problem 4 x + 8 = 0 by setting the first derivative to 0.
To continue, tap... x = − 2
Locate the values at which the derivative is ambiguous.
All real numbers fall under the expression's domain, with the exception of cases where it is undefined. In this instance, the phrase is defined even if there is no real number.
At each x value where the derivative is 0 or undefined, evaluate 2 x 2 + 8 x 7.
( − 2 , − 15 ).
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This figure is a right triangular prism. The sides of its triangular bases are each 5 cm and the height of the triangular base is approximately 4.3 cm. The length of the prism between the bases is 8 cm. What is the approximate surface area of this prism?
The approximate surface area of the right triangular prism is 141.5 cm².
How to find surface area of a triangular prism?The surface area of a triangular prism can be found as follows;
surface area of a triangular prism = (perimeter × length) + (2 × base area)
Therefore,
perimeter of the triangular base = 5 + 5 + 5
perimeter of the triangular base = 15 cm
length = 8 cm
The base area = 1 / 2 bh
where,
b = baseh = heightThe base area = 1 / 2 × 4.3 × 5
The base area = 1 / 2 × 21.5
The base area = 10.75 cm²
Hence,
surface area of a triangular prism = (15 × 8) + 2(10.75)
surface area of a triangular prism = 21.5 + 120
surface area of a triangular prism = 141.5 cm²
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Answer:
Step-by-step explanation:
The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1400, which was tobe divided equally among the members going. Prior to the trip, 5 members decided not to go. If thecost per person increased by $14, how many people went on the expedition?
originally, the cost was to be divided among all members
[tex]\frac{1400}{m}=x[/tex]Where m is the number of members and x was the cost per person originally
When 5 people decided not to go, x was increased $14 and m decreased 5...
[tex]\frac{1400}{m-5}=x+14[/tex]Now, we have two equations that we need to solve...
[tex]\frac{1400}{m}=x,\: \frac{1400}{m-5}=x+14[/tex][tex]\begin{gathered} \frac{1400}{m}=x \\ - \\ \underline{\frac{1400}{m-5}=x+14} \\ \frac{1400}{m}-\frac{1400}{m-5}=x-\mleft(x+14\mright) \end{gathered}[/tex]if we subtract the two expressions, we get the above
Now, we simplify...
[tex]\begin{gathered} \frac{1400}{m}-\frac{1400}{m-5}=x-\mleft(x+14\mright) \\ -\frac{7000}{m\left(m-5\right)}=-14 \end{gathered}[/tex]Now, we solve for m
[tex]\begin{gathered} -\frac{7000}{m\left(m-5\right)}=-14 \\ -\frac{7000}{m\left(m-5\right)}m\mleft(m-5\mright)=-14m\mleft(m-5\mright) \\ -7000=-14m\mleft(m-5\mright) \\ -7000=-14m^2+70m \\ -14m^2+70m=-7000 \\ -14m^2+70m+7000=-7000+7000 \\ -14m^2+70m+7000=0 \\ m_{1,\: 2}=\frac{-70\pm\sqrt{70^2-4\left(-14\right)\cdot\:7000}}{2\left(-14\right)} \\ m_{1,\: 2}=\frac{-70\pm\:630}{2\left(-14\right)} \\ m_1=\frac{-70+630}{2\left(-14\right)},\: m_2=\frac{-70-630}{2\left(-14\right)} \\ m1=-20,\: m2=25 \end{gathered}[/tex]we obtain that m=25, meaning there are 25 members, so 25-5=20, this is, 20 people went to the expedition
Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65. What will be the size of Kathleen’s total interest when she retires?
Simple interest is the cost of borrowing money without accounting for the effects of compounding.12672 is the size of Kathleen’s total interest when she retires.
What is Simple Interest?Simple interest is the cost of borrowing money without accounting for the effects of compounding.
Given that Kathleen begins working and at age 32 she invests $6000.00 into a retirement account that pays an APR of 6.4% compounded monthly. She expects to retire at age 65.
Let us calculate the age or time
65-32 =33 years
A=P(1+rt)
A= Final Amount
P=Principle amount=6000
r = rate of interest=6.4%
t is time =33 years
Substitute these values in Formula.
Convert 6.4% to decimal number by dividing with 100.
A=6000(1+0.064(33))
A=6000(1+2.112)
A=6000(3.112)
A=18672
The final Amount she got is 18,672.
To find the interest amount we have to substitute initial amount from final amount.
18672-6000
=12672
Hence 12672 is the size of Kathleen’s total interest when she retires.
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Find the distance between point A and point c
Answer:
Option C: Square root of 74
Step-by-step explanation:
Use the distance formula
Solve for x (Simplify your answer. Type an integer or a decimal. Round to 3 decimal places if needed.
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]e^{ln3x}=e^{ln(x+6)}[/tex]STEP 2: Simplify the expression
[tex]\begin{gathered} e^{\ln \left(3x\right)}=e^{\ln \left(x+6\right)} \\ Apply\text{ exponent rules} \\ \ln \left(3x\right)=\ln \left(x+6\right) \\ By\text{ simplification,} \\ x=3 \end{gathered}[/tex]Hence, x = 3
Write two linear functions, f(x) and g(x). For example, f(x)=
3x-7-and glx) = -2x+5. Then see whether f(x)= (-g(x)) is equivalent to f(x) + g(x) hint : To find -g(x), just change the signs of all the terms in g(x). Discuss whether you think your results would apply to every function.
The most appropriate choice for functions will be given by -
f (x) - (-g(x)) = f(x) + g(x) holds for f(x)=3x-7-and g(x) = -2x+5.
f (x) - (-g(x)) = f(x) + g(x) holds for every functions
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
For f(x) - (-g(x))
-g(x) = -(-2x + 5)
= 2x - 5
f (x) - (-g(x)) = (3x - 7) - (2x - 5)
3x - 7 - 2x + 5
x - 2
For f(x) + g(x)
f(x) + g(x) = (3x - 7) + (-2x + 5)
= 3x - 7 - 2x + 5
= x - 2
So f (x) - (-g(x)) = f(x) + g(x) holds here
Since addition and subtractions can be done on functions,
f (x) - (-g(x)) = f(x) + g(x) holds for every functions.
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Which of these transactions types INCREASE how much you owe the credit card company? (Choose 4)
1. Balance Transfers
2. Purchases
3. Interest Charged
4. Cash Advances
5. Payments
The following table shows a proportional relationshipbetween w and z.w2182.455819Write an equation to describe the relationship betweenwand z.
As it is a proportional relationship then this relationship can be described by a line. To find the equation of the line that passes through the points shown in the table, you can first find the slope and then use the point-slope formula.
I need help with part A bit if u can help me with every I will give you 5 stars ⭐️ this is my homework
SOLUTION
From the diagram of the box plot
A. The IQR for the male's data is approximately 14 - 5 = 9
B. The median for female is 7
The median for male is estimated 10
Difference 10 - 7 = 3.
C. The mean would be better to compare males with females because from the box plot diagram, more males saw the movie than females.
D. The possible reason for the outlier in the data set could be due to more females attending the movie than normal.
Kaylee obtains a loan with simple interest to buy a car that costs $8,500. If Kaylee pays $1,020 in interest during the four-year term of the loan, what was the rate of simple interest?A.0.03%B.3%C.8.3%D.12%
Answer : r = 3%
[tex]\begin{gathered} I\text{ = }\frac{P\text{ X R X T}}{100} \\ \text{Where I = interest, P = principal, R = rate, and T= time} \\ I\text{ = \$1,020} \\ P\text{ = \$8,500} \\ T\text{ = 4} \\ 1020\text{ = }\frac{8500\text{ x r x 4}}{100} \\ 1020\text{ x 100 = 8500 x 4 x r} \\ r\text{ = }\frac{8500\text{ x 4}}{1020\text{ x 100}} \\ r\text{ =}\frac{34000}{102000} \\ r\text{ = }0.333 \\ r\text{ = }3^{} \\ r\text{ = 3\%} \end{gathered}[/tex]Pls tell me the answer it is due in 20 min pls pls pls
I WILL GIVE YOU A TONE OF BRAINLY POINTS AND FIRST ONE TO AMSWER GETS BRAINLYIEST
Answer:
100 is the number
Step-by-step explanation:
For this equation, it may be helpful to replace words with symbols.
The question is:
if 6% of x is the same as 5% of 120, then what is x?
The comma splits the sentence into two parts
if 6% of x is the same as 5% of 120 is the main focus, and the second part requires you to find x.
In the question "if 6% of x is the same as 5% of 120"
the word "of" can be replaced with " * ", and the words "is the same as" can be replaced with "=". The if can be dropped
The question becomes:
6% * x = 5% * 120
This equation can be easily solved.
6% = 0.06
5% = 0.05
So,
0.06x=0.05*120
0.06 x = 6
x = 6 / 0.06
x = 100
What was the new balance to start the
next bank statement?
$913.40
$672.40
$554.54
Answer:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
Step-by-step explanation:
Assuming that the amount shown is an addition to the bank account, you add all those and get 2140.34 dollars to start the next statement.
Question 2 of 3 Which decimal is equivalent to ( 8 × 3 ) ( 1 10 × 1 10 ) ?
The expression's decimal is equivalent to (B) 0.24.
What do we mean by decimal numbers? A decimal is a number that is divided into two parts: a whole and a fraction. Between integers, decimal numbers are used to express the numerical value of whole and partially whole quantities. One of the number types in algebra that has a whole number and a fractional portion separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.So, ( 8 × 3 ) ( 1/10 × 1/10 ):
Solve as follows:
(8 x 3) x (1/10 × 1/10)24 x 1/10024/1000.24Therefore, the expression's decimal is equivalent to (B) 0.24.
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The correct question is given below;
Which of the following decimals is equivalent to (8 x 3) (1/10 × 1/10)
A. 0.024
B. 0.24
C. 2.4
D. 24.0
Identify the information given to you in the application problem below. Use thatinformation to answer the questions that follow on Practical Domain and PracticalRange.Round your answers to two decimal places as needed.The cost to fill your motor home's propane tank is determined by the functionC(9) = 3.37g where C is the output (cost in $) and g is the input (gallons of gas).The propane tank can hold a maximum of 17 gallonsIdentify the practical domain of this function by filling in the blanks below.Minimum Gallons Purchased 59 s Maximum Gallons PurchasedPractical Domain:
Solution:
The cost to fill the propane tank is modeled by the function;
[tex]\begin{gathered} C(g)=3.37g \\ \\ \text{ Where }C=cost(\text{ \$})\text{ and }g=gallon\text{ \lparen of gas\rparen} \end{gathered}[/tex]The practical domain of this function is;
[tex]0\leq g\leq17[/tex]Hence, the range of this function is;
[tex]\begin{gathered} \text{ Minimum cost:} \\ C(0)=3.37(0) \\ \\ C(0)=0 \\ \\ Maximum\text{ cost:} \\ C(17)=3.37(17) \\ \\ C(17)=57.29 \end{gathered}[/tex]Thus, the practical range is;
[tex]0\leq C(g)\leq57.29[/tex]rosa has 3 3/4 pounds of dough. she use 3/4 of a pound for one medium of loaf of bread. how many medium loaves of brrad could be me from rosa's dough?2 3/16353 9/16
The number of pounds of doughs available is given as:
[tex]3\frac{3}{4}[/tex]The fraction of a pound used for one medium is given as:
[tex]\frac{3}{4}[/tex]f(x)=9-x^2Average rate of change x=0 to x=3x=-1 to x=5x=-2 to ×=2
f(x)=9-x^2
Average rate of change
x=0 to x=3
x=-1 to x=5
x=-2 to ×=2
we know that
The average rate of change is equal to
[tex]\frac{f\mleft(b\mright)-f(a)}{b-a}[/tex]Part 1) we have
a=0
b=3
f(a)=f(0)=9-(0)^2=9
f(b)=f(3)=9-(3^2)=0
substitute the given values in the expression above
[tex]\frac{0-9}{3-0}=-\frac{9}{3}=-3[/tex]the rate of change is -3
Part 2) we have
a=-1
b=5
f(a)=f(-1)=9-(-1)^2=8
f(b)=f(5)=9-(5)^2=-16
substitute the given values in the expression above
[tex]-\frac{16-8}{5-(-1)}=\frac{8}{6}=\frac{4}{3}[/tex]the rate of change is 4/3
Part 3) we have
a=-2
b=2
f(a)=f(-2)=9-(-2)^2=5
f(b)=f(2)=9-(2)^2=5
substitute
[tex]\frac{5-5}{2-(-2)}=\frac{0}{4}=0[/tex]the rate of change is zero
One number is 8 more than another. Their product is -16.
Answer:
The two numbers are 4 and -4
Step-by-step explanation:
Turn the words into equations: let's assign one number to be x and the other to be y
x+8=y
x*y=-16
To solve, substitute the value of y in the first equation into y in the second equation.
This gives x*(x+8)=-16
Simplifying gives x^2+8x=-16
x^2+8x+16=0
(x+4)^2=0
x=-4
plug this value of x back into the first equation, -4+8=y, y is 4
Now to make sure the answer is correct: 4 is 8 more than -4, and 4*-4 does equal 16
WILL GIVE BRAINLYEST 200 POINTS!!!1
The range will be impacted by A. The range will increase by 12.
What is a range?A range simply means the difference between the highest and the lowest number.
Highest number = 34
Lowest number = 15
Range = 34 - 15 = 19
When the highest number is 46, the range will be:
= Highest number - Lowest number
= 46 - 15
= 31
The difference will be:
= 31 - 19
= 12
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Answer:
The range will be impacted by A. The range will increase by 12.What is a range?A range simply means the difference between the highest and the lowest number.Highest number = 34Lowest number = 15Range = 34 - 15 = 19When the highest number is 46, the range will be:= Highest number - Lowest number= 46 - 15= 31The difference will be:= 31 - 19= 12
Step-by-step explanation:
Express 5√27 in the form n√3, where n is a positive integer.
Answer:
n = 15Step-by-step explanation:
See the steps below:
[tex]5\sqrt{27} =[/tex][tex]5\sqrt{3^2*3} =[/tex][tex]5*3\sqrt{3} =[/tex][tex]15\sqrt{3}[/tex]The value of n is 15.
triangle ABC has side lengths 10 14 and 26 do the silence form a Pythagorean triple explain
Solution:
Given the side lengths of a triangle ABC;
[tex]a=10,b=14,c=26[/tex]The side lengths form a Pythagorean triple if ithe square of the longest side is equal to the sum of squares of the remaining two sides.
Thus;
[tex]\begin{gathered} 10^2+14^2=100+196 \\ \\ 10^2+14^2=296 \\ \\ 296\ne29^2 \\ \\ \text{ Thus;} \\ \\ 10^2+14^2\ne26^2 \end{gathered}[/tex]Hence, they do not form a Pythagorean triple.
CORRECT OPTION: (B) No, they do not form a Pythagorean triple.
[tex]10^{2}+14^{2}\ne26^{2}[/tex]
Solve for x.5/6x = 15
The answer is 18
You first multiply both sides by 6 which will make 15, now 90
then divide both sides by 5 so that will make 90, 18 thus x=18 is correct
Heather, Tom, and Kareem have a total of $86 in their wallets. Heather has $9 less than Kareem. Tom has 3 times what Kareem has. How much does each have?
Answer: Heather: $10, Kareem: $19, Tom: $57
Step-by-step explanation:
Complete the table below by writing the symbols for the cation and anion that make up each ionic compound. The first row has been completed for you.
The cations and Anions for the given compounds are;
1) CuS: Cation; Cu²⁺ and Anion: Su²⁻
2) (NH₄)₂O; Cation; NH₄⁺ and Anion: O²⁻
3)Mn₃(PO₄)₂; Cation; Mn²⁺ and Anion: PO₄³⁻
4) VBr₅; Cation; V⁵⁺ and Anion: Br⁻
How to Identify Anions and Cations?Cations are defined as Positively charged ions that are formed by loss of electrons by an atom. In a cation, number of electrons are less than number of protons.
Anions are defined as Negatively charged ions that are formed by gaining of electron by an atom. In anions, number of electrons are more than the number of protons.
Thus;
1) CuS
Cation; Cu²⁺
Anion: Su²⁻
2) (NH₄)₂O
Cation; NH₄⁺
Anion: O²⁻
3) Mn₃(PO₄)₂
Cation; Mn²⁺
Anion: PO₄³⁻
4) VBr₅
Cation; V⁵⁺
Anion: Br⁻
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help meeee pleasee!!!
thank youu
Answer:
Domain: A, [tex](-\infty, \infty)[/tex]
Range: [tex][4, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
The function y=f(x)y=f(x) is graphed below. Plot a line segment connecting the points on ff where x=-6x=−6 and x=2.x=2. Use the line segment to determine the average rate of change of the function f(x)f(x) on the interval -6\le x \le 2.−6≤x≤2.
The average rate of change of the function f(x) on the interval−6≤x≤2 is -0.5
This is further explained below.
What is the average rate?Generally, The average rate of reaction is referred to as the change in concentration of any of the reactants or any of the products per unit of time during a specific period of time. This change may occur at any point throughout the reaction.
A single rate is applicable to property that is located in more than one place and that is calculated by weighting the separate rates that are calculated for each location.
In conclusion, The average rate of change on x e(a, b)
[tex]\begin{aligned}m &=\frac{f(b)-f(a)}{b-a} \\\\m &=\frac{f(2)-f(-6)}{2-(-6)} \\\\&=\frac{2-(-(-6))}{8}=\frac{6}{2} \\\\=-0.5\\\\\end{aligned}[/tex]
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maths lit inflation g11I from South Africa we use Rands
It is given that the price of the box increases from R17.99 to R19.99.
It is required to find the inflation rate for the period.
Recall the formula for the Inflation Rate:
[tex]\frac{\text{ Current price}-\text{ Initial price}}{\text{ Initial price}}\times100\%[/tex]Substitute the given prices:
[tex]\frac{19.99-17.99}{17.99}\times100\%=\frac{2}{17.99}\times100\%=\frac{200}{17.99}\%\approx11.1\%[/tex]The answer is about 11.1%.9.) The line plot shows the number of pounds of fish eaten by each dolphin at the zoo. Fish Eaten by Dolphins (pounds) XXX X х x x 16 20 24 28 32 36 Which stem and leaf plot best represents the data in the line plot? Fish Eaten by Dolphins (pounds) Fish Eaten by Dolphins (pounds) Stem Leaf Stem Leaf 1 889 1 2 3 88 0026 1113 3 KEY 2|0 - 20 pounds KEY 2|0 - 20 pounds Fish Eaten by Dolphins (pounds) Fish Eaten by Dolphin (pounds) Stem Leaf Stem Leaf 1 D 7 78 015 0003 89 0 26 2 3 KEY = 20 pounds 2|0 - 20 pounds
C
1) Writing down the data gathered from that :
lbs number of fishes
18 2
19 1
20 1
26 1
31 3
34 1
2) Examining the steam and plot graphs we can state that the best represents those collected data is the option C
Note how many times those data are enlisted, and you can conclude that. On the left the tens and on the right the units, just like the "key" displays.
3) Hence, the answer is C
