Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents
. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.
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Which of these ordered pairs is a solution to the linear inequality y ≤ 4x – 3?
Responses
(1, 4)
(1, 4)
(1, 5)
(1, 5)
(–2, 5)
(–2, 5),
(2, 5)
Answer:
(2, 5)
Step-by-step explanation:
You want the ordered pair that is a solution to y ≤ 4x -3 from those on the list:
(1, 4)(1, 5)(-2, 5)(2, 5)GraphThe attachment shows a graph of the inequality, along with the offered solution points. The only solution among those shown is (2, 5). That solution lies on the boundary line. The "≤" symbol means the boundary line is included in the solution set.
CalculatorWe can use a calculator to check the solutions, too. Rearranging, we have ...
4x -3 -y ≥ 0
The calculator in the second attachment is able to make this calculation using the list of x-values and the list of y-values. The solution list only has one number that is not less than zero. That corresponds to (x, y) = (2, 5).
__
Additional comment
We like to avoid having to enter the same equation over and over with different data. That is why we have chosen the solution methods here. A spreadsheet can repeat the calculation and comparison for you, too.
#95141404393
a tank in the form of a truncated cone is formed by rotating the segment between (2, 0) and (4, 4) around the y-axis. it is filled with sludge (density 80 lbs/ft3). if the sludge is pumped 4 feet upwards into a tank truck, how much work was required?
The work required to pump the sludge is approximately 21449.6 ft-lbs.
To calculate the work required to pump the sludge, we need to determine the volume of the sludge and then multiply it by the weight of the sludge.
First, let's find the volume of the sludge in the tank. Since the tank is formed by rotating the segment between (2, 0) and (4, 4) around the y-axis, it forms a frustum of a cone. The formula for the volume of a frustum of a cone is:
V = (1/3) * π * h * (R^2 + r^2 + R*r),
where h is the height of the frustum, R is the radius of the larger base, and r is the radius of the smaller base.
In this case, the height of the frustum is the difference in y-coordinates between the two points: h = 4 - 0 = 4 ft.
The radius of the larger base, R, is the y-coordinate of the point (4, 4): R = 4 ft.
The radius of the smaller base, r, is the y-coordinate of the point (2, 0): r = 0 ft.
Substituting these values into the volume formula, we have:
V = (1/3) * π * 4 * (16 + 0 + 0) = (4/3) * π * 16 = 67.03 ft^3 (approximately).
Next, we need to calculate the weight of the sludge, which is the volume multiplied by the density:
Weight = Volume * Density = 67.03 ft^3 * 80 lbs/ft^3 = 5362.4 lbs (approximately).
Finally, we can calculate the work required to pump the sludge 4 feet upwards. The work is given by the formula:
Work = Force * Distance,
where Force is the weight of the sludge and Distance is the vertical distance it is pumped.
Work = Weight * Distance = 5362.4 lbs * 4 ft = 21449.6 ft-lbs (approximately).
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in the xy-plane, exactly how many x-intercepts does the graph of f of x equals, x times, open parenthesis, x minus 4, close parenthesis, squared, times, open parenthesis, x minus 5, close parenthesis, cubed have?
The function has three x-intercepts: x=0, x=4, and x=5. The graph of f(x) has three x-intercepts in the xy-plane.
To find the x-intercepts of a function, we need to set the value of y to zero and solve for x. In this case, the function is f(x) = x(x-4)^2(x-5)^3. To find the x-intercepts, we set f(x) = 0 and solve for x.
First, we notice that each factor is squared or cubed, which means that they cannot be negative. Therefore, we only need to consider the positive values of x.
Next, we see that the factor x will make the whole expression zero when x=0.
The factors (x-4)^2 and (x-5)^3 will make the expression zero when x=4 and x=5, respectively.
Therefore, the function has three x-intercepts: x=0, x=4, and x=5.
In conclusion, the graph of f(x) has three x-intercepts in the xy-plane. Includes the terms "parenthesis" and "squared."
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The mass of a substance varies directly as the volume of the substance. If a mass of 30 kg of a substance has a volume of 6 liters, what is the volume of 65 kg of the substance?
Answer:
The volume of 65 kg of the substance is 13 liters.
Step-by-step explanation:
If a substance's mass varies directly from its volume, it means that the ratio of mass to volume remains constant. In this case, we can calculate the continuous ratio and then use it to find the volume.
Given:
Mass1 = 30 kg
Volume1 = 6 liters
Let's denote the constant ratio as k.
Mass1 / Volume1 = k
30 kg / 6 liters = k
k = 5 kg/liter
Now, we can find the volume2 for a mass of 65 kg using the constant ratio:
Mass2 = 65 kg
Volume2 = ?
Mass2 / Volume2 = k
65 kg / Volume2 = 5 kg/liter
To find Volume2, we can cross multiply:
65 kg = 5 kg/liter * Volume2
Volume2 = 65 kg / 5 kg/liter
Volume2 = 13 liters
What type of number is 1.overline 00 Choose all answers that apply:
1.) Whole number
2.) Integer
3.) Rational
4.) Irrational.
Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.
The number 1.overline00 represents a repeating decimal. To understand its nature, let's break it down.
The overline above the zeros indicates that the zeros repeat infinitely. Therefore, 1.overline00 can be represented as 1.000000... with the zeros repeating indefinitely.
1.) Whole number: A whole number is a non-negative integer. Since 1.overline00 is greater than 1, it is not a whole number.
2.) Integer: An integer includes both positive and negative whole numbers, including zero. As 1.overline00 is greater than 1, it is not an integer.
3.) Rational: A rational number can be expressed as the ratio of two integers, where the denominator is not zero. To determine if 1.overline00 is rational, we can convert it into a fraction. Let x = 1.overline00. Multiplying both sides by 100, we get 100x = 100.overline00. Subtracting the original equation from this new equation, we get 100x - x = 100.overline00 - 1.overline00, which simplifies to 99x = 99. Therefore, x = 1. Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.
4.) Irrational: An irrational number cannot be expressed as the ratio of two integers. Since we have determined that 1.overline00 is rational, it is not irrational.
Since 1 can be expressed as the ratio of two integers (1/1), 1.overline00 is a rational number.
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I don’t even know if I’ve done this problem right or not please help
Step-by-step explanation:
I believe there is something missing from the description.
I base my solution and explanation on the following assumptions :
the angle theta is at the origin (0, 0).not only passes the terminal side through (20, -21), but so does also the circle around our trigonometric triangle.in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.
the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.
Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :
distance² = (x1 - x2)² + (y1 - y2)²
in our case
distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841
distance = radius = 29
remember, sine is the up/down leg, cosine is the left/right leg.
so,
sin(theta) = -21/29
FYI : theta ≈ -46.4°
cos(theta) = 20/29
tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =
= -21/20
you were right about tan(theta), not about sin(theta) and cos(theta).
if you mistook theta for a 0, you were still wrong :
sin(0) = 0, cos(0) = 1.
200 bats in a colony are affected by a disease which causes their population to decrease by 8% every day.
the following equation represents the bat colony population as the disease effect's them
f (x)= 200 (0.92)^x
Does this equation represent exponential growth or exponential decay. Explain how you know using the function itself.
15 POINTS!!!!!
Answer:
Exponential decay--------------------------
The first explanation comes from the information given in the question.
It says the population decreases.
From the function itself, we look at the base of the exponent. The function is representing a growth if the base is greater than 1 and decay if the base is less than 1.
In our case 0.92 < 1, hence the function represents exponential decay.
the grade point averages of the gourmet society are uniformly distributed between 2.5 and 3.5. a. find the probability distribution function, f(x) for this scenario. b. using part (a), find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2
The probability that a randomly chosen member of the society has a grade point average between 3 and 3.2 is 0.2 or 20%.
The probability distribution function (pdf), f(x), for the grade point averages of the gourmet society can be represented by a uniform distribution between 2.5 and 3.5. In a uniform distribution, the probability density is constant within the range and zero outside the range. The formula for the pdf is:
f(x) = 1 / (b - a)
where a is the lower bound (2.5 in this case) and b is the upper bound (3.5 in this case). Therefore, for this scenario:
f(x) = 1 / (3.5 - 2.5) = 1
To find the probability that a randomly chosen member of the society has a grade point average between 3 and 3.2, we need to calculate the area under the probability distribution curve within that range. Since the probability density is constant within the range, the probability is equal to the width of the range divided by the total width of the distribution.
The width of the range is 3.2 - 3 = 0.2, and the total width of the distribution is 3.5 - 2.5 = 1. Therefore, the probability is:
Probability = (width of range) / (total width)
= 0.2 / 1
= 0.2
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Problems 19-23 use the following scenario: A design engineer is measuring the drag force (i.e., the
force resisting motion) on a robotic submarine. As the submarine moves through the water at v
meters per second m
it experiences a drag force of F newtons (N). The table below represents
the design engineer's measurements.
Drag Force vs. Speed
Speed (in
8
10
m
F Drag Force (in N)
720
1100
The drag force can be modeled by a quadratic equation of the form F=bv+cv².
IVE
n.
19. Using (8, 720), create an equation in terms of b and c.
720=6(8) + C² (8) ²
20. Using (10, 1100), create an equation in terms of b and c.
720= 8b+ C4 C
1100=b (10) + c(10) ²
1100 = 10b + 1979 an
21. Solve the system of equations from #19 and # 20 for b and c.
720 = 8b+ Cec
2. Write a function F which serves as a model for profit.
1100-106+100c
What value of speed, in meters per second, corresponds a drag force of 120N? Includ
your answer.
An
engineer
makes a model of a bridge
using a scale of 1 inch = 4 yards.
The
length of the
actual
bridge is 60
yards.
What is the
length of the
model?
The length of the model when the scale given is used would be = 240 yards.
How to calculate the length of a model of a bridge?To calculate the length of the model, the formula for scale factor should be used. That is;
Scale factor = Actual length/Model length
The scale factor = 1/4
Actual length = 60 yards
Model length = ?
That is;
1/4 = 60/?
Model length = 60×4
= 240 yards
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Calculate the relative frequency of the data to determine which association the two-way table suggests.
A. None of the associations listed are correct.
B. Those who have a brother tend not to have a sister.
C. Those who have a brother tend to have a sister.
D. Those who do not have a brother tend not to have a sister.
The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.
The table provides information about whether individuals have a brother and a sister.
Based on the options given, let's calculate the relative frequencies to see which association is suggested:
Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)
Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)
Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)
Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)
By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.
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How many different possible outcomes are there if you spin a spinner labeled Red, Blue, Yellow five times?
The number of different possible outcomes if you spin a spinner labeled Red, Blue, Yellow five times (excluding outcomes where the same color is spun five times) is 243 x 1/10 = 24.3, which we can round down to 24.
If you spin a spinner labeled Red, Blue, Yellow five times, there are a total of 3^5 (three raised to the power of five) different possible outcomes.
This is because each spin has three possible outcomes and the number of possible outcomes is calculated by multiplying the number of outcomes for each spin together.
Therefore, 3 x 3 x 3 x 3 x 3 = 243. However, this includes outcomes where the same color is spun five times, which we want to exclude.
To calculate this, we can use the formula for combinations: nCr = n! / (r! * (n-r)!). In this case, we want to find the number of combinations of 3 colors taken 5 at a time, which is 3C5 = 3! / (5! * (3-5)!) = 3! / (-2! * 5!) = 1/10.
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reatest, or the mean of
node: The number that appea
POL
oss
Find the mean for 3, 9, 5, 4, 9.
Di please find mean of this question?
Answer:
The Mean is 6.
Step-by-step explanation:
6. How many full revolutions
does a car tire with a
diameter of 25 inches
make when the car
travels one mile?
Answer:
5
Step-by-step explanation:
im right
true or false: double integral can be used to compute the area of a region d in a plane simply by integrating the function f(x,y)
True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.
However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.
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help fast and whoever gets it correct gets brainlyest
solve for x in the following equation
A. X = 16.5
B. X.= 4.125
C. X= -3
D. X= -12
Answer:
C. x = -3
Step-by-step explanation:
Given equation:
[tex]10x+57=9-6x[/tex]
Add 6x to both sides of the equation:
[tex]10x+57+6x=9-6x+6x[/tex]
[tex]16x+57=9[/tex]
Subtract 57 from both sides of the equation:
[tex]16x+57-57=9-57[/tex]
[tex]16x=-48[/tex]
Divide both sides by 16:
[tex]\dfrac{16x}{16}=\dfrac{-48}{16}[/tex]
[tex]x=-3[/tex]
Therefore, the solution to the equation is x = -3.
Hello !
Answer:
[tex] \boxed{\sf Option \: C\text{:} \: x= -3} [/tex]
Step-by-step explanation:
Solve the equation by isolating the variable 'x'.
[tex] \\ [/tex]
We are given the following equation:
[tex] \sf 10x + 57 = 9 - 6x [/tex]
[tex] \\ [/tex]
Subtract 57 from both sides and combine like terms:
[tex] \sf 10x + 57 - 57 = 9 - 6x - 57 \\ \sf 10x = -6x - 48 [/tex]
[tex] \\ [/tex]
Add 6x to both sides of the equation and combine like terms:
[tex] \sf 10x + 6x = -6x - 48 + 6x \\ \sf 16x = -48 [/tex]
[tex] \\ [/tex]
Finally, divide both sides by 16, which is the coefficient of the variable.
[tex] \sf \dfrac{16x}{16} = \dfrac{-48}{16} \\ \\ \boxed{\sf x= -3} [/tex]
Have a nice day ;)
Answer: =
24
X
Submit Answer
62
H
word
The value of x, which is the radius of this cone is 64 units.
How to calculate the volume of a cone?In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:
Volume of cone, V = 1/3 × πr²h
Where:
V represent the volume of a cone.h represents the height.r represents the radius.By substituting the given parameters into the formula for the volume of a cone, we have the following;
512π = 1/3 × π × x² × 24
512π = π × x × 8
Radius, x = 512/8
Radius, x = 64 units
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Complete Question:
The volume of the right cone below is 512π units³. Find the value of x.
Describe, in your own words, what "convenience sampling" is
Answer: Put this in your own words:
Convenience sampling is like staying in a certain area of a mall and giving samples to people as the come by you stay there at that one place because it is convenient because you don't want to move from that spot so you stay at that spot and only that spot. Convenience sampling is also like ordering food because it is convenient and you don't want to cook.
Step-by-step explanation:
A cans good company manufuctured a cylinderical can of height 10cm and radus 4 cm find surface area
To find the surface area of a cylindrical can, we need to calculate the sum of the areas of its curved surface and its two circular bases.
The curved surface area (CSA) of a cylinder can be calculated using the formula:
CSA = 2πrh
In this case, the height (h) of the can is 10 cm and the radius (r) is 4 cm.
Using the formula, we can calculate the curved surface area:
CSA = 2 × 3.14 × 4 cm × 10 cm
CSA = 251.2 cm²
The area of each circular base can be calculated using the formula:
Base Area = πr²
Substituting the radius (r = 4 cm) into the formula, we get:
Base Area = 3.14 × (4 cm)²
Base Area = 50.24 cm²
Since the can has two circular bases, the total area of the bases is 2 times the base area, which is:
2 × 50.24 cm² = 100.48 cm²
To find the total surface area, we add the curved surface area and the area of the bases:
Total Surface Area = CSA + 2 × Base Area
Total Surface Area = 251.2 cm² + 100.48 cm²
Total Surface Area = 351.68 cm²
Therefore, the surface area of the cylindrical can is approximately 351.68 cm².
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PLEASE HELP ME
What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
a cylinder with a radius labeled 2.6 meters and height labeled 6.1 meters
82 square meters
91 square meters
96 square meters
142 square meters
The surface area of the cylinder, rounded to the nearest square meter, is: D. 142 square meters
What is the Surface Area of a Cylinder?The surface area of a cylinder can be calculated by using the formula expressed as:
SA = 2[tex]\pi[/tex]r(h + r), where r is the radius and h is the height.
Given the following:
[tex]\pi[/tex] = 3.14
radius (r) = 2.6 m
height of the cylinder (h) = 6.1 m
Plug in the values:
[tex]\sf SA = 2 \times 3.14 \times 2.6 \times (6.1 + 2.6)[/tex]
[tex]\sf SA \thickapprox 142[/tex] square meters (rounded to the nearest square meter)
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the mean number of words per minute (wpm) typed by a speed typist is 135 with a variance of 100 . what is the probability that the sample mean would be greater than 135.7 wpm if 43 speed typists are randomly selected? round your answer to four decimal places.
The probability that the sample mean would be greater than 135.7 WPM is 0.1686.
Calculate the standard deviation:
The standard deviation of the WPM typed by a speed typist is √100 = 10.
Calculate the z-score
The z-score is calculated by subtracting the population mean (135) from the sample mean (135.7) and dividing it by the standard deviation (10).
z = (135.7 - 135) / 10 = 0.07
Calculate the probability
The probability of the sample mean being greater than 135.7 WPM can be calculated using the z-score.
P(x > 135.7) = 1 - P(x ≤ 135.7)
P(x > 135.7) = 1 - 0.8314 = 0.1686
Therefore, the probability that the sample mean would be greater than 135.7 WPM if 43 speed typists are randomly selected is 0.1686, rounded to four decimal places.
Complete Question:
The mean number of words per minute WPM typed by a speed typist is 135 with a variance of 100. What is the probability that the sample mean would be greater than 135.7 WPM if 43 speed typist are randomly selected? round your answer to four decimal places.
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Let R be the region in the first quadrant bounded by the graph of y = 2 \sqrt x, the horizontal line y = 6, and the y-axis, as shown in the figure.
a) Find the area of R.
b) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the horizontal line y = 7.
c) Write, but do not evaluate, an integral expression that gives the volume of the solid generated when R is rotated about the y-axis.
a) To find the area of region R, we need to calculate the area between the curves y = 2√x and y = 6 in the first quadrant. The region is bounded by the y-axis and the horizontal line y = 6.
To find the area, we integrate the difference between the upper and lower curves with respect to x:
Area = ∫[0 to a] (6 - 2√x) dx,
where 'a' is the x-coordinate where the curves intersect.
b) To find the volume of the solid generated when region R is rotated about the horizontal line y = 7, we can use the method of cylindrical shells. Each cylindrical shell has a height of 6 - 7 = -1 (as y = 6 is below y = 7) and a radius equal to x.
The volume is given by the integral:
Volume = ∫[0 to a] 2πx(6 - 7) dx,
where 'a' is the x-coordinate where the curves intersect.
c) To find the volume of the solid generated when region R is rotated about the y-axis, we can use the method of disks. Each disk has a radius equal to y and a thickness given by dx.
The volume is given by the integral:
Volume = ∫[0 to b] π(y^2) dx,
where 'b' is the y-coordinate where the curves intersect.
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Acceptance sampling. A company produces large cases of incandescent light bulbs. If there is a 1% chance that any one light bulb is defective, what is the probability that among 83 randomly sampled lightbulbs. A. . 1 or less are defective?
b. . 2 or more are defective?
Light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808. light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)= 1-0.1808=0.8192.
a. The probability that 1 or less light bulbs are defective among 83 sampled light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808.
b. The probability that 2 or more light bulbs are defective among 83 sampled light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)=1-0.1808=0.8192.
In acceptance sampling, a sample is taken from a large batch of items to determine if the entire batch should be accepted or rejected based on the number of defective items in the sample. In this problem, the probability of a light bulb being defective is given as 1%, and we are asked to find the probabilities of having 1 or less defective light bulbs or 2 or more defective light bulbs among a sample of 83 light bulbs. We can use the binomial distribution to calculate these probabilities, where X is the number of defective light bulbs in the sample. The probability of having 1 or less defective light bulbs can be calculated as the sum of the probabilities of having 0 or 1 defective light bulbs, and the probability of having 2 or more defective light bulbs can be calculated as 1 minus the probability of having 1 or less defective light bulbs.
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2.1 You are given that m is an even integer and n is an odd integer. Which of these is an
odd integer?
A: 3m + 4n
B: 5mn
C: (m + 3n)²
D: m³n²
E: 5m + 6n
The only odd integer among the choices is 5mn.
To determine which expression is an odd integer,
we need to know that the sum of an even integer and an odd integer is always odd, and the product of an even integer and an odd integer is always even.
A: 3m + 4n = 2m + m + 4n is even
since it's the sum of two even integers.
B: 5mn is odd since it's the product of an odd and an even integer.
C: (m + 3n)² = m² + 6mn + 9n² is odd since it's the sum of two odd integers and an even integer.
D: m³n² = m * m² * n² is even since it's the product of an even integer and two odd integers.
E: 5m + 6n = 2(2m + 3n) + m is odd since it's the sum of two even integers and an odd integer.
Therefore, the only odd integer among the choices is 5mn.
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total cost
of the wall = answer
Answer:
64 pounds
Step-by-step explanation:
so first what you have to do is find the perimeter of the barn:
2l+2w
2*12)+2*4)= 32 m
Then it costs 2 pounds per meter
So they you multiply
32m * 2 pounds
64 pounds
I need some help please, which figure is a translation of figure A?
1) Figure B
2) Figure C
3) Figure D
Answer: Figure C
Step-by-step explanation:
Figure C is a translation of Figure A because it moved down. Figure A moved down 5 units in order to be Figure C. A translation is moving in a direction. Figure B and D have both been altered some other way, but Figure C has just been moved down.
Hellooe what r the answers to these
1) The value of cos θ is,
2) The value of sin θ is,
3) The value of cos θ is,
We have to given that;
The value of sin θ is,
⇒ sin θ = 3/5
Hence,
cos θ = √1 - sin²θ
cos θ = √1 - 9/25
cos θ = √16/9
cos θ = 4/3
Since, It is quadrant II.
Hence,
cos θ = - 4/3
Since, cos θ = - 5/12
Hence,
sin θ = √1 - cos²θ
sin θ = √1 - 25/144
sin θ = √119/144
Since, It is quadrant III,
Hence,
sin θ = - √119/12
The value of sin θ is,
⇒ sin θ = - 15/17
Hence,
cos θ = √1 - sin²θ
cos θ = √1 - 225/289
cos θ = √64/289
cos θ = 8/17
Since, It is quadrant IV.
Hence,
cos θ = 8/17
Since, Value of sine is always positive,
And, Values of cosine is always greater than - 1.
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I really need help in this question! Lots of points as a reward for answer and I will give brainiest for best answer possible!
a) Marcus' result is likely to be more reliable.
b) Because the sample was bigger.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
The higher the total number of outcomes, the more reliable the probability calculated is.
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Solve an equation that can be used to determine the value of k.
(11k-23)
Y
Z
(5k - 3)°
(14k - 4)°
X W
Answer:
k = 11Y = 52°Z = 98°∠WXZ = 150°Step-by-step explanation:
You want the value of the variable k and the angle measures around triangle XYZ in the given figure.
Exterior angleThe exterior angle at X is equal to the sum of the remote interior angles at Y and Z:
14k -4 = (5x -3) +(11k -23)
14k -4 = 16k -26
7k -2 = 8k -13 . . . . . . divide by 2 (because we can)
11 = k . . . . . . . . . . add 13-7k
The value of k is 11.
Angle YY = (5k -3)° = (5·11 -3)°
Y = 52°
Angle ZZ = (11k -23)° = (11·11 -23)°
Z = 98°
Angle WXZangle WXZ = Y +Z = 52° +98°
angle WXZ = 150°
__
Additional comment
The exterior angle at X is the supplement of the adjacent interior angle X. That interior angle is also the supplement of the sum of angles Y and Z. Two angles are equal when their supplements are equal. Hence angle WXZ is the sum of angles Y and Z.
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Select the values that make the inequality
3
�
≥
−
72
3d≥−72 true. Then write an equivalent inequality, in terms of
�
d.
The values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent Inequality in terms of d is d ≥ -24.
To make the inequality 3d ≥ -72 true, we need to find values of d that satisfy the inequality.
Dividing both sides of the inequality by 3, we get:
d ≥ -24
Therefore, any value of d that is greater than or equal to -24 will satisfy the inequality.
An equivalent inequality in terms of d would be:
d + 24 ≥ 0
We can simplify this inequality by subtracting 24 from both sides:
d ≥ -24
This is the same inequality we found earlier, which means that any value of d greater than or equal to -24 will make the inequality true.
the values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent inequality in terms of d is d ≥ -24.
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