An anthill has a volume of 8792 mm^3 of dirt. It’s radius is 20 mm.
Use 3.14 for pi and round your answer to the nearest mm if necessary.
Answers
The height of the cone is 11 mm and the slant height of the cone is 23 mm and the ant crawls 31 mm to get from the base of the cone to the top of the hill.
What is the volume of the right circular cone?
A right circular cone is a three-dimensional geometric shape that has a circular base and a vertex that is located directly above the center of the base. The axis of the cone is a line that passes through the vertex and the center of the base.
The volume of a right circular cone can be found using the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume of the cone, r is the radius of the circular base, and h is the height of the cone.
1) To find the height of the cone, we need to use the formula for the volume of a cone, which is [tex]V = (1/3)\pi r^2h[/tex]. Rearranging this formula, we get:
[tex]h = 3V / \pi r^2[/tex]
Substituting the given values, we get:
[tex]h = 3(8792) / (3.14)(20^2)[/tex]
h ≈ 11
Therefore, the height of the cone is approximately 11 mm.
2) To find the slant height of the cone, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In the case of the cone, the slant height is the hypotenuse of a right triangle formed by the height and the radius of the base. Therefore, we have:
[tex]s^2 = r^2 + h^2[/tex]
Substituting the values we found in part 1, we get:
[tex]s^2 = 20^2 + 11^2[/tex]
s ≈ 23
Therefore, the slant height of the cone is approximately 23 mm.
3) To find the distance the ant crawls to get from the base of the cone to the top of the hill, we can use the Pythagorean theorem again. This time, we need to find the distance along the slant height from the base of the cone to the top of the hill. This distance is the hypotenuse of a right triangle formed by the distance from the base to the apex (which is the height of the cone) and the radius of the base. Therefore, we have:
[tex]d^2 = r^2 + s^2[/tex]
Substituting the values we found in parts 1 and 2, we get:
[tex]d^2 = 20^2 + 23^2[/tex]
d ≈ 31
Therefore, the ant crawls approximately 31 mm to get from the base of the cone to the top of the hill.
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Related Questions
Kylie invested $2,800 in an account paying an interest rate of 5. 5 % compounded annually. Ariana invested $2,800 in an account paying an interest rate of 5. 75% compounded continuously. After 12 years, how much more money would Ariana have in her account than Kylie, to the nearest dollar?
Answers
After 12 years, Ariana would have 366.65 more in her account than Kylie, to the nearest dollar.
The formula used to calculate the amount of money Ariana would have in her account after 12 years is [tex]A = Pe^rt[/tex], where A is the amount of money, P is the principal amount (initial investment), e is the mathematical constant (2.71828), r is the rate at which interest is compounded, and t is the time (in years).
Kylie's total amount after 12 years would be calculated using [tex]A = 2800(1.055)^12[/tex], while Ariana's total amount would be calculated using [tex]A = 2800(2.71828)^(0.0575*12)[/tex].
After substituting the values into the formulas, Kylie would have 4,841.22 in her account and Ariana would have 5,207.87 in her account. This means that Ariana would have 366.65 more than Kylie in her account, to the nearest dollar.
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One of the legs of a right triangle measures 16 cm and the other leg measures 10 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answers
Answer:
We can use the Pythagorean theorem to find the length of the hypotenuse:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Plugging in the given values, we get:
c^2 = 16^2 + 10^2
c^2 = 256 + 100
c^2 = 356
Taking the square root of both sides, we get:
c = sqrt(356)
c ≈ 18.9
Therefore, the length of the hypotenuse is approximately 18.9 cm.
1. Currently in a hypothetical country 5% of the population suffers from Covid-19. Suppose that the antibody test to detect this disease has an 90% chance of detecting the disease if the person has it (sensitivity of the test) and a 95%% chance of correctly indicating that the disease is absent if the person really does not have the disease (specificity of the test). What is the probability that randomly selected person gets true negative results?
Answers
The probability that a randomly chosen individual will experience actual unfavorable effects is roughly 0.9025, or 90.25%.
What do we mean when we claim a test is 99% accurate?The percentage of genuine positive results—both true positive and true negative—in the chosen population is represented by the accuracy score's numerical number. 99% of the time, whether the test result is positive or negative, it is accurate.
We can write: Applying the law of total probability
P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A),
To calculate P(B|¬A,¬T), the probability that the test is negative given that the person does not have Covid-19 and the test is negative, we can use the complement rule:
P(B|¬A,¬T) = 1 - P(¬B|¬A,¬T),
P(¬B|¬A,¬T) = 1 - P(B|¬A,¬T) = 1 - 0.95 = 0.05.
P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A)
= (1 - P(¬B|¬A,¬T))P(¬T|¬A) + P(B|¬A,T)P(T|¬A)
= (1 - 0.05) x 0.95 + 0 x 0.1
= 0.9025.
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Find the area of the region bounded by the x-axis, line x=2, line x=6, and lines y=x+3, and y=10-x.
Answers
Answer:
A=∫
1
3
x
2
dx
A=[
3
x
3
]
1
3
A=(
3
27
−
3
1
)
A=
3
26
The ratio of the measures of two angles that form a linear pair are 1:17. What is the measure of the larger of the two angles
Answers
The measure of the smaller angle is 10 degrees. We find the measure of the larger angle, we can substitute x = 10 into the expression, the measure of the larger angle is 170 degrees.
When two angles form a linear pair, they are adjacent angles that share a common side and form a straight line. The sum of the measures of these two angles is always 180 degrees.
Let x be the measure of the smaller angle in this problem. Since the ratio of the measures of the two angles is 1:17, we can express the measure of the larger angle in terms of x by multiplying 17 to x. Thus, the measure of the larger angle is 17x.
To find the value of x, we can use the fact that the sum of the measures of the two angles is 180 degrees. So we have:
x + 17x = 180
Simplifying the equation, we get:
18x = 180
Dividing both sides by 18, we obtain:
x = 10
Therefore, the measure of the smaller angle is 10 degrees. To find the measure of the larger angle, we can substitute x = 10 into the expression we derived earlier for the measure of the larger angle:
17x = 17(10) = 170 degrees
Hence, the measure of the larger angle is 170 degrees.
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A book sold 42800 copies in its first month of release. Suppose this represents 7. 3 of the number of copies sold to date. How many copies have been sold to date?
Answers
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets. So far, 312440 copies have been sold.
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per 100 is what the word percent means.
In mathematics, the word "of" is also regarded as one of the arithmetic operations, denoting multiplication between brackets.
We are given that the copies sold on first release date= 42800 copies.
And this is the 7.3 of the number of copies sold on date.
So, let the number of copies sold out on date is x.
Therefore, x= 7.3*42800 OR [tex]x= \frac{73}{10} * 42800= 73*4280= 312440[/tex]
Hence, the number of copies sold out on the date are 312440.
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can yall help me with this I have been up since 7 in the morning and I need some help with this do you think you can help me
Answers
Answer: (3/6) then (2/6)
Step-by-step explanation:
FRACTIONS: YOU TIMES IT SO THE DENOMINATOR IS THE SAME APPLY THE NUMBER YOU TIMED BY THE NUMERATOR.
Which of the following expressions are equivalent to a - b? A a Choose all answers that apply: B a + b b a = b None of the above + 0 look at picture giving 80 points
Answers
Answer:
None of the above
Step-by-step explanation:
The absolute value of a-b is equal to none of the above. say A was -4, and b was -1. -4 minus -1 is -3. absolute value of -3 is 3. so lets see if any problems equal 3. |a+b| = 5 (absolute value of -4+-1). a-b is -3. ((-4)-(-1))
13
Less than
DRAG AND
DROP ITEMS
HERE
Drag the expressions to the table to show whether the product is less than greater
than or equal to
E
Equal to
DRAG AND
DROP ITEMS
HERE
CLEAR
Greater than
DRAG AND
DROP ITEMS
HERE
CHECK
Answers
The first and fifth expressions are equal to the fraction, the second expression is less than the fraction and the third, fourth, and sixth expressions are greater than the fraction.
How to know if a number is greater, less than, or equal to another number?In this case, to better understand the numbers and expressions given, let's simplify each of the expressions.
3/4 or 0.75
Firs expression: 7/7 x 3/ 4 = 1 x 0.75 = Equal to
Second expression: 1/3 x 3/4 = 0.33 x 0.75 = 0.24 = Less than
Third expression: 9/7 x 3/4 = 1.28 x 0.75 = 0.96 = Greater than
Fourth expression: 3/4 x 3/4 = 0.75 x 0.75 = 1.5 = Greater than
Fifth expression: 5/5 x 3/4 = 1 x 0.75 = 0.75 = Equal to
Sixth expression: 5/2 x 3/4 = 2.5 x 0.75 = 1.5= Greater than
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Use the Special Integration Formulas (Theorem 8.2) to find the indefinite integral. (Use C for the constant of integration.) ∫ 49−5x 2 dx ∫ 3x 2 −1 dx
Answers
Simplifying the expression, we get: ∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C
what is integration?
Integration is a fundamental concept in calculus that involves finding the integral of a function. The integral of a function is essentially the opposite of differentiation, and it involves finding the area under the curve of the function.
we have:
∫(a - bx^2) dx = ax - (b/3)x^3 + C
where C is the constant of integration.
Applying this formula to the first integral, we have:
∫(49 - 5x^2) dx = 49x - (5/3)x^3 + C1
where C1 is the constant of integration for the first integral.
Similarly, applying Theorem 8.2 to the second integral, we have:
∫(3x^2 - 1) dx = x^3 - x + C2
where C2 is the constant of integration for the second integral.
Therefore, the indefinite integral of the given expression is:
∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = 49x - (5/3)x^3 + C1 + x^3 - x + C2
where C = C1 + C2 is the constant of integration for the entire expression.
Therefore Simplifying the expression, we get:
∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C
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what is the mean absolute division of 16 10 22 18 4 18 14 24 16 22
Answers
the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.
To find the mean absolute deviation of a set of numbers, we first need to calculate the mean of the set.
The mean of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is:
Mean = (16 + 10 + 22 + 18 + 4 + 18 + 14 + 24 + 16 + 22) / 10 = 16.4
Next, we need to calculate the absolute deviation of each number from the mean. The absolute deviation is the absolute value of the difference between the number and the mean.
The absolute deviations for each number in the set are:
|16 - 16.4| = 0.4
|10 - 16.4| = 6.4
|22 - 16.4| = 5.6
|18 - 16.4| = 1.6
|4 - 16.4| = 12.4
|18 - 16.4| = 1.6
|14 - 16.4| = 2.4
|24 - 16.4| = 7.6
|16 - 16.4| = 0.4
|22 - 16.4| = 5.6
Now, we need to find the mean of the absolute deviations.
Mean absolute deviation = (0.4 + 6.4 + 5.6 + 1.6 + 12.4 + 1.6 + 2.4 + 7.6 + 0.4 + 5.6) / 10
Mean absolute deviation = 4.68
Therefore, the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.
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Write out the sample space for the given experiment. Use the following letters to indicate each choice: Y for yellow, W for white, R for red, U for unfinished, T for teak, and C for cherry.
While renovating your house, you have a choice of paint colors for your game room: yellow, white, or red. You also have the following options for the finish on your entertainment center: unfinished, teak, or cherry.
Answers
The sample space can then be written as: S = {(Y,U), (Y,T), (Y,C), (W,U), (W,T), (W,C), (R,U), (R,T), (R,C)}Thus, the sample space consists of nine possible outcomes or options.
The sample space for this experiment is composed of all the possible combinations of the two variables (paint color and finish). The possible combinations are:
Y + U
Y + T
Y + C
W + U
W + T
W + C
R + U
R + T
R + C
Therefore, the sample space is {Y + U, Y + T, Y + C, W + U, W + T, W + C, R + U, R + T, R + C}.
Here, the experiment involves choosing a paint color and a finish for a game room and entertainment center respectively. We are given that there are three paint color options and three finish options. Therefore, the sample space can be written as follows:
Let Y, W, and R represent the paint colors yellow, white, and red respectively. Let U, T, and C represent the finish options unfinished, teak, and cherry respectively.
Each outcome is an ordered pair, where the first element represents the paint color option and the second element represents the finish option.
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4. A submarine is traveling a 375 feet below sea leven
rises183 feet and then dives 228 feet if the subm
come safely to the surface at 30 feet per second how many seconds will it take to reach the surface?
97
Answers
The submarine will take 14 seconds to safely reach the surface.
What is Speed?Speed is a measure of how quickly an object is moving, calculated as the distance traveled per unit time.
The submarine rises 183 feet, which means its depth decreases by 183 feet. Therefore, its depth is now 375 - 183 = 192 feet below sea level.
The submarine then dives 228 feet, which means its depth increases by 228 feet. Therefore, its depth is now 192 + 228 = 420 feet below sea level.
To reach the surface, the submarine needs to ascend a distance of 420 feet.
The speed of the submarine is given as 30 feet per second. Therefore, the time it will take for the submarine to reach the surface can be calculated as:
[tex]Time = \frac{Distance}{Speed} = \frac{420}{30}[/tex]
= 14 seconds
Therefore, it will take the submarine 14 seconds to safely reach the surface.
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HELP PLEASE ASAP
Carson wants to solve this system of equations.
=2+5−6
=−1
He solves 2+5−6=0 to find the -values, and then substitutes those values into =−1 to find the -values.
Use the drop-down menus to complete the explanation of why Carson’s work cannot be used to find the solution of the system of equations.
Answers
Carson's work cannot be used to find the solution of the system of equations because
The equation x² + 5x - 6 = 0 has two solutions, but only one of them may satisfy the equation y = x - 1.
What is system of equations?
A system of equations is a set of two or more equations that need to be solved simultaneously. The solution to a system of equations is the set of values that make all the equations in the system true. Systems of equations can be solved using a variety of methods, including substitution, elimination, and graphing.
A system of equations can be represented using algebraic notation. For example, consider the following system of two linear equations in two variables x and y:
2x + 3y = 8
4x - 5y = -7
Why Carson's work cannot be used to find the solution of the system of equations ?
The equation x² + 5x - 6 = 0 has two solutions, but only one of them may satisfy the equation y = x - 1.
Substituting the x-values found from solving the quadratic equation into the equation y = x - 1 does not necessarily give the correct y-values for the corresponding x-values that satisfy both equations simultaneously.
Carson should have substituted the x-values found from solving the quadratic equation into the equation y = x² + 5x - 6 instead of y = x - 1 to find the correct y-values that satisfy both equations simultaneously.
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Jeremy has 5.902 kg of trail mix, bought 0.890 kg more and was given 1.5 kg. How
Answers
2 * 2 * 2 * 2 + 20 * 5 + 15 = ?
Answers
Answer:131
Step-by-step explanation:
2 * 2 * 2 * 2 + 20 * 5 + 15 = 2^4+100+15=16+115=131
Answer:
131
Step-by-step explanation:
2 * 2 * 2 * 2 + 20 * 5 + 15 = (remember PEMDAS)
16 + 100 + 15 =
131
There are 8 finalists in a science fair competition. How many ways can they stand on the stage?
Answers
In total, there are 8! (8 factorial) ways that the 8 finalists can stand on the stage. 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320. This means that there are 40,320 possible combinations in which the 8 finalists can stand on the stage.
To calculate this, we can use the formula n!, which stands for n factorial. n! is the product of all the numbers from n down to 1, so 8! is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. This formula can be used to find the total number of combinations that 8 people can stand in on the stage.
It's important to remember that the order matters in this case, so a configuration where the finalists are standing in a line is different from a configuration where they are standing in a circle.
In conclusion, there are 40,320 ways in which the 8 finalists can stand on the stage. This can be determined by using the formula n!, which stands for n factorial.
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2 screenshots!!
giving brai. to whoever can solve both of them correct
Answers
1) 6 3/7
2) 7 1/2
3) 2 7/13
4) 4
Find the quotient (same page as find the product) :
1) 3
2) 3/19
3) 18/35
4) 4 4/9
Find the quotient (beginning of the other page) :
1) 11 3/7
2) 35/43
3) 24/25
4) 6
Find the quotient (end of the other page) :
1) 2
2) 5 1/11
3) 11 1/2
4) 4 9/34
A quick quiz consists of a multiple-choice question with 6 possible answers followed by a multiple-choice question with 3 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "%" symbol.
prob = %
Answers
The probability of correctly answering both questions with random guesses is 5.6%.
There are 6 possible answers, so the probability of randomly guessing the correct answer is 1/6. Similarly, for the second question, there are 3 possible answers, so the probability of randomly guessing the correct answer is 1/3.
Since the two questions are independent events, meaning that the outcome of one question does not affect the outcome of the other question, we can find the probability of both events occurring by multiplying their probabilities together. Therefore, the probability of randomly guessing both answers correctly is:
P(both answers correct) = P(first answer correct) * P(second answer correct)
= (1/6) * (1/3)
= 1/18
The probability is 1/18 or about 0.056 or 5.6% when rounded to one decimal place.
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ABC and EDC are straight lines
AE and BD are parallel
angle ABD=125°
Angle BCD= 30°
work out the size of x
Answers
Therefore , the solution of the given problem of angles comes out to be x has a value of 150°.
An angle meaning is what?The two sides of a tilt in Euclidean geometry are actually spherical faces that divide at the centre and top of barrier. At the point where two rays meet, they might combine to form an angle. Angle is another outcome of two entities interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.
Here,
Since AE and BD are parallel, we can calculate the value of angle ABD using the alternate internal angles theorem:
=> BCD x ABD = 180
=>ABD = 150°, ABD + 30° Equals 180°.
Now, we can use the knowledge that a triangle's angles sum to 180 degrees to determine what angle AED is worth:
180° from ABD + AED + EDC is 150° from
=>AED + 180° is 180°.
=>AED = -150°
=>AED Plus BAE = 180
=> BAE + 30° = 180°
=> BAE = 150°
In order to determine the value of angle AEB, we can use the knowledge that the angles in a triangular sum to 180°:
=>AED 180° BAE AEB
=> AEB + 150° + 30° = 180°
=>AEB = 0°
.Points A, E, and B are collinear because angle AEB is 0°, and angle x equals angle ECD:
=> Angle BCD x = 180° - 30° x = 150° x = ECD = 180°
Consequently, x has a value of 150°.
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i need too find the missing side lengths does anyone know the answer!
Answers
Answer:
Step-by-step explanation:
[tex]sin45=\frac{x}{4}[/tex] [tex](sin=\frac{opposite}{hypotenuse})[/tex]
[tex]x=4sin45[/tex]
[tex]=\frac{4}{\sqrt{2}}[/tex]
[tex]=\frac{4}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]=\frac{4\sqrt{2} }{2}[/tex]
[tex]=2\sqrt{2}[/tex]
[tex]cos45=\frac{y}{4}[/tex] [tex](cos=\frac{adjacent}{hypotenuse})[/tex]
[tex]y=4cos45[/tex]
[tex]=\frac{4}{\sqrt{2}}[/tex]
[tex]=2\sqrt{2}[/tex]
Using transformations, create a design for fabric that represents you as a person to be used on project runway. How will you combine transformations to move your design around the fabric? what combination of transformations was used to create your design?
Answers
Combined translation, rotation, reflection, and enlargement to create a vibrant average pattern on fabric that represents me.
My design would consist of a colorful pattern with a variety of forms, including circles, triangles, squares, and stars. I would mix several transformations, such as translation, rotation, reflection, and enlargement, to get this design. I would first create the shapes and then move them across the cloth using translation and transformation. The forms would then be rotated using the rotation transformation. I would also apply the reflection transformation to the same forms to produce a mirror appearance. Ultimately, I would enhance certain forms while reducing others using the transformation. The cloth would have a distinctive and dynamic appearance that symbolizes me as a person thanks to this mix of alterations.
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Answer this ASAP will give the brainliest answer
Given that y = 9 cm and θ = 25°, work out x rounded to 1 DP.
Answers
In response to the query, we can state that Therefore, the value of x trigonometry rounded to 1 decimal place is 19.4 cm.
what is trigonometry?The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, roughly in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric shapes.
Based on the information given in the diagram, we can use trigonometry to find the value of x.
tan(θ) = opposite / adjacent
tan(25°) = y / x
x = y / tan(θ)
x = 9 / tan(25°)
x ≈ 19.4 cm (rounded to 1 decimal place)
Therefore, the value of x rounded to 1 decimal place is 19.4 cm.
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The following table specifies the joint distribution of Age group (3 levels) and Education level (4
levels) for U.S. adults.
Education Level
Age group Not HS grad HS only Some college College grad
25–44 77 101 99 123
45–64 123 171 46 60
65+ 101 59 20 20
(a) Summarize the association between these variables by reporting the 2 ×3 table of local odds
ratios
θij = πij πi+1,j+1
πi,j+1πi+1,j
for i = 1,2 and j = 1,2,3 .
Identify the odds ratio corresponding to the strongest of these pairwise associations, and
carefully interpret that odds ratio.
(b) Summarize the association between these variables by reporting the 2×3 table of odds ratios
θij = πij π14
πi4π1j
for i = 2,3 and j = 1,2,3 ;
that is, treating the youngest age group and highest education level as baseline categories
for comparison. Identify the odds ratio corresponding to the strongest of these pairwise
associations, and carefully interpret that odds ratio.
Answers
(a) 25-44
(b) 45-64
(a) The 2×3 table of local odds ratios for the association between age group and education level is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.78, which indicates that adults aged 45-64 are 78% more likely to have a high school diploma than adults who are 25-44.
(b) The 2×3 table of odds ratios for the association between age group and education level when treating the youngest age group and highest education level as the baseline categories for comparison is as follows:
The odds ratio corresponding to the strongest of these pairwise associations is 1.48, which indicates that adults aged 25-44 are 48% more likely to have a high school diploma than adults aged 45-64.
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Jean drove 66 miles per hour for a total of 396 miles on a trip. She used the equation below to calculate the time, t, it would take her to complete the trip. What is the constant of proportionality in the equation?
396 = 66t
A. t
B. 396
C. 66
D. 6
Answers
The equation given is:
396 = 66t
This equation relates the distance traveled (396 miles) to the rate of travel (66 miles per hour) and the time it takes to travel that distance (t hours).
We can rearrange this equation to solve for the constant of proportionality, which is the rate of travel:
66t = 396
Dividing both sides by 66, we get:
t = 6
Therefore, the constant of proportionality in the equation is 66. The correct answer is C.
Point A (-3,-3) to A' is a glide reflection where the translation is (x+2, y) and the
line of reflection is y=1? What are the new coordinates?
O(-3,8)
O(-2,-2)
O (5,-1)
O (-1,5)
Answers
The new coordinates is A'(-1,5) which is glide reflection of point A(-3,-3) where the translation is (x+2,y) and the line of reflection is y = 1.
What is Glide Reflection?Glide Reflection, it is known as composition of transformations.
In glide reflection, before reflected over a line it translation is first performed on the figure.
The coordinate of A are given as (-3,-3).
The rule of translation is (x, y) → (x+2,1) and the line of reflection is y=1.
Now,
Applying the rule of translation, we get;
A = (-3, -3) → (-3+2, -3) = (-1, -3)
Since, -3 which is 4 unit below line of reflection,
then,
after reflection, over the line y=1 we get, the reflected point A' would be 4 units above line of reflection
so, A' (-1, 1+4) =(-1, 5)
Therefore, the coordinate of A' (-1, 5).
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Find the function value.
csc330° =
2
-2√3/3
2√3/3
-2
Answers
The function value is csc 330° = -2.
A function formula: what is it?Function establishes the relationship between input and output. The x-intercept, y-intercept, and slope of any function are calculated using function formulas. You could also figure out the vertex of a quadratic function. Moreover, a graph of the function can be created for a range of x values.
Since the sine of 360 degrees (which has a sine of 0) is similar to 30 degrees being subtracted from it, we can determine using the unit circle that the sine of 330 degrees is equal to -1/2 and thus the sine function is negative in the fourth quadrant. The reciprocal of sine 330 degrees, which is -2/1 or -2, is the cosecant of 330 degrees.
Thus, csc 330° = -2.
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A random sample of 120 students at a certain high school was asked if they spend more than 4 hours a night on homework. Assume the true proportion of students that spend more than 4 hours a night on homework is 15%, which of the following is closest to the probability that more than 25 students in a sample of 120 students would respond that they spend more than 4 hours a night on homework? * 0.9632 O 0.0368 0.3236 0.6764 None of these
Answers
The probability that more than 25 students in a sample of 120 students would respond that they spend more than 4 hours a night on homework is given as follows:
0.0367 = 3.67%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The estimate and the sample size for this problem are given as follows:
p = 0.15, n = 120.
Hence the standard error is of:
s = sqrt(0.15 x 0.85/120)
s = 0.0326.
More than 25 students is a sample proportion above 25/120 = 0.2083, hence the probability is one subtracted by the p-value of Z when X = 0.2083, hence:
Z = (0.2083 - 0.15)/0.0326
Z = 1.79
Z = 1.79 has a p-value of 0.9633.
Hence:
1 - 0.9633 = 0.0367 = 3.67%.
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What is the correlation?
A.Positive Trend
B.Negative Trend
C.No Trend
If it has one, what would be the equation for line of best fit?
A. y=3x
B.y=3/4x+1
C.y=10
D.y=1/4x
Answers
The correlation here in the provided graph is a positive trend and the equation for line of best fit will be as follows:
y = 1/4x
Define correlation?Correlation is a statistical method for determining the association or relationship between two variables. To put it another way, the correlation coefficient formula facilitates the calculation of the correlation coefficient, which assesses the degree to which one variable depends on another.
The correlation coefficient is a numerical indicator of correlation. Between -1 and 1, the correlation coefficient is found. An inverse association between two variables is shown by a negative correlation coefficient. A high correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero-correlation coefficient.
Here in the question,
The graph shows a positive trend as its increasing upwards. The equation for the line of best fit will be y =1/4x.
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In triangle FGH, what is m∠F + m∠G + m∠H
?
°
Answers
Since, the triangle FGH is a right angle triangle, The angles of the ∠F = 62°, ∠G = 90° and ∠H = 28°.
Right Angle Triangle:
A right triangle (American English) or right triangle (UK), or more formally an orthogonal triangle, formerly known as a right triangle, is a triangle in which one angle is a right angle (i.e. say an angle of 90 degrees), i.e. two of its sides are perpendicular. The relationship between the sides of a right triangle and the other angles is the basis of trigonometry.
According to the Question:
Interior angles of a triangle add up to 90 degrees
∠F + ∠ G + ∠H = 180
⇒ 9x - 1 + 90 + 3x + 7 = 180
⇒ 12x + 96 = 180
⇒ 12x = 180 - 96
⇒ 12x = 84
⇒ x = 84/12
⇒ x = 7
Therefore,
∠F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62
And, ∠G = 90
And, ∠ H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28
If we add the angles :
62 + 90 + 28 = 180°
Complete Question:
Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?
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