Seating arrangement would best suit a family restaurant is c) a space with all booths.
ABOUT FAMILY STYLE RESTAURANTSThis restaurant with a comfortable atmosphere usually serves food in large quantities by placing it in the middle of the table.
So, each family member can take food from the middle and enjoy it on their respective plates. This concept is exactly the same as how to eat at home with the family.
Apart from that, the characteristics of this restaurant are almost the same as a casual dining restaurant, the difference is the absence of alcoholic beverages in family restaurants.
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The hypotenuse of a 45°-45°-90° triangle measures 10 StartRoot 5 EndRoot in.
A right triangle is shown. The hypotenuse has a length of 10 StartRoot 5 EndRoot and the lengths of the other 2 sides are congruent.
What is the length of one leg of the triangle?
Answer:
5 StartRoot 10 EndRoot
Step-by-step explanation:
we know that
The legs of a 45°-45°-90° triangle are congruent
Let
x ----> the length of one leg of the triangle
Applying the Pythagorean Theorem
where
c is the hypotenuse
a and b are the legs
we have
substitute
Simplify
5 StartRoot 10 EndRoot
Trapezoid WHNT id shown where R is the midpoint of HN, Y is the midpoint of WT.
WH = 10x +2.6,
NH = 11x- 7.4,
TN 23x -3.9,
RY = 18x- 4.1, and
WT = 8x + 5.2.
Answer:
It looks like you're trying to solve a problem involving geometry and algebra. To solve this problem, you need to use the information given in the statements to find the value of x and then use that value to find the lengths of the sides of the trapezoid.
Starting with the first statement, we have:
WH = 10x + 2.6
NH = 11x - 7.4
Next, we can use the information about Y being the midpoint of WT to find the value of WT:
WT = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2
Using the information about R being the midpoint of HN, we can find the value of HN:
HN = 2 * RY = 2 * (18x - 4.1) = 36x - 8.2
Finally, using the information about TN, we can find the value of TN:
TN = 23x - 3.9
With these values, we can now find the lengths of the sides of the trapezoid. The length of the top side (WH) is 10x + 2.6, the length of the bottom side (TN) is 23x - 3.9, the length of the left side (NH) is 11x - 7.4, and the length of the right side (WT) is 36x - 8.2.
Note: To fully solve the problem, you will need to use the given equations to find the value of x.
To find the value of x, we need to equate the midpoint formula with the given expressions.
The midpoint formula is (x1 + x2)/2 = x and (y1 + y2)/2 = y.
We can use this formula to find the value of x.
For example, for the midpoint R:
x = (WT + NH)/2
x = (8x + 5.2 + 11x - 7.4)/2
x = (19x - 2.2)/2
x = 9.5x - 1.1
And for the midpoint Y:
y = (WH + TN)/2
y = (10x + 2.6 + 23x - 3.9)/2
y = (33x - 1.65)/2
y = 16.5x - 0.825
Now we have two equations:
9.5x - 1.1 = 16.5x - 0.825
7x = 0.725
x = 0.725/7
x = 0.104285714
So the value of x is approximately 0.104285714.
Answer:
Step-by-step explanation:0.1
The pharmacist has a 2.8 L bottle of cough syrup. If she fills a bottle that is 1,200 ml, how many ml of cough syrup does the pharmacist have left? (1 L = 1,000 ml) 160 ml
Answer:
1600 mL
Step-by-step explanation:
if 1L = 1000mL then:
2.8L is equal to 2800mL
2800 - 1200 = 1600
I need help now please
Answer:8,5
Step-by-step explanation: look at where the dots are and see the numbers
Answer:
AC = 3[tex]\sqrt{5}[/tex] ≈ 6.71
Step-by-step explanation:
using Pythagoras' identity in the right triangle.
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
AC² = AB² + BC² = 6² + 3² = 36 + 9 = 45 ( take square root of both sides )
AC = [tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex] ← exact value
AC ≈ 6.71 ( to the nearest hundredth )
For each pair of equations, determine whether the second equation is the result of a valid operation on the first. If what is the operation.
1. 7 + 5x= 3 - 2x and 7 + 7x = 3
2. 3(x - 4) = 15 and x - 4 = 15
3. x^2 = 6x and x = 6
4. 1/(x - 5) = 10 and 1 = 10(x - 5)
^ this one is a fraction 1 over (x - 5)
The following pairs of equations have its second equation valid
7 + 5x= 3 - 2x and 7 + 7x = 3
1/(x - 5) = 10 and 1 = 10(x - 5)
The invalid equations are;
3(x - 4) = 15 and x - 4 = 15
x^2 = 6x and x = 6
How to calculate using mathematical operation?1. 7 + 5x= 3 - 2x and 7 + 7x = 3
Add 2x to both sides
7 + 5x + 2x = 3
7 + 7x = 3
Valid
2. 3(x - 4) = 15 and x - 4 = 15
3x - 12 = 15
Invalid
3. x^2 = 6x and x = 6
find the square root of both sides
√x² = √6x
x = √6x
Invalid
4. 1/(x - 5) = 10 and 1 = 10(x - 5)
cross product
1 × 1 = 10(x - 5)
1 = 10(x - 5)
Valid
Therefore, 7 + 5x= 3 - 2x and 7 + 7x = 3;
1/(x - 5) = 10 and 1 = 10(x - 5) are the valid equations.
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Given the km represents an angle bias for, find the value of x and KL
Answer:
Answer is in attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do note that to solve this question, there are multiple ways (using Pythagoras' Theorem), this is only one of the ways.
Stacey is designing a custom rug for a client. the current design is a rectangle with a width of 8 feet and a length of 5 feet. the client wants the rug to be larger but doesn't want the width to exceed 12 feet. select any of the scale factors that stacey could use to dilate the current dimensions and meet the customer's requests.
Answer:87
Step-by-step explanation:
The variable whose effect on the response variable is to be assessed by the experimenter is called
The factor is the variable that the experimenter will use to judge its impact on the response variable.
A dependent variable is one that is altered as a result of the modification of an independent variable. The outcome you're trying to measure "depends" on your independent variable. Response variables in statistics are another name for dependent variables (they respond to a change in another variable).
The terms are the numbers or the variables added together, factors are the numbers or the variables that are multiplied together and the coefficient is the number multiplied to the variable.The coefficient of a variable term is that word's numerical factor.
A factor is a type of statistical data that is used to hold categorical variables. Categorical variables can be categorised into only a few groups. Continuous variables, on the other hand, are infinitely variable.The variable being measured or tested in an experiment is known as the dependent variable.
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for that, she needs 20 grams of a 52% solution of salt. she has two bottles of salt water. one bottle contains a 40% salt solution and the other a 70% salt solution. how much of each must she use to make the solution she needs?
The solution used to make 40% of salt solution is 12 grams and 70% of salt solution is 8 grams.
Let us consider 'a' represents the 40% of salt in water.
And 'b' represents the 70% of salt in water.
Total salt required to make 52% salt solution = 20 grams
Required equations is :
a + b = 20
⇒ a = 20 - b ___( 1 )
40% of a + 70% of b = 52% of 20 grams
⇒ 0.40a + 0.70b = 10.4 ___( 2 )
Substitute the value of 'a' in equation ( 2 ) from (1) we get,
0.40( 20 - b ) + 0.70b = 10.4
⇒8 - 0.40b + 0.70b = 10.4
⇒ 0.30b = 10.4 - 8
⇒ b = 2.4 / 0.30
⇒ b = 8
⇒ a = 12
Therefore, the solution used by Serena for 40% is 12 grams and 70% solution is 8 grams.
The above question is incomplete , the complete question is:
Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?
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Graph a quadratic function with a vertex of (3, -7). Type your equation below.
The quadratic equation can be written in vertex form as:
y = (x - 3)^2 - 7
How to write the quadratic equation?A general quadratic equation with a leading coefficient a and a vertex (h, k) can be written as:
y = a*(x - h)^2 + k
If particularly we take a = 1 (we could take any value here, because the problem doesn't say anything about the leading coefficient).
And the vertex is (3, -7)
Then the quadratic equation can be:
y = (x - 3)^2 - 7
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how many nickels and dimes
Answer:
12 nickles and 9 dimes
Step-by-step explanation:
First, let's use the first equation, n + d = 21, to solve for d in terms of n:
n + d = 21 [Subtract n from both sides]
d = 21 - n
Now that we have found d in terms of n, let's plug d into the second equation, 0.05n + 0.1d = 1.5:
0.05n + 0.1d = 1.5 [Plug in d]
0.05n + 0.1(21 - n) = 1.5 [Distribute 0.1 to (21-n)]
0.05n + 2.1 - 0.1n = 1.5 [Combine like terms]
-0.05n + 2.1 = 1.5 [Subtract 2.1 from both sides]
-0.05n = -0.6 [Divide both sides by -0.05]
n = 12
Now that we have found the amount of nickles Donna had, let's use the first equation, n + d = 21, to solve for d, the amount of dimes she used.
n + d = 21 [Plug in n]
12 + d = 21 [Subtract 12 from both sides]
d = 9
So, Donna must have bought her candy bar using 12 nickles and 9 dimes.
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What is halfway between 0.2 and 0.3
Help plsss
Answer:
0.25
Step-by-step explanation:
You are finding the average of the two numbers by finding the halfway point. So you do 0.2+0.3 = 0.5 and then you divide by 2. 0.5/2 = 0.25
Hope this helped :)
a vertical asymptote is a vertical line that the graph of the function approaches as x tends to positive or negative infinity. b. a vertical asymptote is a vertical line x
A vertical asymptote basically means of a graph on a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.
In a graph a vertical asymptote is a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a. And similarly the horizontal asymptote in a graph is a horizontal line y = b where the graph approaches the line as the inputs approach ∞ or –∞.
At x = a in a graph where a is a zero for a factor in the denominator the removable discontinuity occur that is common with a factor in the numerator.
Factor the numerator and denominator.
It is set it equal to zero and solve if any factors are common to both the numerator and denominator.
This is removable discontinuity type location.
In mathematics a graph is defined as a diagrametical or a pictorial representation that helps to represents data or values in an organized manner. The points that are shown on the graph are use to mark of represent the various value or relation between two value .
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A builder is using the drawing below to build a house. If the owner decides to increase the living room dimensions by 20%, what is the new length and width of the living room floor?a. 14.4 feet x 9.6 feetb. 144 feet x 96 feetc. 13.2 feet x 8.2 feetd. 10 feet x 8 feet
Percentage increment means the part of original value is added to the value. The new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long. The option A is the correct option.
The length of the living room is 12 feet.
The width of the living room is 8 feet.
The owner increases the 20 percent of length and 20% width.
Suppose new length is feet long. As the owner increases the 20 percent of length. Thus the new length will be sum of original length and the 20 percent of it. Hence,
l=12+12/100*12
l=14.4
Thus the new length of the living room is 14.4 feet long.
Suppose new width is feet long. As the owner increases the 20 percent of width. Thus the new width will be sum of original width and the 20 percent of it. Hence,
w=8+20/100*8
w=9.6
the new width of the living room is 1.6 feet long.
Hence the new length of the living room is 14.4 feet long and new width of the living room is 1.6 feet long.
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which equation is true??? A 3/4 = 9/16 B 6/8 = 4/3 C 3/5 = 8/10 D 12/16 = 36/48
Answer:
D) 12/16 = 36/48
Step-by-step explanation:
They are equivalent fractions, unlike the other options. Both of these fractions simplify to 1/3 so they are indeed equivalent.
Answer:
12/16 = 36/48
Step-by-step explanation:
because 12/16 multiplyed by 3 is 36/48
A new product price is increased from $5 to $6. What is the percent of change?
Answer:
Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.
Or you could do it this way:
Step 1: Divide new value by old value: $6/$5 = 1.2
Step 2: Convert to percentage: 1.2×100 = 120% (i.e. $6 is 120% of $5)
Step 3: Subtract 100%: 120% − 100% = 20%, and that means a 20% rise.
Answer:
20%
Step-by-step explanation:
$5 to $6 is a $1 increase
Divide by old value: $1/$5=.2=20%
To check: $5 times 1.2 (120%)=6
2nd Method:
Divide by new vlaue: $6/$5=1.2
1.2=120%
120%-100%=20%
Identify the graph of the solution set of 13 > 5 + 4x.
The requried graph of the solution of a set of given inequality 13 > 5+ 4x is shown.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
here,
Given inequality,
13 > 5 + 4x
Simplify the above expression,
Subtract -5 from both sides,
13 - 5 > 5 - 5 + 4x
8 > 4x
Divide by 4 into both sides
2 > x
The graph of the solution to the given inequality is less than 2, and line x = 2 will be a dotted line [value no included in x < 2]
Thus, the graph of the inequality has been shown.
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heart failure is due to either natural occurrences (89%) or outside factors (11%). outside factors are related to induced substances or foreign objects. natural occurrences are caused by arterial blockage, disease, and infection. suppose that 15 patients will visit an emergency room with heart failure. assume that causes of heart failure between individuals are independent. (a) what is the probability that 3 individuals have conditions caused by outside factors? round your answers to three decimal places (e.g. 0.987). probability
The probability that 3 individuals have conditions caused by outside factors is 0.1496
The proportion of heart failures due to outside factors, p = 11% = 0.11
Sample size, n = 15
The formula for binomial distribution is:
P(x) = ⁿCₓ pˣ (1 - p)ⁿ⁻ˣ
Here, x = Number of heart failures.
We are asked to determine the probability that 3 individuals have conditions caused by outside factors
So, here x = 3
P(3) = ¹⁵C₃ p³ (1 - p)¹⁵⁻³
P(3) = ¹⁵C₃ (0.11)³ (1 - 0.11)¹²
P(3) = ¹⁵C₃ (0.11)³ (0.89)¹²
P(3) = 455 (0.11)³ (0.89)¹²
P(3) = 0.1496
Hence, the probability that 3 individuals have conditions caused by outside factors is 0.1496
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a football field is supposed to be exactly 120yd long, including the end zones. how many inches is this? (1yd
The length of a football field, including the end zones, is 120 yards, which is equal to 4320 inches.
To calculate this, we can use the conversion rate of 1 yard equal to 3 feet and 1 foot equal to 12 inches. This means that 1 yard is equal to 36 inches. To convert 120 yards to inches, we can multiply 120 by 36, resulting in 4320 inches.
To explain this mathematically, we can use the formula:
Inches = Yards x (Feet/Yard) x (Inches/Foot)where Inches/Foot = 12 and Feet/Yard = 3.
Plugging in the appropriate variables, we can calculate the number of inches in a football field as:
Inches = 120 x 3 x 12 = 4320 inches.
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To select 10 students our of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. What type of sample is this? A. Stratified Random Sample B. Multistage Sample C. Simple Random Sample D. Cluster Sample E. Systematic Random Sample
Simple Random sampling as each student is getting equal opportunity to get selected.
Describe random sampling.
A selection of participants from a community are chosen at random by the investigator using simple random sampling, a sort of sampling techniques. Every individual in the population has the same chance of being chosen. Then, information is gathered from as much of this randomly selected subgroup as possible.
Which four forms of random sampling are there?
Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are the four main random (probability) sampling techniques.
What benefit may simple random sampling provide?
The benefits of a simple random sample include its simplicity and accuracy of depiction. Simple random sampling is the easiest way to select a study sample from a bigger population.
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Between which two numbers will you find in 5.634x10 to the 2 power
The number 5.634x10 to the 2nd power can be expressed as 563.4. The numbers between which 563.4 falls are 560 and 567.
The table shows values for functions f(x) and g(x) .
What are the known solutions to f(x)=g(x) ?
Select each correct answer.
1
3
7
9
11
The solution is, The value of x where f(x) = g(x) is 3.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
Functions and values
According to the given question, we are to find the value of x for which the function f(x) is equal to g(x)
From the given table, we need to find the point where the values of f(x) = g(x). The value of x at this point is the solution.
Therefore from the table, the value of x where f(x) = g(x) is 3
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uppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. find the probability that the person selected is female.
There is a 50% chance that the person selected is female.
Let's assume that there are 50 students in the class and of them, 25 are female and 25 are male.
The probability that the person selected is female will be calculated by the formula P(Female) = 25/50 = 0.5
Therefore, the probability that the person selected is female is 0.5 or 50%. This means that if a person is randomly selected from the front, middle portion of the class, there is a 50% chance that the person selected is female.
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Complete question:
What is the gender ratio of the people in the class?
If you help you get a ice cream cake
1: The number of dogs is greater than 20
2: The temperature was less than 80°
3: The cost of the bike is atleast $100.
4: The grocery list does not exceed 15 items. The speed limit is not more than 40mph
Which graph represents the inequality y is less than negative one-third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
The graph represents the inequality, the graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
What is linear inequality?According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. Any of the symbols for inequality, including greater than (>), less than (<), greater than or equal to (≥), less than or equal to (≤), or not equal to (≠).
Given the phrase, y is less than negative one-third times x plus 1
negative one-third times x plus 1,
-1/3x + 1
y < -1/3x + 1
to plot the coordinates consider,
y = -1/3x + 1
when x = 0, y = 1
and when y = 0,
0 = -1/3x + 1
-1/3x = -1
x = 3
x 0 3
y 1 0
and the graph says y is less than negative one-third times x plus 1,
so the shaded portion will be below the line, and the graph is attached for the condition.
Hence option D is correct.
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A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 81 long and 55 wide. What is the length of a training track running around the field?
The length of a training track running around the field is 334.7m.
What is Rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
What is semicircle?A semicircle is created when a circle is divided in half along its diameter. There is an equal distribution of each half. A semicircle is a circle that has been folded in half; it is sometimes referred to as a half-disk.
here, we have,
GIven that;
length of rectangle = 81m
width of rectangle = 55m
Length of track running around the field = 2 x length of field + circumference of two semicircles
= 2 x 81 +pi x 55
= 162 + 3.14 x 55
= 334.7m
∴ the length of a training track field is 334.7m
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the measures of the angles in a triangle are in a ratio of 2:2:4. find the exterior angle that is adjacent to the largest triangle.
The exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.
The exterior angle adjacent to the largest interior angle in a triangle is equal to the sum of the other two interior angles.
Let's call the measures of the angles in the triangle x, x, and 2x. Then,
x + x + 2x = 180 degrees,
so 4x = 180 degrees, and
x = 45 degrees.
The largest interior angle is 2x, or 90 degrees. The exterior angle that is adjacent to this angle is equal to 180 degrees minus the interior angle, which is 180 - 90 = 90 degrees.
So the exterior angle adjacent to the largest interior angle in a triangle with a 2:2:4 angle ratio is 90 degrees.
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market research indicates that a new product has the potential to make the company an additional $3.8 million, with a standard deviation of $1.8 million. if this estimate was based on a sample of 10 customers, what would be the 90% confidence interval?
The 90% confidence interval is (2.76, 4.84).
The standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range.
Standard deviation may be abbreviated SD and is most commonly represented in mathematical texts and equations by the lower-case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
Mean [tex]$(\overline{\mathbf{x}})[/tex] =3.8, sample standard deviation [tex]$(\mathrm{s})[/tex] =1.8, sample size [tex]$(\mathrm{n})[/tex] = 10
since population standard deviation [tex]$(\sigma)$[/tex] is unknown and the value of [tex]$\mathrm{n}$[/tex] is less than 30, use. [tex]$\mathrm{t}$[/tex] - distribution
degrees of freedom =10-1=9
for 90% confidence level with degrees of freedom = 9
[tex]$t_{\frac{\alpha}{2}}=1.833[/tex] (from t- table)
formula: confidence interval for population mean. [tex]$\mu=\bar{x} \pm t_{\frac{\alpha}{2}} *\left\{\frac{s}{\sqrt{n}}\right\}$[/tex]
= 3.8 ± 1.833×[tex]\left\{\frac{1.8}{\sqrt{10}}\right\}$[/tex]
= 3.8 ± 1.04
= (3.8 - 1.04, 3.8 + 1.04)
= (2.76, 4.84)
Therefore, the 90% confidence interval is (2.76, 4.84).
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bacteria growth the number of bacteria in a culture is increasing according to the law of exponential growth. there are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. (a) find the initial population. (b) write an exponential growth model for the bacteria population. let represent time in hours. (c) use the model to determine the number of bacteria after 8 hours. (d) after how many hours will the bacteria count be 25,000
a) The initial population is [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex].
b) The exponential growth model for the bacteria population is N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex].
c) The number of bacteria after 8 hours is N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex].
d) After t = ln(25,000 / [tex]N_0[/tex]) / k hours the bacteria count will be 25,000.
(a) To calculate the beginning population, we must first establish the bacterium population's exponential growth rate. Assume that the initial bacterial population is [tex]N_0[/tex]. The exponential growth model is given by:
N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
Where N is the number of bacteria at time t, [tex]N_0[/tex] is the starting population, e is the natural logarithm base, k is the growth rate constant, and t is time in hours.
We have two data sets: N = 125 after two hours and N = 350 after four hours. We can solve using these two equations [tex]N_0[/tex] and k.
(125) = [tex]N_0[/tex] × [tex]e^{(2k)}[/tex]
(350) = [tex]N_0[/tex] × [tex]e^{(4k)}[/tex]
Dividing the second equation by the first equation:
(350/125) = [tex]e^{(2k)}[/tex]
Taking the natural logarithm of both sides:
ln(350/125) = 2k
Solving for k:
k = ln(350/125) / 2
Now that we have k, we can plug it into either equation and solve for it. [tex]N_0[/tex]:
[tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex]
(b) The bacterium population's exponential growth model is:
N = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
Where [tex]N_0[/tex] = 125 / [tex]e^{(2k)}[/tex] and k = ln(350/125) / 2
(c) To calculate the number of bacteria present after 8 hours, we use the exponential growth model with t = 8:
N = [tex]N_0[/tex] × [tex]e^{(8k)}[/tex]
(d) To calculate the time when the bacterium count reaches 25,000, enter N = 25,000 into the exponentially growing model and solve for t:
25,000 = [tex]N_0[/tex] × [tex]e^{(kt)}[/tex]
t = ln(25,000 / [tex]N_0[/tex]) / k
However, in the absence of a specified growth rate constant (k) and starting population ([tex]N_0[/tex]), we are unable to determine a precise value for t.
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The question is -
The number of bacteria in the culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.
(a) Find the initial population.
(b) Write an exponential growth model for the bacteria population. (Let t represent time in hours)
(c) Use the model to determine the number of bacteria after 8 hours.
(d) After how many hours will the bacteria count be 25,000?
Sally is near the end of a three year lease on a car with an original msrp of $38,000. her leasing company claims that the car is now worth only $28,500. which percentage represents the residual value of sally’s leased car? a. 25% b. 33% c. 67% d. 75% please select the best answer from the choices provided a b c d
The right answer is D.
Detailed explanation:
$35,000. Original cost of the vehicle
The car's current value is $28,500.
The residual worth of Sally's leased vehicle is equal to x.
Current Price x * 38,000 = 28,500 x = 28,500/38,000 x = 0.75 Residual value * Original Price
Since we must determine the proportion
Divide the residual value by 100, or 0.75 * 100, to get 75%.
The right answer is D.
What exactly does leasing mean?A lease is a contract in which the owner of an asset (the lessor) agrees to let the lessee use it in exchange for a specific amount of money (the rent), which may or may not be based on any factors, for a specified amount of time (the lease term), which may or may not be flexible.
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