At the beginning of an environmental study, a forest covered an area of 1500 km^2. Since then, this area has decreased by 7.75% each year.
Let t be the number of years since the start of the study. Let y be the area that the forest covers in km^2.
Write an exponential function showing the relationship between y and t.
If "t" number of years the study started and "y" denote the forest cover area, then the exponential-function representing the relation between "y" and "t" is y = 1500 × [tex](0.9225)^{t}[/tex].
An "Exponential-Function" is a mathematical expression in which a constant (called the base) is raised to a variable power.
In this case, we want to find an exponential function that relates the area of a forest (y) to the number of years since the start of an environmental study (t).
We know that the forest is decreasing by 7.75% each year, which means that the area of the forest after "t years" will be some percentage of its original area.
The formula for an exponential function is y = a × [tex]b^{t}[/tex], where "a" = initial value and "b" = growth or decay factor.
In this case, the initial area of the forest is = 1500 km², and
The forest is decreasing by 7.75% each year.
So, the "decay-factor" is = 1 - 0.0775 = 0.9225,
The exponential function that relates the area of the forest (y) to the number of years since the start of the study (t) is:
⇒ y = 1500 × [tex](0.9225)^{t}[/tex],
Therefore, the required "exponential-function" is y = 1500 × [tex](0.9225)^{t}[/tex].
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Graph the function f(t)=e0.4t
Answer:
here is the graph for it
Step-by-step explanation:
Quadrilateral EFGH is a rhombus which addition fact would prove that EFGH is a square
the answer choices are in the photo below I will give brainlyest to right answer
Option C) EG bisects ZFEH would prove that EFGH is a square.
What is quadrilateral?In geometry, a quadrilateral is a polygon with four sides and four vertices (corners). It is a two-dimensional shape with four straight sides, and the sum of its interior angles is equal to 360 degrees. Some common types of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. Each type of quadrilateral has its own unique set of properties, such as congruent sides and angles, parallel sides, or perpendicular diagonals. Quadrilaterals are used in many areas of mathematics, as well as in engineering, architecture, and other fields.
Here,
A rhombus has opposite sides congruent, but its angles are not necessarily right angles. However, if the diagonals of a rhombus are perpendicular bisectors of each other, then the rhombus is a square.
If EG bisects ZFEH, then the opposite angles of the rhombus are congruent and the diagonals of the rhombus are perpendicular bisectors of each other. This means that EFGH is a square, and all its sides and angles are congruent.
Options A), B), and D) do not provide any information about the shape of EFGH.
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Which graph represents the function f(x) = 2^x-1 + 2?
The graph that represents the exponential function f(x) = 2^(x - 1) + 2 is given as follows:
Graph A.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The function for this problem is defined as follows:
f(x) = 2^(x - 1) + 2
It has an horizontal asymptote at y = 2, which removes the option C.
The parameter b is of b = 2, meaning that the function is increasing, which removes option D.
The numeric value of the function when x = 0 is given as follows:
f(0) = 2^(0 - 1) + 2
f(0) = 1/2 + 2
f(0) = 5/2
f(0) = 2.5.
Hence graph A is correct.
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a group of students was to clean up to two areas in their school. area a was 1 1 2 times of area b. in the morning (half of a day), the number of students cleaning area a was 3 times that of the number of students in area b. in the afternoon (another half of a day), 7 12 of the students worked in area a while the rest of them in area b. at the end of the day, area a was done, but area b still needed 4 students to work one more day before it was done. how many were there in this group of students?
the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students,
How to solve the problem?
Let's use the following variables to represent the unknowns in the problem:
Let A be the area of area A
Let B be the area of area B
Let x be the number of students working in area B in the morning
Let 3x be the number of students working in area A in the morning
Let y be the total number of students in the group
From the problem statement, we know that A = 1.5B (since area A is 1.5 times area B). We also know that in the morning, the number of students working in area A is 3 times the number of students working in area B. This can be expressed as:
3x = y/2 (since half of the students work in the morning)
In the afternoon, 7/12 of the students work in area A, so the number of students working in area B is:
(1-7/12)y = 5/12y
At the end of the day, area A is done and area B still needs 4 more students to work for another day. This means that the amount of work done by the students in area B is (y/2 - 3x) + (5/12y - 4B) = B, since the total work needed to be done in area B is B and the amount of work done by the students in area A is y/2 - 3x.
Substituting A = 1.5B and 3x = y/2, we can solve for y:
(y/2 - 3x) + (5/12y - 4B) = B
y/2 - 3(y/2)/3 + 5/12y - 4B = B
y/2 - y/2 + 5/12y = 5B
17/12y = 5B
y = (5/17)12B
Therefore, the total number of students in the group is (5/17)12B. We don't have a specific value for B, so we can't give a specific answer for the number of students, but we can say that the number of students is proportional to the area of area B. If we know the area of area B, we can use the equation above to find the total number of students in the group.
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Find the standard form of the equation of the hyperbola with the given characteristics.
Vertices:
(1, −2), (5, −2);
passes through the point
(−3, 6)
The standard form of the hyperbola is:
(x-3)²/4 - (y+2)²/(64/35) = 1
How to solve
Given vertices (1, -2) and (5, -2), the center is (3, -2) and the semi-major axis, a = 2.
The hyperbola is horizontal.
Using point (-3, 6), we find the semi-minor axis, b² = 64/35.
The standard form of the hyperbola is:
(x-3)²/4 - (y+2)²/(64/35) = 1
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What is the solution to the system of equations graphed below?
3
2
68 x
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph.
How to obtain the solution to the system of equations?In this problem, the graph of the system of equations is given, hence we use it to obtain the solution.
The solution of the system of equations is given by the point of intersection of all the equations that compose the graph, that is, the point where all the curves cross each other.
The point of intersection represents the solution of the system of equations as it is the input values for which all the equations have the same output value.
Missing InformationThe problem is incomplete, hence the procedure to obtain the solution of the system of equations from the graph is presented.
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2.2.3 quiz: angle theorems what is the value of y? OA.50
its c please mark me as a brainliest
Write an equation for the function graphed below
The given graph represents the function with the equation f(x) = 12(x - 1)/[(x + 2)(x - 3)].
To write an equation for the function, we first observe that the vertical asymptotes occur at x = -2 and x = 3, indicating that the denominator (Q(X)) has roots at x = -2 and x = 3. Hence, the equation of the denominator is:
Q(X) = (x + 2)(x - 3)
Furthermore, from the graph, we can see that the zero of the function occurs at x = 3, indicating that the numerator (P(X)) has the factor (x - 3). Let a be the leading coefficient of P(X), so we can write:
P(X) = a(x - 1)(x - 3)
To find the value of a, we use the fact that the y-intercept of the function is (0, -2). Substituting x = 0 and f(0) = -2 into the equation of the function, we get:
-2 = a(-1)/[(2)(-3)]
Simplifying this equation gives us:
a = -2/(2*3) = -1/3
Substituting this value of a into the equation for P(X), we get:
P(X) = (-1/3)(x - 1)(x - 3)
Substituting the equations for P(X) and Q(X) into the formula for f(x), we get:
f(x) = (-4)(x - 1)/[(x + 2)(x - 3)]
Simplifying this equation gives us:
f(x) = -4(x - 1)/[(x + 2)(x - 3)]
Therefore, the equation of the function graphed in the figure is f(x) = -4(x - 1)/[(x + 2)(x - 3)].
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What is the vertex form of function f? f (x) = 2x^2 + 6x + 5
Answer:
y = 2(x + 1.5)² + 0.5
Step-by-step explanation:
"To convert the standard form y = ax² + bx + c to vertex form:
Extract a from the first two terms: y = a[x² + (b/a)x] + c.
Add and subtract (b/(2a))² inside the bracket: y = a[x² + (b/a)x + (b/(2a))² - (b/(2a))²] + c.
Use the short multiplication formula: y = a[(x + b/(2a))² - (b/(2a))²] + c.
Expand the bracket: y = a(x + b/(2a))² - b²/(4a) + c.
This is your vertex form with h = -b/(2a) and k = c - b²/(4a)."
^^ not my explanation!!
Name an acute angle and give its measure.
Angle: ______ Measure: _____
Name an obtuse angle and give its measure. (2 points)
Angle: _____ Measure: _____
Name one right angle. (1 point
Name one straight angle. (1 point)
11. Angle KEF = 40°, Angle KEJ = 50°
12. Angle HEF = 115°, Angle KED = 140°
13. Angle JEF = 90°, Angle KEF = 90°
14. Angle DEF = 180°
Define the term geometry?The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.
11. Acute angles: Those angles are less than 90 degree angles.
Angle KEF = 40°
Angle KEJ = 50°
Angle KEH = 75°
Angle JEH = 25°
Angle HED = 65°
12. Obtuse angles: Those angles are more than 90 degree angles.
Angle HEF = 115°
Angle KED = 140°
13. Right angle: Those angles are 90 degree angle.
Angle JEF = 90°
Angle KEF = 90°
14. Straight angle: Those angles make 180 degree angle.
Angle DEF = 180°
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Denzel used the spinner shown below to compare theoretical probability and experimental probability. He spun the spinner 180 times and recorded the letter that it landed on each time. The results are shown in the table..
Which statement correctly compares the theoretical probability and experimental probability for one of the letters on the spinner?
A. The theoretical probability of landing on a C is greater than the experimental probability of landing on an C.
B. The theoretical probability of landing on a D is greater than the experimental probability of landing on an D.
C. The theoretical probability of landing on a B is less than the experimental probability of landing on an B.
D. The theoretical probability of landing on an A is less than the experimental probability of landing on an A.
Answer:
C
Step-by-step explanation:
The theoretical probability of landing on A, B, C, or D is all 1/4. This would also mean the theoretical probability is 45/180. Statement C is the only one that is true.
I am confused on how to solve the table and find the velocity
Answer:
Step-by-step explanation:
y = 5x^3 - x
Slope of a secant
= (y2 - y1)/(x2-x1) where (x1, y1) and (x2, y2) are the 2 points.
Slope for the interval (1, 2)
= [5(2)^3 - 2)- (5(1)^3 - 1)] / (2-1)
= 34
Slope for interval (1, 1.5)
= [5(1.5)^3 - 1.5)- (5(1)^3 - 1)] / (1.5-1)
= 22.75
In the same way we get the slopes of the intervals:
(1, 1.1):- 15.55
(1, 1,01):- 15.15
(1, 1.001):- 15.015
So the answer is 15.
The sum of two numbers exceeds a third number by four. If the sum of the three numbers is at least 20 and 28,find any three intgral values satisfying the inequality .
Answer:
Let the three numbers be x, y, and z.
We are given that x + y = z + 4.
We are also given that x + y + z >= 20 and x + y + z <= 28.
Combining these two inequalities, we get:
z + 4 + z >= 20
2z >= 16
z >= 8
Since z is an integer, z can be 8, 9, 10, 11, 12, 13, 14, 15, 16, or 17.
For each value of z, we can find the corresponding values of x and y using the equation x + y = z + 4.
For example, if z = 8, then x + y = 12.
So, the three integral values satisfying the inequality are 8, 4, and 0.
Another example is z = 15.
In this case, x + y = 19.
So, the three integral values satisfying the inequality are 15, 2, and 2.
There are many other possible solutions.
Draw a bar chart to show how the price increased
The bar chart showing the growth of the price per tone of ground nut over the years is attached accordingly.
What is a bar chart?A bar chart, sometimes known as a bar graph, is a type of chart or graph that displays categorical data using rectangular bars with heights or lengths proportionate to the values they represent. The bars can be plotted horizontally or vertically. A vertical bar chart is also known as a column chart.
From the bar chart, is clarer to see that the price of ground nut per tone increased steadily year on year.
By the year 2008, it had hit record high of 100,000 per ton.
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answer this please and thank you
Answer:
2800=1.4tons
Step-by-step explanation:
2000Ib=1ton
please answer question on picture
The probability that Mason does not arrive at work by 9 a.m. is given as follows:
p = 17/50.
How to calculate a probability?A probability is calculated dividing the desired number of outcomes by the total number of outcomes.
The outcomes relating to the bus not arriving on time are divided as follows:
1 - 3/4 = 1/4 of 4/5. -> bus arrives on time.1 - 3/10 = 7/10 of 1 - 4/5 = 1/5. -> bus does not arrive on time.Hence the probability is given as follows:
p = 1/4 x 4/5 + 7/10 x 1/5
p = 1/5 + 7/50
p = 10/50 + 7/50
p = 17/50.
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How likely is it that
at least > or them are vowe tiles?
) Which simulation could be used to fairly represent the situation?
There is a probability of 0.117 for at least 2 of the tiles to be vowel tiles.
Given that,
Probability that the tiles getting is a vowel tile is 30%.
P(V) = 30% = 0.3
That is there will be only 3 tiles out of 10 tiles which are vowels.
Out of 8, there will be 8 × 0.3 = 2.4 tiles which are vowels.
There would be either 2 or 3 vowels.
Probability that at least 2 of them is vowel tiles is,
Probability = (0.3)² + (0.3)³
= 0.117
Here,
The simulation which can be used to fairly represent the situation is,
Use a computer to randomly generate 8 numbers from 1 to 10. Each time 1, 2 or 3 appears, it represents a vowel tile.
Hence, the required probability is 0.117.
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PLS REPLY FAST NO EXPLAINATION NEEDED
Tony solved the equation below by completing the square, but he got the incorrect solution. In which step did Tony first make an error?
Step 1 : x 2 + 4 x = 77
Step 2 : x 2 + 4 x + 4 = 81
Step 3 : ( x + 2 ) 2 = 81
Step 4 : x + 2 = ± 81
Step 5 : x = 79 , x = − 83
The error made by Tony is in Step 4, where he wrote "x + 2 = ± 81". The correct step should be:
Step 4: Take the square root of both sides to solve for x.
√((x + 2)^2) = √81
In this step, Tony should have taken the square root of both sides, but he made the mistake of only taking the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
The correct step should be:
x + 2 = ±9
Step 5: Solve for x.
x + 2 = 9 or x + 2 = -9
Step 6: Subtract 2 from both sides to isolate x.
x = 9 - 2 or x = -9 - 2
This will give the correct solutions:
x = 7 or x = -11
So, the error made by Tony occurred in Step 4 where he only took the square root of the right-hand side and neglected to take the square root of the left-hand side correctly.
Hope this helps!
The probability that a certain state will be hit by a major tornado (category F4 or F5) in any single year is
parts (a) through (d) below.
1/20
Complete
(Simplify your answer. Round to five decimal places as needed.)
- What is the probability that the state will be hit by a major tornado in three consecutive years?
(Simplify your answer. Round to five decimal places as needed.)
What is the probability that the state will not be hit by a major tornado in the next ten years?
(Round to three decimal places as needed.)
What is the probability that the state will be hit by a major tornado at least once in the next ten years?
(Round to three decimal places as needed.)
the probability of a major tornado in three consecutive years is 1/8000. the probability of not having a major tornado in the next ten years is approximately 0.328. he probability of having at least one major tornado in the next ten years is approximately 0.672.
How to the probabilities in the question(a) The probability of a major tornado in any single year is 1/20. To find the probability of a major tornado in three consecutive years, we multiply the probabilities together:
P(major tornado in 3 consecutive years) = (1/20) * (1/20) * (1/20) = 1/8000
So the probability of a major tornado in three consecutive years is 1/8000.
(b) The probability of not having a major tornado in any single year is 19/20. To find the probability of not having a major tornado in the next ten years, we raise this probability to the power of 10:
P(no major tornado in next 10 years) = (19/20)^10 ≈ 0.328
So the probability of not having a major tornado in the next ten years is approximately 0.328.
(c) To find the probability of having at least one major tornado in the next ten years, we can subtract the probability of having no major tornadoes in the next ten years from 1:
P(at least one major tornado in next 10 years) = 1 - P(no major tornado in next 10 years)
P(at least one major tornado in next 10 years) = 1 - (19/20)^10 ≈ 0.672
So the probability of having at least one major tornado in the next ten years is approximately 0.672.
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If JK is tangent to circle L, find x.
x =
(60 POINTs will give BRAINIEST FOR EFFORT)
Answer:
x ≈ 11.87 units-----------------------
Tangent line is perpendicular to radius at the point of tangency.
Hence we have:
MJ ⊥ KJTherefore ΔMKJ is a right triangle.
Radius is 11, so diameter is 22, this is one of legs and its hypotenuse is 25 units.
Use Pythagorean theorem to find the missing leg:
x² = 25² - 22²x² = 141x = √141x ≈ 11.87 units (rounded)matrix A = 2 -7 matrix B = -9 5
6 1 1 -1
If X - A = B, what is X?
Sonic Corporation purchased and installed electronic payment equipment at its drive-in restaurants in San Marcos, TX, at a cost of $37,800. The equipment has an estimated residual value of $2,400. The equipment is expected to process 261,000 payments over its three-year useful life. Per year, expected payment transactions are 62,640, year 1; 143,550, year 2; and 54,810, year 3.
Complete a depreciation schedule for each of the alternative methods.
1. Straight-line.
2. Units-of-production.
3. Double-declining-balance.
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Complete a depreciation schedule for each of the alternative methods.Method of the straight line:
Annual depreciation = (Cost - Residual value) / Useful life
Annual depreciation = ($37,800 - $2,400) / 3 years = $11,800 per year
Schedule of depreciation: shown in the below table
Units-of-production method:
Depreciation per unit = (Cost - Residual value) / Total units of production
Depreciation per unit = ($37,800 - $2,400) / 261,000 = $0.139 per unit
Depreciation schedule:
Double-declining-balance method:
Depreciation rate = 2 / Useful life
Depreciation rate = 2 / 3 = 0.667 or 66.7%
Depreciation schedule: shown in the below table
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Function f has a vertex. Can the function be increasing over its entire domain? Can it be decreasing over its entire domain? Explain.
Choose the correct answer below.
A. A function with a vertex is always increasing if the y-coordinate of the vertex is positive and is always decreasing if the y-coordinate of the vertex is negative.
B. A function with a vertex is constant. So, the function can neither be increasing nor decreasing.
C. A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its
entire domain.
D. A function with a vertex can be always increasing as long as the function approaches positive infinity in both directions and can be always decreasing as long as the
function approaches negative infinity in both directions.
A function with a vertex must switch from increasing to decreasing or vice versa at the vertex. So, the function cannot be only increasing or only decreasing over its entire domain.
Given data ,
A function with a vertex, also known as a vertex form of a quadratic function, is a function of the form f(x) = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. The vertex is the point on the parabola where it changes direction from increasing to decreasing or vice versa.
It is impossible for a function with a vertex to increase continuously if its whole domain shows an increase in the function. Similar to the last example, a function with a vertex cannot decrease throughout its whole domain because that would imply that the function is constantly decreasing.
Hence , a function with a vertex must switch from increasing to decreasing or vice versa at the vertex, and it cannot be only increasing or only decreasing over its entire domain.
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Given that a line has a slope of 1/2 and
its y-intercept is the point (0, 7), write
the equation of the line in slope-
intercept form, y = mx + b.
A. y= (1/2)x
B. 7 = (1/2)x+ 0
C. y= (1/2)x+ 7
D. y= 7x+ ½
I will give brainliest and ratings if you get this correct
Answer:
below
Step-by-step explanation:
To show that (AB)^-1 = B^-1A^-1, we need to show that:
(AB)(B^-1A^-1) = (B^-1A^-1)(AB) = I
where I is the identity matrix.
Using the associative property of matrix multiplication, we can simplify the left-hand side of the equation as:
(AB)(B^-1A^-1) = A(BB^-1)A^-1 = AIA^-1 = AA^-1 = I
Similarly, using the associative property of matrix multiplication, we can simplify the right-hand side of the equation as:
(B^-1A^-1)(AB) = B^-1(A^-1A)B = B^-1IAB = BB^-1 = I
Therefore, we have shown that (AB)^-1 = B^-1A^-1.
To show this identity, we need to demonstrate that:
(AB)^-1 = B^-1 A^-1
To do this, we start by multiplying both sides of the equation by (AB):
(AB)^-1 (AB) = B^-1 A^-1 (AB)
On the left side, we know that (AB)^-1 is the inverse of AB. So we can simplify to:
I = B^-1 A^-1 (AB)
Where I is the identity matrix. We can now simplify the right side by rearranging the terms:
B^-1 A^-1 (AB) = B^-1 (A^-1 A) B
Since A^-1 A = I, we can simplify further to:
B^-1 (A^-1 A) B = B^-1 IB = B^-1 B = I
Therefore, we have shown that:
(AB)^-1 = B^-1 A^-1
Q.E.D.
A triangle has a base of 12 cm and an area of 18 cm².
Find the height of the triangle:
Height = cm
Answer:
3cm
Step-by-step explanation:
triangle formula is height times base divided by two and divide base by two. then its 6 and divide 6 from 18. so the answer is 3cm
A company reports the following beginning inventory and two purchases for the month of January on January 26th the company says $420 units ending inventory at January 31st totals $170 units assume the Perpetual inventory system is used determine the cost to assigned to the ending inventory will cost or assigned based on the lifo method
The cost assigned to the ending inventory will cost or assigned based on the lifo method is attached.
What is the inventory about?Denoting the valuation of inventories a business owns at the completion of any accounting term – be it monthly, quarterly, or annually – ending inventory speaks to the cost of items that have yet to be sold or used in the creation of goods and services.
Checking a company's economic performance is contingent on examining its ending inventory since this element impacts cost of goods sold (COGS) substantially; many corporations' COGS are worked out by subtracting the cost of goods distributed over a period from the overall cost of goods available for sale during that same interval.
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Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
y = 11.46 e1.107x
y = 0.45x1.903
y = –109.41 + 14.59x
y = –477.38 + 237.66 ln x
The regression equation that fits the scenario will be y = 11.46 e1.107x
How to explain the equationUtilizing this method with the provided information, we attain the regression equation:
ln y = 2.4502 + 0.0515x
It should be noted that to find the exponential equation, we can elevate both sides of the equation:
y = e^(2.4502 + 0.0515x) = 11.46 * e^(1.107x)
Consequently, the mathematical model that is most suitable for the mentioned data is:
y = 11.46 * e^(1.107x)
The coefficient of determination (R-squared) for said model is 0.994, thus indicating an incredibly strong fit.
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A new hair cream was just given to a random sample of
500 people that are either bald, or currently losing their hair. The results showed that
175 of people either started growing back hair or stopped losing their hair, and the results had a margin of error of 0.065
.
If the new hair cream will be administered to 7810
people, how many are expected to see improvement?
Between [DROPDOWN1] and [DROPDOWN2] are predicted to see an improvement in their baldness.
Between 2226 and 3241 people are predicted to see an improvement in their baldness.
How to obtain the amounts?The expected amount of people expected to see improvement is obtained applying the proportions in the context of the problem.
The sample proportion is given as follows:
175/500 = 0.35.
Considering the margin of error, the bounds are given as follows:
0.35 - 0.065 = 0.285.0.35 + 0.065 = 0.415.Hence the amounts out of 7810 people are obtained as follows:
0.285 x 7810 = 2226 people.0.415 x 7810 = 3241 peopleMore can be learned about proportions at https://brainly.com/question/24372153
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