The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:
P(x > 52) = 1 - P(x ≤ 52)
P(x ≤ 52) = (52 - 58) / 6 = -1
P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.
Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.
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Find the missing angle. Round your
answer to the nearest tenth.
tº
11 mi
5 mi
Answer:
24.4 degrees
Step-by-step explanation:
This is a right triangle so you can use trig to solve. If you take the arctan of 5/11 you get 24.4(rounded to the nearest tenth)
In the figure here, a small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h1=5.4 m and h2=2.8 m. What are the speeds of the block at (a) point B and (b) point C? (c) Does the block reach point D? (d) If, so what is its speed there; if not, how far through the section of friction does it travel?
A small block is sent through point A with a speed of 6.8 m/s. Its path is without friction until it reaches the section of length L=14 m, where the coefficient of kinetic friction is 0.78. The indicated height are h₁ =5.4 m and h₂=2.8 m. The speeds of the block at (a) Point B is 108m/s and (b) Point C is 7.6m/s
The velocity of an object (usually denoted v) is the amount of its position change over time ; therefore it is a scalar quantity. The average speed of an object over a time interval is the distance traveled by the object divided by the duration of the interval; the instantaneous speed remains zero.
(a) At B the speed is :
V = [tex]\sqrt{V^{2}+2gh_1 }[/tex]
⇒ V = [tex]\sqrt{(6.8m/s)+ 2(9.8m/s^2) (5.4)}[/tex]
⇒ V = 108.44 m/s
⇒ V = 108 m/s
(b) Here, matters is the difference in heights (between A and C):
[tex]V = \sqrt{V_0^{2}+2g(h_1+h_2) }[/tex]
⇒ [tex]V = \sqrt{(6.8)+2 (9.8) (5.4- 2.8) }[/tex]
⇒ [tex]V = \sqrt{6.8 +2(9.8)(2.6)}[/tex]
⇒ √57.76 = 7.6m/s
(c) Using the results from part (b), we see that its kinetic energy is just at the beginning of its "rough glide" (horizontally to D) is:
1/2 m(7.6m/s)² = 28.88m (with SI units understood).
We note that this kinetic energy will turn entirely into thermal energy
28.88m = μₙ mgd
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Ñamandu es un genio dibujó un cuadrado de x cm cada lado en la parte superior del cuadrado partió en tres partes iguales quedando el corte expresado de esta manera x bajo 3 unió el primer punto de corte con el vértice del lado paralelo trazando un segmento a lo que llamó y Descubre que figuras se forman y entra el perímetro de cada figura formado
The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).
When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.
Using the Pythagorean theorem, we can solve for y:
y^2 = (x/3)^2 + x^2
y^2 = x^2/9 + x^2
y^2 = (10x^2)/9
y = x×sqrt(10)/3
Now we can find the perimeter of each figure that is created
Perimeter of the original square = 4x
Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3
Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)
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Reggie is rolling a block with the number 1,2,3,4, and 5 on it. Kaitlyn is drawing one desk from a basket of three disks: one blue, one red, and one yellow. use the tree diagram below to answer the question. What is the probability that they end up with a yellow disk
The probability of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
What is probability?Probabilistic theory is a branch of mathematics that calculates the chance of an event or a claim being true. A risk is a number between 0 and 1, where 1 represents certainty and a probability of about 0 shows how likely an event appears to be to occur. Probability is a mathematical term for the likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1, or as percentages ranging from 0% to 100%. The proportion of occurrences among equally likely choices that result in a certain event in compared to all possible outcomes.
the answers to the questions:
a) The chance of getting a yellow disc is 1/6 + 1/6 = 1/3. This is because there are two methods to acquire a yellow disc: receive an even number and then choose the yellow disc, or get an odd number and then choose the yellow disc.
b) The chance of getting a blue disc is 1/6 + 1/6 = 1/3. This is because there are two methods to receive a blue disc: get an even number and then choose the blue disc, or get an odd number and then choose the blue disc.
c) The chance of getting an odd number with a red disc is (1/6 + 1/6) 1/3 = 1/18. This is because there are two ways to acquire an odd number, and there is only one way to get a red disc for each of those two methods.
d) The chance of getting an even number and a yellow disc is 1/6 1/3 = 1/18. This is due to the fact that there is only one method to obtain an even number and a yellow disc.
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Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to:
Venus
Jupiter
Earth
The Sun
Sgr A has a diameter of about 27.3 million miles; that's roughly the same distance from Mercury to The Sun.
What is distance?Distance is a measurement of how far apart two objects or points are, either numerically or rarely qualitatively. Distance can relate to a physical length in physics or to an estimate based on other factors in everyday language (e.g. "two counties over"). The term is frequently used metaphorically to refer to a measurement of the difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation, as spatial cognition is a rich source of conceptual metaphors in human thought (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize the majority of these ideas of distance, both literal and figurative.
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The stem-and-leaf plot below gives the number of minutes that customers waited for their orders at two restaurants. There were 13 wait times recorded for the first restaurant and 16 for the second. Use the plot to answer the questions.
Answer: The first restaurant had a greater median time
the range for the first restaurant is 35 minutes and the range for the second restaurant is 39 minutes
The second restaurant had more wait times from 30-39 minutes
All 5 students in Mr. Arthur's class score 50 on a test. What is the average score on this test?
If all the 5 students in Mr. Arthur's class scores 50 on a test then the average score of the test is 50.
To find the average score on the test, we need to sum up the scores of all the students and then divide by the number of students.
In this case, all 5 students scored 50 on the test.
So the total score of all 5 students is:
Total score = 5 x 50 = 250
The average score is then calculated by dividing the total score by the number of students:
Average score = Total score / Number of students
Average score = 250 / 5
Average score = 50
Therefore, the average score on the test is 50.
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Can some one solve this and show their work plssss
Answer:
For WXYZ to be a parallelogram, both pairs of opposite sides must be parallel.
So, we have 7m + 4 = 9m and 5y + 13 - (2n - 1) = 6y - 8 - (n + 6).
Solving the first equation, we get m = 2.
Solving the second equation, we get y - n = 4.
Thus, for WXYZ to be a parallelogram, m = 2 and y - n = 4, so option B is correct.
What is the composition of linear transformation matrix?
A linear transformation matrix is a square matrix that represents a linear transformation of a vector space. The composition of linear transformation matrices is equivalent to the composition of linear transformations they represent.
In general, the composition of two linear transformations A and B can be represented by the matrix product AB. Therefore, the composition of two linear transformation matrices, say A and B, would be the matrix product AB.
Linear transformations are functions that map vectors from one vector space to another in a linear way. These transformations can be represented by matrices, which can be composed to represent the composition of linear transformations.
The composition of two linear transformations represented by matrices involves multiplying the matrices together. To perform this multiplication, we need to ensure that the number of columns in the first matrix matches the number of rows in the second matrix. The resulting matrix will have the same number of rows as the first matrix and the same number of columns as the second matrix.
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At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation: Given a positive constant € and the two equations below, what is the relationship between X and Y? Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y 1 . X Y Submit
The relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows X = Y/2
At times, the relationship between a dependent and an independent variable is expressed as a logarithmic equation. For this question, given a positive constant € and the two equations below, we can find the relationship between X and Y. Equation 1: Log(c) = X/2 Equation 2: Log(c^2) = Y.We can use the basic properties of logarithms to solve this problem. To do so, we need to understand what logarithms are first.Logarithms are the opposite of exponentials. They allow us to find the exponent needed to produce a given value. For instance, log base 2 of 8 is 3 since 2^3 = 8.
A logarithm is represented as log_bx where b is the base and x is the argument or the number being passed to the logarithm.In equation 1, we are given that log(c) = x/2. To isolate x, we need to exponentiate both sides with base e.e^(log(c)) = e^(x/2)This gives us c = e^(x/2).We can rewrite this expression as c^2 = e^x. Now we use equation 2 which states that log(c^2) = y. This is equivalent to 2log(c) = y.Using equation 1, we can substitute log(c) for x/2.2log(c) = y2(x/2) = yx = y/2So the relationship between X and Y is X = Y/2. Therefore, we can conclude that the relationship between a dependent and an independent variable expressed as a logarithmic equation is as follows: X = Y/2.
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suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. if the population grows to 500 after one year, what will the population be after another three years?
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.
What is the logistic model?A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.
Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:
[tex]P(t) = K / (1 + Ae^{-rt})[/tex]
where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.
Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].
[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]
Now, solve for A by dividing both sides by 2000 / (1 + A):
[tex]1 + A = 4A = 3[/tex]
Substitute the value of A back into the logistic model equation:
[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]
Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):
[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]
[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]
Solve the first equation for r:
[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]
Solve for e using the quadratic formula to get:
e = 0.4274 and e = 1.1713
Let e = 0.4274:
[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]
Take the natural logarithm of both sides:
[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]
Use a graphing calculator to solve for r:
[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]; -0.1568 < r < 0.7534
Solve for r using the second year’s data:
[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]
Thus, the population will be 852.78 after another three years.
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Square root of За^2/10b^6
The simplified square expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].
What is square root ?
In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 x 3 = 9.
The square root is denoted by the symbol √, also known as the radical symbol. For instance, the square root of 16 is written as √16 = 4.
The square root can be used to solve various types of equations, including quadratic equations and problems involving areas and volumes. It is also used in various fields such as physics, engineering, and finance.
According to the question:
To simplify the expression [tex]\sqrt{3a^{2}/10b^6}[/tex], we can first separate the numerator and denominator inside the square root:
[tex]\sqrt{3a^2/10b^6} = \sqrt{3a^2}/\sqrt{10b^6}[/tex]
Next, we can simplify the square root of the numerator:
[tex]\sqrt{3a^2} = |3a|,[/tex] where |За| represents the absolute value of За.
Finally, we can simplify the square root of the denominator by factoring out the perfect square[tex]b^2[/tex]:
[tex]\sqrt{10b^6} = \sqrt{10} * \sqrt{b^6} = \sqrt{10} * b^{3}[/tex]
Substituting these values back into the original expression, we get:
[tex]\sqrt{3a^2/10b^6} = |3a| / \(sqrt{10} * b^3[/tex]
Therefore, the simplified expression for[tex]\sqrt{3a^2/10b^6}[/tex] is [tex]|3a| / (\sqrt{10} * b^{3})[/tex].
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which of the following is most likely a population as opposed to a sample? a) respondents to a newspaper survey. b) the first 5 students completing an assignment. c) every third person to arrive at the bank. d) registered voters in a county.
The option that is most likely a population as opposed to a sample is registered voters in a county. The correct answer is Option D.
A population is a group of individuals, objects, or events whose properties are being studied. A sample is a smaller subset of the population that is selected to represent the whole population.
The four options given in the question are all sets of individuals who are being studied, but the difference is how they were selected. Respondents to a newspaper survey, the first 5 students completing an assignment, and every third person to arrive at the bank are all examples of samples because they are subsets of a larger group.
However, registered voters in a county are most likely a population because they are the entire group that is being studied, and there is no need for a subset of this group since the entire population is available. Therefore, option d) registered voters in a county is the most likely population as opposed to a sample.
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5x-2=3(x+4)
What is the value of X
Answer:
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Step-by-step explanation:
[tex]\textsf{For this problem, we are asked to find the value of x.}[/tex]
[tex]\textsf{We should simply isolate the x so that it's only on one side.}[/tex]
[tex]\large\underline{\textsf{How?}}[/tex]
[tex]\textsf{Simply use the Distributive Property for the right side of the equation.}[/tex]
[tex]\textsf{Simplify the equation to where x is by itself.}[/tex]
[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{The Distributive Property is a Property that allow us to distribute expressions further.}[/tex]
[tex]\textsf{Commonly, the form is a(b+c); Where b and c are multiplied by a.}[/tex]
[tex]\large\underline{\textsf{Use the Distributive Property;}}[/tex]
[tex]\mathtt{5x-2=3(x+4)}[/tex]
[tex]\mathtt{5x-2=(3 \times x)+(3 \times 4)}[/tex]
[tex]\mathtt{5x-2=3x+12}[/tex]
[tex]\large\underline{\textsf{Add 2 to Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-2 \ \underline{+ \ 2}=3x+12 \ \underline{+ \ 2}}[/tex]
[tex]\mathtt{5x=3x+14}[/tex]
[tex]\large\underline{\textsf{Subtract 3x from Both Sides of the Equation;}}[/tex]
[tex]\mathtt{5x-3x=3x-3x+14}[/tex]
[tex]\mathtt{2x=14}[/tex]
[tex]\large\underline{\textsf{Divide the Whole Equation by 2;}}[/tex]
[tex]\mathtt{\frac{2x}{2} = \frac{14}{2} }[/tex]
[tex]\large\boxed{\textsf{x = 7}}[/tex]
Answer:
[tex] \sf \: x = 7[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 5x - 2 = 3(x + 4)
Then the value of x will be,
→ 5x - 2 = 3(x + 4)
→ 5x - 2 = 3(x) + 3(4)
→ 5x - 2 = 3x + 12
→ 5x - 3x = 12 + 2
→ 2x = 14
→ x = 14 ÷ 2
→ [ x = 7 ]
Hence, the value of x is 7.
is this relation reflexive? is this relation irreflexive? is this relation total? is this relation transitive?
The relation you have described is neither reflexive, nor irreflexive, nor total, nor transitive.
A relation cannot be both reflexive and irreflexive. Hence, these two properties are mutually exclusive. If it is reflexive, then it is not irreflexive. If it is irreflexive, then it cannot be reflexive. Nonetheless, it is possible for a relation to be neither reflexive nor irreflexive.
A reflexive relation is one in which every element is related to itself. A relation is irreflexive if no element is related to itself. A total relation is one in which every element is related to every other element. A transitive relation is one in which, if element A is related to element B and element B is related to element C, then element A is related to element C.
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About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
The statement that is correct is (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
The binomial distribution can be used to calculate the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success.
The probability of a flight being delayed is 0.24, and the probability of a flight not being delayed is 0.76. Therefore, the probability of exactly 10 flights out of 100 being delayed can be calculated using the binomial distribution with n = 100, k = 10, and p = 0.24.
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Expresa en grados los siguientes radiantes:
1) π RAD=?
2) 3/2π RAD=?
3) π/6 RAD=?
4) π/18 RAD=?
need help finding the letter u
In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd
What is a triangle?A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd
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In the given diagram, ΔHIJ ≈ ΔFIG, the value of u in triangle FIG is calculated as: IG = 8 yd
What is a triangle?A triangle is a geometric shape that is formed by three line segments that intersect at three non-collinear points. The three line segments are called the sides of the triangle, while the three points where they intersect are called the vertices of the triangle.
A triangle is a three-sided polygon formed by three line segments intersecting at three non-collinear points, and it can be classified based on the length of its sides and the measure of its angles.
∆HIJ similar to ∆FIG
HI/FI = IJ/IG
5/10 = 4/IG
IG = 8 yd
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What’s -9.1 times 3.75
Given (x – 7)2 = 36, select the values of x.
Answer:
25
Step-by-step explanation:
2x-14=36
2x=36+14
2x=50
x=25
Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
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In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.
A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:
2000 - 872 - 173 = 955
Therefore, the missing number is 955.
B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:
9180 ÷ 102 = 90
Therefore, the missing number is 90.
C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:
706 + 99 = 805
Therefore, the missing number is 805.
To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.
A) 3 + (5x7) - 2 = 40
B) (3 + 5) × 7 - 2 = 54
C) 3 + (5 × (7-2)) = 28
Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.
An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..
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Complete Question: -
Find unknown numbers of these operations
A ) 872 +. + 173 = 2000
B ) 9180:. = 102
C ). -99 = 706
With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.
A ) 3 + 5 x 7-2 = 40
B ) 3 + 5 × 7-2 = 54
C ) 3 + 5 × 7-2 = 28
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William writes a function f(x) = 2x - 10. He uses an
input-output table to represent the function.
Input: 4
Output: -8
What is the output of William's function when the
input is 4?
Answer: -8
Step-by-step explanation:
When the input is 4, according to the input-output table, the output is -8.
Plugging 4 into the function f(x) = 2x - 10 directly also gives the same result:
f(4) = 2(4) - 10 = 8 - 10 = -2
So the output of William's function when the input is 4 is -8.
Polynomial question
I don't understand this working
Why is b = d = 0 if the function is even?
Please explain the steps to solve a question like this.
To understand why b = d = 0 if the function is even, we need to consider the definition of an even function.Therefore If P(x) is an even function, then b = d = 0.
What is Polynomial?A polynomial is a mathematical expression that consists of variables and coefficients, combined using the operations of addition, subtraction, and multiplication. It can have one or more terms and can be of any degree.
An even function is a function that satisfies the condition f(x) = f(-x) for all x in the domain of the function.
If P(x) is an even function, then we have P(x) = P(-x) for all x. Substituting -x for x in the expression for P(x), we get:
P(-x) = a(-x)⁴ + b(-x)³ + c(-x)² + d(-x) + e
= a(x⁴) - b(x³) + c(x²) - d(x) + e
Since P(x) = P(-x), we can equate the two expressions for P(x) and P(-x) to get:
a(x⁴) + b(x⁴) + c(x²) + d(x) + e = a(x⁴) - b(x³) + c(x²) - d(x) + e
Simplifying this equation, we get:
2b(x³) + 2d(x) = 0
Since this equation holds for all values of x, we can set x = 0 to get:
2d(0) = 0
which implies that d = 0. Similarly, setting x = 1, we get:
2b(1³) + 2d(1) = 0
2b = 0
b = 0
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a circular piece of glass has a radius of 2.1 meters the glass sells for $7.10 per square meter what is the cost of the glass
Answer:
Step-by-step explanation:
The area of a circle is given by the formula:
A = πr^2
where A is the area and r is the radius.
Substituting the given values, we get:
A = π(2.1 m)^2 = 13.85 m^2
So the total cost of the glass with a price of $7.10 per square meter is:
Cost = Price per square meter x Total area
Cost = $7.10/m^2 x 13.85 m^2 = $98.24
Therefore, the cost of the glass is $98.24.
find the ratio of 15 min and 1 hour
Answer:
1 : 4 minutes.
Step-by-step explanation:
Given: 15 minutes / 1 hour.
First convert 1 hour to minutes:
1 hour = 60 minutes
Then write the fraction:
15 : 60
Finally, simplify it:
1 : 4 minutes
B = 75*
C = 50*
A = ?*
Answer: A = 55* or 55 degrees
Step-by-step explanation:
The interior angles of a triangle always have a sum of 180 degrees.
75 + 50 + x = 180
Solve for x
FInal answer: 55 degrees
hope i explained it :)
Given
Δ
ΔACE with vertices A(2, 1), C(2, 4), and E(5, 1)
and
Δ
Δ BCD with vertices B(2, 3), C(2, 4), and D(3, 3)
a) Find each length in simplest form
AC =
BC =
CE =
CD =
b) < C
≅
≅ < C because
c)
Δ
ΔACE
Δ
ΔBCD because
d) < CBD
< A
a) the lengths of each side:
AC = 3, BC = 1, CE = 3, CD = √2.
b) < C ≅ < C, corresponding angles of congruent triangles.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion,
d) ∠CBD ≅ ∠A, vertical angles.
What is the similarity of a triangle?
If the two sides of a triangle are in the same proportion of the two sides of another triangle, and the angle inscribed by the two sides in both triangles are equal, then two triangles are said to be similar.
a)
AC = √[(2-2)² + (4-1)²] = √9 = 3
BC = √[(2-2)² + (4-3)²] = 1
CE = √[(5-2)² + (1-1)²] = 3
CD = √[(3-2)² + (3-4)²] = √2
b) < C ≅ < C because they are corresponding angles of congruent triangles ΔACE and ΔBCD.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion, since AC = BC, CE = CD and < C ≅ < C.
d) < CBD < A because the point B lies on AC, and therefore < A and < CBD are vertical angles, and by definition, vertical angles are congruent.
Hence, a) the lengths of each side:
AC = 3, BC = 1, CE = 3, CD = √2.
b) < C ≅ < C, corresponding angles of congruent triangles.
c) ΔACE ≅ ΔBCD by Side-Angle-Side (SAS) criterion,
d) ∠CBD ≅ ∠A, vertical angles.
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Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. SAS
C. Not similar
B. AA
D. SSS
109⁰
41°
30⁰
30°
The triangles are similar by the AA similarity criterion since they have two pairs of congruent angles (41° and 109°, and 30°). Therefore, the answer is B. AA.
What is triangle?A triangle is a polygon that has three sides, three vertices, and three angles. It is the simplest polygon in Euclidean geometry and one of the most studied shapes in mathematics. The sum of the three angles in a triangle is always 180 degrees, and the length of one side of a triangle is always less than the sum of the other two sides. There are many different types of triangles, including equilateral triangles (where all sides are equal), isosceles triangles (where two sides are equal), and scalene triangles (where no sides are equal). Triangles are used in many areas of mathematics and science, including trigonometry, geometry, and physics.
Here,
To determine whether the two triangles are similar using AA similarity, we need to compare the angles of both triangles.
Triangle 1 has angles 41°, 30°, and 109°.
Triangle 2 has angles 30°, 41°, and 109°.
We see that the two triangles have two pairs of congruent angles, namely 41° and 41°, and 109° and 109°. Therefore, the two triangles are similar by the AA similarity criterion.
Note that the order of the angles does not matter when comparing triangles for similarity.
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three potential employees took an aptitude test. each person took a different version of the test. the scores are reported below. kaitlyn got a score of 74.5 ; this version has a mean of 68.5 and a standard deviation of 12 . kiersten got a score of 244.8 ; this version has a mean of 210 and a standard deviation of 29 . rebecca got a score of 7.24 ; this version has a mean of 6.7 and a standard deviation of 0.3 . if the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job?
Step-by-step explanation:
kaitlyn score is 6 points above the mean
z-score = 6 / 12 = .5
kiersten score is 34.8 above the mean z-score = 34.8/29 = 1.2
rebecca score is .54 above the mean z -score = .54/ .3 = 1.8
rebecca scored the highest percentile (highes z-score) of the three....the best
Dakota earned $6.00 in interest in Account A and 30.00$ in interest in Account B after months. If the simple interest rate is 4% for Account A and 5% for Account B, which account has the greater principal? Explain.
the principal in Account B is 4.8 times the principal in Account A.
How to solve?
Let the principal in Account A be P and the principal in Account B be Q. Also, let n be the number of months.
From the given information, we have:
Interest earned in Account A = $6.00
Interest rate in Account A = 4%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account A = (P × 4%× n) / 12
Substituting the given values, we get:
6.00 = (P × 4% × n) / 12
P× n = 150
Similarly, we have:
Interest earned in Account B = $30.00
Interest rate in Account B = 5%
Number of months = n
Using the formula for simple interest, we have:
Interest earned in Account B = (Q× 5% × n) / 12
Substituting the given values, we get:
30.00 = (Q× 5% ×n) / 12
Q × n = 720
To compare the principals, we can divide the equation for Account B by the equation for Account A:
(Q × n) / (P× n) = 720 / 150
Simplifying, we get:
Q / P = 4.8
Therefore, the principal in Account B is 4.8 times the principal in Account A.
Since the interest rate in Account B is higher than the interest rate in Account A, we can conclude that the principal in Account B is greater than the principal in Account A.
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