Answers
Answer:
A) AAS
B) HL
C) SSS
E) SAS
Step-by-step explanation:
We cannot prove the triangles congruent by AAS because we would need another angle pair that is congruent to each other.
We can prove the triangles congruent by HL because the pairs of hypotenuses and shorter legs are shown to be congruent to each other.
We can prove the triangles are congruent by SSS because every side is congruent to its respective pair.
We cannot prove the triangles congruent by HA because we would need another angle pair that is congruent to each other, like with AAS.
We can prove the triangles are congruent by SAS because two pairs of sides in addition to their respective included angles (the right angles) are congruent to each other.
We cannot prove the triangles congruent by LA because we would need to know by the given information that ∠B≅∠E, but it's not provided.
Therefore, A, B, C, and E are the correct answers.
Related Questions
-8+5(2x+1)=-(7x+9)+x
Answers
The value of x that satisfies the equation -8 + 5(2x + 1) = -(7x + 9) + x is x = 3/4.
To solve the equation -8 + 5(2x + 1) = -(7x + 9) + x, we will simplify the expression step by step and solve for the value of x.
Distribute 5 to the terms within the parentheses: -8 + 10x + 5 = -(7x + 9) + x
Combine like terms on both sides of the equation: -8 + 5 + 10x = -7x - 9 + x
Simplifying further, we have: -3 + 10x = -6x - 9
To eliminate the negative sign on the right side of the equation, we can multiply every term by -1: -3 + 10x = -6x - 9 * -1
This simplifies to: -3 + 10x = -6x + 9
Next, we want to isolate the x terms on one side of the equation and the constant terms on the other side. We can do this by adding 6x to both sides: -3 + 10x + 6x = -6x + 9 + 6x
Simplifying further: 16x - 3 = 9
To isolate the x term, we need to eliminate the constant term on the left side. We can do this by adding 3 to both sides: 16x - 3 + 3 = 9 + 3
Simplifying further: 16x = 12
Finally, we solve for x by dividing both sides of the equation by 16: (16x)/16 = 12/16
The equation simplifies to: x = 3/4
Therefore, the value of x that satisfies the equation -8 + 5(2x + 1) = -(7x + 9) + x is x = 3/4.
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Anumber Y is 15 larger than A Positive number x. If their SUM is not more than 85. What are the Possible values. OF Such Number y ?
Answers
Step-by-step explanation:
y = 15 + x or x = y-15
and x sum to <= 85
x + y <= 85
(y-15) + y <= 85
2y <= 100
y <= 50 The maximum value of y is 50 minimum would be 16 ( since it must be 15 greater than a positive number x (which would be 1 ))
will mark brainleist pls help
Answers
Answer:
x = 31°
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , that is
x + 54° + 95° = 180°
x + 149° = 180° ( subtract 149° from both sides )
x = 31°
You are preparing to buy a house. Your monthly gross income is $3,200. a. What is the maximum amount you can finance (mortgage)? (4 points)
Answers
The maximum amount you can finance is $896.
We are given that;
The monthly gross income = $3,200
Now,
28% of your gross monthly income on your mortgage, including taxes and insurance
The percentage = 28%
3200* 28/100
=32*28
=896
Therefore, by percentage the answer will be $896.
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he quadratic functions f(x) and g(x) are described in the table:
In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units
Answers
In which direction and by how many units should f(x) be shifted to match g(x): A. Left by 4 units.
What is a quadratic function?In Mathematics and Geometry, the standard form of a quadratic function is represented by the following equation;
ax² + bx + c = 0
Based on the information provided about the parent quadratic function f(x), we can logically deduce that it is given by this equation;
f(x) = x²
Next, we would create a quadratic function for g(x) by using the data points provided in the table above;
g(x) = x² + 8x + 16
g(x) = x² + 4x + 4x + 16
g(x) = x(x + 4) + 4(x + 4)
g(x) = (x + 4)(x + 4)
g(x) = (x + 4)²
Therefore, the parent quadratic function must be shifted left by 4 units to create g(x).
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can I please get some help with this
Answers
Apologies for the confusion. The image you provided contains an expression that can be simplified as follows:
√(36 / 12) - 3 × (4 - 3)
Let's break it down step by step:
Simplify the expression inside the square root:
√(36 / 12) = √3
Simplify the multiplication:
-3 × (4 - 3) = -3 × 1 = -3
Subtract the results:
√3 - 3
Therefore, the simplified expression is √3 - 3.
<3
Use limits to find the area of the region between the graph of y=x³+1
and the x-axis on the interval [2, 4], or f(x³ + 1) dx
Answers
Answer:
62
Explanation:
Find the area of the region bounded the graph of y=x³+1 and the x-axis over the interval [2,4].
[tex]\text{\underline{Set up:}}\\\\\Longrightarrow \boxed{\int\limits^4_2 {x^3+1} \, dx}[/tex]
[tex]\text{Now solving...}\\\\\Longrightarrow \int\limits^4_2 {x^3+1} \, dx\\\\\Longrightarrow \frac{1}{4}x^4+x \Big]\limits^4_2\\\\\Longrightarrow [\frac{1}{4}(4)^4+(4)]-[\frac{1}{4}(2)^4+(2)]\\\\\Longrightarrow [68]-[6]\\\\\Longrightarrow \boxed{\boxed{=62}}[/tex]
Thus, the problem is solved.
27. Molander Corporation is a distributor of a sun umbrella used at resort hotels. Data concerning the next month’s budget appear below:
Selling price per unit $ 24
Variable expense per unit $ 14
Fixed expense per month $ 8,900
Unit sales per month 1,040
Required:
1. What is the company’s margin of safety in dollars? (Do not round intermediate calculations.)
2. What is the company’s margin of safety as a percentage of its sales? (Round your percentage answer to 2 decimal places (i.e. .1234 should be entered as 12.34).)
Answers
The breakeven point is 890 units and Molander Corporation's margin of safety is $3,600 in dollars and 14.42% as a percentage of its sales.
To find the breakeven point:
Breakeven Point = Fixed Expenses / Contribution Margin per unit
Contribution Margin per unit = Selling Price per unit - Variable Expense per unit
= $24 - $14
= $10
Breakeven Point = $8,900 / $10
= 890 units
The breakeven point is 890 units.
To calculate the margin of safety:
Margin of Safety = Actual Sales - Breakeven Point
Actual Sales = Unit Sales per month
= 1,040 units
Margin of Safety = 1,040 units - 890 units
= 150 units
Margin of Safety in dollars = Margin of Safety × Selling Price per unit
= 150 units × $24
= $3,600
Margin of Safety as a percentage of sales = (Margin of Safety / Actual Sales) × 100
= (150 units / 1,040 units) * 100
= 14.42% (rounded to 2 decimal places)
Therefore, Molander Corporation's margin of safety is $3,600 in dollars and 14.42% as a percentage of its sales.
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The point U is plotted on the coordinate grid below. Plot the point U', the ref
of U over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
-6 -5 -4 -3 -2 -1
U
2
3
4
5
6
Answers
Answer:
The point U' is (-6, -2).
Step-by-step explanation:
The reflection of point U over the x-axis is the point U' with the same x-coordinate but a y-coordinate that is the opposite of U's y-coordinate. Since the y-coordinate of point U is 3, the y-coordinate of the reflected point U' will be -3. Therefore, the coordinates of U' are (-2, -3).
The graph should show U at the point (2, 3) and U' at the point (2, -3) after being reflected over the x-axis.
find the value of x
Answers
Cross multiply the two as explained below.
Answer:
Option C. 5.5
Step-by-step explanation:
To solve for x in the equation:
[tex]\sf\implies\dfrac{3x - 4}{14} = \dfrac{9}{10}[/tex]
We need to isolate x on one side of the equation.
First, we simplify the left side by solving the division:
[tex]\sf\implies\dfrac{(3x - 4)}{14} = \dfrac{9}{10}[/tex]
Next, we cross-multiply to eliminate the fractions:
[tex]\sf\implies 10(3x - 4) = 14(9)[/tex]
[tex]\sf\implies 30x - 40 = 126[/tex]
Now, we isolate x by adding 40 to both sides of the equation:
[tex]\sf\implies 30x = 166[/tex]
Finally, we solve for x by dividing both sides of the equation by 30:
[tex]\sf\implies x = \dfrac{166}{30}[/tex]
[tex]\sf\implies x = 5.533[/tex]
Therefore, the value of x is approximately 5.533. Thus, the correct option is C. 5.5.
Chi-Chiribi! EmergerOrpheus at your service. Hope it helps!
What is the probability that either event will occur?
A
2
3
B
1
P(A or B) = P(A) + P(B)
P(A or B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Answers
The probability P(A or B) that either event will occur is 0.67
The probability of either event occuring ;Probability is the ratio of required outcome to the total possible outcomes . We could solve the question give. thus:
Total possible outcomes , n(Total) = 3+1+2 = 6
P(A) = n(A)/n(Total) = 3/6 = 0.5
P(B) = n(B)/n(Total) = 1/6 = 0.167
P(A or B) defined as P(A) + P(B) will become ;
P(A) + P(B) = 0.5 + 0.167 = 0.667
Hence, the probability of either A or B occuring rounded to the nearest hundredth is , P(A or B) = 0.67
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1.5 Which of the following set of numbers are integers: -25,31,-100 a) -25 c) -100 Question ? b) 31 d) All of the answers (1) [5]
Answers
Answer:
This question asks which numbers (-25, 31, -100) are integers. The answer is that all of the given numbers are integers.
Step-by-step solution:
An integer is a whole number that can be positive, negative, or zero.
The given numbers are -25, 31, and -100.
To determine whether these numbers are integers, we must check whether they are whole numbers.
Whole numbers are numbers that do not have any fractions or decimals.
-25 and -100 do not have any decimal parts, so they are whole numbers and thus integers.
31 has no decimal parts, so it is also a whole number and an integer.
Therefore, all of the given numbers (-25, 31, -100) are integers.
A correct answer is option (d), "All of the answers".
3. MODELING REAL LIFE An apple growing on a tree
has a circumference of 6 inches. (See Example 2.)
a. The apple has a density of 0.46 gram per cubic
centimeter. Find the mass of the apple.
b. The radius of the apple increases inch per week
for the next five weeks. How does the volume
change during the five-week period? Explain
Answers
a. The mass of the apple is approximately 33.879 grams.
b. The volume of the apple increases by approximately 1.454 cubic inches during the five-week period.
a. To find the mass of the apple, we need to calculate its volume first. The circumference of the apple can be used to determine its radius.
The formula for the circumference of a circle is C = 2πr,
where C is the circumference and r is the radius.
Rearranging the formula, we have r = C / (2π).
Plugging in the given circumference of 6 inches.
we get r = 6 / (2π) ≈ 0.955 inches.
Now, we need to convert the radius from inches to centimeters since the density is given in grams per cubic centimeter.
Since 1 inch is approximately 2.54 centimeters, the radius in centimeters is [tex]0.955 \times 2.54[/tex] ≈ 2.427 cm.
Next, we can calculate the volume of the apple using the formula for the volume of a sphere: V = (4/3)πr³.
Plugging in the radius in centimeters, we get
V ≈ (4/3)π(2.427)³ ≈ 73.682 cm³.
Finally, we can find the mass of the apple by multiplying the volume by the density:
mass = volume [tex]\times[/tex] density
= 73.682 cm³ [tex]\times[/tex] 0.46 g/cm³
≈ 33.879 grams.
Therefore, the mass of the apple is approximately 33.879 grams.
b. The volume of a sphere increases with the cube of its radius.
Since the radius increases by 1/8 inch per week for five weeks, the change in radius would be[tex](1/8) \times 5 = 5/8 inch.[/tex]
Now, let's calculate the change in volume during the five-week period. The formula for the volume of a sphere is V = (4/3)πr³.
Initially, the radius was 0.955 inches.
After five weeks, the radius would be 0.955 + 5/8 inches.
To compare the change in volume, we can calculate the new volume and find the difference:
Change in Volume = New Volume - Initial Volume
Initial Volume = (4/3)π(0.955)³
New Volume = (4/3)π(0.955 + 5/8)³
By subtracting the initial volume from the new volume, we can determine how the volume changes during the five-week period.
Please note that the exact calculation will depend on the precise values used for π and the measurements provided.
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If the average of 9 and x is equal to the average of 7, 3, and x, what is the value of x?
Answers
Hello !
(9 + x)/2 = (7 + 3 + x)/3
3(9 + x) =2(7 + 3 + x)
27 + 3x = 14 + 6 + 2x
27 + 3x = 20 + 2x
27 - 20 = 2x - 3x
7 = -x
x = -7
you can check it works for the 2 averages
HOW DO I SIMPLIFY? I WILL MARK YOU BRAINLIEST! AND EXPLAIN
Answers
Answer:
This is how you simplify it.
Answer:
Step-by-step explanation:
(3x⁵)^3
= {3x}^(15) (According to rule)
Answer = (3x)^(15)
What is the meaning of "the first order predicate calculus"?
Answers
The first order predicate calculus is the mathematical logic that is used to express and analyze propositions involving objects, characteristics, and relations
What is the first order predicate calculus?A foundational framework for mathematical logic that is used to express and analyze propositions involving objects, characteristics, and relations is known as the first-order predicate calculus.
It offers a formal language for expressing statements and a set of inference guidelines for producing reliable results. By incorporating quantifiers like "for all" and "there exists," which allow statements about variables and predicates to be quantified over a domain of objects, first-order logic expands propositional logic.
It enables exact reasoning about intricate systems and structures and forms the basis for mathematical proofs, computer science, artificial intelligence, and different branches of philosophy.
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slope intercept equation of (-5,-7)
Answers
Answer:
[tex]\huge\boxed{\sf y=\frac{9}{5} x + 2}[/tex]
Step-by-step explanation:
Point = (x,y) = (-5, -7)
So,
x = -5, y = -7
General form of slope-intercept equation:y = mx + bWhere m is slope and b is y-intercept.
Finding slope:Along with the already given point, let us take any other point of the line.
Point 1 = (x₁,y₁) = (-5,-7)
Point 2 = (x₂,y₂) = (0,2)
So,
x₁ = -5
y₁ = -7
x₂ = 0
y₂ = 2
[tex]\displaystyle Slope = \frac{y_2-y_1}{x_2-x_1} \\\\Slope = \frac{2-(-7)}{0-(-5)} \\\\Slope = \frac{2+7}{0+5} \\\\\boxed{Slope = \frac{9}{5} }[/tex]
Finding y-intercept:y-intercept is actually the point where x = 0.Here, x = 0 when y = 2.
So,
y-intercept = 2Put slope and y-intercept in general form of slope-intercept equation.
So,
Answer:[tex]\displaystyle y=\frac{9}{5} x + 2\\\\\rule[225]{225}{2}[/tex]
pls solve these equations:
Answers
Step-by-step explanation:
First one:Calculate the difference:
12 × ( -15/12x ) = 7
Multiplying a positive and a negative equals a negative: (+) × (-) = (-)
-12 × 15/12x = 7
Cancel the greatest common factor 12
-5x = 7
Divide both sides of he equation by -5
Solution: x = -7/5
Second one:26 × (7y + 5 +3) = 1300
Divide both sides of the equation by 26
7y + 5 + 3 = 50
add the numbers
7y + 8 = 50
Move the constant to the right hand side and change it's sign.
7y = 50 - 8
Subtract the numbers
7y = 48
Divide both sides of the equation by 7
= y = 6
Third One:Convert the fraction into decimal:
37/10 ÷ (1 2/9 - 0.4)
Convert the mixed number into an improper fraction
37/10 ÷ (11/9 - 0.4)
Convert the decimal into fraction
37/10 ÷ (11/9 - 2/5)
Subtract the fractions
37/10 ÷ 37/45
To divide by a fraction, multiply by the reciprocal of that fraction.
37/ 10 × 45/37
Cancel out the greatest common factor 37
1/10 × 45
Cancel out the greatest common factor 5
1/2 × 9
Calculate the product
Solution: 9/2
Fourth One:Convert the decimal into fraction and mixed fraction into improper fraction.
1/2 + 1/18
________
(7/6 - 7/18) ÷ 14/5
Add and subtract the fractions
5/9
____
7/9 ÷ 14/5
To divide by a fraction, Multiply by the reciprocal of that fraction.
5/9
____
7/9 × 5/14
Cancel out the greatest common factor 7.
5/9
____
1/9 × 5/2
Multiply the fractions
5/9
____
5/18
Simply the complex fraction
Solution: 2
Fifth one:Multiply the brackets
0.5x - 6 + 0.2x + 1.4 = 0.3x + 3.4
Collect like terms and simplify
0.7x - 4.6 = 0.3x + 3.4
Move the variable to the left hand side and move the constant to the right hand side and change the signs.
0.7x - 0.3x = 4.6 + 3.4
Simplify
0.4x = 8
Divide both sides of the equation by 0.4
Solution: x = 20
Thank you!Hank opens a savings account with $850. The account earns 1.2% interest compounded monthly. How much will be in the account after 15 years if he makes no more deposits or withdrawals? Round your answer to the nearest cent.
Answers
After 15 years, the amount in Hank's savings account, with no additional deposits or withdrawals, will be approximately $1,044.50.
To calculate the amount in Hank's savings account after 15 years with monthly compounding interest, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the account
P = the principal amount (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
In this case:
P = $850
r = 1.2% = 0.012 (as a decimal)
n = 12 (monthly compounding)
t = 15 years
Plugging in the values into the formula, we get:
A = 850(1 + 0.012/12)^(12*15)
A = 850(1.001)^180
A ≈ 850 * 1.228824
A ≈ $1,044.50 (rounded to the nearest cent)
Therefore, after 15 years, the amount in Hank's savings account, with no additional deposits or withdrawals, will be approximately $1,044.50.
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The diameter of the sphere is 12.8 cm calculate the value 3.14
Answers
what is needed to be calculated please tell
calculate the size of angle B
Answers
Check the picture below.
Thirteen students in a statistics class were asked how many siblings they have. Their responses are listed below. 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 6 Which of the following boxplots correctly displays the data?
Answers
The box plot which correctly shows displays the given data is the box plot where the whisker ranges from 1 to 6 and the box ranges from 2.5 to 4 with a line at 3.
Given a data set,
0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 5, 5, 6
Box shows the interquartile range.
Starting line of the box is first quartile, middle line is the median and the ending line is the third quartile.
There are 13 data points.
Here median = middle point = 7th point = 3
So the middle line of the box is at 3.
Median divides data plot in to two : 0, 1, 2, 3, 3, 3 and 3, 3, 3, 5, 5, 6.
First quartile is the median of the data points 0, 1, 2, 3, 3, 3.
First quartile, Q1 = average of middle two elements = (2 + 3) / 2 = 2.5
Third quartile is the median of the data points 3, 3, 3, 5, 5, 6.
Third quartile, Q3 = (3 + 5) / 2 = 4
IQR = Q3 - Q1 = 1.5
So the box ranges from 2.5 to 4 with a line at 3.
Now, we have to find the extension of whiskers, that is minimum and maximum value.
Lower whisker = Q1 - 1.5 (IQR) = 0.25
No values less than 0.25 is on the line.
Upper whisker = Q3 + 1.5 (IQR) = 6.25
No values greater than 6.25 will be on the line.
From the data, 0 belong as an outlier outside the whisker.
So whisker ranges from 1 to 6.
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PLS HELP ME ASAP RIGHT NOW
Answers
Answer:
[tex]\huge\boxed{\sf x = 12}[/tex]
Step-by-step explanation:
Let the smaller number be x and greater number be y.
Condition 1:y = 7 + 2x ----------------(1)
Condition 2:x + y = 43 ----------------(2)
Put Eq. (1) in Eq. (2)
x + 7 + 2x = 43
x + 2x + 7 = 43
3x + 7 = 43
Subtract 7 from both sides3x = 43 - 7
3x = 36
Divide both sides by 3x = 36/3
x = 12Put x = 12 in Eq. (1)
y = 7 + 2(12)
y = 7 + 24
y = 31[tex]\rule[225]{225}{2}[/tex]
I don’t understand thus
Answers
The true equations for the given value of x are C, D and E
solving for x in main equation3x = 5
x = 5/3
x = 1.667
Substituting x=1.667 in the equations given in the option
38.75 - 35.25 = 3.5 (False)1.667 + 2 = 3.667 (False)4/3(1.667) = 2.222 (True)9.7 + 1.667 = 11 (True)9(1.667) = 15 (True)The equations C, D and E are true for the value of x in the equation given.
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A solution to an equation Jada solved is −2+3⎯⎯√.
She is trying to determine whether that solution is rational or irrational. Jada knows that −2
is a rational number and 3⎯⎯√
is an irrational number. She also knows that the sum of any two rational numbers is always rational.
a. If we add 2
(a rational number) to −2+3⎯⎯√,
what is the sum? Is the sum rational or irrational?
b. Explain why −2+3⎯⎯√
cannot be rational.
Answers
a. To find the sum of 2 (a rational number) and (-2 + √3), we add them together:
2 + (-2 + √3) = 0 + √3 = √3
The sum is √3. Since √3 is an irrational number, the sum is irrational.
b. The expression -2 + √3 cannot be rational because a rational number can be expressed as the ratio of two integers, while √3 is an irrational number. If -2 + √3 were rational, it could be expressed as a fraction a/b, where a and b are integers. However, we know that √3 is irrational, so it cannot be written as a fraction of two integers. Therefore, -2 + √3 cannot be rational.
Question 2
The down payment makes the monthly loan payment fit into Isabel’s budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment (with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.
Answers
Saving for a down payment was worth it for Isabel. It reduces the total amount paid for the car by lowering the loan amount, resulting in less interest paid over time.
When evaluating whether saving for a down payment on a car was worth it for Isabel, we need to consider the difference in the total amount paid for the car in two scenarios: with a down payment and without a down payment. Let's analyze the two scenarios to make a judgment.
Scenario 1: With a down payment
In this scenario, Isabel saved up and made a down payment on the car. As a result, her monthly loan payment fits within her budget. By making a down payment, she reduces the principal amount borrowed and, subsequently, the interest charged on the loan.
The benefits of saving for a down payment include:
Lower loan amount: By making a down payment, Isabel reduces the total amount borrowed from the lender.
Reduced interest: With a lower loan amount, the interest charged on the loan is also reduced.
Shorter loan term: A down payment can help Isabel secure a shorter loan term, reducing the overall interest paid over time.
Scenario 2: Without a down payment
In this scenario, Isabel does not make a down payment and finances the entire purchase price of the car. As a result, her monthly loan payment may be higher, as she is borrowing a larger sum and potentially paying more interest over the loan term.
The drawbacks of not saving for a down payment include:
Higher loan amount: Without a down payment, the entire purchase price is financed, leading to a higher loan amount.
Increased interest: With a higher loan amount, more interest may accumulate over the loan term, resulting in a higher total cost of the car.
By comparing the two scenarios, we can assess the impact on the total amount paid for the car. Generally, having a down payment reduces the loan amount, decreases interest charges, and may result in a shorter loan term. This, in turn, can lead to substantial savings in the long run.
To determine the exact difference in the total amount paid for the car in each scenario, we would need specific details such as the purchase price of the car, the interest rate, and the loan term. With these figures, we could calculate the total cost of the car, including interest, in both scenarios and compare the results. Based on this analysis, we can then determine if saving for a down payment was worth it for Isabel.
In conclusion, saving for a down payment on a car can offer financial benefits such as lower loan amounts, reduced interest charges, and potentially shorter loan terms. Considering the potential cost savings and improved financial stability, it is generally advisable for Isabel to save for a down payment, making it worth the effort and consideration.
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Question
The down payment makes the monthly loan payment fit into Isabel's budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.
The rate of change of a population P of an environment is determined by the logistic formula
dP/dt =0.04P(1-P/20000)
where t is in years since the beginning of 2015. So P (1) is the population at the beginning of 2016. Suppose P (0) = 1000.
(a) Calculate P′(0)
(b) Use the number from the previous part to estimate the population in the middle of 2015. That is, estimate P (0.5)
(c) What assumption is made in the computation in the previous part? Use the formula given for P ′ to see whether or not the assumption is true, to within 1%
Answers
We first need to understand the logistic formula used for modeling population growth. The formula is:
P'(t) = rP(t)(1 - P(t)/K),
where P'(t) represents the rate of change of the population, P(t) is the population at time t, r is the intrinsic growth rate, and K is the carrying capacity of the environment.
(a) To calculate P'(0), we need the values for r, P(0), and K. P(0) refers to the initial population.
(c) The assumption made in the computation is that the population grows continuously and the rate is proportional to both the population size and the remaining capacity for growth.
To verify this assumption, we can plug in the given values and compare the result with the actual data. If the difference is within 1%, the assumption holds true.
Please provide the required values for r, P(0), and K to proceed with the calculations.
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3^3-8×3? evaluate it
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Answer:
3³-8*3 = 3
Step-by-step explanation:
Use order of operations:
P -> Parentheses
E -> Exponents
M -> Multiplication (left to right)
D -> Division (left to right)
A -> Addition (left to right)
S -> Subtraction (left to right)
3³=27 is done first because of the exponent. Next, we would do 8*3=24 because that has multiplication. Finally, we do 27-24=3 because of subtracting being the last step in PEMDAS.
Therefore, the final answer is 3
Write the expression for the following statement without
any spaces:
the sum of 64y and 3, cubed can be expressed as
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The expression of the statement that is given above can be written as follows: 262144y³ + 27.
How to determine a way to express the given statement?To determine how to express the given statement the following should be carried out.
When a number is said to be cubed, it means that the number should be times by itself three consecutive times.
That is (64y + 3)³. This means that various components should be multiplied by itself three times. That is,
= 64×64×64(y)³ + 3×3×3
= 262144y³ + 27.
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Pls help me with this 2 questions, thanks
Answers
[Top Question] Answer: A. |-6| + |3|
Step-by-step explanation:
First, we realize they are both on the same y-axis as they both have y-values of 4. This means that we can "ignore" the y-value and focus on the x-value. To find the distance between these two points, we will find the absolute value of the x-values and add them together. This gives us answer option A;
A. |-6| + |3|
[Bottom Question] Answer: 36 [tex]\frac{3}{4}[/tex] units²
Step-by-step explanation:
To find the area of a parallelogram, we multiply the base by the height. I will change 8 [tex]\frac{3}{4}[/tex] into 8.75 and 4 [tex]\frac{1}{5}[/tex] into 4.2 to make multiplying with a calculator easier.
A = bh
A = (8.75 units)(4.2 units)
A = 36.75 units² = 36 [tex]\frac{3}{4}[/tex] units²