The population will exceed 2627 after approximately 6.08 units of time.
What is logarithm?A lοgarithm is a mathematical functiοn that tells us what expοnent is needed tο prοduce a given number, when that number is expressed as a pοwer οf a fixed base. In οther wοrds, lοgarithms tell us hοw many times we need tο multiply the base by itself tο get the desired number.
To solve for t when the population exceeds 2627, we can set the equation equal to 2627 and solve for t:
p(t) = 1000\(e^{(0.21t)}\) = 2627
Dividing both sides by 1000, we get:
\(e^{(0.21t)}\) = 2.627
Taking the natural logarithm of both sides, we get:
0.21t = ln(2.627)
Solving for t, we get: t = ln(2.627)/0.21 ≈ 6.08
Therefore, the population will exceed 2627 after approximately 6.08 units of time.
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Please help! In the figure below, what is the length of EG
Answer:
Step-by-step explanation:
The triangles are similar because they have two sides and the angle between them (EFG) respectively equals, and it’s evident the factor between the two triangles is 2. So EG=2CB=2*8=16
Answer:
the value of EG is 20.
Step-by-step explanation:
3×4 = 12, AB and EF is similar but the value of AB is multiplied by 4 to become 12 for EF.
similarly, 4×4 = 16, BC and FG is similar but the value of BC is multiplied by 4 to become 16 for FG..
In this way, AC and EG are also similar so 5×4 = 20.
All the values are multiplied by 4 ...
Which point on the graph tells you the amount of sugar you'll
use if you don't make any pies?
Total Cups of Sugar
The point on the graph that tells you the amount of sugar you'll use if you don't make any pies is (0, 0).
What is a proportional relationship?In Mathematics, a proportional relationship is a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y represent the amount of sugar.x represent the number of pies.k is the constant of proportionality.In order to have a proportional relationship, the variables representing the amount of sugar and time must have the same constant of proportionality:
Constant of proportionality, k = y/x
Constant of proportionality, k = 4/3
Constant of proportionality, k = 12.
Therefore, the required equation is given by:
y = kx
y = 4x/3
When x = 0, the value of y is given by:
y = 4(0)/3
y = 0 pies.
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how many decimal points are in 131.6
Answer:
It just has 1 decimal point
Step-by-step explanation:
If it was a number like 14.454, then that would have 3 decimal points
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The amount of cabling that you need in feet is 15 ft.
The amount of cabling you have in feet is 18. 3 feet.
You therefore have enough cabling to run the network line.
How to find the cabling ?The total amount of cabling that you will need in feet is :
= 5 ft + 10 ft
= 15 ft
You have 220 inches in cabling on hand so this figure in feet is :
= 220 / 12 inch per feet
= 18. 3 ft
This is more than the required 15 ft so there is enough cabling.
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The table represents the function f(x). x 0 1 4 9 16 f(x) -4 -3 -2 -1 0 If g(x) =4/x-8 , which statement is true? A. The y-intercept of g(x) is less than the y-intercept of f(x). B. The y-intercept of g(x) is equal to the y-intercept of f(x). C. The x-intercept of g(x) is equal to the x-intercept of f(x). D. The x-intercept of g(x) is greater than the x-intercept of f(x).
The y-intercept of g(x) is less than the y-intercept of f(x). The y-intercept of g(x) is -1/2, which is greater than the y-intercept of f(x), which is -4. So, the correct answer is A. The y-intercept of g(x) is less than the y-intercept of f(x).
To determine the y-intercept and x-intercept of the function g(x) = 4/(x - 8), we need to find the values of x for which g(x) equals zero and the value of g(x) when x equals zero.
First, let's find the x-intercept of g(x), which is the value of x for which g(x) equals zero. Setting g(x) = 0 and solving for x, we have:
0 = 4/(x - 8)
This equation has no solutions because a fraction can only be zero if its numerator is zero, but in this case, the numerator (4) is always non-zero. Therefore, g(x) does not have an x-intercept.
Next, let's find the y-intercept of g(x), which is the value of g(x) when x equals zero:
g(0) = 4/(0 - 8)
g(0) = 4/(-8)
g(0) = -1/2
Therefore, the y-intercept of g(x) is -1/2.
Now, let's compare the y-intercepts of g(x) and f(x). From the given table, we see that the y-intercept of f(x) is -4.
Since -4 is not equal to -1/2, we can conclude that statement B, "The y-intercept of g(x) is equal to the y-intercept of f(x)," is false.
To summarize, the correct answer is: A. The y-intercept of g(x) is less than the y-intercept of f(x).
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The data in the tables below were collected from first year students at a community college. The variable is “number of credit cards.” Two of the probabilities are missing.
Number of credit cards 0 1 2 3 4 5
Number of students 122 40 28 2 2 6
Based on this data, we can estimate the probability that a randomly selected student has X number of credit cards using relative frequencies to create a probability distribution. Note: There are 200 students.
Number of credit cards 0 1 2 3 4 5
Probability 0.14 0.01 0.01 0.03
Use this information to answer the first two questions below.
What is P(0)? (Hint: Find the relative frequency for this outcome. There are 200 students in the data set.)
The probability that number of credit cards is 0 is 0.61
What is Probability ?Probability is the likeliness of an event to happen ,
It has a range from 0 to 1 , where 0 indicates uncertainty while 1 indicates certainty
The data for the college students is given and it has been asked to determine P(0)
The total students are 200
and the students that have no credit card from the data is 122
Therefore
P(0) = 122/200 = 0.61
Therefore the probability that number of credit cards is 0 is 0.61
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Consider the function f(x)=2x−−√−8. If f−1(x) is the inverse function of f(x), find f−1(2)
\(f^(-1)(2) = 6\), which is consistent with our earlier result.
What is inverse function?A function that "undoes" another function is known as an inverse function. If f(x) is a function, then f(x inverse, )'s indicated by f-1(x), is a function that accepts f(x output )'s as an input and outputs f(x initial )'s input.
Given the function f(x) = √(2x - 8), if f^(-1)(x) is the inverse function of f(x), what is \(f^(-1)(2)\)?
Solution:
To find f^(-1)(2), we need to find the value of x such that \(f(x) = 2\) . We can set up an equation:
\(f(x) = \sqrt(2x - 8) = 2\)
Squaring both sides, we get:
\(2x - 8 = 4\)
\(2x = 12\)
\(x = 6\)
Therefore, \(f^(-1)(2) = 6.\)
We can also verify this result by using the definition of an inverse function. If f^(-1)(x) is the inverse function of f(x), then by definition:
\(f(f^(-1)(x)) = x\)
We can substitute x = 2 and solve for f^(-1)(2):
\(f(f^(-1)(2)) = 2\)
\(f^(-1)(2) = (f(6))^(-1)\)
f(6) = √(2(6) - 8) = √4 = 2
Therefore,\(f^(-1)(2) = 6\), which is consistent with our earlier result.
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PLEASE HELP ASAP THIS IS FOR ALGEBRA PLEASE EXPLAIN AS WELL
5. What is the next term of the sequence -3, 6, -12, 24,…?
Answer:
-48
Step-by-step explanation:
we can see each number is getting doubled but flipped from negative and positive and vise versa. aka getting multiple by negative 2
we can also double check our work by multiplying each number in the sequence we have by -2 and make sure it follows the sequence.
Urgent help,
Translate the following words into equations step 2 solve the equation.
8 more than a number is equal to 15
The product of 7 and a number is 35
Answer:
x+8=15
-8. -8
x=7
7x=35
7. 7
x=5
Would this be right? If not can someone please explain why if I did something incorrect?
Answer:
Yes, this would be right.
The plot below shows the amount of time Mira spent on
5
55 math problems.
All measurements are rounded to the nearest
1
4
4
1
start fraction, 1, divided by, 4, end fraction minute.
A line plot labeled Time per problem (minutes) shows, moving left to right, labeled tick marks at seven, seven and a half, eight, eight and a half, nine, nine and a half, and ten. An unlabeled tick mark appears between each labeled tick mark. Dots are plotted as follows: 2 dots above the unlabeled tick mark between eight and eight and a half and 3 dots above nine and a half.
A line plot labeled Time per problem (minutes) shows, moving left to right, labeled tick marks at seven, seven and a half, eight, eight and a half, nine, nine and a half, and ten.
If Mira had spent the same total amount of time, but spent an equal amount of time on each problem, how many minutes would each problem have taken?
If Mira had spent the same total amount of time but an equal amount of time on each problem, each problem would have taken around 2.36 minutes.
In the given plot, Mira spent varying amounts of time on each of the 55 math problems. To find out how many minutes each problem would have taken if Mira had spent an equal amount of time on each problem, we need to calculate the total time she spent and divide it by the number of problems.
Looking at the plot, we can estimate the total time Mira spent by counting the dots above each tick mark and multiplying them by the corresponding time interval. Let's break it down step by step:
The tick marks on the plot are at 7, 7.5, 8, 8.5, 9, 9.5, and 10 minutes per problem.
There are 2 dots above the unlabeled tick mark between 8 and 8.5 minutes per problem. We can assume it represents 8.25 minutes.
There are 3 dots above the 9.5 minutes per problem tick mark.
Now, let's calculate the total time Mira spent:
(7 * 2) + (7.5 * 2) + (8 * 2) + (8.25 * 2) + (9 * 2) + (9.5 * 3) + (10 * 2) = 129.5 minutes.
Since Mira spent a total of 129.5 minutes on 55 problems, each problem would have taken approximately 2.36 minutes (rounded to two decimal places) if she had spent an equal amount of time on each problem.
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How long would it take for Pedro to finish reading a 1210- page book with a number of pages left after t minutes is given by a function f(t) = - 4t + 140. How long will it take for Pedro to finish reading the remaining pages? What is the domain of the function?
If a covert promoter charges $65 per ticket for a concert. The promoter’s cost will be $5500 plus $4 per ticket. Write an equation for the profit function
the equation will be 61n - 5500
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
If a covert promoter charges $65 per ticket for a concert. The promoter’s cost will be $5500 plus $4 per ticket.
Here it is: r(n) - c(n)
which goes to
65n - (4n + 5500)
=61n - 5500
Hence, the equation will be 61n - 5500
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expand and simplify (x+5)(x-1)
The expanded and simplified form of the expression (x + 5)(x - 1) is x² - x + 5x - 5.
What is the expanded form of the expression?Given the expression in the question;
(x + 5)(x - 1)
To expand and simplify the expression (x+5)(x-1),
we use the distributive property:
(x + 5)(x - 1)
x(x - 1) + 5(x - 1)
Now we can simplify each term by using the distributive property again:
x(x - 1) = x² - x
5(x - 1) = 5x - 5
Putting these terms back together, we have:
(x+5)(x-1) = x² - x + 5x - 5
Combining like terms, we get:
(x+5)(x-1) = x² + 4x - 5
Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.
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56) A tire retailer plans to sell
$100,000 worth of tires in
January. Planned reductions are
$15,000; planned inventory for
January Ist is $300,000 and for
January 31st is $350,000. As of
January 8th, the retailer has
ordered $15,000 for January
delivery. What is the open-to-
buy for the rest of the month?
Answer:
/
Step-by-step explanation:
− 9 ≤ − 3 x + 6 or −9≤−3x+6or
Answer:
- 9 ≤ − 3 x + 6
Step-by-step explanation:
- 9 ≤ − 3 x + 6
-6 from both sides
-15 ≤ -3x
divide by -3 from both sides
5 ≤ x
4. Calculate the Social Security and Medicare tax that would be applied to an annual salary of $56,400.
Answer:759
Step-by-step explanation:
3/8 + 4/5 please help me
\(\cfrac{3}{8}+\cfrac{4}{5}\implies \cfrac{(5)3~~ + ~~(8)4}{\underset{\textit{using this LCD}}{40}}\implies \cfrac{15+32}{40}\implies \cfrac{47}{40}\implies 1\frac{7}{40}\)
Answer:
47/40
Step-by-step explanation:
\((\frac{3}{8}\cdot\frac{5}{5})+(\frac{4}{5}\cdot\frac{8}{8})=\frac{15}{40}+\frac{32}{40}=\frac{47}{40}\)
Given the diagram below, what is mD?
Answer:
A
Step-by-step explanation:
Answer:
A. 72
Step-by-step explanation:
There are two ways to solve this problem. First of all, this quadrilateral is a trapezoid because the top two angles are congruent and there is one pair of parallel lines. One way to solve the problem is to remember all trapezoids have a measure of 360. So, mD=360-(108+108+72); this equals 72. Additionally, in a trapezoid, the bottom two angles are always congruent; therefore, angle D must equal 72 degrees.
What is the radius of a circle with a diameter of 15 centimeters?
Answer:
radius is 7.5cm
Step-by-step explanation:
Convert diameter to centimeter.
Answer:
radius is 7.5 cm
Step-by-step explanation:
Convert diameter to centimeter
Hope You Your Get You Answer Right
what is the lowest number that must be added to 2000 so that the sum is divisible exactly by 10 12 16 and 18
6TH GRADE MATH Find the length of x!!! Btw if the numbers are long just round to the nearest hundredth
Answer:
11.67
Step-by-step explanation:
Assume the triangles are similar.
10/6 = x/7
6x = 70
x = 70/6
x = 11.67
A cold front moves through the area quickly. In the morning, the temperature is 82
degrees F and after 6 hours the temperature has dropped to 58 degrees F. If the
temperature dropped at a steady rate, how much did it drop each hour?
The temperature dropped by 4 degrees Fahrenheit per hour during the 6-hour period.
What is the drop in temperature?The temperature drop each hour is calculated as follows;
temperature drop per hour = (change in temperature) / (time elapsed)
change in temperature = final temperature - initial temperature
change in temperature = 58 degrees F - 82 degrees F
change in temperature = -24 degrees F
The time elapsed = 6 hours
The change in temperature or drop in temperature is calculated as;
temperature drop per hour = (-24 degrees F) / (6 hours)
temperature drop per hour = -4 degrees F/hour
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An electronics store advertised a television as $17 a day for 30 days rather than the full price of $510. Why did the store choose to advertise the television this way?
A.Because it looks like a deal
B. Because they accept partial payments
C.To help customers pay for it
D.To show the daily consumption cost
Answer:
A.Because it looks like a deal
Step-by-step explanation:
17$ a day for 30 days is just multiplication which ends up with 510$ which is the full price they only put the ad up to make it seem like a deal. Understand well il break it down for you take the seventeen and 30. multiply the 7 and the 30 then 10 and the 30. add both of the products together to get 510 or 510$.
Selma wants to know if seventh-grade students prefer to do their math homework in silence or with background music. She polled the 21 students in her music class. Seven students preferred to do their math homework in silence, and fourteen students preferred to do their math homework with background music. What type of sampling is demonstrated in the situation above?
A. random sampling
B. census
C. convenience sampling
D. Systematic Sampling
Answer:
D.
Step-by-step explanation:
She used systematic sampling by asking the class to vote by using a type voting system this will help by choosing the highest number as the vote she will go through with.
Find x of angle. 74° 74° 3x + 23 9x - 73
Answer: 169
Step-by-step explanation: 3x + 23 9x - 73= 242-73= 169
Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an (x , y) point
\(y = - {x}^{2} + 8x - 23\)
solve 7(x-3)+x+22=17 for x.
Answer:
x=-13/4
Step-by-step explanation:
hope this helps :)
Answer:
x = 1
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
(x-3)+x+22-(17)=0
Step by step solution :
STEP 1:
Pulling out like terms
1.1 Pull out like factors :
2x + 2 = 2 • (x + 1)
Equation at the end of step 1:
STEP 2:
Equations which are never true:
2.1 Solve : 2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : x+1 = 0
Subtract 1 from both sides of the equation :
x = 1
One Solution Was Made :
x = 1
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help i hill give brainliest
Answer:
530.66 cm²
Step-by-step explanation:
take half the diameter of 26 and that gives you the radius of 13
A =π· r²
A = 3.14 x 169
A cone has a volume of 6 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of? (1 point)
Answer:
18 cubic inches
Step-by-step explanation:
The formulas for the volumes of a cone and a cylinder can be used to answer this question.
Volume formulasThe volume of a cone is given by ...
V = 1/3πr²h . . . . . volume of cone with radius r and height h
The volume of a cylinder is given by ...
V = πr²h . . . . . volume of a cylinder with radius r and height h
Relation between volumesComparing the formulas, we see that the volume of a cone is 1/3 the volume of a cylinder with the same radius and height.
(cone volume) = 1/3(cylinder volume)
Multiplying this equation by 3 gives ...
3×(cone volume) = (cylinder volume)
Using the given value for cone volume, we have ...
cylinder volume = 3×(6 in³) = 18 in³
The volume of the cylinder is 18 cubic inches.