A culture started with 4,000 bacteria. After 5 hours, it grew to 4,800 bacteria. Predict how many bacteria will be present after 15 Hours.
Round your answer to the nearest whole number
Answer:
6900 rounded answer -
Step-by-step explanation:
Plato users, correct.
Seascapes rent small fishing boats for a day-long fishing trips. each boat can carry only 1200 lb of people and gear for safety reasons. Assume the average weight of a person is 150 lb. each group will require 200 pounds of gear for the boat plus 10 lb of gear for each person.
A) create any quality describing the restrictions on the number of people that can possibly fit in a rented boat.
B) several groups of people wish to rent a boat Group one has 4 people group two has 5 people group three has 8 people. Determine which of the groups, if any, can safely run a boat what is the maximum number of people that may rent a boat.
A. We are given that each person weighs 150 lb, each gear
per person weighs 10 lb, and a total of 200 pounds of gear for the boat itself.
Since each person only carries one gear, therefore total weight per person in 160 lb (weight of person + weight of gear).
So let us say that x is the number of persons, the inequality equation is:
160 x + 200 ≤ 1200
B. There are three groups that wish to rent the boat.
> Solve the inequality equation when x = 4
160 (4) + 200 ≤ 1200
840 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 5
160 (5) + 200 ≤ 1200
1000 ≤ 1200 (TRUE)
> Solve the inequality equation when x = 8
160 (8) + 200 ≤ 1200
1480 ≤ 1200 (FALSE)
So only the 4 people group and 5 people group can safely run the boat.
C. Find the maximum number of people that may safely use the boat, solve for x:
160 x + 200 ≤ 1200
160 x ≤ 1000
x ≤ 6.25
Therefore the maximum number of people that can safely use the boat is 6 people.
A mathematical inequality is created to determine that a maximum of 6 people can rent a boat based on the safety weight limit of 1200 lb. Of the groups provided, only groups with 4 or 5 people can safely rent the boat, while the group with 8 people cannot due to exceeding the weight limit.
To determine the restrictions on the number of people that can possibly fit in a rented boat given the safety weight limit, we start by creating an inequality. Let p represent the number of people, then the total weight of the people is 150 lb times p, and the total gear weight is 200 lb for the boat plus 10 lb per person. The inequality can be represented as:
150p + 10p + 200 \<= 1200
Simplifying the inequality gives us:
160p \<= 1000
Dividing both sides by 160:
p \<= 1000 / 160
p \<= 6.25
Since we cannot have a fraction of a person, the maximum number of people allowed is 6.
For part B, we evaluate if the groups mentioned can safely rent a boat:
Group 1 (4 people): 150(4) + 10(4) + 200 = 840 lb \<= 1200 lb - they can rent.
Group 2 (5 people): 150(5) + 10(5) + 200 = 1000 lb \<= 1200 lb - they can rent.
Group 3 (8 people): 150(8) + 10(8) + 200 = 1480 lb > 1200 lb - they cannot rent as it exceeds the limit.
The maximum number of people who may rent a boat based on the given restrictions and average weights is 6 people.
Simplify an expression
Answer:
[tex]\frac{20+2k}{3k+12}[/tex]
Step-by-step explanation:
Since there is no equals sign here, we are not solving this. The only way to simplify is to get a common denominator and write the expression as a single expression. We can begin by noting that the second term has a k in the numerator and in the denominator, and those cancel each other out. That is the first simplification we can perform. That leaves us with:
[tex]\frac{4}{k+4}+\frac{2}{3}[/tex]
In the first term, the denominator is k + 4, in the second term it is just 3. Therefore, the common denominator is 3(k+4). We are missing the 3 in the denominator of the first term, so we will multiply in 3/3 by that term. We are missing a (k + 4) in the second term, so we will multiply in (k + 4)/(k + 4) by that term:
[tex](\frac{3}{3})(\frac{4}{k+4})+(\frac{k+4}{k+4})(\frac{2}{3})[/tex]
Multiplying fractions requires that I multiply straight across the top and straight across the bottom. That gives me:
[tex]\frac{12}{3k+12}+\frac{2k+8}{3k+12}[/tex]
Now that the denominators are the same, I can put everything on top of that single denominator:
[tex]\frac{12+2k+8}{3k+12}[/tex]
Th final simplification requires that I combine like terms:
[tex]\frac{20+2k}{3k+12}[/tex]
Maddie has a retangular garden in her backyard. The perimeter of the garden is eighty-two feet. The width is five shorter than the length. What are the length and width of the garden?
what is the sale tax on item that costs $33.50. if the sale tax is 0.06 on every $1?
a video store sold 2 vhs tapes for every 4 dvds if 564 dvds were sold how many vhs tapes were sold?
To find the number of VHS tapes sold when 564 DVDs were sold, divide the number of DVDs by 2.
Explanation:To solve this problem, we can set up a ratio comparing the number of VHS tapes sold to the number of DVDs sold. Since the ratio is given as 2 VHS tapes to every 4 DVDs, we can simplify it to 1 VHS tape to every 2 DVDs. If 564 DVDs were sold, we can divide this number by 2 to find the number of VHS tapes sold:
564 DVDs ÷ 2 = 282 VHS tapes
Therefore, 282 VHS tapes were sold.
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PLEASE HELP!!!
Taylor bought 200 shares of stock for $18.12 per share last year. He paid his broker a flat fee of $30. He sold the stock this morning for $21 per share, and paid his broker 0.5% commission.
a. What were Taylor's net proceeds?
b. What was his capital gain?
Taylor's net proceeds from the sale of his stock are $4179, after paying his broker's 0.5% commission. His capital gain on the investment is $525, calculated by subtracting the total purchase cost, including the initial broker's flat fee, from the net proceeds of the sale.
a. What were Taylor's net proceeds?
To calculate Taylor's net proceeds, we need to consider the initial cost of buying the shares, any fees paid to the broker, and the amount earned from selling the shares. Here's the breakdown:
Determine initial cost: 200 shares x $18.12 per share = $3624
Add broker's fee when buying: $3624 + $30 = $3654
Subtract broker's fee when selling: $42 (0.5% of $8400 from selling 200 shares at $21 per share)
Calculate net proceeds: $8400 - $42 = $8358
b. What was his capital gain?
To find Taylor's capital gain, subtract the total cost (initial purchase cost + fees) from the total earnings after selling the shares. The calculation is as follows:
How can u tell
Whether 1080 is cube number
The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
the number is 1080
Split into prime factors
1080 = 2*2*2*3*3*3*5
so, we have,
Its not a cube
because although there are 2 triplicates there is also a 5.
as, we know that,
Note 2*2*2*3*3*3 is a cube.
so, 1080 = 2*2*2*3*3*3*5, is not a cube number.
Hence, The solution is, 1080 = 2*2*2*3*3*3*5, is not a cube number.
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Evaluate the expression. (26÷13)⋅(−7)+14−4 Enter your answer in the box
The value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
What is the value of the expression?When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.
PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
The expression is given below.
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
Simplify the expression, then the value of the expression will be
⇒ (26 ÷ 13) ⋅ (−7) + 14 − 4
⇒ (2) ⋅ (−7) + 14 − 4
⇒ −14 + 14 − 4
⇒ − 4
Then the value of the expression (26 ÷ 13) ⋅ (−7) + 14 − 4 will be negative four.
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A corporation employs 2000 male and 500 female engineers. a stratified random sample of 200 male and 50 female engineers gives each engineer 1 chance in 10 to be chosen. this sample design gives every individual in the population the same chance to be chosen for the sample. is it an srs? explain your answer.
No, the sample design is not a simple random sample (SRS), but a stratified random sample. In an SRS, every individual in the population has an equal chance of being chosen for the sample.
Explanation:The given sample design is not a simple random sample (SRS). In an SRS, every individual in the population has an equal chance of being chosen for the sample. However, in this case, the sample design is a stratified random sample. It involves dividing the population into groups (in this case, male and female engineers) and then selecting a sample from each group using a different sampling rate.
To determine if a sample design is an SRS, we need to ensure that each individual in the population has an equal chance of being chosen, and this probability is the same for every individual. In the case of the given example, the sample design does not meet these criteria, making it not an SRS.
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Which transformation is not isometric?
Find the product: 5(−3)(−2)
PLEASE HELP ASAP!
4x-3y+6z=18,-x+5y+4z=48,6x-2y+5z=0 what are x,y,and z?
Write your answer in standard form with integer coefficients.
2x + 3y = 30 ; (2,-5)
A stack of two hundred fifty cards is placed next to a ruler, and the height of stack is measured to be 5 8 58 inches.
If a triangle has an angle greater than 90 degrees, then it is not a right triangle true or false?
Jake has $11 left in his pocket. he spent $3 on a bus ticket, $5 on lunch, and $5 on a movie. how much money did he have at the beginning of the day?
Answer:
Jake had twenty-four dollars ($24) at the beginning of the day.
Step-by-step explanation:
Jake has $11 dollars left in his pocket, after spending 3 dollars on a bus ticket, 5 dollars on lunch, and 5 more dollars on a movie. 3+5+5 is equal to 13, therefore if after spending 13 dollars Jake still has 11 dollars, which means that at the beginning of the day Jake had 24 dollars (11+13).
The regular price of a jacket is $42.75. during a sale, the jacket was marked 12% off. what was the price of the jacket during the sale? (1 point) $5.13 $30.75 $37.62 $42.63
Divide 42 in a ratio of 1:2:3?
Write the equation of the piecewise function ƒ that is represented by its graph.
Piecewise function with 3 pieces: [tex]x^2+1, 4x-8, 2[/tex]
The piecewise function ƒ that is represented by the graph in the image is:
ƒ(x) =
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
This is because the graph of the function consists of three distinct pieces:
For 0≤x<4, the graph is a parabola with vertex at (0,1) and opening upwards. This suggests that the function is of the form [tex]ax^{2} +bx+c.[/tex]
We can find the values of a, b, and c by substituting the points (0,1), (1,1), and (4,16) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]a \cdot 0^2 + b \cdot 0 + c = 1[/tex]
[tex]a \cdot 1^2 + b \cdot 1 + c = 1 \\[/tex]
[tex]a \cdot 4^2 + b \cdot 4 + c = 16[/tex]
\end{cases}
Solving this system gives us a=1, b=0, and c=1, so the equation of the function for this interval is [tex]x^{2} +1[/tex].
For 4≤x<5, the graph is a line with slope 4 and y-intercept −8.
This suggests that the function is of the form mx+b.
We can find the values of m and b by substituting the points (4,2) and (5,25) into the equation.
This gives us the system of equations:
\begin{cases}
[tex]4m+b = 2 \\[/tex]
5m+b = 25
\end{cases}
Solving this system gives us m=4 and b=−8, so the equation of the function for this interval is 4x−8.
For x=5, the graph is a horizontal line at y=26.
This suggests that the function is of the form c.
We can find the value of c by simply looking at the graph.
This gives us c=26, so the equation of the function for this interval is 26.
Therefore, the complete piecewise function is:
ƒ(x) =
\begin{cases}
[tex]x^2+1, & \text{if } 0 \le x < 4 \\[/tex]
[tex]4x-8, & \text{if } 4 \le x < 5 \\[/tex]
[tex]5^2+1 = 26, & \text{if } x = 5[/tex]
\end{cases}
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Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.what fraction of the whole pie is each slice?
If Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that, Harry has 1/4 of apple pie that he wants to cut into 3 equal slices.
We have to apply the ratio which is the comparison of two quantities to determine how many times one obtains the other.
Suppose the fraction of the whole pie is each slice will be x,
x = 1/4 / 3
x = 1 /12
Thus, if Harry has 1/4 of apple pie that he wants to cut into 3 equal slices. The fraction of the whole pie in each slice will be 1/12.
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#2
Point C has a _____ abscissa and a _____ ordinate.
positive, negative
negative, positive
negative, negative
positive, positive
What does negative 2 over 3 > −1 indicate about the positions of negative 2 over 3 and −1 on the number line?
Answer:
Step-by-step explanation:
At a certain college, there are 600 freshman, 400 sophomores, 300 juniors, and 200 seniors. if one student is selected at random, what is the probability that the student is a sophomore?
(60 POINTS! I NEED HELP NOW PLEASE!)
Given a polynomial function f(x), describe the effects on the y-intercept, regions where the graph is increasing and decreasing, and the end behavior when the following changes are made. Make sure to account for even and odd functions.
-When f(x) becomes f(x) -3
-When f(x) becomes -2 * f(x)
How to solve 2(2d+4)=-3(d+2) ?
a physicist working in a large labortory has found out that the light particles traveling in a particle accelerator increase velocity in a manner that can be described by linear function -4x+3y=15, where x is time and y is velocity in kilometers per hour. use this function to determine when a certain particle will reach 30 km/hr
List -0.3 , 0.5 ,0.55 ,-0.35 from least to greatest
Please help!!!!!
The function graphed shows the total cost for a taxi cab ride for x miles.
Select from the drop-down menus to correctly identify the taxi cab ride information provided by the graph.
The slope is ________
a. 5
b. 3
c. 2.5
d. 0.2
The slope represents _______
a. the total cost of the taxi ride
b. total number of miles traveled
c. cost per mile traveled
d. the initial cost of the taxi ride
The slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
What is slope of line ?
Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.
The function graphed shows the total cost for a taxi cab ride for x miles the cost in taxi is shown in y axis and the distance covered by taxi in x axis. Now, to find put the slope we must two coordinates which can be found out from the graph easy by observation as (0,3) and (2,8).
How using slope formula to find the slope of line :
[tex]\begin{aligned}\frac{y_{2}-y_{1}}{x_{2}-x_{1}}&=\frac{8-3}{2-0}\\&=\frac{5}{2}\\&=2.5\end{aligned}[/tex]
It represents the cost of taxi per mile of distance travelled.
Therefore, the slope of the line between cost of taxi and distance is 2.5 and it represents the cost of taxi per mile of distance travelled.
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Average precipitation for the first 7 months of the year, the average precipitation in toledo, ohio, is 19.32 inches. if the average precipitation is normally distributed with a standard deviation of 2.44 inches, find these probabilities.
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.b) 0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.Normal Probability Distribution
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
The mean is of 19.32 inches, hence [tex]\mu = 19.32[/tex].The standard deviation is of 2.44 inches, hence [tex]\sigma = 2.44[/tex].Item a:
The probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months is 1 subtracted by the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{18 - 19.32}{2.44}[/tex]
[tex]Z = -0.54[/tex]
[tex]Z = -0.54[/tex] has a p-value of 0.2946.
1 - 0.2946 = 0.7054.
0.7054 = 70.54% probability that a randomly selected year will have precipitation greater than 18 inches for the first 7 months.
Item b:
Now, we want the probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months, hence:
[tex]n = 5, s = \frac{2.44}{\sqrt{5}}[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 19.32}{\frac{2.44}{\sqrt{5}}}[/tex]
[tex]Z = -1.21[/tex]
[tex]Z = -1.21[/tex] has a p-value of 0.1131.
1 - 0.1131 = 0.8869.
0.8869 = 88.69% probability that five randomly selected years will have an average precipitation greater than 18 inches for the first 7 months.
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