Answer:
k = 0.2980
Step-by-step explanation:
Given:
number of months t =3
number of hits y = 10000
The equation is modeled as
[tex]y= 4090e^{kt}[/tex]
We need to find value of k.
Now Substituting the values in above equation we get.
[tex]10000= 4090e^3k\\e^{3k}=\frac{10000}{4090}\\\\[/tex]
Now taking Anti log on both side to remove e we get,
[tex]3k = \ ln \frac{10000}{4090}\\\\3k = 0.8940\\k = \frac{0.8940}{3}= 0.2980[/tex]
Hence the value of k = 0.2980.
The value of k is 0.2981.
We are given that in the website's third month (t = 3), there were 10,000 hits. We need to find the value of k.
1. First, substitute y = 10000 and t = 3 into the given equation:
10000 = 4090e3k
2. Next, solve for the exponential term:
10000 / 4090 = e3k
This simplifies to:
10 / 4.09 = e3k
2.444 = e3k
3. Take the natural logarithm (ln) of both sides to solve for k:
ln(2.444) = 3k
Calculating ln(2.444) yields approximately 0.8944.
0.8944 = 3k
4. Finally, solve for k:
k = 0.8944 / 3
k ≈ 0.2981
Therefore, the value of k, rounded to four decimal places, is approximately 0.2981.
Please answer this correctly
Is the answer
12:59pm
8:27am
3:59pm
9:13am
Answer:
3:59 PM
Step-by-step explanation:
When the plane arrives in Fargo, the time is 13:59 or 1:59 PM in pacific time. From the pacific to central, you add 2 hours. 1:59 + 2 hours is 3:59 PM.
Which measure is greatest, the amount of milk cottage cheese, or strawberries? 3/4 cup milk 2/6 cup cottage cheese 8/12 cup strawberries
Answer:
3/4 cup milk
Step-by-step explanation:
I order to be able to compare quantities that come in fraction form, the best is to write all of them as equivalent fractions with the same denominator. That way just looking at the magnitude of the numerators will allow us to give the answer.
the fractions to consider are: [tex]\frac{3}{4} \,,\, \frac{2}{6} \,, \, and\, \frac{8}{12}[/tex]
so the denominators in question are: 4, 6, and 12.
We see that 12 is the Least Common Denominator (LCD) of these three, since 4 divides perfectly 12, 6 divides 12 perfectly, and 12 divides itself perfectly as well.
Now, the initial fractions can be re-written with equivalent fractions showing denominator 12.We do such by multiplying numerator and denominator of the first fraction by "3" in order to get a "12" in the denominator. By multiplying the second fraction by 2 in numerator and denominator to get a "12" in the denominator. Notice that we don't need to modify the third fraction since it is already expressed with denominator 12:
[tex]\frac{3}{4} \,,\, \frac{2}{6} \,, \, and\, \frac{8}{12}=\\=\,\frac{9}{12} \,,\, \frac{4}{12} \,, \, and\, \frac{8}{12}[/tex]
Therefore, the greatest of these is the first fraction, that shows a "9" in the numerator (the largest of the three numerators)
An ice cream factory makes 350 quarts of ice cream in 2 hours. How many quarts could be made in 36 hours? What was that rate per day?
Answer:
36 hours - 6,300
24 hours - 4,200
In 36 hours, 6300 quarts of ice cream could be made. The rate per day would be 6300 quarts per day.
350 quarts of ice cream are made in 2 hours. To find out how many quarts could be made in 36 hours, we can set up a proportion: 350 quarts / 2 hours = x quarts / 36 hours. Solving for x gives us 6300 quarts in 36 hours. To find the rate per day, we divide the total quarts made in 36 hours by the number of days: 6300 quarts / 1 day = 6300 quarts per day.
A customer bought a car and paid $1,080 in sales tax.The rate is 6%?
The price of car is $18000
Step-by-step explanation:
Given
Sales tax on car = $1080
Rate = 6%
Let x be the price of the car
We know that as the rate of sale tax is 6%, 6% of x is 1080
Using mathematical notation
0.06x = 1080
Dividing both sides by 0.06
[tex]\frac{0.06x}{0.06} = \frac{1080}{0.06}\\\\x = 18000[/tex]
Hence,
The price of car is $18000
Keywords: Rate of tax, Percentage
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negative 8 minus the product of three and a number is 19
Answer: -8 - (3 x N) = 19
n = number
Step-by-step explanation: i think thats how u write it
Answer:
[tex](-8)-3n=19[/tex]
Step-by-step explanation:
In the equation, the difference of -8 and the product of 3 and n (refering to "the number" in the question) equals 19.
Hope this helps
Which of the following shows an equivalent expression to
[(5.3). 12] if only the associative property was used to transform the expression?
The equivalent expression using associative property is [tex]5 \times(3 \times 12)[/tex]
Solution:Given expression is [(5.3). 12]
We are asked to write a equivalent expression using associative property
The associative property states that you can add or multiply regardless of how the numbers are grouped. By 'grouped' we mean 'how you use parenthesis'. In other words, if you are adding or multiplying it does not matter where you put the parenthesis
Associative property is as follow:-
a + (b + c) = (a + b) + c { for Addition}
(a x b) x c = a x (b x c) { for multiplication}
The given expression is [(5.3). 12], which can be written as
[tex](5 \times 3) \times 12=5 \times(3 \times 12)[/tex]
NEED HELP FAST!!!!! The graph below compares plant height to the age of the plant, in weeks. Y=1.3x-0.8 Based on the graph, which is the best prediction of the height of the plant at 5 weeks?
A.)4 inches
B.) 5 inches
C.)6 inches
D.)7 inches
will award with brainllest
Answer:
C) 6 inches
Step-by-step explanation:
Given function:
[tex]Y=1.3x-0.8[/tex]
The function compares plant height in inches to the age of plant in weeks.
So, we can say
[tex]Y[/tex] represents height of plant in inches.
[tex]x[/tex] represents age of the plant in weeks.
In order to predict the height of the plant in 5 weeks, we will plugin [tex]x=5[/tex] in the given function and evaluate [tex]Y[/tex]
⇒ [tex]Y=1.3(5)-0.8[/tex]
⇒ [tex]Y=6.5-0.8[/tex]
⇒ [tex]Y=5.7[/tex] inches
Thus the approximate height of plant in 5 weeks would be [tex]\approx 6[/tex] inches
Answer:
C: 6
Step-by-step explanation:
2. Tom is planting 24 vegetables in his garden.
He arranges them into rows and columns.
If there are 4 vegetables in each row, how
many columns are there?
Write the division sentence, then draw an array to
support your answer.
Answer: 6 columns.
Step-by-step explanation:
24 ÷ 4 = 6
Answer:
6
Step-by-step explanation:
24 divided by 4 = 6
mr.rogers is buying candy for his class. he'll distribute the candy equally among his 25 scholars, and he wants each scholar to recieve at least 3 pieces of candy. he's also going to keep 5 pieces for himself. write an inequality statenent to represent the least number of candies that mr.rogers can buy
25 scholars × 3 candies = 75 candies
5 candies for himself = 80
Answer: 80 candies
An inequality statement to represent the least number of candies that Mr.Rogers can buy is 80≥x.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given that, Mr.Rogers distribute the candy equally among his 25 scholars.
Let the total number of candies be x.
Here, inequality is 25×3+5≥x
80≥x
Therefore, an inequality statement to represent the least number of candies that Mr.Rogers can buy is 80≥x.
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Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each. Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella does because Stella only has enough supplies to make 40 pies. let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes.
Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.
Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.
Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.
Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.
Answer:
Jamie: His inequality would look like this: 25x >= 600
Stella: Her inequality would look like this: 15y >= 600
Her limitations would be listed as: y=40
Yep. Stella has plenty of money by baking 40 pies; $600.
We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.
Since the cost for washing one car is $25
Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.
Since the cost for making one pie is $15
Therefore, the cost of making y pies is 15y.
Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600
We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So.... y<=40
Bam.
In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40
The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.
Step-by-step explanation:
4. Given ABC with vertices at A(1,-4), B(-1,-2), and C(-2,-5), prove or disprove that ABC is isosceles
Answer: ABC is isosceles
Step-by-step explanation:
The coordinate of points given are:
A(1,-4)
B(-1, -2 )
C ( -2 , -5 )
For ABC to be isosceles , then AB must be equal to BC or AB = AC
The next thing to do is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
Calculating AB first , we have
[tex]\sqrt{(-1-1)^{2}+(-2+4)^{2} }[/tex]
= [tex]\sqrt{4+4}[/tex]
=[tex]\sqrt{8}[/tex]
Therefore:
AB = [tex]\sqrt{8}[/tex]
Calculating BC , we have :
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
D = [tex]\sqrt{(-2+1)^{2}+(-5+2)^{2} }[/tex]
D = [tex]\sqrt{10}[/tex]
Therefore:
BC = [tex]\sqrt{10}[/tex]
Calculating AC , we have :
D = [tex]\sqrt{(x_{2}-x_{1}) ^{2}+(y_{2}-y_{1}) ^{2}}[/tex]
D = [tex]\sqrt{(-2-1)^{2}+(-5+4)^{2} }[/tex]
D = [tex]\sqrt{10}[/tex]
Therefore:
AC = [tex]\sqrt{10}[/tex]
Since AC = BC then triangle ABC is isosceles
Practice Analytic Geometry
1. Find the midpoint of the line segment defined by the points: (sqrt 2, 0) and (0, -sqrt 2)
Answer is ((sqrt 2)/2, (-sqrt2)/2)
2. Find the distance of the line segment joining the two points: (5,4) and (-2,1)
Answer is sqrt 58
3. Find the distance of the line segment joining the two points: (1/2, -5/2) and (-4/3, -1/6)
Answer is (sqrt 317)/6
4. Given triangle ABC with vertices at A (1,-4), B (-1, -2), and C (-2,-5), prove or disprove that triangle ABC is an isosceles
Answer triangle ABC is isosceles since AB = sqrt 8, BC = sqrt 10, and AC = sqrt 10
In Quadrilateral ABCD, AB|CD and mZ5
What is mZ5?
Answer:
∠5 = 27°
Step-by-step explanation:
CDB = ABD (alternate angle)
∠2 = ∠5
∠5 = 27°
(Correct me if i am wrong)
Answer:
∠5 = 27°
Step-by-step explanation:
CDB = ABD (alternate angle)
∠2 = ∠5
∠5 = 27°
What is 5,841 divided by 62
it's 94.20967742 if you simplify it you will get 94.21
5,841 divided by 62 equals 94 with a remainder of 13. You can find this using long division, where 62 goes into 584 (from 5,841) nine times and then into 261 (the remainder with the next digit) four times.
Explanation:To find the result of 5,841 divided by 62, we can use long division. Let's break down the problem step by step:
Place 5,841 under the division bar and 62 outside, to the left.First, determine how many times 62 goes into 584 (the first three digits of 5,841). It goes in 9 times because 9 * 62 = 558. Place the 9 above the division bar, above the 4.Subtract 558 from 584 to get 26 and bring down the next digit from 5,841, which is 1, giving us 261.Now, see how many times 62 can fit into 261. It goes in 4 times (4 * 62 = 248), so we place a 4 above the division bar, to the right of the 9.Subtract 248 from 261 to get a remainder of 13.Since there are no more digits to bring down, we have completed the long division. So, 5,841 divided by 62 equals 94 with a remainder of 13.To express this as a decimal, we could continue the division process by adding a decimal point and zeros to the dividend, but that is not requested in this problem.
What is the value of x?
6x - 3
3x + 6
Enter your answer in the box.
5x
Answer:
Step-by-step explanation:
The correct answer is x = 3
The value of x in the equilateral triangle is 3 units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the perimeter of any planer figure except a circle is the sum of the lengths of all the sides and we also know that an equilateral triangle has equal sides and equal angles.
∴ We can equate any of the two sides of the given equilateral triangle.
So, 5x = 6x - 3.
5x - 6x = - 3.
- x = - 3.
x = 3.
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how would i distribute 2.5(-y+2)
How to distribute 2.5(-y + 2)
= (2.5 * -y) + (2.5 * 2)
= -2.5y + 5
Distributive Property is when you multiply different addends from a sum then add them.
______
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If 168 chocolate chips weigh 5
ounces. How many chocolate chips are in an ounce?
Answer:
About 34
Step-by-step explanation:
There are 168 chocolate chips in 5 ounces. That means you want to know how many chips there are per ounce. Divide 168 by 5 and you get approximately 34 chocolate chips per ounce (33.6 if you need this)
Answer:
34
Step-by-step explanation:
All you have to do is divide
168 / 5 = 33.6
so about 34 chocolate chips in an ounce
The ages of five friends are 20,31,28,31 and 25. How many of the friends are older than the average (arithmetic mean) age?
Answer:
3 friends
Step-by-step explanation:
The mean age is 27 so 3 friends are above that age.
The average age of the friends is 27. Only two of the friends, both aged 31, are older than the average age.
Explanation:To find out how many of the friends are older than the average age, we need to first find the arithmetic mean of the ages. We do this by adding up all the ages and dividing by the number of ages. So, (20+31+28+31+25)/5 = 27. Once we have the average, we can see that the ages of 31 and 31 are larger than the average of 27. Therefore, there are 2 friends whose ages are older than the average.
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The total of monthly payments for a three-year loan is $22,317.12. The APR is 4%. How much money was originally borrowed?
Answer:
$717336
Step-by-step explanation:
The total of monthly payments for a 3-year loan is $22317.12.
So, the total amount has to pay back in 3 years is $(22317.12 × 12 × 3) = $803416.32.
Let the amount of money that was originally borrowed is $x and the given APR is 4%.
Then we can write, [tex]x(1 + \frac{4 \times 3}{100}) = 803416.32[/tex]
⇒ 1.12x = 803416.32
⇒ x = $717336 (answer)
Divide the following by hand (long division). (Show your work )
585 ÷ 13
Answer: 45
Step-by-step explanation: To divide this start with finding how many times 585 goes into 13 which is 0. I put a picture for you to look at.
A rectangular garden measures 5m by 7m. Both dimensions are to be extended by the same amount so that the area of the garden is doubled. By how much should the dimensions increase
Final answer:
To double the area of the rectangular garden, the dimensions should increase by 5 meters.
Explanation:
To double the area of the rectangular garden, we need to find the increase in dimensions that will result in double the original area. The original dimensions are 5m by 7m, so the original area is 5m x 7m = 35 square meters. To double this area, the new area should be 35 square meters x 2 = 70 square meters. Let's assume the increase in dimensions is 'x'. The new dimensions will be (5m + x) by (7m + x). We can set up the equation:
(5m + x)(7m + x) = 70 square meters
Expanding and simplifying the equation, we get:
35m + 5x + 7x + x^2 = 70 square meters
Combining like terms, we have:
x^2 + 12x + 35 = 70 square meters
Next, we rearrange the equation into standard form:
x^2 + 12x + 35 - 70 = 0
Simplifying further, we get:
x^2 + 12x - 35 = 0
Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation gives us:
(x + 7)(x - 5) = 0
Setting each factor equal to zero, we have:
x + 7 = 0 or x - 5 = 0
Solving for 'x', we get:
x = -7 or x = 5
Since a negative value doesn't make sense in this context, we can conclude that the dimensions should increase by 5 meters.
Nathan went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 25 grams of sugar and each bottle of juice has 35 grams of sugar. Nathan purchased 3 more bottles of juice than bottles of soda and they all collectively contain 405 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system.
25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.
Step-by-step explanation:
Given,
Sugar contained by each soda bottle = 25 grams
Sugar contained by each juice bottle = 35 grams
Let,
x be the number of soda bottles.
y be the number of juice bottles.
According to given statement;
25x+35y=405 Eqn 1
y= x+3 Eqn 2
25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.
Keywords: Linear equation, substitution method
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Delia has 493 stamps in her stamp collection. She can put 16 stamps on each page of an album. How many pages can she fill completely.
Answer:30
Step-by-step explanation:
it’s division. there’s some left over but they wouldn’t make a complete page.
493/16=30.8....
Jody's older brother is only three years less than twice Jody's age. If the sum of their ages is 30, then what is the age of jodys brother
Answer: 19
Step-by-step explanation:
j+2j-3 = 30
3j = 33
j = 11
and
b = 2j-3
b = 2(11)-3
b = 19
Answer:19
Step-by-step explanation:
An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at the same rate of descent. Write an equation to represent the height of the airplane in feet above the ground f(x) in relationship to time in minutes x
[tex]f = 30000 - (2000 \times m)[/tex] is an equation to represent the height of the airplane in feet above the ground f(x) in relationship to time in minutes x
Step-by-step explanation:
As given that the plane is at 30000 feet above the grounds. And starts descending at the rate of 2000 feet/ min
So, let us consider the below,
H= height in feet above ground
r = rate of descent
m = minutes
So, now frame the required equation format with the given data as follows,
[tex]H = 30000 - (2000 \times m)[/tex]
Leonard it sells small watermelons for seven dollars each and large watermelons for $10 each one day the number of small watermelons he saw was 15 more than the number of large watermelons and he made a total of $394 how many small and how many large watermelons a did he sell?
What are the intercepts of the graphed function?
O
O
x-intercept = (-1,0)
y-intercept = (-3,0)
x-intercept = (0, -1)
y-intercept = (0, -3)
x-intercept = (0, -1)
y-intercept = (-3, 0)
x-intercept = (1, 0)
y-intercept = (0,-3)
O
O
Answer:
x-intercept = (1, 0)
y-intercept = (0, −3)
Step-by-step explanation:
These is the only answer that make the most sense:
x-intercept: [tex]\displaystyle 0 = y[/tex]
y-intercept: [tex]\displaystyle 0 = x[/tex]
I am joyous to assist you anytime.
The intercepts of the graph function are:
The x-intercept is (-1, 0).
The y-intercept is (0, 3).
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
From the graph,
The x-intercept is the point when y = 0.
The y-intercept is the point when x = 0.
So,
The x-intercept is (-1, 0).
The y-intercept is (0, 3).
Thus,
The intercepts of the graph function is:
The x-intercept is (-1, 0).
The y-intercept is (0, 3).
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what is 29 divided by 11
Answer:
2.63
Step-by-step explanation:
29/11=2.63
Answer:
2.64
Step-by-step explanation:
First you Set the problem up like
11/29
then you take
11/29
11x2= 22
29
-
22
=
7
i dont understand this question, and needs to be done by tomorrow morning please help
Answer:
ABCD and EFGH
ABCD and PQRS (or EFGH and PQRS)
Dilate by a scale factor of 3
Step-by-step explanation:
Congruent means they have the same shape and size.
Similar means they have the same shape, but not necessarily the same size.
The orientation (rotation angle) or position do not matter.
EFGH is reflected and rotated, so it maintains the same shape and size as ABCD. Therefore, they are congruent.
PQRS is scaled and translated, so it has the same shape, but different size than ABCD. Therefore, they are similar but not congruent.
Also, PQRS is similar to EFGH, but not congruent.
To make EFGH congruent to PQRS, we need to make it the same size. So we need to scale EFGH by a factor of 3.
The ratio of men to women working for a company is 2 to 3. If there are 42 women for the company what is the total number of employees
Answer:
70 people
Step-by-step explanation:
Final answer:
The total number of employees at the company is calculated using the given ratio of men to women, 2 to 3, along with the information that there are 42 women. By converting the ratio into actual numbers, we find that there are 28 men and 42 women, totaling 70 employees.
Explanation:
The question asks about the total number of employees in a company given the ratio of men to women and the number of women. To find the answer, we will use the ratio of men to women, which is 2 to 3, and the information that there are 42 women working for the company.
Since the ratio of men to women is 2 to 3, this implies there are 2 men for every 3 women in the company.If there are 42 women, and the ratio of women to the total number of employees is 3 parts, we can find out how many parts represent the men. One part would be 42 women divided by 3, which is 14 men.According to the ratio, there are 2 parts for men, therefore, 2 parts times 14 give us 28 men.To find total number of employees, we add the number of men and women, which is 28 men plus 42 women, equating to 70 employees.24.3 ounces for $8.76 or 32.6 ounces for $16.95 I need to use the unit rate to answer this questions and I'm really bad at this.
Answer:
8.76/24.3= 0.36
16.95/32.6= 0.519 round up to make 0.52
Step-by-step explanation:
8.76/24.3= 0.36
16.95/32.6= 0.519