Answers
In response to the stated question, we may state that The equivalent trigonometry expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
tan(A + B) = (tan A + tan B)/(1 - tan A tan B)
Set A = 90 degrees and B = b degrees:
tan(90 + b) = (tan 90 + tan b)/(1 - tan 90 tan b)
tan(90 + b) = (undefined + tan b)/(1 - undefined tan b)
tan(90 + b) = -cot b
7/tan b + 7tan b
= 7/(tan b) + 7(tan(90 + b) - 1)
= 7/(tan b) + 7(-cot b - 1)
= (7 - 7tan b cot b)/sin b
The equivalent expression of 7/tan b + 7tan b is (7 - 7tan b cot b)/sin b.
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Related Questions
Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answers
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
What does replacement value in math? Say if you have to find a replacement value for the variable X, what does that mean?
Answers
A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.
What is an expression?An expression is a combination of numbers, variables, and/or operators that represents a mathematical relationship or calculation. An expression can be as simple as a single number or variable, or it can be more complex and involve multiple operations and variables.
What is a variable?A variable is a symbol or letter that represents a quantity or value that can change or vary in different contexts.
In the given question,
A replacement value is a value that can be substituted for a variable in an equation or expression in order to solve for that variable or simplify the expression.
For example, suppose you have the equation 2x + 3 = 7, and you want to solve for x.
To do so, you can use a replacement value.
You can subtract 3 from both sides of the equation to isolate the term with x, which gives you:
2x = 4
Now, you can divide both sides of the equation by 2 to solve for x:
x = 2
In this case, the replacement value was the number 2, which was substituted for the variable x in the equation in order to solve for x.
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g suppose x and y are two random variables. you don't know their distribution, but someone tells you e[x]
Answers
When x and y are independent variables with x having uniform distribution (0,1) and y having exponential distribution respectively, then e (X+Y) is 3/2, E(XY) is 1/2, E (x-y)2 is 4/3, and e (x2 e24) is -1/3 22etyx u (0,1) > Independent y exp (1) > Independent
The exponential distribution is a continuous probability distribution used in probability theory and statistics that frequently addresses the amount of time until a given event occurs. Events occur continually, independently, and at a steady average pace during this process.
E (x) = 0+1/2 = 1/2
v (x) = [1 – 0]2 / 12 = 1/12
E x2 = v (x) + [Ex]2
= 1/12 + 1/4 = 1+3/12 = 4/12 = 1/3
E (y) = 1 v(y)=1
E y2= 1+1= 2
Eety = ∫0etye-ydy
Eety = ∫0e-y (1 – t)dy
a : E (x+y) = E (x) + E(y)
E (x+y) = 1/2+1 = 3/2
b: E (xy) = E (x) E(y) = 1/2 x 1 = 1/2
c: E (x+y)2 = E (x2 - 2xy+ y2)
= 1/3 - 2 x 1/2 + 2
= 1/3 + 1 = 4/3
d. E x2e24
= 1/3 x -1 = - 1/3
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They did not explain why that was right. What kind of explanation is that?
Answers
An explanation without explaining why that was right is called
dogmatic explanation.
What is a dogmatic statement?An explanation without a reason why it is true is called a dogmatic statement.
We have,
Dogmatic statement:
This is a statement that is presented as true without providing any evidence or logical reasoning to support it.
It is often based on personal beliefs, opinions, or assumptions rather than objective facts or evidence.
Dogmatic statements can be problematic in academic or scientific contexts, where claims must be supported by evidence and logical reasoning.
It is important to be critical and skeptical of dogmatic statements and to seek out evidence and logical reasoning before accepting any claim as true.
Thus,
An explanation without explaining why that was right is called
dogmatic ex[planation.
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A research study is conducted to establish if keeping a dog away from human beings during the day time and freeing it at night conditions them to become brave and aggressive to trespassers. To ascertain the claims, two dogs are kept away from human beings during the day and freed at night. Two other dogs are kept in an environment in which they regularly engage with human beings at both the day and the eveningWhich of the following choices is the best description of the research design for this study? A Sample survey
B Controlled experiment
C Observational study
D None of these
Answers
The best description of the research design for this study is a controlled experiment.
What is a controlled experiment?
A controlled experiment is a type of scientific investigation in which an independent variable is manipulated and the dependent variable is measured while controlling for other variables that may affect the outcome.
Finding the best description of the research design for this study :
In this research study, the researchers are manipulating the environment in which the dogs are kept. Two dogs are kept away from human beings during the day and freed at night, while the other two dogs are kept in an environment where they regularly engage with human beings at both the day and the evening. By doing this, the researchers can observe and measure the behavior of the dogs in both groups and determine if there is a difference in their behavior towards trespassers.
This research design is a controlled experiment because the researchers are manipulating one variable, which is the environment in which the dogs are kept, while keeping other variables constant. This allows them to establish cause-and-effect relationships between the independent variable (environment) and the dependent variable (dog behavior).
In conclusion, the research design for this study is a controlled experiment because it involves manipulating the environment in which the dogs are kept and measuring their behavior while controlling for other variables that may affect the outcome.
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( [9(1) g(n) = g(n − 1) (-4) Find an explicit formula for g(n). g(n): g(1) = -29 1
Answers
Answer:
To find an explicit formula for g(n), we can start by using the recursive formula to generate some terms of the sequence:
g(1) = -29
g(2) = g(1) * (-4) = -29 * (-4) = 116
g(3) = g(2) * (-4) = 116 * (-4) = -464
g(4) = g(3) * (-4) = -464 * (-4) = 1856
We can see that each term in the sequence is obtained by multiplying the previous term by -4. More generally, we can write:
g(n) = (-4)^(n-1) * g(1)
Substituting g(1) = -29 and simplifying, we get:
g(n) = (-4)^(n-1) * (-29)
Thus, the explicit formula for g(n) is:
g(n) = -29 * (-4)^(n-1)
Note that this formula gives the same values as the recursive formula for all positive integers n.
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Which of the following shows the correct evaluation for the exponential expression 1 over 5 to the power of 3 ? (2 points) a 1 over 5 times 3 equals 3 over 5 b 1 over 5 times 1 over 5 times 1 over 5 equals 1 over 125 c 1 over 5 plus 3 equals 3 and 1 over 5 d 1 over 5 divided by 3 equals 1 over 15
Answers
Answer:
b 1 over 5 times 1 over 5 times 1 over 5 equals 1 over 125
Find the standard normal area for each of the following: round your answers to 4 decimal places
Answers
The answers to 4 decimal places are=
(a) 0.0884
(b) 0.0190
(c) 0.9596
(d) 0.2921
What is area?A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
According to our question-
a= 2.25-1.25
0.0884
b= 3.04-2.04
0.0190
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What value of Y and Z will make DEF correspond to JKI?
Answers
[tex]\bold{Solution:}[/tex]
[tex]\Delta[/tex][tex]DE[/tex][tex]F[/tex] congruent to [tex]\Delta[/tex][tex]JKI[/tex]
[tex]\bold{FD=JI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]z + 22 = 3z[/tex]
[tex]\text{or,} \ z-3 z= -22[/tex]
[tex]\text{or,} \ -2z = -22[/tex]
[tex]\text{or,} \ z = \bold{11}[/tex]
[tex]\bold{EF=KI} \text{(corresponding angles of congruent triangles)}[/tex]
[tex]5y+13=6y[/tex]
[tex]\bold{y=13}[/tex]
A researcher tests whether cocaine use increases impulsive behavior in a sample of cocaine-dependent and cocaine-inexperienced mice.
Independent Variable: ________
Quasi-Independent Variable: ________
Dependent Variable: ________
Answers
Answer:
Independent variable: Cocaine Use
Quasi-Independent Variable: Cocaine-dependent and cocaine-inexperienced mice
Dependent variable: Increase in impulsive behavior
Independent Variable: Cocaine use
Quasi-Independent Variable: Cocaine-dependent and cocaine-inexperienced mice (this is a quasi-independent variable because the researcher cannot manipulate whether a mouse is cocaine-dependent or not)
Dependent Variable: Impulsive behavior
to enter their home the clayton family enters a 4 digit code how many codes are possible.
Answers
A Clayton family can therefore employ 10,000 different codes to access their house.
What makes fingers digits?In actuality, the habit of numbering to ten on the fingers is what gave rise to the custom of calling numbers by their digits. The English term "number" is derived from the Latin word digits, which originally meant "finger or toe." If the code is made up of four digits, and each digit can be any number from 0 to 9, then there are 10 possible choices for each of the four digits.
Hence, there are a total of the following codes:
10 x 10 x 10 x 10 = 10,000
Hence, the Clayton family has 10,000 different possible entry codes.
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x±Z./
x±t./
A highway safety researcher is studying the design of a freeway sign and is interested
in the mean maximum distance at which drivers are able to read the sign. The
maximum distances (in feet) at which a random sample of 9 drivers can read the sign are as follows:
400 600 600 600 650 500 345 500 440
The mean of the sample of 9 distances is 512 feet with a standard deviation of 105
feet.
(a) What assumption must you make before constructing a confidence interval?
•The population distribution is Uniform.
•The population distribution is Normal.
(b) At the 90% confidence level what is the margin of error on your estimate of the true mean maximum distance at which drivers can read the sign.
Answer= feet (round to the nearest whole number)
(c) Construct a 90% confidence interval estimate of the true mean maximum
distance at which drivers can read the sign.
Lower value= feet (round to the nearest whole number)
Upper value= feet (round to the nearest whole number)
(d) There is a 10% chance the error on the estimate is bigger than what value?
Answer= feet (round to the nearest whole number)
(e) The researcher wants to reduce the margin of error to only 15 feet at the 90% confidence level. How many additional drivers need to be sampled? Assume the sample standard deviation is a close estimate of the population standard deviation.
Answer=
Answers
In response to the stated question, we may state that The margin of error function is equal to the highest mistake on the estimate.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
(a) The population distribution must be assumed to be normal before generating a confidence interval.
(b) The margin of error with 90% confidence is provided by:
Error Margin = Z (/2) * (/n)
Where Z (/2) is the confidence level/2 crucial value, is the population standard deviation (unknown), and n is the sample size.
Error Margin = t (/2, n-1) * (s/n)
Where t (/2, n-1) is the critical value for the degrees of freedom /2 and n-1, and s is the sample standard deviation.
(d) The margin of error is equal to the highest mistake on the estimate.
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Raul's favorite gummy bear colors are yellow and red. He bought a package of gummy bears that only had his favorite colors. When he counted the gummy bears, he had 20 red and 23 yellow. What is the ratio of red gummy bears to yellow gummy bears?
Question 2 options:
23/20
23/43
20/23
20/43
Answers
The ratio between the number of red gummy bears to the number of yellow gummy bears is of:
20/23.
How to obtain the ratio?The ratio between the number of red gummy bears and the number of yellow gummy bears is obtained applying the proportions in the context of the problem.
To obtain the ratio between two amounts A and B, you need to divide the first amount by the second amount. The result of this division will give you the ratio of the two amounts.
The amounts for this problem are given as follows:
Amount A: 20 red gummy bears.Amount B: 23 yellow gummy bears.Hence the ratio between these two amounts is given as follows:
20/23.
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Use the product of powers property to simplify the numeric expression. 2^2/5/2^1/10
Answers
Answer:
[tex] 2^\frac{3}{10} [/tex]
Step-by-step explanation:
[tex] \dfrac{2^\frac{2}{5}}{2^\frac{1}{10}} = [/tex]
[tex]= 2^{\frac{2}{5} - \frac{1}{10}}[/tex]
[tex]= 2^{\frac{4}{10} - \frac{1}{10}}[/tex]
[tex] = 2^\frac{3}{10} [/tex]
Mary is 21 years old. She buys 50/100/25 liability insurance, and collision and
comprehensive insurance, each with $500 deductibles. What is her total annual
premium? Round to the nearest dollar. Do not state the units. Be sure to show work.
Liability Insurance
Type Amount Premium
25/50 $240
50/100 $385
100/300 $450
Property damage 25 $210
50 $150
100 $140
Collision and comprehensive premiums
$250 $172 $112
$500 $102 $87
$750 $85 $52
Rating factor
Age
17-20 male Female
3.1 1.64
21-24. 2.53. 1.22
25-29 1.73 1.0
Answers
According to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
What is multiplication ?In mathematics, multiplication is an arithmetic operation that combines two or more numbers to produce a product. It is represented by the symbol "×" or "*", or by placing the numbers next to each other with no symbol between them.
According to the given information:Mary is 21 years old, so according to the rating factor table, her rating factor is 1.22 for a female.
For liability insurance, Mary has chosen the 50/100/25 coverage, which means $50,000 for bodily injury per person, $100,000 for bodily injury per accident, and $25,000 for property damage per accident. The premium for this coverage is $385.
For collision and comprehensive insurance, Mary has chosen a $500 deductible, so her premiums are $102 for collision and $87 for comprehensive.
To find the total annual premium, we add up the premiums for liability insurance and collision/comprehensive insurance:
Total premium = Liability premium + Collision premium + Comprehensive premium
Total premium = $385 + $102 + $87
Total premium = $574
Therefore, according to the given information, Mary's total annual premium is $574 (rounded to the nearest dollar).
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LOOK AT THE PHOTO PLS
Answers
Answer: 0.27272727 or 0.27 (with a dash on top of 27)
Step-by-step explanation:
A rectangle has an area of 24 square yards.the dimensions are whole numbers what are all the possible dimensions of the rectangle
Answers
Answer:
4 combination if order doesn't matter, 8 if order matter (for example is not the same 1x24 or 24x1)
Step-by-step explanation:
1x24
2x12
3x8
4x6
IF order matter also:
6x4
8x3
12x2
24x1
find the two numbers whose ratio is 3:7 and their difference is 20
Answers
Answer:
the two numbers are 15 and 35, and their ratio is 3:7, and their difference is 20.
Step-by-step explanation:
A shopkeeper sold 20 mobile sets of same brand for Rs 3,00,0000 at the same rate in a week. (a)What is the selling price of each mobile set? b, If he bought each mobile set for Rs 12,500, find his profit or loss percent. c, If each mobile set is 12 cm long, 6 cm broad and 1 cm thick, find the ratio of it length to the breadth.
Answers
Answer: 2:1
Step-by-step explanation:
a) The total selling price of 20 mobile sets is Rs. 3,00,000. Therefore, the selling price of each mobile set is:
Selling price of each mobile set = Total selling price ÷ Number of mobile sets sold
= 3,00,000 ÷ 20
= Rs. 15,000
Therefore, the selling price of each mobile set is Rs. 15,000.
b) The cost of each mobile set is given as Rs. 12,500. The total cost of 20 mobile sets is:
Total cost = Cost of each mobile set × Number of mobile sets sold
= 12,500 × 20
= Rs. 2,50,000
The profit made by the shopkeeper is the difference between the selling price and the cost price of the mobile sets:
Profit = Selling price - Cost price
= 3,00,000 - 2,50,000
= Rs. 50,000
Therefore, the profit made by the shopkeeper is Rs. 50,000.
The profit percent is given by:
Profit percent = (Profit ÷ Cost price) × 100
= (50,000 ÷ 2,50,000) × 100
= 20%
Therefore, the shopkeeper made a profit of 20%.
c) The ratio of the length to the breadth of each mobile set is:
Length:breadth = 12:6
= 2:1
Therefore, the ratio of the length to the breadth of each mobile set is 2:1.
Answer:
Step-by-step explanation:
a) To find the selling price of each mobile set, we need to divide the total amount sold by the number of mobile sets sold:
Selling price of each mobile set = Total amount sold / Number of mobile sets sold
Selling price of each mobile set = Rs 3,00,000 / 20
Selling price of each mobile set = Rs 15,000
Therefore, the selling price of each mobile set is Rs 15,000.
b) The cost price of each mobile set is Rs 12,500.
Profit or loss percent = [(Selling price - Cost price) / Cost price] x 100
Profit or loss percent = [(15,000 - 12,500) / 12,500] x 100
Profit or loss percent = 20%
Therefore, the shopkeeper has made a profit of 20%.
c) The ratio of the length to the breadth of the mobile set is:
Length : Breadth = 12 cm : 6 cm
Simplifying the ratio by dividing both sides by 6:
Length : Breadth = 2 : 1
Therefore, the ratio of the length to the breadth of the mobile set is 2 : 1.
Let V,Wbe vector spaces and T:V→Wa linear transformation, then Tis injective iff Tpreserves linear independence".
Answers
The statement "T is injective iff T preserves linear independence" means that T maps distinct vectors in V to distinct vectors in W and that if a set of vectors in V is linearly independent, then their images under T are also linearly independent.
Now, let V and W be two vector spaces and let T: V→W be a linear transformation. We say that T is injective if and only if every distinct vector in V gets mapped to a distinct vector in W.
Now, the statement "T preserves linear independence" means that if a set of vectors in V is linearly independent, then their images under T (i.e., the vectors they get mapped to in W) are also linearly independent.
To see why this is true, suppose we have a linearly independent set of vectors v₁, v₂, ..., vₙ in V. If we assume that their images under T are linearly dependent, then there exist coefficients c₁, c₂, ..., cₙ such that
c₁Tv₁ + c₂Tv₂ + ... + cₙTvₙ = 0
But since T is linear, this is equivalent to
T(c₁v₁ + c₂v₂ + ... + cₙvₙ) = 0
which implies that c₁v₁ + c₂v₂ + ... + cₙvₙ = 0. But this contradicts the assumption that v₁, v₂, ..., vₙ are linearly independent. Therefore, their images under T must also be linearly independent.
Conversely, if T is injective, then it preserves linear independence because distinct vectors in V get mapped to distinct vectors in W. Therefore, if a set of vectors in V is linearly independent, then their images under T must also be linearly independent.
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Help please! I have no idea!!!! PLEASEE
Answers
To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0.
What is graph?
In mathematics, a graph is a visual representation of a set of data, typically as a set of points or lines on a coordinate plane. Graphs are used to represent various types of data, such as numerical values, functions, relationships, and patterns.
Assuming that the graph is a coordinate plane with the x-axis and y-axis, do the following:
To highlight the point (9, 8) on the graph in red, locate the point (9, 8) on the coordinate plane and mark it with a red color.
To highlight the point (20, f(20)) on the graph in green, you need to know the value of f(20) first. Once you have that value, locate the point (20, f(20)) on the coordinate plane and mark it with a green color.
To highlight the line y = 5 on the graph in blue, draw a straight line passing through all points whose y-coordinate is 5. This line should be parallel to the x-axis and should be marked with a blue color.
Therefore To highlight the line y = 0 on the graph in black/grey, draw a straight line passing through all points whose y-coordinate is 0. This line should be parallel to the x-axis and should be marked with a black/grey color.
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Pls help me! I only have 1 chances
Answers
Answer:
Neither parallel or perpendicular
Step-by-step explanation:
Parallel lines have the same slope. Perpendicular slopes are the negative reciprocals of each other.
30y +25x = -180 Subtract 25x from both sides
30y + 25x - 25x = -25x - 180
30y = -25x - 180 Divide all the way through by 30
[tex]\frac{30y}{30}[/tex] = [tex]\frac{-25}{30}[/tex] - [tex]\frac{180}{30}[/tex]
y = [tex]\frac{-5}{6}[/tex] - 6
y = [tex]\frac{-6}{5}[/tex] x + 6
Comparing the 2 equations, we have slope of
[tex]\frac{-5}{6}[/tex] and [tex]\frac{-6}{5}[/tex]
These slopes are not the same so they are not parallel.
These slopes are not negative reciprocals. so they are not perpendicular.
Perpendicular slopes would be [tex]\frac{-5}{6}[/tex] and [tex]\frac{6}{5}[/tex] or [tex]\frac{-6}{5}[/tex] and [tex]\frac{5}{6}[/tex]. One slope would have to be negative and the other slope would have to be positive which they are not.
Helping in the name of Jesus.
g suppose that x and y are i.i.d. bernoulli(p) random variables (i.e., with the same value of p, 0
Answers
The product of expected value of xy is p^2.
If x and y are i.i.d. Bernoulli(p) random variables, then the probability mass function of each variable is:
P(x=1) = p
P(x=0) = 1-p
P(y=1) = p
P(y=0) = 1-p
To find the expected value of the product xy, we can use the definition of expected value:
E[xy] = Σ Σ xy P(x,y)
where the summation is over all possible values of x and y.
Since x and y can only take on the values of 0 or 1, there are only four possible outcomes:
x=0, y=0
x=0, y=1
x=1, y=0
x=1, y=1
We can calculate the probability of each outcome using the probability mass function:
P(x=0, y=0) = P(x=0)P(y=0) = (1-p)(1-p)
P(x=0, y=1) = P(x=0)P(y=1) = (1-p)p
P(x=1, y=0) = P(x=1)P(y=0) = p(1-p)
P(x=1, y=1) = P(x=1)P(y=1) = p^2
Therefore, we have:
E[xy] = (0)(0)(1-p)(1-p) + (0)(1)(1-p)p + (1)(0)p(1-p) + (1)(1)p^2
E[xy] = 0 + 0 + 0 + p^2
E[xy] = p^2
So the expected value of xy is p^2.
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____The given question is incomplete, the complete question is given below:
g suppose that x and y are i.i.d. bernoulli(p) random variables (i.e., with the same value of p, 0. find the product of expected value of xy.
I will mark you brainiest!
Name the transformation that maps the rectangle onto itself.
A) Rotation 90º clockwise about the origin.
B) Reflection over the x-axis.
C) Rotation 90º counterclockwise about the origin.
D) None of these choices are correct.
E) Translation up 4 and right 8.
Answers
Answer:
B
Step-by-step explanation:
It's like a piece of paper, fold it in half
i need the answer to this question
Answers
The measure of angle BAC is 55°, which is closest to option B (50°).
What is a tangent angle?The ratio of the length of the side directly opposite an acute angle to the side directly adjacent to the angle is known as the tangent in trigonometry. Only triangles with straight angles can have this.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
To determine the size of angle ABC, we can use the knowledge that a triangle's total angles equal 180°. Because the straight line formed by angles ABD and BCD, we have:
[tex]Angle ABC = 180° - Angles ABD and BCD.[/tex]
[tex]Angle ABC = 180° - 35° - 90°Angle ABC = 55°[/tex]
Given that triangle ABC has two angles, we can use the knowledge that a triangle's total of angles equals 180° to determine the size of angle BAC:
[tex]Angle BAC = 180° - Angle ABC - Angle ACBAngle BAC = 180° - 55° - 70°Angle BAC = 55°[/tex]
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It is most similar to option B (50°) when the angle BAC is 55°.
What is a tangent angle?
The tangent in trigonometry is the length of the side directly opposite an acute angle divided by the length of the side directly next to the angle.
This property can only be found in triangles with straight angles.
Let's give the angles shown in the diagram the following labels:
Angle ACD = 55°
Angle ABD = 35°
Angle BCD = 90°
We can use the fact that a triangle's total number of angles is 180° to calculate the size of angle ABC. due to the fact that the straight line created by angles ABD and BCD
Triangle ABC has two angles, so we can use the fact that a triangle's sum of angles is 180° to calculate the size of angle BAC.
Therefore, the BAC measurement is 55°, which is closest to option B's 50°.C is 55°, which is closest to option B (50°).
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A test consists of 30 multiple choice questions, each with five possible answers, only one of which is correct. find the mean and the standard deviation of the number of correct answers. round the answers to the nearest hundredth.
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The mean and standard deviation for 30 multiple-choice questions for the number of correct answers is Mean(μ) = 6 and Standard deviation(σ) = 2.19.
What is mean?
A collection of values are averaged to form the mean. The total points were divided by the total scores. When population samples are tiny, the mean is sensitive to extreme scores. For example, if two students in a class of 20 earned significantly higher than the rest, the mean will be skewed higher than the other students' scores might suggest. When using means, larger sample sizes are preferable.
Define standard deviation.
In statistics, a measure of variability known as the standard deviation ( standard deviation ) is frequently used. It demonstrates how different things are from the norm. (mean). When the SD is low, the data tend to be close to the mean, while when it is high, the data are dispersed over a wide variety of values.
Given: number of questions(n) = 30, p = [tex]\frac{1}{5}[/tex], q = [tex]\frac{4}{5}[/tex]
Mean μ = n*p
= 30 *[tex]\frac{1}{5}[/tex]
μ = 6
Standard deviation σ = [tex]\sqrt{n*p*q}[/tex]
= [tex]\sqrt{30*\frac{1}{5}*\frac{4}{5}}[/tex]
= [tex]\sqrt{4.8}[/tex]
σ = 2.19
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PLEASE HELPPPP 30 POINTS!
Answers
Answer:
56
90
56
Step-by-step explanation:
easy easy lol.
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As a sound wave travels, what happens to the particles in the medium it travels through i need help
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As a sound wave travels, the particles in the medium it travels through vibrate back and forth in the same direction as the wave travels.
How to explain what happens to the mediumAs a sound wave travels through a medium, such as air or water, the particles in the medium vibrate back and forth in the same direction as the wave travels.
However, the particles themselves do not actually move along with the wave. Instead, the wave causes a disturbance in the particles, which then passes from one particle to the next, resulting in a wave-like pattern of motion that travels through the medium.
In other words, the sound wave is a disturbance that travels through the medium, causing the particles in the medium to oscillate back and forth around their equilibrium positions.
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For each of the following find:
I. lim f (x) as x approaches a from the negative
II. lim f (x) as x approaches a from the positive
III. lim f (x) as x approaches a
a. f(x)={ sin x/3, if x< or equal to pi a=pi
{ x(root3)/(2pi), if x>pi
b. f(x)= (x^2-36)/root(x^2-12x+36) a=6
Answers
Answer:
a. For the function:
f(x) = { sin x/3, if x ≤ π
{ x√3/2π, if x > π
I. To find lim f(x) as x approaches π from the negative side, we need to evaluate f(x) for values of x that are slightly less than π. In this case, since sin(x/3) is a continuous function, we can simply evaluate it at x = π:
lim f(x) as x approaches π- = f(π-) = sin(π/3) = √3/2
II. To find lim f(x) as x approaches π from the positive side, we need to evaluate f(x) for values of x that are slightly greater than π. In this case, we can simply evaluate the other part of the piecewise function at x = π:
lim f(x) as x approaches π+ = f(π+) = π√3/2π = √3/2
III. To find lim f(x) as x approaches π, we need to check whether the left-hand and right-hand limits are equal. In this case, since both the left- and right-hand limits exist and are equal, we have:
lim f(x) as x approaches π = √3/2
b. For the function:
f(x) = (x^2 - 36)/√(x^2 - 12x + 36)
I. To find lim f(x) as x approaches 6 from the negative side, we need to evaluate f(x) for values of x that are slightly less than 6. In this case, we can substitute x = 6 - h, where h is a positive number approaching zero, to get:
lim f(x) as x approaches 6- = lim f(6 - h) as h approaches 0
Substituting x = 6 - h into the function, we get:
f(6 - h) = [(6 - h)^2 - 36]/√[(6 - h)^2 - 12(6 - h) + 36]
= [h^2 - 12h]/√[h^2]
Simplifying the numerator and denominator separately, we get:
f(6 - h) = h(h - 12)/|h|
Since h approaches 0 from the positive side, we have:
lim f(6 - h) as h approaches 0+ = lim h(h - 12)/h as h approaches 0+ = lim (h - 12) as h approaches 0+ = -12
II. To find lim f(x) as x approaches 6 from the positive side, we need to evaluate f(x) for values of x that are slightly greater than 6. In this case, we can substitute x = 6 + h, where h is a positive number approaching zero, to get:
lim f(x) as x approaches 6+ = lim f(6 + h) as h approaches 0
Substituting x = 6 + h into the function, we get:
f(6 + h) = [(6 + h)^2 - 36]/√[(6 + h)^2 - 12(6 + h) + 36]
= [h^2 + 12h]/√[h^2]
Simplifying the numerator and denominator separately, we get:
f(6 + h) = h(h + 12)/|h|
Since h approaches 0 from the positive side, we have:
lim f(6 + h) as h approaches 0+ = lim h(h +
Step-by-step explanation:
Which graph represents this equation?
= 3/2x^2 - 6x
Answers
The parabola is passing through (0, 0) and (9, 0).
What is the parabola?The locus of a moving point is the location that maintains a constant distance between a stationary point and a predetermined line.
The directrix is a non-moving line, while the focus is a non-moving point.
As you can see, the quadratic variable is not, which modifies the figure's orientation.
This parabola doesn't actually represent a function because it will open horizontally, specifically toward negative infinity, as the graphic linked illustrates.
The vertical line test will reveal that the vertical line in question intercepts the figure in two places, proving that it is not a function.
According to our question-
The equation of the parabola is given below.
y = (3/2)x² - 6x
Then the factor of the equation will be
y = 3x (x / 2 - 3)
Then the zeroes of the function will be
y = 0
x = 0, 9
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