We will substitute he value 3 for a.
We will substitute he value 4 for b.
Required function is[tex]f(n) = 3(4)^{(n-1)}[/tex]
What is function?
A function is a mathematical concept that maps an input value or set of values to a unique output value or set of values. In computer programming, a function is a block of code that can be called by its name, and may take inputs (arguments) and return outputs.
We can observe that each term in the sequence is obtained by multiplying the previous term by 4. Therefore, the common ratio of the sequence is 4.
To write the explicit formula for the nth term, we can use the formula for a geometric sequence,
[tex]f(n) = a(b)^{(n-1)}[/tex]
We know that f(1) = 3, so we can substitute n=1 into the formula to get,
[tex]f(1) = a(b)^{(1-1)} = a[/tex]
Therefore, a = 3.
We also know that the common ratio between consecutive terms is 4. We can use this information to find the value of b,
12/3 = 4
48/12 = 4
192/48 = 4
768/192 = 4
The ratio between consecutive terms is 4, so b = 4.
Putting it all together, the explicit formula for the nth term in the sequence is [tex]f(n) = 3(4)^{(n-1)}[/tex]
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Correct question is "The first five terms of a sequence are shown
3, 12, 48, 192, 768, ...
We are going to write an explicit function to model the value of the nth term in the
sequence such that f(1) = 3.[tex]a(b)^{n-1}[/tex]
Our function will be written in this form: f(n)
What value will we substitute in for a?
What value will we substitute in for b?
What will be the function?"
what is the base 8 representation of 1100111 base 2
Answer:
147
My teacher has been trying to help me learn this and it has been working.
60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°
The value of y is 4, so the answer is option A: y = 4.
What is trigonometric ratios ?
Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Using the given diagram, we can use the trigonometric ratios to find the value of y.
First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:
sin(30°) = opposite/hypotenuse
sin(30°) = y/8
y/8 = 1/2
y = 8/2
y = 4
Therefore, the value of y is 4, so the answer is option A: y = 4.
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What is the volume of a cube with a length of 11 meters? Volume V = $³ V = /w/z V = Bh V=²h Cube Rectangular prism Triangular prism Cylinder OA) 33 m³ B) 121 m³ C) 1,221 m² D) 1,331 m³ or V = Bh
Answer:
The volume of a cube with a length of 11 meters is 33 m³.
A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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What is M in triangle properties
I hope this helps you.
how long does it take for a deposit of $1300 to double at 9% compounded continuously?
how many years does it take to double? years _ days _
8. The percentage of the moon's surface that is visible to someone on the Earth varies due to
the time since the previous full moon. The moon passes through a full cycle in 28 days. The
maximum percentage of the moon's surface that is visible from Earth is 50%. Find a function
for the percentage, P, of the surface that is visible as a function of the number of days, t,
since the previous full moon.
A functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
What is a functiοn?In the case οf a functiοn frοm οne set tο the οther, each element οf X receives exactly οne element οf Y. The functiοn's dοmain and cοdοmain are respectively referred tο as the sets X and Y as a whοle. Functiοns were first used tο describe the idealized relatiοnship between twο varying quantities.
Here, we have
Given:
Tο find the percentage οf the full mοοn, we can write an equatiοn in the fοrm P = Acοs(Bt) + C
After 14 days, the percentage οf the mοοn is zerο
A = (max-min)/2 = 50/2 = 25
The periοd = 28 days
P = Acοs(BT = t) + c
B = 2π/periοd = 2π/28 = π/14
c = min + A = 0 + 25 = 25
We get,
P = 25cοs(π/14t) + 25,
Here, p is the percentage οf the mοοn visible cοmpared tο the previοus full mοοn.
Hence, a functiοn fοr the percentage is P = 25cοs(π/14t) + 25.
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Spencer is working with his finande advisor to create some personal financial goals for the next year. One of his goals is to reduce the amount of debt
he has. Which statement could
his goal specific and timely?
He should focus intust his student loan debt and give himself a deadline of five years.
B. He should ask
end to be his accountability partner and remind him of his goal every two weeks.
le should review.
current finances to determine how much he can allocate to his goal.
He should pay
the minimum payment on his credit card statement each month.
Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.
Step-by-step explanation:
Mohal plans to repaint some classroom bookcases. He has 1 1/8 gallons of paint. All of the bookcases are the same size and each requires 1/8 gallon of paint. How many bookcases will he be able to paint?
Mohal will be able to paint 9 bookcases for the amount of paint.
What is fraction?An expression for a portion of a whole is a fraction. It is represented by the numerator above the denominator, with a horizontal line separating the two numbers. In mathematics, fractions are used to represent fractions of a whole or values that are not whole numbers. Like whole numbers, they can be multiplied, split, added, and subtracted. Ratios and proportions, which are crucial ideas in many branches of mathematics and science, are also represented by fractions.
Given that, he has 1 1 /8 gallons of paint.
Thus, number of bookcases are:
1 1/8 ÷ 1/8 = (9/8) ÷ (1/8) = 9
Hence, Mohal will be able to paint 9 bookcases for the amount of paint.
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solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
The expression 12x +8 is equivalent to the expression a(bc+c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4). Which statement best explains whether the students answer is correct or incorrect
The student's is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
What is expression?Expression is the communication of emotion or ideas through words, art, music, or other forms of communication. It is the way in which a person or artist conveys their thoughts and feelings in a creative and meaningful way. Expression can be seen in the form of art, writing, music, dance, and other creative outlets. Expression is a powerful tool that can be used to communicate a message or to evoke a feeling in the audience. Expression can be used to inspire, educate, motivate, and even to heal. Expression is a way to connect people and cultures, and a way to share stories and experiences. It is a way to express oneself in a meaningful and powerful way.
This is because 12z+8 can be written as 2z(6x+4), where the greatest common factor of 12 and 8 (2z) is factored out.
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Complete Question:
The expression 12z+8 is equivalent to the expression a (bx + c), where b and c are constants and have no common factors. A student wrote the answer as 2 (6x+4).
Which statement best explains whether the student's answer is correct or incorrect?
OA. The student's answer is incorrect because the greatest common factor of 12 and 8 is 2z, so the correct expression is 2x (6x+4).
OB. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4z, so the correct expression is 4z (3x+2).
C. The student's answer is incorrect because the greatest common factor of 12 and 8 is 4, so the correct expression is 4 (3x+2).
OD. The student's answer is incorrect because the greatest common factor of 12 and 8 is 8, so the correct expression is 8 (4x+1).
Is the vertex from if
y=-.29 (x) ^2 +8 what is factored form
Please help it’s due today!!!!
I will mark you brainless
Answer: Vertex is (0,8)
Could someone help me find the answers and show me how they got it it’s a review for a quiz I have to take for tomorrow
Area of composite shape = 12 + 9
= 21 cm²
How to solve
Area of composite shapes:
13) Figure 1:
Figure1 is a rectangle.
l = 4 cm & w = 2 cm
Area of figure1 = l * w
= 4 * 2
= 8 cm²
Figure2:
Figure2 is a parallelogram
base = b = 4 cm
h = 4 cm
Area of figure2 = b * h
= 4 * 4
= 16 cm²
Area of composite shape = 8 + 16
= 24 cm²
14) Figure1:
Figure 1 is a trapezium. a & b are parallel sides and h is the height
a = 4 cm ; b = 6 cm; h = 4 -2 = 2 cm
Figure2:
Figure2 is a rectangle. l = 6 cm ; w = 2 cm
Area of figure2 = 6*2
= 12 cm²
Area of composite shape = 10 + 12
= 22 cm²
15) Figure 1 & figure 2:
Figure 1 and figure 2 are congruent triangles
base = b = 3 cm & h= 4 cm
= b *h
= 3 * 4
= 12 cm²
Figure3:
Figure 3 is a square.
side = 3 cm
Area of figure3 = side *side
= 3 * 3
= 9 cm²
Area of composite shape = 12 + 9
= 21 cm²
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A quadrilateral is shown.
H
6.5
5.51
What is the area of the quadrilateral? Enter the answer in the box.
The calculated area of the quadrilateral is 35.82 square units.
What is the area of the quadrilateral?Given that
BAse = 6.5
Height = 5.51
To find the area of a quadrilateral, we need to multiply the base by the height.
Area of quadrilateral = base x height
Substituting the given values, we get:
Area = 6.5 x 5.51
Area = 35.815
Rounding to the nearest hundredth, the area of the quadrilateral is 35.82 square units.
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A container in the shape of a rectangular prism has a height of 2 feet. Its length is four
times its width. The volume of the container is 200 cubic feet. Find the length and width of
the container.
Answer: length = 20 feet and width = 5 feet
Step-by-step explanation: Volume is equal to volume = height * width * length. The questions tells us the total volume is 200 cubic feet and that the lenght is equal to length = 4w. Set up the equation 4w * w * 2 = 200 cubic feet. Multiply to get 8w^2 = 200 and solve for w.
4)
Northbrook Middle School surveyed 325 students to learn more about their after-schoo
activities. They found that 90 students are in a club and play a sport. 140 total students
play a sport and 200 total students are in a club. Construct a two-way relative freques
table summarizing the data.
Plays a Sport
In a Club
Not In a Club
Total
Doesn't Play a
Sport
Total
Th two-way relative frequency table has been attached at the end of the solution. The relative frequencies were obtained by dividing each frequency by the total number of students (325).
What is frequency?Frequency refers to the number of times that a particular event or value occurs within a specific dataset or sample. In statistics, frequency is often used to represent the distribution of values in a dataset, and it can be displayed using tools such as frequency tables, histograms, or frequency polygons.
90 students are in a club and play a sport.
140 total students play a sport.
Therefore, 140 - 90 = 50 students play a sport but are not in a club.
The total number of students who play a sport is 140 + 50 = 190.
200 total students are in a club.
Therefore, 200 - 90 = 110 students are in a club but do not play a sport.
The total number of students who do not play a sport is 325 - 190 = 135.
The relative frequency of students who play a sport and are in a club is 90/325 = 0.277.
This table tends to show the proportion of students in each category and how they overlap with the other category. For example, we can see that 27.7% of the students play a sport and are in a club, while 15.4% of the students do not play a sport but are in a club. We can also see that 21.5% of the students play a sport but are not in a club, while 35.4% of the students do not play a sport and are not in a club.
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The supply and demand for a product are related to price by the following equations, where y is the price, in dollars, and x is the number of units, in thousands. Find the equilibrium point for this product.
y=300+40x
y=9300-50x
helpp..
Answer: At equilibrium, the supply and demand are equal, so we can set the two equations equal to each other:
300 + 40x = 9300 - 50x
Simplifying and solving for x:
90x = 9000
x = 100
Now that we know x, we can use either equation to find y:
y = 300 + 40(100) = 4300
So the equilibrium point is when x = 100 and y = 4300.
Step-by-step explanation:
If you are performing a right-tailed z-statistic test with a sample size n = 100 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = 2.88, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.
What is null hypothesis?A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.
1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.
2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.
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3. In a sports centre, the ages of 100 people were recorded as follows: Age Under 20 years 20 to 29 years 30 t0 39 years 40 to 59 years 60 years and over Number of people 30 15 12 14 29 Fri, 24 Mar 2023 Angle (i) complete the table above to show the angle for each categ rounded off to the nearest degree. (ii) construct a pie chart using the circle below.
100 people = 360° of circle
For n people, the degree for the circle is (n×360)÷100
30 people = (30×360)÷100 = 108°
15 people = 54°
12 people = 43.2° ≅ 43°
14 people = 50.4° ≅ 50°
29 people = 104.4° ≅ 104°
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
__
Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)
PLEASE HELP !!
(Do not guess please and thank you )
Step-by-step explanation:
A = π r²
r = 3 inches
A = 3.14 × (3)²
A = 3.14 × 9
A = 28.29 square inches
A car park changes £1.50 to each car entering.
The payment station only accepts £1 coins and 50p coins.
Here are the coins collected from the payment station on particular day:
Number of £1 coins 172
Number of 50p coins 256
Assuming each driver paid the exact amount due on that day, work out the percentage of the drivers that paid with three 50p coins.
Answer:
84 paid with three 50p coins.
What is the solution to the equation 3/5x-4-3√7x+8?
A x = -6
B x=-1
C x = 1
D x = 2
The solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To solve the equation 3/5x - 4 - 3√7x + 8 = 0:
First, simplify the expression by combining like terms:
3/5x - 3√7x + 4 = 0 + 8
3/5x - 3√7x + 4 = 8
Next, move the constant term to the right side:
3/5x - 3√7x = 8 - 4
3/5x - 3√7x = 4
Factor out x from the left side:
x(3/5 - 3√7) = 4
Divide both sides by (3/5 - 3√7):
x = 4 / (3/5 - 3√7)
To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator, which is (3/5 + 3√7):
x = 4(3/5 + 3√7) / [(3/5 - 3√7)(3/5 + 3√7)]
x = 12/5 + 12√7/5 / (9/25 - 63/25)
x = 12/5 + 12√7/5 / (-54/25)
x = -10√7/9
Therefore, the solution to the equation 3/5x - 4 - 3√7x + 8 = 0 is x = -10√7/9, which is not one of the options provided.
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What is the approximate distance from the origin to the point (-2, -7, -4)? Round to the nearest tenth
O 3.6 units
O 7.6 units
O 8.3 units
O 9.4 units
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
Distance between two points formula:In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.
The formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Here we have
The point (-2, -7, -4)
We need to find the distance between the origin to the point
Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)
Using the distance formula,
d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]
d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]
d = √ [(2)² + (7)²+ (4)² ]
d = √ [4 + 49 + 16 ]
d = √69 = 8.3066
d = 8.3
Therefore,
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
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3. Find the probability of randomly entering each room in the maze shown at right.
a. P(A)
b. P(B)
The probabilities of randomly entering each room in the maze shown at right are:
P(A) = 5/18
P(B) = 1
What is the probability?The probabilities can be determined from the formulas below:
P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3
P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1
To calculate the probabilities, we need to simplify the expressions and do the arithmetic.
Using the formulas you provided:
P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18
P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1
Therefore, the probabilities, evaluated to their simplest form, are:
P(A) = 5/18
P(B) = 1
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An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,124 customers, 7751 are good risks, 2426 are medium risks, and 947 are poor risks. As part of an audit, one customer is chosen at random. Round your answers to four decimal places if necessary.
a) What is the probability that the customer is a good risk?
b) What is the probability that the customer is not a poor risk?
Answer:
Step-by-step explanation:
a) The probability that the customer is a good risk is given by the ratio of the number of good risks to the total number of customers. Therefore:
P(customer is a good risk) = 7751/11124 = 0.6968 (rounded to four decimal places)
b) The probability that the customer is not a poor risk is equal to the probability that the customer is a good risk or a medium risk. Therefore:
P(customer is not a poor risk) = P(customer is a good risk or a medium risk)
= P(customer is a good risk) + P(customer is a medium risk)
= (7751 + 2426) / 11124
= 0.9239 (rounded to four decimal places)
50 Points! 2 Multiple choice algebra questions. Photo attached. For questions 5 and 6, use the graph. Determine the values of x between which a real zero is located. Estimate the x-coordinate at which a relative minimum occurs. Thank you!
5. The real zero occurs located
C. between -2 and -16. The x-coordinate at which a relative minimum occurs is at
B. 2What is real zero and relative minimum in a graphIn the context of a graph of a function
A real zero, also known as a root or a solution, is a value of the independent variable (usually denoted as x) for which the value of the dependent variable (usually denoted as y) is equal to zero.
Geometrically, a real zero corresponds to the x-coordinate of a point where the graph of the function intersects the x-axis.
A relative minimum, on the other hand, is a point on the graph where the function has a local minimum value.
Geometrically, a relative minimum corresponds to a point where the graph changes from decreasing to increasing, and is located at the bottom of a valley or a trough.
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In 1991, the moose population in a park was measured to be 4330. By 1999, the population was measured again to be 5850. Assume population continues to change linearly.
A)find a formula for the moose population,P since 1991.
B)what does your model predict the moose population to be in 2002?
Answer:
a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.
b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.
Step-by-step explanation:
What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65
A child has wooden blocks with the letters shown below. Find the probability that the child randomly arranges the letters in the order TIGER. Find your answer as a fraction.
the probability that the child randomly arranges the letters in the order TIGER is 1/120.
What is Probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
There are 5 blocks with 5 different letters. Since we want the child to arrange the letters in the order TIGER, there is only one way to arrange them correctly out of a total of 5! = 120 possible arrangements.
Therefore, the probability that the child randomly arranges the letters in the order TIGER is 1/120.
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