Answer:
1.38 pm.
Step-by-step explanation:
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he has made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
So the time when he finishes 60 cupcakes is 1.08 + 30
= 1.38 pm.
The 60 cupcakes will be decorated at 1.38 pm.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
After 1.05 PM the rate at which he decorates the cakes is 10 - 5 = 5 cakes per 3 minutes = 5/3 cakes per minute. At 1.08 pm he made 10 cupcakes.
At 1.08 he has to decorate another 50 cakes so the time he will take to do these is 50 / 5/3 = 50 * 3/5 = 30 minutes.
The time when he finishes 60 cupcakes is:-
1.08 + 30 = 1.38 pm.
Therefore, 60 cupcakes will be decorated at 1.38 pm.
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In 2017, Moreno Cheeses had a net income of $42,390, paid preferred dividends of $6,000 and 18,000 shares of common stock outstanding. What was their earnings per share for 2017?a) $1.69 b) $2.69 c) $2.02 d) $2.36
Answer:
Option c.
Step-by-step explanation:
In 2017, Moreno Cheeses had a net income of $42,390, paid preferred dividends of $6,000.
value of the shares = Net income - preferred dividends
= 42,390 - 6,000
= $36,390
To find their earnings per share = [tex]\frac{\text{Value of the shares}}{\text{total number of shares}}[/tex]
= [tex]\frac{36,390}{1,8000}[/tex]
= $2.02 per share
Option c) $2.02 per share
given line ac with line ab=2x-4, bc=4x and ac=2x+12 find ac
Answer:
The answer to your question is: AC = 20
Step-by-step explanation:
Data
AB = 2x - 4
BC = 4x
AC = 2x + 12
AC = ?
AB + BC = AC
2x - 4 + 4x = 2x + 12
6x - 4 = 2x + 12
6x - 2x = 12 + 4
4x = 16
x = 16/4
x = 4
AB = 2(4) - 4 = 8 - 4 = 4
BC = 4(4) = 16
AC = 2(4) + 12 = 8 + 12 = 20
4 + 16 = 20
20 = 20
4. A number of whales were asked about things that they dislike
19 dislike giant squids
6 dislike giant squids and pollution and Captain Ahab
24 dislike Captain Ahab
1 dislike pollution but don't s dislike giant squids and don't dislike Captain Akab
11 dislike Captain Ahab and giant squids
3 dislike pollution and Captain Ahab but don't dislike giant squids
20 dislike pollution
5 have no dislikes
A How many whales were surveyed?
B. How many dislike at least one of those three tags?
C. How many dislike Captain Ahab but don't dislike giant squids?
D. How many dislike giant squids or pollution?
6. A number of classicists were asked to identify their favorite epic poets. The results
The question is solved by carefully analyzing the given figures and working step by step to avoid double counting of items. Adding numbers to find total whales and then subtracting or combining them as required gives the specific group numbers.
Explanation:This question requires calculations around the given number of whales and their specific dislikes. Let's address each part of the question step by step:
A. To find out the total number of whales surveyed, we add all the mentioned whales together, including those with no dislikes.
B. To find out the number of whales disliking at least one thing, we subtract the whales with no dislikes from the total number of whales.
C. To find out the number of whales that dislike Captain Ahab but not giant squids, we need to remove the whales that dislike both these things.
D. To determine the number of whales that dislike either giant squids or pollution, we need to avoid counting the whales that dislike both twice.
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What is the converse and the truth value of the converse of the following conditional:
If an angle is 60 degrees, then it is acute.
Answer:
converse: If an angle is acute, then it is 60°.the converse is FALSEStep-by-step explanation:
The converse of a conditional swaps the "if" and "then" clauses. Here, that makes the converse read ...
If an angle is acute, then it is 60 degrees.
Since an acute angle may have any non-negative measure less than 90°, it is not true that its measure is necessarily 60°.
If x and y are linearly independent, and if {x, y, z} is linearly dependent, then z is in Span{x, y}.Choose the correct answer below.True / False.
The correct answer is True, as z must be expressible as a linear combination of the linearly independent vectors x and y, putting z in the Span{x, y}.
Explanation:If x and y are linearly independent, and if the set {x, y, z} is linearly dependent, then it must be the case that z can be expressed as a linear combination of x and y. This is because in a linearly dependent set, at least one of the vectors can be written as a combination of the others. Since x and y are linearly independent, they cannot be written in terms of each other, leaving z to be the vector that depends on x and y. Therefore, z is in the Span{x, y}. The correct answer to the question is True.
A submarine traveling 200 meters below the surface of the ocean increases its depth by 45 meters. Adam says that the new location of the submarine is -155 meters. Describe an error Adam could have made that would result in the answer he gave
Answer:
The error that Adam could have made is added 45 to the depth of
submarine instead of adding -45
Step-by-step explanation:
* Lets explain how to solve the problem
- A submarine traveling 200 meters below the surface of the ocean
- Increases its depth by 45 meters
- Adam says that the new location of the submarine is -155 meters
- We need to know the error of Adam
∵ We consider the surface of the ocean is the zero level
∵ The submarine is 200 meters below the surface of the ocean
∵ Below means negative
∴ The depth of submarine is -200 meters
∵ It increases the depth by 45 meters
- That means it travels down another 45 meters
∵ Down means negative
∴ The depth of submarine = -200 + (-45) = -245 meters
∴ The depth of submarine is 245 below the surface of the ocean
- Adam could thought that the submarine traveled up for 45 meters
then he add 45 to -200
∵ -200 + 45 = -155 meters
∴ The error that Adam could have made is added 45 to the
depth of submarine instead of adding -45
Final answer:
Adam incorrectly subtracted the increased depth from the initial depth, but the correct method is to add the increased depth to the initial negative depth, resulting in a depth of -245 meters.
Explanation:
The error Adam made in his calculation is that he subtracted the increased depth from the initial depth, instead of adding it. When a submarine dives deeper from any initial depth below sea level, we must add the increase to the existing negative depth.
The submarine was originally at -200 meters (below the surface), and then it went 45 meters deeper. Thus, the correct new depth is -200 meters - 45 meters = -245 meters.
Prove that quadrilateral ABCD with the vertices A (2,1), B (1,3), C (-5,0) D (-4,-2) is a rectangle. Graph the rectangle and then use appropriate formulas to justify / prove your answer.
Answer:
Just find the distance of the vertices of the quadrilateral ( such as : AB, BC, CD DA )by using distance formula...
Then if opposite sides of quadrilateral is equal then it is rectangle .....
hope you understand...
Sock hop (ExH). You have 10 pairs of socks, fi ve black and fi ve blue, but they are not paired up. Instead, they are all mixed up in a drawer. It ’ s early in the morning, and you don ’ t want to turn on the lights in your dark room. How many socks must you pull out to guarantee that you have a pair of one color? How many must you pull out to have two good pairs (each pair is the same color)? How many must you pull out to be certain you have a pair of black socks?
Final answer:
You need to pull out 6 socks to guarantee a pair of one color, 11 socks to guarantee two pairs, and 7 socks to be certain you have a pair of black socks.
Explanation:
To guarantee that you have a pair of one color when selecting from a mix of 10 pairs of socks (5 black and 5 blue), you must consider the worst-case scenario. This occurs when you alternatively pick one of each color. Therefore, after picking 5 black and 4 blue socks, the next sock you pick will guarantee a pair. So, you need to pull out 6 socks to ensure a pair of one color (5 of one color and 1 of the other).
To have two good pairs, you would continue this pattern. After the first pair is secured with 6 pulls, you would possibly pick the alternating color for the next 4 pulls, and then any subsequent sock would complete a second pair of one color. In total, this would require pulling out 11 socks to ensure two pairs.
To be certain you have a pair of black socks, prepare for the possibility of pulling out all 5 blue socks first. After these 5, the next 2 socks you pull out will be black, giving you at least one pair of black socks. Therefore, you would need to pull out 7 socks to be certain.
Alexis has two ribbons one of the Rubens is 40 cm long and the other is 70 m long she wants to cut a trip into equal pieces of the same like with no ribbon left over what is the longest length she can cut the ribbons in centimeters
Answer: 17.5cm
Steps: 70m = 700cm
40cm = 40cm
700cm/40cm
=17.5cm
vous êtes les bienvenus, baisers cher!
Answer:
40 cm
Step-by-step explanation:
She has one ribbon of 40 cm and another ribbon of 70 m
First, we have to change 70 m to cm, to do this we know that 1m = 100 cm
so we multiply 70*100 = 7,000 cm.
Now we have to find the longest length she can cut the ribbons in centimeters.
To do this we have to find the Greatest Common Factor of 40 and 7000 to know what is the longest length she can cut the ribbons.
To find the Greatest Common Factor we have to find the factors for each number:
Factors of 40:
1, 2, 4, 8, 10, 20, 40
Factors of 7000
1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40
The Greatest Common Factor is 40, so she can have pieces of 40 cm long.
The chance of a hurricane hitting during any year in the area victor will move to is 0.10 . what is the probability victor will have a hurricane five years in a row?
Answer:
10^-5 or 1/100,000
Step-by-step explanation:
That probability of 5 events in a row is the 5th power of the probability of one of them, assuming they are independent.
0.1^5 = (10^-1)^5 = 10^-5
The probability of a hurricane hitting five years in a row, given an annual probability of 0.10, is calculated by raising 0.10 to the power of 5. The result is 0.00001, or 0.001%.
Explanation:The probability of a hurricane hitting during any one year in the designated area is 0.10, making it a fairly rare event. The student wants to know what the probability is that this will occur five years in a row. In probability theory, we calculate the likelihood of independent events happening consecutively by multiplying their individual probabilities together.
In this example, each year is an independent event, meaning one year's hurricane occurrence does not impact the likelihood of a hurricane in the subsequent year. Given that the annual probability of a hurricane is 0.10, if we want to find the probability of a hurricane hitting for five consecutive years, we simply raise this probability to the power of 5.
So, the probability of Victor experiencing a hurricane five years in a row is 0.10 to the power of 5, equivalently written as (0.10)^5.
This equals 0.00001 (or 0.001% if written as a percentage). This demonstrates that the likelihood of experiencing a hurricane five years in a row given an annual probability of 0.10 is quite miniscule.
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Under fair value option, which of the following affects the income the investor recognizes from its ownership in the investee
A. The investees reported income adjusted for excess cost over book value amortization
B. Changes in the fair value of the investors ownership shares of the investee
C. Intra-equity profits from upstream sales
D. Extraordinary items reported by the investee
Answer:
B. Changes in the fair value of the investors ownership shares of the investee
Step-by-step explanation:
The fair value option is defined as the alternative for any business that helps them to record its financial instruments at their fair values.
The answer is : Changes in the fair-value of the investor's ownership in shares of the investee.
Solve using synthetic division:
(x^5+2x^2+2x+1)/(x^2-1)
Answer:
x^3 +x +2 +3/(x -1)
Step-by-step explanation:
Synthetic division can be done using a divisor with a power of the variable other than one, but the most straightforward application of it uses a binomial divisor with a variable coefficient of 1. Fortunately the divisor in this problem is the difference of squares, so can be factored into two divisors. We can make use of synthetic division to divide by one of them, then we can use it again with the other divisor.
= ((x^5 +2x^2 +2x +1)/(x +1)) / (x -1)
= (x^4 -x^3 +x^2 +x +1)/(x -1)
= x^3 +x +2 + 3/(x -1)
The remainder from the second division is simplified by the fact that there is no remainder from the first division. If desired, the final remainder can be expressed over the original divisor as (3x +3)/(x^2 -1) by multiplying numerator and denominator by the first divisor, (x+1).
_____
The synthetic division tableaux are attached. First, we divide by (x+1), then that result is divided by (x-1).
We assume you've been shown how this works. If not, there are numerous web sites and videos that can explain better than is possible in this space.
2. Which memory locations are assigned by the hashing function h(k) = k mod 101 to the records of insurance company customers with these Social Security numbers? a) 104578690 b) 432222187 c) 372201919 d) 501338753
Answer:
Memory Locations assigned
a) 58 b) 60 c) 52 d) 3
Step-by-step explanation:
We are given that:
h(k) = k mod 101
To find the memory location, we need to evaluate the modulus value abbreviated as mod, k modulo n, which returns the value of remainder when k is divided by 101.
a) 104578690
104578690 mod 101 = 58
b) 432222187
432222187 mod 101 = 60
c) 372201919
372201919 mod 101 = 52
d) 501338753
501338753 mod 101 = 3
The memory locations assigned by the hashing function h(k) = k mod 101 to the Social Security numbers are: a) 81, b) 14, c) 15, and d) 38.
Explanation:The hashing function h(k) = k mod 101 assigns memory locations to records based on the modulus operation. To find the memory locations assigned to the Social Security numbers given, we need to calculate the result of k mod 101 for each number.
For Social Security number 104578690, the result is 81.For Social Security number 432222187, the result is 14.For Social Security number 372201919, the result is 15.For Social Security number 501338753, the result is 38.Therefore, the memory locations assigned to the records are:
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Jane spent $40 on flowers. Each small flower cost $2, and each large flower cost $3. Write an equation that describes the relationship between cost and number of flowers purchased, where X is the number of small flowers and Y is the number of large flowers. Choose the best answer.
Answer: Our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]
Step-by-step explanation:
Since we have given that
Total amount he spent on flowers = $40
Let the number of small flowers be 'X'.
Let the number of large flowers be 'Y'.
cost of small flowers = $2
cost of large flowers = $3
According to question, it becomes,
[tex]2X+3Y=40[/tex]
Hence, our required equation describes the relationship between cost and number of flowers purchased is [tex]2X+3Y=40[/tex]
The equation that describes this situation is.
2X + 3Y = 40
How to write the equation?Let's define:
X = number of small flowers
Y = number of large flowers.
We know that Jane spent $40 on the flowers, and each small flower costs $2 and each large flower costs $3, then the total cost of the X and Y flowers is:
2*X + 3*Y
And that must be equal to 40, which is the amount she spent.
2X + 3Y = 40
That is the equation.
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Chelsea walked up a road that has 15% grade to get to her favorite store. That means the slope of the hill was 15/100. At what angle does the road come up from the ground ?
Answer:
[tex]8.53\°[/tex]
Step-by-step explanation:
we know that
The grade of a road can be thought of as rise/run, and you usually see it as a percentage.
So, a 15% grade is the same as a grade of 15/100; for every 15 units the road goes up vertically, it goes 100 units horizontally
see the attached figure to better understand the problem
Let
[tex]\theta[/tex] -----> angle does the road come up from the ground
The tangent of angle theta is equal to the ratio of the opposite side by the adjacent side
[tex]tan(\theta)=\frac{15}{100}[/tex]
[tex]\theta=tan^{-1}(\frac{15}{100})=8.53\°[/tex]
Tickets to a Broadway show cost $35 for adults and $27 for children. The total receipts for 1229 tickets at one performance were $40335. How many adult and child tickets were sold?
Answer:
The number of adults tickets sold was 894 and the number of children tickets sold was 335
Step-by-step explanation:
Let
x ----> the number of adults tickets sold
y ----> the number of children tickets sold
we know that
x+y=1,229 -----> equation A
35x+27y=40,335 ----> equation B
Solve the system by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (894,335)
see the attached figure
therefore
The number of adults tickets sold was 894 and the number of children tickets sold was 335
To solve for the number of adult and child Broadway show tickets sold, we set up and solve a system of equations. After calculation, we find that 894 adult tickets and 335 child tickets were sold.
The question asks to determine the number of adult and child tickets sold when tickets to a Broadway show cost $35 for adults and $27 for children, with a total of 1229 tickets sold for a total amount of $40335. This is a typical example of a system of equations problem.
Step-by-Step Solution:
Let x be the number of adult tickets sold and y be the number of child tickets sold.
We have two equations:
To solve the system, multiply the first equation by -27 to eliminate y:
Add this result to the second equation:
Divide by 8 to find x:
Substitute x = 894 into the first equation to find y:
Therefore, 894 adult tickets and 335 child tickets were sold.
Jackson ran 5/7 of the distance around the school track Sarah around 4/5 of Jackson's distance what fraction of the total distance around the track did Sarah run
Answer:
2/3 of the track
Step-by-step explanation:
5/7 • 4/5 is 2/3 so Sarah ran 2/3 around the track.
Convert 12 over 5 to a decimal using long division. 1.2 2.4 2.6 3.4 LOTS OF POINTS HALPPPPP!!!!!!!!!
Answer: 2.4
Step-by-step explanation:
5 /12-long division think bus stop method
5 goes into 12 twice with 2 remaining
2.
5 / 12.^2000
5 does go into 20 4 times
So you end up with
2. 4
5/12.0
Hope this helps
Answer:
Answer:
12/5=2.4
Showing the work
We know that
12/5
is the same as
12÷5
Then using
Long Division for 12 divided by 5
and rounding to a Max of 3 Decimal Places gives us
=2.4
Good day
Rosa had 3 baskets. She had 35 plums. She put the same number of plums in each basket. Now she has 5 plums left over. How many plums did Rosa put in each basket?
Answer:
10 in each with 5 left over
Step-by-step explanation:
If X - A = B, what is X?
Answer:
The answer to your question is: the first option is correct
Step-by-step explanation:
We know that X - A = B , then X = A + B
A 2 -7 B -9 5
6 1 1 -1
X will be the sum of the two matrix given
X = A + B =
2 - 9 -7 + 5 -7 -2
6 +1 1 - 1 7 0
The first option is correct
Answer:
The first option
Step-by-step explanation:
Ms. Gooden feeds stray cats in the park every evening. She never knows how many cats will come to be fed. The food is always shared equally among the cats that are at the park. One evening, when 6 cups of cat food were shared, each cat received 2 3 cup of cat food. How many cats were fed that evening?
Answer:
9 cats were fed that evening.
Step-by-step explanation:
6 divided by 2/3 equals 9, so 9 cats were fed that evening.
Hope this helps! ☺
Answer:
There are 9 cats in total
Step-by-step explanation:
Let x be the no. of cats
Each cat received cup of food = [tex]\frac{2}{3}[/tex]
Caps received by x cats = [tex]\frac{2}{3}x[/tex]
We are given that 6 cups of cat food were shared
So, [tex]\frac{2}{3}x=6[/tex]
[tex]x=\frac{3}{2} \times 6 [/tex]
[tex]x=9 [/tex]
Hence there are 9 cats in total .
Please help!!!! step by step
Answer:
y=-x-4
Step-by-step explanation:
first-divide the 3 over to the side x is on
then subtract the y over to the other side. THEN MOVE THE X BACK THE THE SIDE WITH 4. tHEN DIVIDE -X BY -1 TO GET RID OF THE NEGATIVE AFTERYOU SHOULD PUT THE NEGATIVE SIGN TO THE X.
Answer:
See the picture please
Step-by-step explanation:
Let F (x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) EverybodycanfoolFred. b) Evelyn can fool everybody. c) Everybody can fool somebody. d) There is no one who can fool everybody. e) Everyone can be fooled by somebody. f) NoonecanfoolbothFredandJerry. g) Nancycanfoolexactlytwopeople.
Answer:
a) ∀x ∃f F(x, f)
b) ∃e ∀y F(e, y)
c) ∀x ∃y F(x, y)
d) ¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)
e) ∃x ∃y F(x, y)
f) ¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]
g) ∃n ∃a ∃b [F(n, a) ∧ F(n, b)]
Step-by-step explanation: F (x, y) "x can fool y,"
domain consists of all people in the world
a) Everybody can fool Fred.
Let's say Fred = f ∈ y
∀x ∃f F(x, f)
b) Evelyn can fool everybody.
Let's say Evelyn = e ∈ x
∃e ∀y F(e, y)
c) Everybody can fool somebody.
∀x ∃y F(x, y)
d) There is no one who can fool everybody.
¬∃x ∀y F(x, y) ≡ ∃x ∀y ¬F(x, y)
e) Everyone can be fooled by somebody.
∃x ∃y F(x, y)
f) No one can fool both Fred and Jerry.
Let's say Fred = f ∈ y
Let's say Jerry = j ∈ y
¬∃x ∃f ∃j [F(x, f) ∧ F(x, j)] ≡ ∃x ∃f ∃j ¬[F(x, f) ∧ F(x, j)]
g) Nancy can fool exactly two people.
Let's say Nancy = n ∈ x
Let's say person 1 = a ∈ y
Let's say person 2 = b ∈ y
∃n ∃a ∃b [F(n, a) ∧ F(n, b)]
The statements are expressed using quantifiers as shown above. The symbols ∀, ∃, ¬, ∧, and → represent "for all," "there exists," "not," "and," and "implies," respectively.
Step 1: Define the domain and predicate.
Domain: All people in the world.
Predicate: F(x, y) means "x can fool y"
Step 2: Express each statement using quantifiers.
a) Everybody can fool Fred: ∀x F(x, Fred)
b) Evelyn can fool everybody: ∀y F(Evelyn, y)
c) Everybody can fool somebody: ∀x ∃y F(x, y)
d) There is no one who can fool everybody: ¬∃x ∀y F(x, y) or ∀x ∃y ¬F(x, y)
e) Everyone can be fooled by somebody: ∀y ∃x F(x, y)
f) No one can fool both Fred and Jerry: ∀x ¬(F(x, Fred) ∧ F(x, Jerry))
g) Nancy can fool exactly two people: ∃y₁ ∃y₂ (y₁ ≠ y₂) (F(Nancy, y₁) ∧ F(Nancy, y₂) ∧ ∀y ((y ≠ y₁ ∧ y ≠ y₂) → ¬F(Nancy, y)))
Complete question:
Let F (x, y) be the statement "x can fool y," where the domain consists of all people in the world. Use quantifiers to express each of these statements. a) Everybody can fool Fred.
b) Evelyn can fool everybody.
c) Everybody can fool somebody.
d) There is no one who can fool everybody.
e) Everyone can be fooled by somebody.
f) No one can fool both Fred and Jerry.
g) Nancy can fool exactly two people.
Every day, there are 3 times more likes on an internet video of a cat which is modeled by the function c(n) = (3)n − 1, where n is the number of days since the video posted. On the first day, there were 143 likes. What is the function that shows the number of likes each day?
A. c(n) = (3)(143)^{n-1}
B. c(n) = 143^{n-1}
C. c(n) = (3)143 − n
D.143(3)^{n-1}
The function that represents the number of likes each day is[tex]\(c(n) = 143(3)^{n-1}\)[/tex]. Therefore, the correct answer is option D.
The function [tex]\(c(n) = (3)n - 1\)[/tex] models the number of likes each day, where [tex]\(n\)[/tex] is the number of days since the video was posted.
On the first day, there were 143 likes.
To find the function that shows the number of likes each day, we need to substitute [tex]\(n = 1\)[/tex] into the given function and solve for the number of likes.
Substituting [tex]\(n = 1\) into \(c(n) = (3)n - 1\)[/tex], we get:
[tex]\[c(1) = (3)(1) - 1\][/tex]
[tex]\[c(1) = 3 - 1\][/tex]
[tex]\[c(1) = 2\][/tex]
So, on the first day[tex](\(n = 1\)),[/tex] there were 2 likes. Since the problem states that there were actually 143 likes on the first day, the correct function should take this into account. Therefore, the correct function is:
[tex]\[c(n) = 143(3)^{n - 1}\][/tex]
Thus, the correct option is:
[tex]D. \(143(3)^{n-1}\)[/tex]
The correct function modeling the number of likes each day with 143 initial likes and tripling daily is: [tex]\[ c(n) = 143 \times 3^{n-1} \][/tex]
This aligns with the given exponential growth pattern.
To determine which function models the number of likes each day, let's consider the following:
- The initial number of likes is 143. This is the base case.
- The function is described as having 3 times more likes each day. This suggests an exponential growth pattern.
To derive the correct function, we need to incorporate this growth rate into the initial likes:
Given the base case (the first day) has 143 likes, and the number of likes triples each day, the correct function should start with the initial likes (143) and then account for the exponential increase by multiplying by the growth factor raised to the appropriate power.
This can be represented mathematically as:
[tex]\[ c(n) = 143 \times 3^{n-1}. \][/tex]
Let's break it down:
- Exponential Growth: Multiplying by 3 every day suggests exponential growth with a base of 3.
- Initial Value : The function starts with 143 likes.
- Days Since Posting : The exponent n-1 accounts for the base case.
If n = 1 , then [tex]\( 3^{n-1} = 3^{0} = 1,[/tex] which preserves the initial value of 143.
This leads us to option D , which correctly models the number of likes each day:
[tex]\[ c(n) = 143 \times 3^{n-1}.[/tex]
Question :
Every day, there are 3 times more likes on an internet video of a cat which is modeled by the function c(n) = (3)n − 1, where n is the number of days since the video posted. On the first day, there were 143 likes. What is the function that shows the number of likes each day?
A. c(n) = (3)(143)^{n-1}
B. c(n) = 143^{n-1}
C. c(n) = (3)143 − n
D.143(3)^{n-1}
Write your own word problem that can be translated into the mathematical sentence 2x + 4 = 10. What does the variable x represent in your problem?
Answer:
A number
Step-by-step explanation:
the sum of four and two of a number = equals ten
The created word problem involves Sam and his apples. Here, the variable 'x' represents the number of apples Sam's friend has. By solving the equation, we deduce that Sam's friend has 3 apples, so Sam originally had 10 apples.
Explanation:Let's create a word problem for the equation 2x + 4 = 10:
Sam has twice as many apples as his friend. If Sam gives 4 apples to his friend, he will only have 10 apples left. How many apples did Sam have originally?
In this problem, the variable 'x' represents the number of apples Sam's friend has. Therefore, to solve the problem, you would subtract 4 from both sides of the equation to get 2x = 10 - 4. Simplifying gives you 2x = 6. Finally, dividing both sides of the equation by 2 gives you x = 3. So, Sam's friend has 3 apples, meaning Sam originally had 2 * 3 + 4 = 10 apples.
Learn more about Linear Equations here:https://brainly.com/question/32634451
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Lana has 18 pencils, 24 erasers and 36 crayons that she wants to put evenly into her pencil boxes. If she put the same number of each type of item in her pencil boxes, what is the most number of pencil boxes will she fit
Answer:
6
Step-by-step explanation:
The largest factor that is common to all these numbers is 6. That is the number of pencil boxes Lana can fill.
18 = 6×3
24 = 6×4
36 = 6×6
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Each of her six (6) pencil boxes will have 3 pencils, 4 erasers, and 6 crayons.
Natalie reads for 6/8 hour on 6 days each week. How many hours does Natalie read each week? Enter your answer by filling in the boxes.
Multiply the time per day by the number of days per week.
6/8 x 6 = (6 x 6)/8 = 36/8 = 4 1/2 hours a week.
Hey!
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Answer:
[tex]\large\boxed{Natalie~reads~4~\frac{1}{2}~hours~a~week! }[/tex]
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Solution:
~Turn six into improper fraction
6 = 6/1
~Multiply
6/8 * 6/1 = 38/8
~Simplify
38/8 = 4 1/2
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Hope This Helped! Good Luck!
Martina, Hong, and Felipe sent a total of 91 text messages over their cell phones during the weekend. Hong sent 9 more messages than Martina. Felipe sent 2 times as many messages as Hong. How many messages did they each send?
Answer:
M = 16
H = 25
F = 50
Step-by-step explanation:
Let's use for abbreviation M for Martina's messages, H for Hong's messages and F for Felipe's messages.
Now we need to write the given information as equations.
Martina, Hong, and Felipe sent a total of 91 text messages
(1) M + H + F = 91
Hong sent 9 more messages than Martina.
(2) H = M + 9
Felipe sent 2 times as many messages as Hong
(3) F = 2 * H
Now with this system, we need to replace the letters to leave only M in the first equation.
(4) M + (M + 9) + (2*(M + 9) = 91
(5) 4*M + 27 = 91
(6) M = (91-27) / 4
Then we find the answer:
M = 16
H = 25
F = 50
The number of text messages sent by Martina, Hong, and Felipe, you solve the equation m + (m + 9) + 2(m + 9) = 91, which results in Martina sending 16 messages, Hong sending 25, and Felipe sending 50.
The problem involves solving a system of equations to find out how many text messages Martina, Hong, and Felipe each sent. Let's define Martina's number of messages as m.
Then Hong's number would be m + 9, and Felipe sent 2(m + 9) because he sent twice as many as Hong.
The total number of messages sent by all three is given as 91. This gives us the equation: m + (m + 9) + 2(m + 9) = 91. Simplifying, we get:
m + m + 9 + 2m + 18 = 91
4m + 27 = 91
4m = 64
m = 16.
Now that we've found Martina's number, we can calculate the others:
Hong: 16 + 9 = 25
Felipe: 2 * 25 = 50. So, Martina sent 16 messages, Hong sent 25, and Felipe sent 50.
Use the rules of exponents to simplify the expressions. (Please show the answer in fraction or whole number form and simplify all math that can be done.) 2/2 to the power of -4
Answer: 1
Step-by-step explanation:
Ok so 2/2=1
So 1^-4 is
(-1)(-1)(-1)(-1)=1
A telephone pole is supported by a steel cable which extends from the top of the pole to a point on the ground 3 meters from its base. When Leah walks 2.5 meters from the base of the pole toward the point where the cable is attached to the ground, her head just touches the cable. Leah is 1.5 meters tall. How many meters tall is the pole?
We find that the telephone pole is 1.8 meters tall.
To figure out the height of the telephone pole, we can use similar triangles. Picture a right triangle formed by the telephone pole, the ground, and the wire, and another smaller triangle formed by Leah standing 2.5 meters from the pole, reaching the point where her head touches the wire 1.5 meters above the ground. Because these two triangles are similar, we can set up a proportion.
The large triangle's height is the height of the pole (H), and its base is 3 meters. The smaller triangle's height is Leah's height (1.5 meters), and its base is 2.5 meters. Using the similar triangles:
H (height of the pole) / 3 meters (distance from pole to cable ground attachment) = 1.5 meters (Leah's height) / 2.5 meters (Leah's distance from the pole)
H / 3 = 1.5 / 2.5
H = (1.5 / 2.5) * 3
H = 1.8 meters
Therefore, the telephone pole is 1.8 meters tall.