The smallest angle is 5° when each of those angles was divided into 5 equal parts.
What is an Angle ?In Geometry, an angle is a figure which is produced by two rays, which share a common point called a vertex. The two rays stand in for the angle's two sides. The Roman word "Angulus," which means "corner," is where the term "angle" originates. The intersection of two curves in this plane results in the angles. Angles of several kinds can be generated on a planar surface. As follows:
Acute Angle
Obtuse Angle
Right Angle
Reflex Angle
Straight Angle
Full Angle
Obtuse Angle :An angle greater than 90° but less than 180° is referred to as a "obtuse angle." An obtuse angle is between a right angle and a straight angle.
Now in this question,
Starting with an obtuse angle of 150°, bisecting it gives two angles of 75° each.
Trisecting each of these angles gives three angles of 25° each.
Dividing each of these angles into 5 equal parts gives angles of 5° each.
Therefore, the smallest angle is 5°.
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Please help and answer A and B!
a) The value of the bulldozer at any time t should be given by the equation,
V = 140500- 5600t
b) The value of the bulldozer after 7 years is $1,01,300
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a)To answer the problem above, we make the assumption first that the depreciation is a straight-line method in order to solve for the depreciation rate.
d = (140500 - 17300)/ 22 = 5600
The value of the bulldozer at any time t should be given by the equation,
V = 140500- 5600t
b) Substitute t=7 into the equation
V = 140500- 5600(7)
= 140500- 39200
= 1,01,300
The value of the bulldozer after 7 years is $1,01,300
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Decide whether Rolle's Theorem can be applied to f(x) = x2 - 3 on the interval [-2, 2]. If Rolle's Theorem can be applied, find all value(s) of c in the interval such that f '(c) = 0. Rolle's theorem can be applied; c = 0
Rolle's theorem can be applied; c = -2, 2
Rolle's theorem cannot be applied because f '(c) ≠ 0
Rolle's theorem cannot be applied because f(-2) ≠ f(2)
Therefore , the solution of the given problem of function comes out to be the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.
Explain Function.The study of numbers and their variable, as well as in out environment, architecture, and both real and imagined places, are all covered in the mathematics curriculum. A function range illustrates visually how the amounts of the inputs and the corresponding outputs for each are related. Simply stated, a function is a set of inputs that, when combined, produce specific outputs for each input. Each position is given a locale, region, or range.
Here,
Rolle's Theorem can be applied to $f(x) = x^2 - 3$ on the interval [-2, 2]. This is because f(x) satisfies the following conditions of Rolle's Theorem:
1 ) f(x) is continuous on the interval [-2, 2]
2 ) f(x) is differentiable on the interval (-2, 2)
3) f(-2) = 1 and f(2) = 1
Since f(-2) = f(2), there must exist at least one point c in the interval (-2, 2) such that f'(c) = 0.
Taking the derivative of f(x) with respect to x, we get f'(x) = 2x. Setting f'(c) = 0, we have:
2c = 0
Solving for c, we get c = 0.
Therefore, the value of c for which f'(c) = 0 in the interval [-2, 2] is c = 0.
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The area of the circle is 4pix^2+12pix+9pi what is the least possible integer value of x for the circle to exist
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
What is the area of the circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle. Then the area of the circle will be
A = πr² square units
The area of the circle is 4π x² + 12πx + 9π. Then the radius is given as,
A = 4π x² + 12πx + 9π
πr² = π [(2x)² + 2 · 2x · 3 + 3²]
r² = (2x + 3)²
r = 2x + 3
The value of the radius should be more than zero. Then we have
r > 0
2x + 3 > 0
x > - 3/2
The expression for the radius of the circle is 2x + 3. And the least possible integer value of x for the circle to exist will be greater than - 3/2.
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The complete question is given below.
The area of a circle is 4π x 2 + 12πx + 9π.
a. What is an expression for the radius of the circle?
b. What is the least possible integer value of x for the circle to exist? Explain.
Two items are omitted from each of the following summaries of balance sheet and income statement data for two proprietorships for the year 2022, Greene’s Goods and Solar Enterprises.
Greene’sGoods
SolarEnterprises
Beginning of year:
Total assets
$110,000
$129,000
Total liabilities
85,000
(c)
Total owner’s equity
(a)
80,000
End of year:
Total assets
160,000
180,000
Total liabilities
120,000
50,000
Total owner’s equity
40,000
130,000
Changes during year in owner’s equity:
Additional investment
(b)
25,000
Drawings
37,000
(d)
Total revenues
220,000
100,000
Total expenses
175,000
60,000
The missing amounts are a) $79,000, b) $22,000, c) $51,000, d) $15,000 and e) $6,000.
We have,
The theory used in this question is the basic accounting equation which states that Assets = Liabilities + Equity.
This equation can be used to determine the missing amounts in the summaries of Greene's Goods and Solar Enterprises.
Step 1: Start with the beginning of year data for Greene's Goods. We know that the Total Assets = $110,000, Total Liabilities = $85,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.
Assets = Liabilities + Equity
110,000 = 85,000 + Equity
Equity = 25,000
Step 2: Now look at the ending of year data for Solar Enterprises. We know that the Total Assets = $180,000, Total Liabilities = $50,000 and that the Total Owner's Equity is missing. We can use the basic accounting equation to solve for Total Owner's Equity.
Assets = Liabilities + Equity
180,000 = 50,000 + Equity
Equity = 130,000
Step 3: Lastly, look at the changes in owner's equity for each proprietorship. For Greene's Goods, we know that Additional Investment = $7,000 and Drawings = $37,000. We can use the basic accounting equation to solve for the missing amount.
Change in Equity = Additional Investment + Drawings
Change in Equity = 7000 + 37000
Change in Equity = $44,000
For Solar Enterprises, we know that Additional Investment
= $25,000 and Drawings = $15,000.
We can use the basic accounting equation to solve for the missing amount.
Change in Equity = Additional Investment + Drawings
Change in Equity = 25000 + 15000
Change in Equity = $40,000
Therefore, the missing amounts are:
a) $79,000
b) $22,000
c) $51,000
d) $15,000
e) $6,000
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Write the slope-intercept form of the equation of the line described.
2) through: (4, 3), parallel to x=0
quick caveat, there's no slope-intercept form per se for a vertical line, Check the picture below.
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U = 1, 2, 3, 4, 5, 6, 7, 8, 9
A = 1, 2, 5, 6
B = 2, 3, 4, 6, 7
C = 5, 6, 7, 8
Find ∪∩A′BC′.
The elements in C U (B' ∩ A') is {5, 6, 7, 8, 9}.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, and the complement of sets.
We have,
U = {1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 5, 6}
B = {2, 3, 4, 6, 7}
C = {5, 6, 7, 8}
Now,
A' = U - A = {3, 4, 7, 8, 9}
B' = U - B = {1, 5, 8, 9}
C' = U - C = {1, 2, 3, 4, 9}
Now,
(B' ∩ A')
= {1, 5, 8, 9} ∩ {3, 4, 7, 8, 9}
= {8, 9}
And,
C U (B' ∩ A')
= {5, 6, 7, 8} U {8, 9}
= {5, 6, 7, 8, 9}
Thus,
C U (B' ∩ A') = {5, 6, 7, 8, 9}
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The complete question:
Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows.
U = 1, 2, 3, 4, 5, 6, 7, 8, 9
A = 1, 2, 5, 6
B = 2, 3, 4, 6, 7
C = 5, 6, 7, 8
Find C U (B' ∩ A').
six sigma in 9 minutes | what is six sigma? | six sigma explained | six sigma training | simplilearn
Six Sigma is a data-driven methodology for process improvement that aims to minimize defects and reduce variation in processes.
Explanation of six sigma.Six Sigma is a data-driven methodology for process improvement that aims to minimize defects and reduce variation in processes. It is a systematic approach to quality management that uses data and statistical analysis to identify and eliminate the root causes of defects and minimize errors in processes.
Six Sigma is based on the DMAIC (Define, Measure, Analyze, Improve, Control) methodology, which involves the following steps:
Define: Identify the problem and determine the goals of the project.
Measure: Gather data and establish a baseline for the process.
Analyze: Use statistical tools and techniques to understand the sources of variation in the process.
Improve: Develop and implement solutions to eliminate the sources of variation and reduce defects.
Control: Monitor and control the process to ensure sustained improvement.
Six Sigma uses a range of tools and techniques, including process maps, statistical analysis, and design of experiments, to achieve its goals. It is designed to be a highly disciplined approach to process improvement, and Six Sigma practitioners must be trained and certified to use the methodology effectively.
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ASAP!! Please help!!
If on the scale of a map, 3/4 inch equals 72 miles, what is the actual distance between two cities that are 3 7/8 inches apart on the map?
Answer:
The actual distance between two cities that are 3 7/8 inches apart on the map is 279 miles.
Step-by-step explanation:
To find the actual distance between two cities, we need to convert the distance on the map to miles. The scale of the map is 3/4 inch equals 72 miles, which means 1 inch on the map is equal to 72/3=24 miles.
So, the actual distance between two cities on the map that are 3 7/8 inches apart is 24 * 3 7/8 = 279 miles.
The coordinate plane shown below is a graph of a relation.
What is the range of the graph?
The range of the function, given the graph of a relation, can be found to be −2 ≤ y ≤ 7 .
How to find the range of a graph ?Graphs can be used to determine a function's domain and range. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.
The range here would therefore be the y - values that the relations fall within. The lowest y - value is - 2 as no relation goes below this. The highest y - value is 7.
The range is therefore -2 ≤ y ≤ 7.
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IS THIS CORRECT PLEASE HELP MEEEEEEEEEE
The following statements are either true or false;
Chemicals in the environment can cause mutation - TrueDifferences in characteristics within a specie is known as variation - TrueFossils cannot be dated - FalseIf an organism cannot adapt fast enough, they may become extinct - TrueOrganisms evolve because of natural selection - True What is mutation?Mutation can be defined as the altering or the change in the DNA sequence or arrangement of a cell.
variation can be defined as any difference between cells, organisms, or groups of organisms of any species caused by genetic differences or environmental factors.
Fossils refers to the remains of plants and animals whose bodies were buried in sand, mud, seas, lakes and rivers over a long period of time.
Therefore, the statement Fossils cannot be dated is false because fossils can be dated to upto 10,000 years ago.
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h(x)=-x+3 complete the function table
Answer:
Here is the function table for the given equation:
x H(x)
1 2
2 1
3 0
4 -1
5 -2
Note: The table shows the result of the equation H(x) = -x + 3 for different values of x.
Step-by-step explanation:
The vector [-14,-7,19] is a linear combination of vectors [-3,-3,-3] and [10,9,-10] if and only if the matrix equation Ax = b has a solution x where A = [? ?] and b = [?] [? ?] [?] [? ?] [?]T
A = [[-3, 10], [-3, 9], [-3, -10]], b = [-14, -7, 19] Ax = b's matrix equation has a solution in the form of T. x.
Only if the matrix equation Ax = b has a solution x is the vector [-14,-7,19] a linear combination of the vectors [-3,-3,-3] and [10,9,-10]. The vector [-14,-7,19] must be transposed for this to hold true, and A must be the matrix of coefficients of the linear combination of the two vectors. As a result, A is a 3x2 matrix and its formula is as follows: A = [[-3, 10], [-3, 9], [-3, -10]], and b = [-14, -7, 19]T. The vector [-14,-7,19] is a linear combination of the two vectors [-3,-3,-3] and [10,9,-10] if there is a solution x to the matrix equation Ax = b.
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There are 12 inches in 1 ft. what fact family would you use to find the number of inches in 2 ft.
The offered statement states that there's 12 inches throughout 1 foot and 24 inches in 2 feet.
What does inch serve?In the United States, Quebec, and the United Kingdom, the inch is a widely used conventional measure of length. In Japan, particularly for display screens, it is utilized for electrical components as well. The inch is also a commonly-used informal unit of measurement for display screens throughout most of continental Europe. Half, quarter, eighth, and sixteenths are the minor fractions that make up an inch. The size of both the line indicating each lowers as the sum or length does. Millimeters are used to divide centimeters (10 per centimeter).
In 1 feet there are 12 Inches.
12 inches/foot * 2 feet = 24 inches
So, 2 feet is equal to 24 inches.
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2
Ghana Railways Co-operation has 20 trains for its operation. It is observed that x trains can
accommodate 2 passengers, y trains 3 passengers and z trains 5 passengers. However, the total
number of passengers always present at Ghana Railways is 64. During market day, 3 of x trains, 2
of y trains and 4 of 2 trains for a total of 10 trains were used. Determine the values of x, y and z.
The number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.
What do you mean by equation?It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.
Let x, y and z be the number of trains that can accommodate 2 passengers, 3 passengers and 5 passengers, respectively.
From the information given, we have:
x + y + z = 20 (the total number of trains)
2x + 3y + 5z = 64 (the total number of passengers)
We also know that 10 trains were used during market day:
3 of the x trains, 2 of the y trains and 4 of the z trains.
So, we have:
2x + y + 5z = 10
Solving these three equations simultaneously, we can find the values of x, y and z:
Subtracting the first equation from the third equation:
0 + y + 4z = -10
y + 4z = -10
Subtracting 2 times the first equation from the second equation:
-x + 3y + 4z = 32
y + 4z = 42
Subtracting the last two equations:
x = 32
Substituting the value of x back into the first equation:
32 + y + z = 20
y + z = -12
Substituting the value of y and z back into the third equation:
2x + y + 5z = 10
64 + y + 5z = 10
y + 5z = -54
Solving these two equations simultaneously, we can find the values of y and z:
Subtracting the second equation from the last equation:
4z = -44
z = -11
Substituting the value of z back into the second equation:
y + 5z = -54
y - 55 = -54
y = 1
Therefore, the number of trains that can accommodate 2 passengers is x = 32, the number of trains that can accommodate 3 passengers is y = 1, and the number of trains that can accommodate 5 passengers is z = -11.
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In 2008, the per capita consumption of soft drinks in Country A was reported to be 18.88 gallons. Assume that the per capita consumption of soft drinks in Country A is approximately normally distributed, with a mean of 18.88 gallons and a standard deviation of 4 gallons. Complete parts (a) through (d) below.
a. What is the probability that someone in Country A consumed more than 15 gallons of soft drinks in 2008?
b. What is the probability that someone in Country A consumed between 5 and 9 gallons of soft drinks in 2008?
c. What is the probability that someone in Country A consumed less than 9 gallons of soft drinks in 2008?
d. 99% of the people in Country A consumed less than how many gallons of soft drinks?
On solving the provided question, we can say that Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\ = 0.9645 and Probability(5<x<9) = P(x<9) - P(x<5) = 0.0101 and P(x<9) = 0.0106
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Probability(x>11) = 1 - P(x[tex]\leq 11[/tex])\
= 0.9645
Probability(5<x<9) = P(x<9) - P(x<5)
= 0.0101
P(x<9) = 0.0106
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In exercises 17-20, approximate the logarithm using the properties of logarithms, given the values logb2 = 0.3562, logb3 = 0.5646, and logb = 0.8271. Round your result to four decimal places.
I only need 19 and 20!
19. logb 16/25
20. logb [tex]\sqrt{3}[/tex]
The solution of the logarithmic expressions will be:-
19) 2logb4 - 2logb5
20) (1/2)logb (3)
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the two expressions are logb 16/25 and logb √3.
The expressions will be solved as:-
E = logb 16/25
E = logb 16 - logb 25
E = logb 4² - logb 5²
E = 2logb 4 - 2logb 5
The second expression will be solved as:-
E = logb √3.
E = ( 1 / 2 ) logb 3
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Yemi sold 100 books at ₦4.25each for a publishing company that gives 12%commission. how many commission would he get
The amount of commission Yemi gets is, ₦51
What is the percentage?Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".
Given that,
Yemi sold 100 books at ₦4.25 each,
So,
the total sales revenue is,
⇒ 100 x ₦4.25
⇒ ₦425
The publishing company gives a 12% commission on sales,
So, Yemi's commission would be,
⇒ 12/100 x ₦425
⇒ ₦51
Therefore, Yemi would get a commission of ₦51.
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kenneth wants to solve the system of equations shown below he made two
tables showing the value if y for different values of x
The solutions to the system of equations are the values of x for which f(x) and g(x) have the same value according to the table.
How to obtain the solution to the system of equations?When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.
At these intersections point, the functions have the same numeric value, which are the points looked at to find the solution on a table.
From the table given by the image presented at the end of the answer, the solutions are given as follows:
x = 1, as both f(x) and g(x) have a numeric value of 14 at x = 1.x = 9, as both f(x) and g(x) have a numeric value of 6 at x = 9.Missing InformationThe problem is incomplete, hence the solution was given in general terms, with an example problem solved.
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At first, Mrs. Hanrahan's students thought that a linear model might describe the relationship between a pendulum's length and its period pretty well. After fitting a least-squares regression model to data, they decided that a better model be available. Perform this analysis yourself, and explain why the students didn't favor the linear model.
The relationship between pendulum length and period is nonlinear. As the period is dependent on the square root of the length.
To anatomize this relationship, the scholars would need to gather data on pendulum length and period, also fit a regression model.However, the residuals from the model would be erratically distributed around zero, If the relationship is direct.
If the relationship is nonlinear, the residuals would parade a pattern, indicating that a direct model is not the swish fit. In this case, a nonlinear model analogous as the square root of pendulum length would give a better fit for the data. The scholars probably set up that the residuals from the direct model were not erratically distributed, hence they didn't favor the direct model.
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A radio-controlled helicopter sells for $20, but needs a lithium battery that costs 25% of that price. A sales tax of 6% will be added to the cost of both items. What is the total cost of the helicopter, battery and tax? Complete the explanation.
Answer:
$26.50
Step-by-step explanation:
Helicopter is $20.
The battery is 25% of 20.
25% of 20
= .25 • 20
= 5
The battery will be $5.
The total purchase will be 20 + 5, that is,
$25
Calculating the tax:
6% of $25
= .06 • 25
= 1.5
Add the tax onto the total.
$25 + $1.50
= 26.50
The helicopter, battery and tax all adds up to $26.50
Pre-calc. WIll give brainliest
Answer:
[tex]S_{18}=-792[/tex]
Step-by-step explanation:
The given arithmetic series is:
24 + 16 + 8 + ...From inspection of the given series, the first term is 24.
The common difference is the difference between consecutive terms.
Therefore, the common difference of the given series is -8 as each term is 8 less than the previous term.
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
To find the sum of the first 18 terms of the given series, substitute a = 24, d = -8 and n = 18 into the sum formula.
[tex]\implies S_{18}=\dfrac{1}{2}(18)\left[2(24)+(18-1)(-8)\right][/tex]
[tex]\implies S_{18}=9\left[48+(17)(-8)\right][/tex]
[tex]\implies S_{18}=9\left[48-136\right][/tex]
[tex]\implies S_{18}=9\left[-88\right][/tex]
[tex]\implies S_{18}=-792[/tex]
Therefore, the sum of the first 18 terms of the given arithmetic series is -792.
The ratio of boys to girls on a softball team was 5:3. For every 35 girls how many ratio of boys will be there?
Answer:
let the boys and girls be 5x and 3x
the ratio of boys to girls= 5:3
the total girls = 35
the ratio of boys to girls = the total girls
5 =35
3 x
5x = 105
x= 105÷5
x= 25
5x= 5×25= 125
3x= 3× 25 = 75
The graph of the exponential function f is shown. Find f(-7)
The value of f(-7) from the graoh is 1/128
How to determine unknown point on exponential graphExponential function typically refers to the positive-valued function of a real variable, although it can be extended to complex numbers or generalized to other mathematical objects like matrices.
From the given graph, we need to determine then value f(-7). The function f(-7), is the equivalent value on the y-axis if the value of x is -7.
The standard exponential equation is y = ab^x
Using the coordinate points (0, 1) and (-2, 4), the resulting equations are:
1 = ab^0
4 = ab^-2
From equation 1, a = 1
4 = b^-2
b^2 = 1/4
b = 1/2
The exponential function will be y = (1/2)^x
f(-7) = (1/2)^-7
f(-7) = 1/128
Hence the resulting value of f(-7) is 1/128
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explain why A*B*C and (A*B)*C are not same
Suppose that 3 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 53 cm.
(a) How much work is needed to stretch the spring from 41 cm to 45 cm? (Round your answer to two decimal places.)
_____ J
(b) How far beyond its natural length will a force of 30 N keep the spring stretched? (Round your answer one decimal place.)
_____ cm
a ) Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J
b ) 1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.
A spring has a spring constant k,
It takes force kx to extend the spring's length.
A spring stretched length x has energy kx²/2.
Work of 3J gave the spring energy k(53-36)²/2.
Therefore,
3 = k(53-36)²/2
k = 6/289 N/cm
Work is needed to stretch the spring from 41 cm to 45 cm
At 41 cm the spring has energy k(41-36)²/2.
At 45 cm the spring has energy k(45-36)²/2.
The extra energy is given by,
(6/289)(45-36)²/2 - (6/289)(41-36)²/2
= (6/289) * 81/2 - (6/289) * 25/2
= 243/289 - 75/289
= 168/289
= 0.58J
Work is needed to stretch the spring from 41 cm to 45 cm is 0.58J
The natural length will a force of 30 N keep the spring stretched,
30 = kx
x = 30/k
= 1445 cm
1445 cm far beyond its natural length will a force of 30 N keep the spring stretched.
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What is the smallest integer value for IK for which parallelogram IJKL will have an obtuse angle at J ? A. 12 B. 13 C. 14 D. 15
The smallest integer value for IK is (c) 14
How to determine the smallest integer valueFrom the question, we have the following parameters that can be used in our computation:
The parallelogram
The value of IK can be calculated as
IK^2 = 5^2 + 12^2 - 5 * 12cos(J)
IK^2 = 169 - 60cos(J)
If J is obtuse, then cos(J) is a negative value,
This means that IK^2 must be greater than 169 and therefore IK must be greater than 13.
The smallest integer value greater than 13 is 14,
So your answer is (c). IK = 14
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A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row. If a person is aiming to park in first row, what is his probability in decimal form of getting a parking spot?
The probability in decimal form of getting a parking spot is, 0.2
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
A parking lot is arranged with 9 parking spots in the first row, 15 parking spots in the second row, and 21 parking spots in the third row.
Hence, Total parkin spots = 9 + 15 + 21
= 45
And, Number of spots in first row = 9
Thus, The probability in decimal form of getting a parking spot when a person is aiming to park in first row is,
⇒ 9 / 45
⇒ 1/5
⇒ 0.2
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Two ordinary fair dice are thrown. The resulting score is found as follows.
• If the two dice show different numbers, the score is the smaller of the two numbers.
• If the two dice show equal numbers, the score is 0.
(i) Draw up the probability distribution table for the score.
The probability distribution table is shown below
How to determine the probability distribution tableFrom the question, we have the following parameters that can be used in our computation:
Dice = 2
This means that
Sample size = 6 * 6
Sample size = 36
So, the number of outcomes is 36
To determine the distribution table, we need to identify that the dice are distinct.
This means that (1, 2) and (2, 1) are not the same outcomes
We can create a probability distribution table for the score by listing all possible outcomes and their probabilities, and then determining the score for each outcome based on the rules given.
So, we have
Outcomes Probability
(1, 1) 1/36
(1, 2) 1/36
(1, 3) 1/36
(1, 4) 1/36
(1, 5) 1/36
(1, 6) 1/36
........
(6, 1) 1/36
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what is 4+4?????????????????????????????????????
Answer:
Step-by-step explanation:
uhhhhh 8 lol
Use an equation to find the value of k so that the line that passes through (k,4) and (3,-2) has a slope of m=-1
K=
Step-by-step explanation:
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