(a) The value of sin 2θ is -3√(91)/50.
(b) θ/2 is located in the third quadrant.
(c) The value of cos θ/2 is -√65/10.
What is the value of the sine and cosine functions?We know that cos θ = 3/10, so we can find sin θ using the Pythagorean identity:
sin² θ + cos² θ = 1
sin²θ + (3/10)² = 1
sin²θ = 1 - (3/10)² = 91/100
sin θ = ±√(91)/10
Since 3π/2 < θ < 2π,
we know that sin θ < 0, so sin θ = -√(91)/10.
a) To find sin 2θ, we can use the double angle formula:
sin 2θ = 2 sin θ cos θ
sin 2θ = 2 (-√(91)/10) (3/10)
sin 2θ = -3√(91)/50
b) To find the quadrant in which θ/2 is located, we first need to find θ/2:
θ/2 = (3π/2 + 2π)/2 = 5π/4
5π/4 is in the third quadrant, so θ/2 is located in the third quadrant.
c) To find cos θ/2, we can use the half angle formula:
cos θ/2 = ±√((1 + cos θ)/2)
Since 3π/2 < θ < 2π, we know that cos θ < 0, so we take the negative square root:
cos θ/2 = -√((1 + 3/10)/2)
cos θ/2 = -√(13/20)
Simplifying the radical by dividing both numerator and denominator by 4:
cos θ/2 = -√(13)/2√5
Multiplying numerator and denominator by √5 to rationalize the denominator:
cos θ/2 = -√65/10
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In PQR, PQ= 5.4, QR= 3.6, and PR=6.2. To the nearest Tenth, what is M∠R
Therefore , the solution of the given problem of angles comes out to be M∠R measured at 45.4 degrees, to the closest tenth.
An angle meaning is what?The intersection of the lines that form a skew's ends determines the size of its biggest and smallest walls. There's a possibility that two paths will intersect at a junction. Angle is another outcome of two things interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by placing two line beams in various configurations between their ends.
Here,
To determine the size of angle R in triangular PQR, we can apply the Law of Cosines:
=> cos(R) = (PQ₂ + PR₂ - QR₂) / (2 * PQ * PR)
=> cos(R) = (5.4₂ + 6.2₂ - 3.6₂) / (2 * 5.4 * 6.2)
=> cos(R) = 0.6960917
When we calculate the inverse cosine of both sides, we obtain:
=> R = cos⁻¹(0.6960917)
=> R equals 45.4 degrees
Angle R in triangle PQR is therefore measured at 45.4 degrees, to the closest tenth.
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Jen is studying how years of drought conditions have caused the water level of Richland Reservoir to drop. At the start of the study, the water in the reservoir was 65 meters deep. Jen observed that the depth of the water dropped by about 0.8 meters the first month of the study. She wants to know what the depth of the water will be if it continues dropping at the same rate. You can use a function to approximate the depth of the water in the reservoir x months after the start of the study. Write an equation for the function.
The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
What is a linear function?
A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.
We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:
D(x) = 65 - 0.8x
where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.
Therefore, the equation for the function is D(x) = 65 - 0.8x.
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Lyla invests $2,500 into a savings account
which earns 5% per year. In 15 years, how
much will Lyla's investment be worth if interest
is compounded semiannually (twice a year)?
Round to the nearest dollar.
Answer:
The formula for compound interest is given by:
A = P(1 + r/n)^(nt)
Where:
A = the amount of money accumulated after n years
P = the principal (initial investment)
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 = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:
A = 2500(1 + 0.05/2)^(2*15)
A ≈ $5,551.33
Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.
A circular flower bed is 20 m in diameter and has a circular sidewalk around it that is 2m wide. Find the area of the sidewalk in square meters. Use 3.14 for
According to the solving the area of the sidewalk is 138.16 square meters.
What is an area?Size of a location on a surface is expressed in terms of area. As opposed to surface area, which refers to the area of an open surface or the border of a three-dimensional object, plane region or plane size refers to the area of a shape or planar lamina.
According to the given information:The width of the circular sidewalk is 2 m, which means that the radius of the entire area, including the flower bed and the sidewalk, is 10 m + 2 m = 12 m.
To find the area of the sidewalk, we need to subtract the area of the flower bed from the area of the larger circle.
Area of larger circle = πr²
= 3.14 x 12²
= 452.16 square meters (rounded to two decimal places)
Area of flower bed = πr²
= 3.14 x 10²
= 314 square meters
Area of the sidewalk = Area of larger circle - Area of flower bed
= 452.16 - 314
= 138.16 square meters (rounded to two decimal places)
Therefore, the area of the sidewalk is 138.16 square meters.
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Your tank has a volume of 10 L at the surface (1 atm pressure). You reach a depth of 66 ft. What is the
pressure? What is the volume?
the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.
EquationsTo find the pressure at a depth of 66 ft in a liquid, we can use the formula:
pressure = density x gravity x depth
Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².
First, we need to convert 66 ft to meters:
66 ft x 0.3048 m/ft = 20.1168 m
Then, we can find the pressure at this depth:
pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa
To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.
We can rearrange this equation to solve for V₂:
V₂ = (P₁ x V₁) / P₂
Substituting the values, we get:
V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L
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A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make 1728 mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value 3.14 for X, and round up your answer to the next square meter.?
Answer:
1759 square meters
Step-by-step explanation:
You want the surface area of a cuboid with a half-cylinder top.
Lateral areaThe lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.
P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters
LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²
End areaThe end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.
EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²
Total areaThe total area of 1 mailbox is ...
LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²
Then the area of 1728 mailboxes is ...
1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²
About 1759 square meters of aluminum will be needed for the 1728 mailboxes.
__
Additional comment
This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.
Lola hosts a podcast about computers, and Franco hosts a podcast about parenting. Both podcasts have a set duration for each episode. Last year, Lola released 17 episodes and Franco released 43 episodes, for a total of 5,645 minutes of content. This year, Lola released 36 episodes and Franco released 43 episodes, which lasted a total of 6,956 minutes. How long is each episode?
Answer:
Let's denote the duration of each episode of Lola's podcast by "L" and the duration of each episode of Franco's podcast by "F".
From the information given, we can write two equations based on the total duration of content for the two years:
17L + 43F = 5,645 (equation 1)
36L + 43F = 6,956 (equation 2)
To solve for L and F, we can eliminate F by subtracting equation 1 from equation 2:
(36L + 43F) - (17L + 43F) = 6,956 - 5,645
Simplifying, we get:
19L = 1,311
Therefore, the duration of each episode of Lola's podcast (L) is:
L = 1,311 / 19
L ≈ 69.0 minutes
To find the duration of each episode of Franco's podcast (F), we can substitute the value of L into either equation 1 or 2:
17L + 43F = 5,645
17(69.0) + 43F = 5,645
1,173 + 43F = 5,645
43F = 4,472
F = 4,472 / 43
F ≈ 104.0 minutes
Therefore, each episode of Lola's podcast is approximately 69.0 minutes long, and each episode of Franco's podcast is approximately 104.0 minutes long.
Find the product……..
The product of the expressions are;
Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)
Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)
Step 4: 3/x + 5
How to determine the productIt is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.
From the information given, we have the fraction;
4x + 8/x² + 5x + 6 × 3x + 9/4x + 20
To determine the product, let us reduce the expressions to their lowest forms, we have;
4x + 8 = 4(x + 2)
x² + 5x + 6 = (x + 2)(x + 3)
3x + 9 = 3(x +3)
4x + 20 = 4(x + 5)
Substitute the expressions
4(x + 2)/(x + 2)(x + 3) × 3(x +3)/4(x + 5)
divide the common terms
4(x + 3) × 3(x + 3)/4(x + 5)
Divide further, we have.
3/x + 5
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Can some one help with this problem
Step-by-step explanation:
Area of the trapezoid = height x average of bases
area = 4 x (8+13)/2) = 42 in^2
Area of triangle = 1/2 base * height = 1/2 (13-8) * 4 = 10 in^2
what is required for a current to flow?
A. Electrons, protons, and an energy source
B. An insulator, battery, and recipient
C. A recipient, a connection, and something made out of rubber
D. An Energy source, a recipient, and a connection
Therefore , the solution of the given problem of unitary method comes out to be enable the current to travel, a connection, such as a wire or conductor, is required.
What is a unitary method?Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.
Here,
D. In order for a current to move, there must be an energy source, a recipient, and a connection.
Current is the movement of charged ions through a conductor, most frequently electrons.
The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.
The current has a route through a recipient, which can be a machine or a circuit.
In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.
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If ƒ is an entire function such that lim_|z|-->00 |ƒ (z)| = ∞ then?.
ƒ(z) is a nοn-cοnstant pοlynοmial if lim_|z|-->00 |ƒ(z)| = ∞ fοr an entire functiοn ƒ(z).
Hοw tο calculate entire functiοn such that lim_|z|-->00 |ƒ (z)| = ∞?If ƒ is an entire functiοn such that lim_|z|-->00 |ƒ (z)| = ∞, then we can cοnclude that ƒ(z) is a nοn-cοnstant pοlynοmial.
Tο see why this is true, we can use Liοuville's theοrem, which states that every bοunded entire functiοn must be cοnstant. Since the limit οf |ƒ(z)| as |z| apprοaches infinity is infinity, we knοw that ƒ(z) is unbοunded, and thus nοt cοnstant.
Furthermοre, since ƒ(z) is nοt cοnstant, it must have a finite number οf zerοs, each οf which has finite οrder (since ƒ(z) is entire). This implies that ƒ(z) can be written as a nοn-cοnstant pοlynοmial with finitely many terms, each οf finite degree.
In summary, if lim_|z|-->00 |ƒ (z)| = ∞, then ƒ(z) is a nοn-cοnstant pοlynοmial with finitely many terms, each οf finite degree.
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A line has a slope of 5/6
and passes through the point (7,6). Write its equation in slope-intercept form.
Answer:
y = 5/6x + 1/6
Step-by-step explanation:
m = 5/6, x = 7, y = 6
y = mx + b
6 = 5/6(7) + b
b = 6 - 35/6
b = 36/6 - 35/6 = 1/6
y = 5/6x + 1/6
Answer:
Below
Step-by-step explanation:
Here is another way:
Start with point ( 7,6) slope ( m= 5/6) form :
(y-6) = 5/6 ( x-7) expand
y-6 = 5/6 x - 35/6 add 6 to both sides
y = 5/6 x + 1/6 Done.
13. The profit, in thousands of dollars, from the sale of x kilogram of coffee bean can be modelled by the function () = 5−400 +600 . a) State the asymptotes and the intercepts. Then, sketch a graph of this function using its key features. (5 pts) b) State the domain and range in this context. (2 points) c) Explain the significance of the horizontal asymptote. (1 point) d) Algebraically, find how much amount of tuna fish, in kg, should be sold to have a profit of exactly $4000? (4 points) SOLUTION
Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
PLS HELP MEEEEEEEEEEEEEEEEEE I CAN'T ANSWER
A. Tell whether distance, speed, or time is asked in each given situation.
_____1. How long will it take Zihann to arrive at school if she walks a constants 2 kilometers per hour?
_____2. How far do you need to travel at an average speed for 5 hours?
_____3. How fast should you travel to arrive at your destination that is 2.5 hours away?
_____4. If Carla travels a distance of 150 kilometers and arrive after 3 hours, how fast did she drive?
_____5. If Alwyn drove at an average speed to travel a certain distance, how long did it take him to travel?
the length of a rectangle is 9 centimeters less than its width. what are the rectangles dimension if its area is 90.
Length of rectangle in cm:
Width of rectangle in cm:
Let the width of the rectangle be "X". Then the length of the rectangle will be (X-9).
Formula to find the area of a rectangle is given by-
[tex] \small \underline{ \boxed{ \sf{ \pmb{Area_{(rectangle)} = Length\times Width }}}}\\[/tex]
On substituting the values-
[tex] \:\:\:\:\:\:\longrightarrow \sf {Area_{(rectangle)} = X \times \bigg(X-9\bigg)}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {90 = X^2 -9X}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X =90}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-9X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X^2-15X+6X -90=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {X\bigg(X-15\bigg) +6\times \bigg(X-15\bigg)=0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \sf {\bigg(X-15\bigg) \times \bigg(X+6\bigg) =0}\\[/tex]
[tex] \:\:\:\:\:\:\longrightarrow \boxed{ \tt{ \pmb{ \red{X = 15\: Or,\: -6}}}}\\[/tex]
Since,width cannot be (Negative) , so the width will be 15cm.And the length will be (X-9)= (15-9)=6cm.
what is the answer of 10.9% of $8.85
Answer:
To find 10.9% of $8.85 we can convert the percentage into a decimal:
10.9% = 0.109
0.109x8.85 = $0.964
=$0.96 (Rounded to 2 decimal places)
Note: For questions 13–21, remember to show all of the steps that you use to solve the problem. You can use the comments field to explain our work. Your teacher will review each step of your responses to ensure your receive proper credit for your answers.
Note: Your teacher will grade your response to this question to ensure you receive proper credit for your answer.
Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She decides to use the scale 1 in. = 4 in. Is this a reasonable scale?
SOMEONE, PLEASE HELP! I WILL MAKE BRAINLIST!!!
Answer:
This isn't a reasonable scale
Step-by-step explanation:
Using the scale 1 in. = 4 in., the width of the scaled down painting will be:
48 in. ÷ 4 = 12 in.
And the height of the scaled down painting will be:
120 in. ÷ 4 = 30 in.
So the scaled down painting will be 12 in. wide and 30 in. tall. Since Sarah's paper is 12 in. wide and 24 in. tall, the scaled down painting will fit within the paper's width but will be taller than the paper.
Therefore, the scale is not reasonable because the scaled down painting will not fit within the dimensions of Sarah's paper.
is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 26 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
Answer:
x is first angle
y is second angle
and z is third angle
Step-by-step explanation:
This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.
please help immediately
please go to my profile and answer the other I need them asap.
10³•10⁵•10³
Step-by-step explanation:
10³means 10×3,10⁵means 10×5and 10³means 10×3 30+50+30=110
can someone please prove this
The proof that ΔABC ≅ ΔDCB (congruent) in a parallelogram is because they are alternate interior angles.
How to prove alternate interior angles?If AABC is a parallelogram, then AB and AC are parallel. Therefore, angle BAC is equal to angle BDC since they are alternate interior angles.
Similarly, angle ABC is equal to angle ADC since they are also alternate interior angles.
Now, using the angle-angle-side (AAS) postulate to show that ΔABC and ΔDCB are congruent.
Since angle BAC = angle BDC and angle ABC = angle ADC, angle A = angle D, angle B = angle C, and side AB = side DC.
Therefore, ΔABC ≅ ΔDCB.
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Image transcribed:
8. Prove ΔABC≅ΔDCB (parallelogram)
In one town 44% of voters are democrats if two voters are randomly selected for a survey find the probability that they are both Democrats assume events are independent round to the nearest thousand if necessary
the probability that they are both Democrats. round to the nearest thousandth if necessary is 0.194
The probability that BOTH is democrats means the probability of "one being democrat" AND "another also being democrat".
The AND means we need to MULTIPLY the individual probability of a person being a democrat.
The probability that a voter is democrat is 44% (0.44) -- stated in the problem
Now, the Probability of BOTH being Democrats is simply MULTIPLYING 0.44 with 0.44
Rounded to the nearest thousandth, 0.194
The last answer choice is correct.
the complete question is-
In one town 44% of all voters are Democrats if two voters are randomly selected for a survey find the probability that they are both Democrats. round to the nearest thousandth if necessary.
0.189
0.880
0.440
0.194
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7 x 10 the the power of -5
Answer:
0.00005
Step-by-step explanation:
you move 5 decimal places left starting from 7 and right it as a decimal.
Ans=0.00007
Simplify the expression below.
5^2 + 9^2
To simplify the expression 5^2 + 9^2, we can evaluate the squares of 5 and 9 and then add the results:
5^2 = 5 x 5 = 25
9^2 = 9 x 9 = 81
So, 5^2 + 9^2 = 25 + 81 = 106
Therefore, the simplified form of the expression 5^2 + 9^2 is 106.
COMM 291C Applications of Statistics in Business
Winter 2023
Assignment 07
1. A fish tank is filled with the fish of three different species, and each fish comes in three sizes. The
counts of all the fish are summarized in the following contingency table:
Small Medium Large Total
Goldfish 48 45 19 112
Guppy 70 42 19 131
Gourami 40 9 10 59
Total 158 96 48 302
a. If I randomly catch any one fish from this tank, what is the probability that the caught
fish is medium-sized? Show your calculations. (1)
b. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
medium-sized guppy? Show your calculations. (1)
c. If I randomly catch one medium-sized fish from this tank, what is the probability that the
caught fish is a guppy? Show your calculations. (1)
d. If I randomly catch one guppy from this tank, what is the probability that the caught fish
is medium-sized? Show your calculations. (1)
e. If I randomly catch one fish from this tank, what is the probability that the caught fish is a
not a goldfish? Show your calculations. (1)
f. Are two events, randomly catching a guppy and randomly catching a medium-sized fish,
independent? Explain how you know. (2)
a) If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.
c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e) the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent
Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.
The explanation to the above probability answer are given below:
a)
From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:
Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish
Probability of catching a medium-sized fish = 96 / 302
Probability of catching a medium-sized fish = 0.3182
Therefore, the probability of catching a medium-sized fish from the tank is 0.3182
b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:
Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish
Probability of catching a medium-sized guppy = 42 / 302
Probability of catching a medium-sized guppy = 0.1391
Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.
c)
From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:
Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish
Probability of catching a guppy given a medium-sized fish = 42 / 96
Probability of catching a guppy given a medium-sized fish = 0.4375
Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.
d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.
From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:
Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies
Probability of catching a medium-sized guppy given a guppy = 42 / 131
Probability of catching a medium-sized guppy given a guppy = 0.3206
Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.
e)
From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:
Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish
Probability of catching a fish that is not a goldfish = 190 / 302
Probability of catching a fish that is not a goldfish = 0.6291
Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f)
From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.
Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.
If the events are independent, then the product of their individual probabilities should be equal to the joint probability:
P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)
0.4344 x 0.3182 = 0.1391
0.1384 is not equal to 0.1391, which indicates that the two events are not independent.
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what is the average allowance for each student?
$7,$12,$8.50,$10,$7,$8,$10.50,$11
The average allowance for each student is $9.25.
What is the average allowance for each student?To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.
Adding up the allowances:
$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74
There are 8 students, so we divide the total allowance by 8 to get:
$74 / 8 = $9.25
Therefore, the average allowance for each student is $9.25.
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PLEASE HELP! Find missing side lengths of B and C. Explain
Answer:
b=7 & c=7√2
Step-by-step explanation:
b=7 as it is an isosceles triangle
now using Pythagoras theorem,
(c)^2= (7)^2+(7)^2
⇒(c)^2= 49+49
⇒(c)^2= 98
⇒c= √98
⇒c=7√2
Answer:
b = 7c = 7√2Step-by-step explanation:
You want the missing side lengths in an isosceles right triangle with one side given as 7.
Isosceles right triangleThe two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:
b = 7
The hypotenuse of an isosceles right triangle is √2 times the side length:
c = 7√2
__
Additional comment
You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.
c² = 7² + b²
c² = 7² +7² = 2·7²
c = √(2·7²) = 7√2
The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.
The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.
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Answer:
Thank you for your kind words and concern. I appreciate your offer to listen and support others. I think it's important for people to know that they can reach out for help when they're struggling and that there are resources available to them. And as for something that made me happy, I always appreciate it when people show kindness and empathy towards others, and when they're able to make a positive impact in the world.
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Step-by-step explanation:
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A line has the equation y - 6 = 5x + 9 . work out the gradient and the y intercept of the line.
The gradient of the line is 5, and the y-intercept of the line is 15.
EquationsThe given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.
Rearranging the given equation, we get:
y - 6 = 5x + 9
Adding 6 to both sides, we get:
y = 5x + 15
Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.
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Suppose 50 rabbits are on Groff Farm… DOUBLING every SIX MONTHS…
How many rabbits after 5 years?
How many rabbits after 10 years?
Using geometric progression Rabbits after 5 years will be 5120. Rabbits after 10 years will be 52,428,800.
What is geometric progression?When each term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the series. It should be mentioned that the common ratio is obtained by dividing any succeeding term by its preceding term.
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate organizations or groups.
In this question,
The number of rabbits initially=50=a
rabbits after 6 months=100
common ratio=r= 100/50=2
Since it is a geometric progression, the 11th term will give us the number of rabbits after 5 years.
a₁₁=a₁(r)¹¹⁻¹
=50(2)¹⁰=5120
the 21th term will give us the number of rabbits after 10 years.
a₂₁=a₁(r)²¹⁻¹
=50(2)²⁰=52,428,800
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rx+sy=24
4x+16y=120
In the system of equations above, r and s are
constants. If the system has an infinite number of
solutions, what is the value of rs
?
The values of r and s, considering that the system has an infinite number of solutions, are given as follows:
r = 4/5.s = 16/5.How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The number of solutions of a system of two linear functions is given as follows:
Infinity solutions: same slope and intercept.Zero solutions: same slope, difference intercepts.One solution: different slopes.For this problem, the system has an infinite number of solutions, meaning that the equations are multiples, thus the values of r and s are given as follows:
120/24 = 5.r = 4/5.s = 16/5.More can be learned about linear functions at https://brainly.com/question/24808124
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