Solve the exponential equation algebraically and use a graphing utility
400/1+e^-x= 350
Answers
[tex]400=350(1+e^{-x} )[/tex]
[tex]400=350+350e^{-x} [/tex]
[tex]50=350e^{-x} [/tex]
[tex]350e ^{-x} =50[/tex]
[tex]e^{-x} = \frac{50}{350} [/tex]
[tex]e ^{-x} = \frac{1}{7} [/tex]
[tex]ln(e ^{-x} )=ln( \frac{1}{7} )[/tex]
[tex]-x=ln( \frac{1}{7} )[/tex]
[tex]x=-ln( \frac{1}{7} )[/tex]
[tex]x=1.95[/tex]
Now to find the solution using a graphing utility, just type the equation and look for the point in which the graph intercepts the x-axis as shown in the picture. The point in which the graph intercepts the x-axis is a zero of the function, and therefore the solution.
Related Questions
What is the probability of flipping a coin six times in a row and getting three heads and three tails?
Answers
Final answer:
The probability of flipping a coin six times and getting exactly three heads and three tails is calculated using the binomial formula and is found to be 31.25%.
Explanation:
The probability of flipping a coin six times and getting exactly three heads and three tails can be calculated using the binomial probability formula, which is P(x; n, p) = (n choose x) * p^x * (1-p)^(n-x), where 'n' is the number of trials, 'x' is the number of successes, and 'p' is the probability of success on any given trial.
In this instance, since we are flipping a fair coin, the probability 'p' of getting heads (success) on any single flip is 0.5. We want to find the likelihood of getting 'x' = 3 heads out of 'n' = 6 flips. Therefore, the equation becomes:
P(3; 6, 0.5) = (6 choose 3) * 0.5^3 * 0.5^(6-3)
The combination (6 choose 3) calculates the number of ways to choose 3 successes (heads) from 6 trials, which is 20. Plugging these values into the equation gives:
P(3; 6, 0.5) = 20 * (0.5^3) * (0.5^3) = 20 * (0.125) * (0.125) = 20 * 0.015625
This results in a probability of 0.3125, or 31.25%.
Therefore, the chance of flipping a coin six times and getting three heads and three tails is 31.25%.
You have 10 different video games. how many different ways can you arrange the games side by side on a shelf
Answers
option 1.
for the 1st place 10 games, for the 2d place - 9 games, for the 3d - 8, etc., for the 10th place - 1 game. Then, using the rule of 'logic &': 10*9*8*7*6*5*4*3*2*1=3628800 ways.
option 2.
using formula of permutations (Pₓ=x!): P₁₀=10!=3628800 ways.
Answer: 3628800.
You can arrange the games side by side on a shelf in "3628800" ways.
According to the question,
Number of video games,
10Now,
The amount of possible ways could you place the games side by side on some kind of shelf will be:
= [tex]10![/tex]
= [tex]10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1[/tex]
= [tex]3628800[/tex]
Thus the response above is appropriate.
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Angle D is a vertical angle to F. The measure of D is 53° . What is the measure of F?
Answers
Angle F will have the same measure as angle D, which is 53°, because they are vertical angles and thus congruent.
Explanation:The question asks about the measure of angle F given that it is a vertical angle to angle D, which measures 53°. In geometry, vertical angles (also known as opposite angles) are pairs of non-adjacent angles formed when two lines intersect. Vertical angles are congruent, which means they have the same measure. Therefore, since angle D is 53°, angle F, being its vertical angle, will also have a measure of 53°.
Angle D and angle F are vertical angles, which means they are congruent. If angle D measures 53°, then angle F will also measure 53°. This is because vertical angles are equal in measure.
Find the reference angle for 697 degrees
Answers
what is the coefficient of the term 13a in the expression 13a+6b
Answers
a total of 324 tickets were sold for the school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adults tickets sold how many adult tickets were sold?
Answers
The correct answer is 81
Final answer:
To find the number of adult tickets sold when a total of 324 tickets were sold for a school play and student tickets were three times the number of adult tickets, we set up the equation x + 3x = 324, solved for x, and found out that 81 adult tickets were sold.
Explanation:
The question is asking us to find out how many adult tickets were sold when a total of 324 tickets were sold for a school play, with the number of student tickets being three times the number of adult tickets sold. To solve this, we let x represent the number of adult tickets. Therefore, 3x will represent the number of student tickets since there are three times as many student tickets as adult tickets.
The equation representing the total number of tickets sold would be: x (adult tickets) + 3x (student tickets) = 324. Simplifying, we have 4x = 324. Dividing both sides by 4 gives us x = 81.
Therefore, the number of adult tickets sold is 81.
Factor.x ^2 + 17x + 72
Answers
since we have 1x^2, a and c=1
so factor into (x+b)(x+d)
if we expand, we get
[tex](x+b)(x+d)=x^2+(b+d)x+bd[/tex]
so we need 2 numbers that add to get the middle number and multiply to get the last number
I would factor the last number and see which ones add to the middle one
what 2 numbers multily to get 72 and add to get 17?
hmm, list factor of 72 and add them
1+72=73, nope
2+36=38, nope
3+24=27, nope
4+13=17, yep
so it facotrs to (x+4)(x+13)
Find factors of x^2 and 72, that, when combined, will give you 17x
x ^2 + 17x + 72
x 9
x 8
(x + 9)(x + 8) is your factor.
hope this helps
5x+13≥−37. Find the solution set of the inequality.
Answers
The answer is: x≥-10
The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
5x + 13 ≥ − 37
Simplify the inequality for 'x', then we have
5x + 13 ≥ − 37
5x ≥ − 50
x ≥ − 10
The solution of the inequality 5x + 13 ≥ − 37 will be greater than or equal to negative 10.
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A website is offering a promotion, during which customers can buy up to 100 photos for a flat fee. The cost per photo varies inversely with the number of photos a customer buys, as shown in the table below. What functions model the data?
Answers
we have that
for c=5 and n=20------------> n*c=20*5=100
for c=2.5 and n=40------------> n*c=40*2.5=100
for c=2 and n=50------------> n*c=50*2=100
for c=1.25 and n=80------------> n*c=80*1.25=100
therefore
the function that models the data is n*c=100
the answer is nc=100
Your answer is nc=100
A magazine claims that 75% of all teenage boys have their own cellphones. A researcher wished to test the claim and selected a random sample of 60 teenage boys. She found that 54 had their own cell phones. At α = 0.01, should the claim be rejected?
Answers
Factor each expression: 5a-25
Answers
= 5(a-5)
----------------------
hope it helps
It is 20 minutes after 8:00 what is the correct way to write the time.
Answers
Rhoads earned $324.65 delivering newspapers. She promised her sister 0.2 of her earnings for helping her.How much does Rhoads owe her sister?
Do I have to subtract?? if not help me solve plz
Answers
(owed to sister) = 0.2*(earnings)
.. = 0.2*$324.65
.. = $64.93
Rhoads owes her sister $64.93.
Mrs. Hicks has 35 students in her chemistry class. The ratio of girls to boys is 3:4. How many girls does she have in her class? Let both antecedents represent girls and let both consequence represent total students.
Answers
35/7 = 5
5 * 3 = 15
there are 15 girls
Create a pattern with the rule n x 2 + 1
Answers
The pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
Given:
n × 2 + 1
= 2n + 1
where
n = number of terms
when n = 0
2(0) + 1
0 + 1
= 1
when n = 1
2(1) + 1
= 2 + 1
= 3
when n = 2
2(2) + 1
4 + 1
= 5
when n = 3
2(3) + 1
6 + 1
= 7
when n = 4
2(4) + 1
8 + 1
= 9
Therefore, the pattern that can be created with the rule n x 2 + 1 is 1, 3, 5, 7, 9, 11
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What's the present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?
Answers
General Idea:
We need to make use of the below formula to find the present value.
[tex] PV=\frac{FV}{(1+\frac{r}{n})^{nt}} \\ \\ Where:\\ FV \; is \; Future\; Value\; of \; money\\ r \; is\; Annual\; rate\; of\; interest\\ t\; is\; number\; of\; years\\ n\; is\; Number\; of\; periods\; based\; on\; compounding \; frequency [/tex]
Applying the Concept:
We are given the below information:
[tex] FV= \$11,500\\ \\ t=5\; years\\ \\ r=4.5 \%\\ \\ n=2\; (because\; given\; compounded\; semi-annually) [/tex]
We need to substitute the above information in the formula to find the Present value.
[tex] PV=\frac{11500}{(1+\frac{0.045}{2})^{2 \times 5}} =\frac{11500}{(1+0.0225)^{10}} =\frac{11500}{1.0225^{10}} \\ \\ PV \approx \$9206 [/tex]
CONCLUSION:
The present value of $11,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually is approximately 9206 dollars
a juice can is shaped like a cylinder ]. it is 12 centimeters wide and 16 centimeters tall. find its volume to the nearest whole number . use 3.14
Answers
To find the volume of the cylinder-shaped juice can, calculate using the formula V = π r² h with the radius being half of the can's width and the given height. The volume is found to be approximately 1804 cm³ when rounded to the nearest whole number.
Calculating the Volume of a Cylinder:
To calculate the volume of a cylinder, you should use the formula V = π r² h. First, we need to determine the radius of the juice can. Since it is given that the can is 12 centimeters wide, that means the diameter is 12 centimeters, and therefore, the radius (r) is half of that, which is 6 centimeters. We also have the height (h) of the can, which is 16 centimeters. Plugging these values into the formula gives us:
V = 3.14 × 6² × 16
Now, we calculate:
V = 3.14 × 36 × 16
V = 3.14 × 576
V = 1803.84 centimeters cubed (cm³)
When we round this to the nearest whole number, the volume of the juice can is approximately 1804 cm³.
If a salesperson sells 3/4 of an acre for $80,000, what was the price per square foot rounded to two decimal spaces?
Answers
1 acre=43560 foot
3/4 acre=32670 foot
now we know that
32670 sq foot............................80,000 dollars
1 sq foot...........................................?
the price is=80,000/32670=2.4487
rounded =2.45
Following are the calculation to the given question:
Given:
salesperson sells[tex]\bold{= \frac{3}{4}}[/tex]
acre= 80,000
To find:
price per square foot rounded to two decimal spaces=?
Solution:
Therefore
[tex]1 \ acre=43560\ foot \\\\ \frac{3}{4}\ acre=32670\ foot[/tex]
Calculation
[tex]32670 \ sq \ foot = \$80,000 \\\\1 \ sq \ foot =? \\\\[/tex]
Calculating the price:
[tex]=\frac{80,000}{32670}=2.4487 \approx 2.45[/tex]
Therefore, the final answer is "$2.45".
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which of the following shows an equivalent expression to (5 times 3)times 12 if only associative property was used to transform the expression
Answers
⇒Associative Property states
A × (B ×C)=(A×B)×C=(A×C)×B
Now, we have to find equivalent expression of
[tex](5 \times 3) \times 12 \\\\1.\rightarrow 5 \times (3 \times 12)\\\\2.\rightarrow (5 \times 12) \times 3\\\\3 \rightarrow 180[/tex]
I need help !! This packet is due tomorrow and I have no idea what I’m doing .
Answers
Given: angle M congruent to angle X; angle N congruent to angle Y; YO congruent to NZ.
1. YZ=YO+OZ; reason: segment addition postulate (YZ is made up of YO and OZ).
2. ON=NZ+OZ; reason: segment addition postulate (ON is made up of NZ and OZ).
3. YO=NZ; reason: given.
4. ON=YO+OZ; reason: substitution (since NZ is congruent to YO, we substitute YO for NZ).
5. ON=YZ; reason: substitution (since YZ=YO+OZ, we substitute YZ for YO+OZ).
6. MNO is congruent to XYZ; reason: AAS (we have 2 sides and a non-included angle in each triangle congruent, which is the angle-angle-side theorem).
Answer:
Given is :
∠M≅∠X
∠N≅∠Y
YO≅NZ
We have to prove that ΔMNO≅ΔXYZ
Using segment addition postulate we get YZ=YO+OZ and ON=NZ+OZ and YO=NZ is already given. Using substitution of YO for NZ; we get ON=YO+OZ
Now substituting YZ for YO+OZ we get ON=YZ and also YZ=YO+OZ.
Now applying AAS we get ΔMNO is congruent to ΔXYZ because of angle-angle-side theorem as we have already proved that two sides are congruent and a non-included angle in each triangle is congruent.
What has an infinite number of points extending in opposite directions that has only one dimension
Answers
The answer to your question is a line. A line infinitely extends in opposite directions and it has an infinite number of points. It only has one dimension.
Now because the question doesn't say 'extends infinitely' and it JUST SAYS 'has an infinite number of points, a line segment could be a correct answer too because points are infinitely small. Don't write this answer though because I know the answer your teacher is looking for is a 'line.'
I really hope this helps!
Best wishes :)
Suppose you have two credit cards. The first has a balance of $410 and a credit limit of $1,000. The second has a balance of $510 and a credit limit of $1,000. What is your overall credit utilization? 36% 56% 46% 16% 26%
Answers
In the same way, I will add the balances of each card for a total of $920 and get the percentage of remaining balance:
(sum of balances of two cards) ÷ (sum of credit limits of two cards)
($410 + $510) ÷ ($1000 + $1000) = 0.46 or 46%
Note:
But I have an argument because isn't it that credit utilization is the "percentage used" of the credit limit and for that, I have to subtract 46% from 100% which is 54% and that is not an included in the option
That means you use [tex] \frac{920}{2000} [/tex]. Percent means "out of 100" so we wish to write this fraction with 100 in the denominator (the bottom). We do this by dividing the top (numerator) and bottom (denominator) by the same number. Here we use 20. That gives us [tex]\frac{920}{2000}= \frac{46}{100} =46%[/tex]
what is domain of g(x)= square root plus one
Answers
1. if the given function is
[tex]g(x)= \sqrt{x+1} [/tex]
then
2. domain is x+1≥0; ⇒ x≥-1 or x∈[-1;+oo).
answer: [-1;+oo)
In a multiple regression analysis what would likely be the culprit of a dramatic increase in the P-value of one of the variables?
Answers
This is called multicollinearity.
If there is a high correlation between your independent variables can lead to problems.
It can lead to increased variance of the coefficient estimates and make the estimates very sensitive to minor changes in the model.
What is the area of a figure 36m×21×10×9×8×23×4×7×
Answers
Elias purchases a home for $38,900. The value of the home, in thousands of dollars, since his purchase is shown in the table. Find an exponential function that models the data. Round numerical values to the nearest hundredth. Let x be the number of years since the purchase. The function f(x) =()x models the data. Use the model to predict the home’s value. After 12 years, the home’s value will be about $thousand. After 35 years, the home’s value will be about $thousand.
Answers
Answer:
f(x)=39.59
(1.09)
After 12 years: 111
After 35 years: 808
The exponential function models the data would be f(x) = 39.59 (1.09). After 12 years, the home’s value will be about $111 thousand and After 35 years, it will be about $808 thousand.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Elias purchases a home for $38,900.
Let x be the number of years since the purchase. The function f(x) =()x models the data.
f(x) = 39.59 (1.09)
by using the model to predict the home’s value.
After 12 years, the home’s value will be about $
111 thousand.
After 35 years, the home’s value will be about $
808 thousand.
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The volume v of a right circular cone of radius r and height h is given by v = 1/3 pi r^2 h. suppose that the height decreases from 20 in to 19.95 in and the radius increases from 4 in to 4.05 in. compare the change in volume of the cone with an approximation of this change using a total differential.
Answers
dV = (π/3)*(2r*h*dr +r^2*dh)
The approximate change in volume is
.. ∆V ≈ (π/3)*(2*4*20*0.05 +4^2*(-.05))
.. = (π/3)*(8 - 0.8) = 7.2(π/3) . . . . . in^3
The actual change in volume is
.. (π/3)*(4.05^2*19.95 -4^2*20) = 7.229875(π/3) . . . . . in^3
The actual change in volume is slightly more than the linear approximation would suggest.
George has $23 to spend on art supplies he wants to buy markers papers and glue if the total cost of markers and papers is more than $14 which inequality represents the dollar amount P George can spend on glue
Answers
i think that is the correct answer
Your friend earns $10.50 per hour. This is 125% of her hourly wage last year. How much did your friend earn per hour last year?
Answers
complete the steps to solve the polynomial equation x3-21x=-20 according to the rational root theorem, which number is a potential root of the polynomial?
Answers
potential roots are factors of 20 eg 1, 2 ,4 ,5, 10, 20 and the negative values of these
1 looks like a rots . Try it:-
f(1) = 1 - 21 + 20 = -20+20 = 0
Yes 1 is a solution.
2 is not.
Try 4:-
4^3 - 21*4 + 20 = 64 - 84 + 20 = 0
Try 5 No
Try 10 - N0
20 no.
Try -4 - No
-5:-
Yes
Roots are 1, 4 and -5