Answer:
$17.750 ; 15.979 ; 72
Step-by-step explanation:
Given that :
Cummulative sales, S(t) is represented by the equation :
S(t) = 72/(1 + 9e^-0.36t)
Cummulative sales after 3 weeks :
Put t = 3 in the equation, as t = time after launch
S(3) = 72/(1 + 9e^-0.36(3))
S(3) = 72 / (1 + 9e^-1.08)
S(3) = 72 / (1 +3.0563597)
S(3) = 72 / 4.0563597
S(3) = 17.749905 = $17.750 thousands
Amount of time required for sales to reach 70000
S(t) = 72/(1 + 9e^-0.36t)
S(t) = 70
70 = 72/(1 + 9e^-0.36t)
70 * (1 + 9e^-0.36t) = 72
(1 + 9e^-0.36t) = 72 / 70
1 + 9e^-0.36t = 1.0285714
9e^-0.36t = 1.0285714 - 1
9e^-0.36t = 0.0285714
e^-0.36t = 0.0285714 / 9
e^-0.36t = 0.0031746
Take the In of both sides ;
In(e^-0.36t) = In(0.0031746)
-0.36t = - 5.752573
t = - 5.752573 / - 0.36
t = 15.979
About 16 weeks
The limiting value in sales :
Take the limit as t - - > ∞
S(t - - > ∞) = 72/(1 + 9e^-0.36t)
Put t = 0
S(0) - - > 72 / (1 + 0)
72 / 1
= 72
Select the correct answer.
Which expression is equivalent to the given expression?
In(2e/x)
A. In 2 - In x
B. In 1 + In 2 - ln x
C. 1 + In 2 - In x
D. In 2 + ln x
Answer:c
Step-by-step explanation:
The equivalent expression is 1 + In 2 - In x.
How to estimate an equivalent to the given expression?Given:
[tex]$\ln \left(\frac{2 e}{x}\right)$[/tex]
Apply log rule:
[tex]$$\log _{C}\left(\frac{a}{b}\right)=\log _{c}(a)-\log _{c}(b)$[/tex]
[tex]$&\ln \left(\frac{2 e}{x}\right)=\ln (2 e)-\ln (x) \\[/tex]
= ln (2e) - ln (x)
Apply log rule:
[tex]$\log _{c}(a b)=\log _{c}(a)+\log _{c}(b)$[/tex]
ln (2e) = ln (2) + ln (e)
= ln (2) + ln (e) - ln (x)
Apply log rule:
[tex]$\log _{a}(a)=1$[/tex]
= ln (2)+1-ln (x)
Therefore, the correct answer is option C. 1 + In 2 - In x.
To learn more about log rule
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How much is six dimes, 8 nickels, and three one-dollar bills? *
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Guide}\downarrow[/tex]
[tex]\large\textsf{Penny: 1 cent} \\\large\textsf{Nickel: 5 cents}\\\large\textsf{Dime: 10 cents}\\\large\textsf{Quarter: 25 cents}\\\large\textsf{Half dollar: 50 cents}\\\large\textsf{1 bill = 1 dollar}[/tex]
[tex]\large\textsf{6 dimes:}\downarrow[/tex]
[tex]\large\textsf{= 10 + 10 + 10 + 10 + 10 + 10}[/tex]
[tex]\large\textsf{= 20 + 20 + 20}[/tex]
[tex]\large\textsf{= 40 + 20}[/tex]
[tex]\large\textsf{= \bf 60}[/tex]
[tex]\large\textsf{6 dimes = \bf 60 cents}[/tex]
[tex]\large\textsf{8 nickels}[/tex]
[tex]\large\textsf{= 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5}[/tex]
[tex]\large\textsf{= 10 + 10 + 10 + 10}[/tex]
[tex]\mathsf{= 20 + 20}[/tex]
[tex]\large\textsf{= \bf 40}[/tex]
[tex]\large\textsf{8 nickels = \bf 40 cents}[/tex]
[tex]\large\textsf{3 one dollar bills}[/tex]
[tex]\large\textsf{= 1 + 1 + 1}[/tex]
[tex]\large\textsf{= 2 + 1 }[/tex]
[tex]\large\textsf{= \bf 3}[/tex]
[tex]\large\textsf{3 one dollar bills = \bf 3 dollars}[/tex]
[tex]\large\textsf{NOW LETS SOLVE FOR YOUR EQUATION}[/tex]
[tex]\large\textsf{3.00 + 0.60 + 0.40}[/tex]
[tex]\large\textsf{= 3.60 + 0.40 }[/tex]
[tex]\large\textsf{= \bf \$4}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your answer is: \huge \bf \$4}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A mother has 6 sons
Each has a sister
How many people are in the family?
A:13.
B)8.
D)7.
C:14.
A. 13
Explanation= 6 (sons) +6 (daughters) +1 (mother) = 13.
(notes: as a father is not within the problem, there is no reason to be in the answer)
Answer:
B)8
A mother has 6 sons. If there is only one sister, than each son has a sister. Don't forget to add the mother. 6 + 1 + 1
Step-by-step explanation:
Which row of the table reveals the y-intercept of function f?
Answer:
No solution is possible from the informatin provided.
Step-by-step explanation:
You didn't include the table,
Answer:
y intercept is found from the pair that has a 0 for the x variable.
Step-by-step explanation:
if a choice was (0,2) this would be the point where the line intercepts the y axis.
x=0 is the position of the vertical line, and 2 is how high up the graph the line passes through the y-axis
Find the missing angle x. Show your work.
What is the solution to the equation 3 + 4/4y = 4?
Answer:
B. y= ¼
Step-by-step explanation:
3 + ^4√4y = 4
^4√4y =4-3
^4√4y = 1
^4√4y =^4√1
so, 4y = 1
y = ¼
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
Consider the following conditional statement. Determine the contrapositive
of the statement and then determine if the contrapositive is true or false.
If two angles are not complements, then their measures do not add up to 180°.
The contrapositive of the statement is true.
The contrapositve of the statement is false.
Answer:
The contrapositive of the statement is true.
Step-by-step explanation:
For a general statement:
p ⇒ q
The contrapositive statement is:
¬q ⇒ ¬p
where:
¬q is the negation of the proposition q.
Here we have the statement:
If two angles are not complements, then their measures do not add up to 180°
So we have:
p = two angles are not complements
q = their measures do not add up to 180°
Then the negations are:
¬p = two angles are complements
¬q = their measures do add up to 180°
The contrapositive statement is:
"if for two angles their measures do add up to 180°, then the two angles are complements"
This is true, if for two angles the sum of their measures is equal to 180°, then these angles are complementary.
Then: The contrapositive of the statement is true.
C. Directions: Complete the table ( Area of a Circle).
Radius Diameter Area
16. _____ 7.5cm _______
17. 10cm _______ _______
18. 21cm ________ _______
pasagot po plss bukas na po pasahan ko
Answer:
3.75cm 44.16cm²
20cm 314cm²
42cm 1384.74cm²
Step-by-step explanation:
Area of a circle = πr²
Where : = π = pi = 3.14
R = radius
the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.
A radius is half of the diameter
16. Radius = 7.5 / 2 = 3.75
Area = 3.14 x 3.75² = 44.16
17. Diameter = 10 x 2 = 20
Area = 10² x 3.14 = 314
18. Diameter = 21 x 2 = 42
Area = 21² x 3.14 = 1384.74
Show A and Show B are two of the most popular television shows of all time. The number of episodes of each show are consecutive even integers whose sum is 570. If there are more episodes of Show A, how many episodes of each were there?
Answer:
A = 286 episodes
B = 284 episodes
Step-by-step explanation:
Let n = the [tex]\text{number of episodes}[/tex] of show B
n + 2 = the [tex]\text{number of episodes}[/tex] of show A
Therefore, according to the question,
The sum of the number of the episodes of each show are consecutive even integers = 570
Therefore,
n + n + 2 = 570
2n + 2 = 570
2n = 568
n = 284
Therefore, the number of episodes for B = 284
The number of episodes for A = n + 2 = 284 + 2
= 286
find the equation of the line passing through points A(3,4) and B(1,10)
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]
Finally, find the equation:
[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]
A group of high school seniors were surveyed on their interests. Of those surveyed, 16 students said they enjoy reading, and 14 said they enjoyed writing. What additional information would you need to know in order to determine how many students said they enjoy both reading and writing?
a) The number of students who enjoy reading only.
b) The number of students who enjoy writing only.
c) The number of students who don't enjoy neither reading nor writing.
d) The number of students said they enjoy either reading or writing.
Answer:
a) The number of students who enjoy reading only.
Answer:
d
Step-by-step explanation
let me know if this is right please
Using the information in the Box-and-Whisker plot below, what is the minimum value?
A. 5
B. 12.5
C. 20
D. 27.5
Answer:
espero ayudarte ..............❤❤
Answer:
b
Step-by-step explanation:
> Next question Get a similar question You this question below Find the distance between the points (-3,-3) and (-5,-1) Distance vo Х Submit Question
Answer:
The answer is the square root of 8, or 2root2.
Step-by-step explanation:
Use the distance formula.
d = sqrt((-3-(-5))^2 + (-3-(-1)))
d = sqrt(2^2 + 2^2)
d = sqrt(4 + 4)
d = sqrt8
d = sqrt4 * sqrt2
d = 2 * sqrt2
What’s the solution
Answer:
x ≥ 12
Step-by-step explanation:
-3/4x +2 ≤ -7
Subtract 2 from each side
-3/4x +2-2 ≤ -7-2
-3/4x ≤ -9
Multiply each side by -4/3, remembering to flip the inequality
-3/4x * -4/3 ≥ - 9 *(-4/3)
x ≥ 12
Answer:
x>=12
Step-by-step explanation:
-3/4x + 2<=-7
-3/4x <= -7 -2
-3/4x<=-9
cross multiply
-3x<=-36
dividing throughout by -3
x>=12
Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco's rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population standard deviation is $10.50 and that spending follows a normal distribution.A. Specify the appropriate null and alternative hypotheses to test whether average spending at the rival's store is more than $130.B. Calculate the value of the test statistic.C. Calculate the p-value. D. Calculate the critical value
Answer:
A. The null hypothesis is [tex]H_0: \mu = 130[/tex].
The alternative hypothesis is [tex]H_a: \mu > 130[/tex]
B. The value of the test statistic is [tex]t = 1[/tex]
C. The p-value is of 0.1636.
D. The critical value is [tex]t_c = 1.711[/tex]
Step-by-step explanation:
Question a:
Customers at Costco spend an average of $130 per trip (The Wall Street Journal, October 6, 2010). One of Costco's rivals would like to determine whether its customers spend more per trip.
At the null hypothesis, we test if the mean is the same as Costco's, that is:
[tex]H_0: \mu = 130[/tex]
At the alternative hypothesis, we test if the mean is more than 130, that is:
[tex]H_a: \mu > 130[/tex]
B. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question.
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
130 is tested at the null hypothesis:
This means that [tex]\mu = 130[/tex]
A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population standard deviation is $10.50 and that spending follows a normal distribution.
This means that [tex]n = 25, X = 135.25, s = 10.50[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{135.25 - 130}{\frac{10.50}{\sqrt{25}}}[/tex]
[tex]t = 1[/tex]
The value of the test statistic is [tex]t = 1[/tex]
C. Calculate the p-value.
Test if the mean is more than a value, so a right-tailed test.
Sample of 25, so 25 - 1 = 24 degrees of freedom.
Test statistic of t = 1.
Using a t-distribution calculator, the p-value is of 0.1636.
D. Calculate the critical value
24 df, using the standard 0.05 significance level.
Using a critical value calculator, the critical value is [tex]t_c = 1.711[/tex]
HW HELP ASAP PLZZZZZ
Answer:
last step is (2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
4x^2 + (10 + 2)x + 5
4x^2 + 10x + 2x + 5
2x(2x + 5) +1(2x + 5)
(2x + 5)(2x + 1)
I need help please no links or I will have you reported
Answer:ʜᴛᴛᴘꜱ://ᴡᴡᴡ.ʏᴏᴜᴛᴜʙᴇ.ᴄᴏᴍ/ᴡᴀᴛᴄʜ?ᴠ=ᴅQᴡ4ᴡ9ᴡɢxᴄQ
Step-by-step explanation:
Heres the answer but its on a another page.
Im joking
here's the answer
the first one is 878 i think that what your looking for at the top
PLS HELP
the simplest form of this product has a numerator of
x + 2
x - 2
( x - 2 ) ( x - 2 )
( x + 2 ) ( x - 2 )
and a denominator of
x - 5
( x - 5 ) ( x - 1 )
x - 1
( x + 5 ) ( x + 1 )
the expression has an excluded value of x
- 5
2
-1
5
(x+2)(x-2) / (x-1)(x-5) this is the simplified form of the expression.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities. It is a way of expressing a number as a quotient of two integers, where the top number is called the numerator, and the bottom number is called the denominator.
x²-3x-10/x²-6x+5 • x-2/x-5
We can factor the numerator and denominator of the first fraction as follows: (x-5)(x+2) / (x-5)(x-1)
Notice that there's a common factor of x-5 in both the numerator and denominator. We can cancel them out, leaving: (x+2) / (x-1)
Now let's simplify the second fraction:
x-2 / x-5
We can't simplify this fraction any further, so we leave it as is.
Putting it all together, we get:
(x+2) / (x-1) * (x-2) / (x-5)
Multiplying the two fractions, we get:
(x+2)(x-2) / (x-1)(x-5)
This is the simplified form of the expression.
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During the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?
Answer:
After three months the value of the food bill will be $ 224.64.
Step-by-step explanation:
Given that during the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month, for state whether this increase was linear or exponential, and determine, if your food bill was $ 130 in one month during this period, what was it three months later, the following calculations must be performed:
A hyperinflation raises prices exponentially (the percentage is calculated based on the increase of the previous month). Thus, to calculate the price of the food bill, the following calculation must be performed:
130 x 1.20 ^ 3 = X
130 x 1.728 = X
224.64 = X
Therefore, after three months the value of the food bill will be $ 224.64.
Figure ABCD is a rectangle find the value of x
Answer:
Espanol la vecsu
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
The diagonals of a rectangle bisect each other , so
DE = EB , that is
7x - 1 = 2x + 4 ( subtract 2x from both sides )
5x - 1 = 4 ( add 1 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
6.
40 x 6+ (9+21)
I need help ASAP please due tomorrow show work
Round the following as specified.
153.38519 to the nearest thousandth.
Answer:
153.3852
Step-by-step explanation:
After the decimal, you count the places. 3 is in the ones place, 8 in the tenths, 5 in the hundreths, and 1 in the thousandths. The thousandths place is what we are rounding, so we look at the next number, 9, which tells us to round the 1 up to 2
Answer:
153.385
Step-by-step explanation:
153.38519
153.38519
The digit to the right of the thousandth (the the one, which is bolded) is less than or equal to 4, which means we round down.
153.38519 ≈ 153.385
Hope this helps.
What happens when the multiplicity of a real root is even?
Answer:
Step-by-step explanation:
The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.
which of the following does not describe a rigid motion transformation
Answer:
The answer to this question is dilating the figure by a scale factor of one half.
five times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits . if four times the value of the digit at ones place is equal to half of the place value of the digit at tens place, find the numbers
9514 1404 393
Answer:
45
Step-by-step explanation:
Let x and y represent the tens and ones digits, respectively. The 5 times the sum of digits is 5(x+y). The value of the digit-reversed number is (10y+x), so the required relation is ...
5(x +y) = (10y +x) -9
The other relationship between the digits is given as ...
4y = 1/2(10x)
A graphing calculator shows the solution to these equations is (x, y) = (4, 5).
The two-digit number is 45.
__
Additional comment
You can solve these equations in any of a variety of ways. Using a graphing calculator to find integer solutions is fast and easy, so is one of my favorites. Here, the coefficients on one equation are not easy multiples of those in the other, so substitution and/or elimination can get messy. In this situation, I like to use the "cross-multiplication" method, which starts with the equations in general form:
4x -5y +9 = 05x -4y +0 = 0From the coefficients of these equations, differences of cross products are formed:
d1 = 4(-4) -(5)(-5) = 9d2 = -5(0) -(-4)(9) = 36d3 = 9(5) -0(4) = 45Then the solutions are the solutions to 1/d1 = x/d2 = y/d3:
x = d2/d1 = 36/9 = 4y= d3/d1 = 45/9 = 5(x, y) = (4, 5) ⇒ the number is 45.
__
This method is one of several variations of Cramer's Rule, the general solution of systems of linear equations using matrix methods.
GIVING OUT BRAINLIEST PLEASE HELP ME!!
Answer: B (0,0) r=4
Step-by-step explanation:
tell whether or not the measurements below form a triangle:
1. 4, 5, 10
2. 12, 26, 20
3. 2, 3, 5
Answer:
Below.
Step-by-step explanation:
If the sum of any 2 sides are less than or equal to the third side then there's no triangle
1. N0 because 4 + 5 < 10
2. YES
3. NO because 2 + 3 = 5.
Answer:
Step-by-step explanation:
1 . 4,5,10 : this measurement does not form a triangle because the sum of two sides is not greater than the third side (longest side)
4 + 5 > 10
9 > 10 (this is not satisfied)
2. 12,26,20 :this measurement forms a triangle beacuse the sum of two sides is greater than the third side
12 + 26 > 20
38 > 20
3 .
2,3,4 : this measurement does not form a triangle because the sum of two sides is not greater than the third side.
2 + 3 > 5
5 > 5 (this is not satisfied)
d= (r+c)t
how do i solve for t?
Answer:
[tex] { \tt{d = (r + c)t}}[/tex]
Divide ( r+c ) on both sides:
[tex]{ \tt{t = { \frac{d}{(r + c)} }}}[/tex]
Answer:
d / ( r + c) = t
Step-by-step explanation:
d = ( r + c ) t
Divide each side by ( r + c)
d / (r + c ) = ( r + c ) t / ( r + c)
d / ( r + c) = t
Antiderivative of Acceleration is???
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
Step-by-step explanation:
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
