Subtracting the death rate from the birth rate of a population calculates its intrinsic growth rate, expressed as dN = (b - d)N, where 'r' is the intrinsic rate of increase.
When you subtract the death rate (D) from the birth rate (B) of a population, you calculate the intrinsic growth rate of the population. The birth rate is typically expressed on a per capita basis, shown as B = bN, where 'b' represents the per capita birth rate and 'N' is the number of individuals in the population. Similarly, the death rate is expressed as D = dN, where 'd' is the per capita death rate. To find the population growth rate at a specific point in time, differential calculus is used to obtain an instant-specific measurement:
dN = (b - d)N
This formula simplifies the relationship between the birth and death rates, where 'b - d' is substituted with 'r', representing the intrinsic rate of increase. Therefore, the correct answer to the student's question is D. the intrinsic growth rate.
Will upvote and tip
A smart phone costs $149.99 before tax. The tax on the smart phone is 7%.
What is the total cost of the smart phone?
Round your answer to the nearest cent.
Answer/Step-by-step explanation:
149.99+(149.99*0.07)=160.4893. Round to $160.49
Find an exact value. cos 15°
The exact value of cos 15° is (√6 - √2)/4.
To find the exact value of cos 15°, we can use the trigonometric identities and special angles to determine its value.
One of the key identities that can be used is the cosine addition formula: cos (A + B) = cos A x cos B - sin A x sin B.
We can rewrite 15° as the sum of two special angles: 15° = 45° - 30°.
Using the cosine addition formula, we have:
cos 15° = cos (45° - 30°) = cos 45° x cos 30° - sin 45° x sin 30°.
Now, we know the exact values of cos 45° (which is (√2)/2), cos 30° (which is (√3)/2), sin 45° (which is (√2)/2), and sin 30° (which is 1/2).
Substituting these values into the equation, we get:
cos 15° = (√2)/2 x (√3)/2 - (√2)/2 x 1/2.
Simplifying further, we have:
cos 15° = (√6 - √2)/4.
This means that cos 15° can be expressed exactly as (√6 - √2)/4 without any decimal approximation.
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Answer:
the answer is check2+check6/4
Step-by-step explanation:
i took an exam and got it right
(i dont know what those check mark things are called or how to put the actual thing on a computer so hopefully you understand the check part)
Which of the following statements is true?
A.A radius is always a chord.
B.A tangent is always a secant.
C.A diameter is always a chord.
D.A chord is always a diameter.
Identify the temperature that is halfway between 0 degrees fahrenheit and 10 degrees fahrenheit
how would you write this in scientific notation
0.2 x 10^6
The number 0.2 x 10⁶ in scientific notation is written as 2 x 10⁵.
To write the number 0.2 x 10⁶ in scientific notation, we need to convert it into a format that has one non-zero digit to the left of the decimal point, followed by the appropriate exponent of 10.
The given number, 0.2 x 10⁶, is already close to scientific notation, however, we typically want the first number to be between 1 and 10. In this case, we can express 0.2 as 2 x 10⁻¹. Multiplying this by 10⁶ gives us:
2 x 10⁻¹ x 10⁶ = 2 x 10⁽⁶⁻¹⁾ = 2 x 10⁵.
So, the number 0.2 x 10⁶ in scientific notation is 2 x 10⁵.
HELPPPPPPPPPPPPP
(3 pt)
Which number sentences show ways to solve the problem?
The 9 members of a conservation club purchased a total of 45 tree saplings. Each member bought the same number of trees to plant in the community. Each tree cost $15. How much did each member pay for the trees?
Choose all answers that are correct.
A.
15 × 9 = 135 and 135 – 75 = 60
B.
3 × 15 = 45 and 45 + 15 = 60
C.
45 ÷ 9 = 5 and 5 × 15 = 75
D.
45 × 15 = 675 and 675 ÷ 9 = 75
is triangle EFG is congruent to triangle STU , what can you conclude about angle E, angle S, angle F and angle T
If triangle EFG is congruent to triangle STU, the following statements are true:
* Angle E = angle S.
* Angle F = angle T.
* Side EF = side ST.
* Side FG = side TU.
* Side EG = side SU.
If triangle EFG is congruent to triangle STU, then we can conclude that the following pairs of angles are congruent:
* Angle E is congruent to angle S.
* Angle F is congruent to angle T.
This is because congruent triangles have corresponding angles that are congruent.
We can also conclude that the following pairs of sides are congruent:
* Side EF is congruent to side ST.
* Side FG is congruent to side TU.
* Side EG is congruent to side SU.
This is because congruent triangles have corresponding sides that are congruent.
Therefore, the following statements are true:
* Angle E = angle S.
* Angle F = angle T.
* Side EF = side ST.
* Side FG = side TU.
* Side EG = side SU.
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A sports store sells bicycle baskets at $40.00 for two. another sports store sells bicycle baskets at $110 for five. which store sells at the better rate?
The solution is store A
The store which sells the bicycle with a better rate is store A with a price of $ 40.00 for two bicycles
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first store be represented as A
Let the second store be represented as B
Now , the equation will be
The price of 2 bicycles at store A = $ 40.00
So ,
The price of 1 bicycle at store A = price of 2 bicycles at store / 2
Substituting the values in the equation , we get
The price of 1 bicycle at store A = 40/2
The price of 1 bicycle at store A = $ 20
Now ,
The price of 5 bicycles at store B = $ 110
So ,
The price of one bicycle at store B = The price of 5 bicycles at store B / 5
Substituting the values in the equation , we get
The price of one bicycle at store B = 110/5
The price of one bicycle at store B = $ 22
And ,
The price of one bicycle at store B > The price of 1 bicycle at store A
22 > 20
Hence , the store A provides better rate for the price of one bicycle
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Draw a scatter plot that shows a person’s height and his or her age, with a description of any trends. Explain how you could use the scatter plot to predict a person’s age given his or her height. How can the information from a scatter plot be used to identify trends and make decisions?
A scatter plot depicting height and age reveals trends: positive correlation if points slope up, negative if down, none if scattered. Regression lines aid age prediction from height. The plot guides decisions by identifying patterns and outliers, supporting informed conclusions based on observed relationships.
Steps to interpret a scatter plot of a person's height and age:
1. **Scatter Plot Description:**
- Axes: Height on the y-axis, Age on the x-axis.
- Each point represents an individual's height and age.
- Scatter points may form a pattern or cluster.
2. **Trends and Interpretation:**
- **Positive Correlation:** If the points generally slope upward from left to right, it suggests a positive correlation—taller people tend to be older.
- **Negative Correlation:** If the points slope downward, it implies a negative correlation—taller people tend to be younger.
- **No Correlation:** If the points seem randomly scattered, there may be no apparent correlation.
3. **Predicting Age from Height:**
- Fit a regression line to the data. A linear regression line can be used to predict age given height.
- For a given height, find the corresponding point on the regression line to estimate the age.
4. **Identifying Trends and Decision Making:**
- **Patterns:** Identify patterns and correlations between variables.
- **Outliers:** Notice any data points significantly deviating from the trend.
- **Decision Support:** Use the trends to make informed decisions. For instance, if there's a correlation between height and age, you might anticipate certain health issues associated with age.
Scatter plots are powerful visual tools to analyze relationships between variables, identify trends, and make predictions or informed decisions based on observed patterns.
a polygon can grow from which of the following
a.one -dimensional objects
b.zero-dimensional objects
c.three-dimensional onjects? ...?
A polygon can grow from one-dimensional objects, which are lines. Zero-dimensional objects, which are points or vertices, also play a role as they define the positions where lines meet, but a polygon cannot directly grow from three-dimensional objects because polygons are two-dimensional shapes.
Explanation:A polygon can grow from one-dimensional objects, specifically from lines. In geometric terms, a polygon is a two-dimensional shape that is formed by connecting straight line segments. Each line segment connects to two others to form the polygon's perimeter. Moreover, the line segments join at their endpoints, known as vertices, which are zero-dimensional objects that contain only a single coordinate pair.
The formation of a polygon from lines is analogous to constructing a shape on a piece of paper by drawing lines that connect to form a closed loop. In this process, the lines are the sides of the polygon, and the points where the lines meet are the vertices. It is not possible for a polygon to directly grow from three-dimensional objects, as polygons are inherently two-dimensional.
For example, to represent a soccer ball in a simplified manner such as in geographic information systems (GIS), we can use polygons in the shape of pentagons and hexagons. The soccer ball itself is a three-dimensional object but the representation involving pentagons and hexagons is a two-dimensional schematic, emphasizing the importance of polygons in various mapping and modeling applications.
Solve the problem.
Find all values of k so that the given points are\sqrt {29} units apart. (-5, 5), (k, 0)
Choose the right answer
a. 3, 7
b. 7
c. -3, -7
d. -7 ...?
Final answer:
The values of k that ensure the points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex]units apart are -3 and -7, derived using the Pythagorean theorem and algebraic manipulation.
Explanation:
To find all values of k so that the points (-5, 5) and (k, 0) are \(\sqrt{29}\) units apart, we use the distance formula derived from Pythagoras’ theorem, which is[tex]d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)[/tex]. Here, [tex]\(x_1 = -5\), \(y_1 = 5\), \(x_2 = k\), and \(y_2 = 0\). Substituting the given values, we get:[/tex]
[tex]\(\sqrt{29} = \sqrt{(k + 5)^2 + (0 - 5)^2}\)[/tex]
Squaring both sides to eliminate the square root gives:
[tex]29 = (k + 5)^2 + 25[/tex]
Subtracting 25 from both sides, we get:
[tex]4 = (k + 5)^2[/tex]
Therefore, \(k + 5 = \pm2\), which simplifies to:
[tex]\(k + 5 = 2\) giving \(k = -3\)[/tex]
[tex]\(k + 5 = -2\) giving \(k = -7\)[/tex]
The values of k are -3 and -7, so the correct option is c. -3, -7.
The correct answer is option (c) -3, -7.
How is it so?
To find the values of k such that the given points (-5, 5) and (k, 0) are [tex]\(\sqrt{29}\)[/tex] units apart, use the distance formula between two points in a plane:
[tex]\[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
Given that the distance between the points is [tex]\(\sqrt{29}\)[/tex], we have:
[tex]\[ \sqrt{(k - (-5))^2 + (0 - 5)^2} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{(k + 5)^2 + 5^2} = \sqrt{29}[/tex]]
[tex]\[ \sqrt{k^2 + 10k + 25 + 25} = \sqrt{29} \][/tex]
[tex]\[ \sqrt{k^2 + 10k + 50} = \sqrt{29} \][/tex]
Squaring both sides to eliminate the square root:
[tex]\[ k^2 + 10k + 50 = 29 \][/tex]
[tex]\[ k^2 + 10k + 21 = 0 \][/tex]
Solve this quadratic equation
[tex]\[ k = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Where a = 1, b = 10, and c = 21.
[tex]\[ k = \frac{-10 \pm \sqrt{10^2 - 4 \cdot 1 \cdot 21}}{2 \cdot 1} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{100 - 84}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm \sqrt{16}}{2} \][/tex]
[tex]\[ k = \frac{-10 \pm 4}{2} \][/tex]
[tex]\[ k = \frac{-10 + 4}{2} \] or \( k = \frac{-10 - 4}{2} \)[/tex]
[tex]\[ k = \frac{-6}{2} \] or \( k = \frac{-14}{2} \)[/tex]
[tex]\[ k = -3 \] \:or \( k = -7 \)[/tex]
So, the correct answer is option (c) -3, -7.
Find the difference.
3x2y - x2y
A. 2
B. 2x2y
C. 3x2y
D. 4x2y
What is 1/10 of 2325
What are the solutions of the equation x4 + 3x2 + 2 = 0? Use u substitution to solve.
The solution to the system of equations are ±2i and ±i
Quartic equationsGiven the quartic equation
x^4 + 3x^2 + 2 = 0
Let u = x^2 to have:
(x^2)^2 + 3x^2 + 2 = 0
u^2 + 3u + 2 = 0
Factorize
u^2 + u +2u + 2 = 0
u(u + 1) + 2(u + 1) = 0
(u + 2)(u + 1) = 0
u = -2 or -1
If u = x^2
-2 = x^2
x = √-2
x = 2i
Similarly
If u = x^2
-1 = x^2
x = √-1
x = i
Hence the solution to the system of equations are ±2i and ±i
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Final answer:
To solve the equation x^4 + 3x^2 + 2 = 0 using u substitution, substitute x^2 for u and solve the quadratic equation. The resulting solutions in the complex number system are x = i, -i, √2i, and -√2i. There are no real solutions for this equation.
Explanation:
The solutions of the equation x4 + 3x2 + 2 = 0 can be found using u substitution. First, let's substitute u for x2, which transforms the original equation into the form u2 + 3u + 2 = 0. This is a quadratic equation, and we can solve it using the quadratic formula or by factoring. Factoring (u + 1)(u + 2) = 0, we get the solutions for u as u = -1 and u = -2. Since u is a substitute for x2, we then solve for x.
For u = -1, the equation x2 = -1 has no real solutions because the square of a real number cannot be negative. However, in the complex number system, the solutions are x = i and x = -i, where i is the square root of -1.
For u = -2, the equation x2 = -2 also has no real solutions, but the complex solutions are x = √2i and x = -√2i.
Therefore, the full set of solutions for the original equation are x = i, -i, √2i, and -√2i.
7 square yards is equal to how many square meters? A. 2.58 square meters B. 3.50 square meters C. 5.85 square meters D. 14.25 square meters C. 5.85 square meters
Final answer:
To convert 7 square yards to square meters, you multiply by the conversion factor, resulting in approximately 5.85 square meters. Hence, the correct answer is C. 5.85 square meters.
Explanation:
7 square yards is equal to how many square meters? To convert square yards to square meters, you can use the conversion factor 1 square yard = 0.83612736 square meters. Therefore, to convert 7 square yards to square meters:
7 sq yards * 0.83612736 sq meters/sq yard = 5.85289152 sq meters
When rounding to two decimal places, this is approximately 5.85 square meters. So, the correct answer would be C. 5.85 square meters.
Shane measured 457 ml of water in a beaker. olga measured 3 times as much water. how much water did they measure altogether
PLEASE HELP!
A 20in. by 24in. photo is reduced so that the length (the longer dimension) is 15in.
What is the width of the reduced photo?
A: 11in
B: 12.5 in
C: 13.5 in
D: 18in
Answer: Option 'B' is correct.
Step-by-step explanation:
Since we have given that
Dimensions of the photo is given by
[tex]20\ in.\ by\ 24\ in.[/tex]
According to question, the photo is reduced so that the longer dimension is 15 inch.
So, Let the width of the reduced photo be x.
So, it becomes,
[tex]\frac{20}{x}=\frac{24}{15}\\\\x=\frac{15\times 20}{24}\\\\x=12.5\ in.[/tex]
So, the width of the reduced photo is 12.5 inch.
Hence, Option 'B' is correct.
According to the Wall Street Journal, 14,200,000 videotape copies of Walt Disney's Fantasia have
been sold to date. Write that number in scientific notation.
A. 1.42 × 10^7
B. 1.42 × 10^6
C. 142 × 1,000,000
D. 142 × 10^7
Heathers desk is 3 feet long about how long is it in meters
What is the Quadratic Formula?
What is the solution to the linear equation?
2/3x –1/2 = 1/3 +5/6 x
A. x=-5
B. x= - 1/6
C.x= 1/6
D. x=5
Answer:
A) -5
Step-by-step explanation:
Evaluate.
2^3+4⋅2−7
A.1
B.5
C.9
D.36
Kenneth is inviting people to his parents' anniversary party and wants to stay at or below his budget of $6,000 for the food. The cost will be $40 for each adult's meal and $15 for each child's meal.
Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.
x = the number of adults
y = the number of children
Two angles of a triangle measures of 70° and 85° which is not the measure of an exterior angle of the triangle
What is the lateral surface area of a cylindrical-shaped candle with a radius of 3 cm and a height of 15 cm? (Use 3.14 for .) A. 847.8 sq cm B. 45 sq cm C. 282.6 sq cm D. 339.12 sq cm
Answer:
its 282.6 sq cm
Step-by-step explanation:
AL=2πrh=2·π·3·15≈282.74334
Your school has a $1200 grant to buy books and magazine subscriptions for the school library. The avarage cost of magazine subscription is $30. Your school decided to spend $870 on books and the remaining amout on magazine subscriptions. How many subscriptions can the school buy?
If deborah ran 3 2/5 miles on monday and on tuesday she ran 4 1/5 miles how many miles did she run on those two days together
Write an algebraic equation for the following. Three times the sum of a number and seven is two less than five times the number.
Evaluate -2x 2 y, if x = -3 and y = -1.
-12
-18
18 im thinking this one
12
How many miles is it from honolulu to turtle bay?
The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
Explanation:The distance from Honolulu to Turtle Bay is approximately 37 miles. To calculate this distance, you can use a map or a GPS tool. The most direct route between the two locations is along the Kamehameha Highway.
It's important to note that the actual distance traveled may vary depending on the specific route taken and any detours or alternate paths chosen.
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