The distance of the end of the trip from the starting point is 193.1321 km.
The ship goes 180 kilometers on bearing after 70 km of subsequent journey.
The starting point in this case is A, and the ending point is C.
We now discover distance AC:
As we can see, a right-angled triangle results.
The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides that make up the right angle is equal to the square of the hypotenuse. This can be expressed mathematically as a^2 + b^2 = c^2, where a and b are the two sides that make up the right angle, and c is the hypotenuse.
Use Pythagoras's principle.
c = √a² + b²
The distance in the Hypotenuse in our case is now.
c = √(70)² + (180)²
c = √4900 + 32400
c = √37,300
c = 193.1321 km
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The complete question is:
A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.
What is the exact area of a circle with a diameter of 12 feet?
367 square feet
817 square feet
324л square feet
1296л square feet
The exact value of the circle is 36π square feet. Option A
How to determine the areaThe formula used for calculating the area of a given circle is expressed with the equation;
A = π(d/2)^2
A = πr²
Such that the parameters are;
A is the area of the circle.π is a constant value of 3.14 r is the radius of the circled is the diameter of the circleThe formula for radius is given as;
radius = diameter/2
divide the values
radius = 6 feet
Substitute the values
Area = 3.14 ×6²
multiply the values
Area = 36π square feet
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A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by
X raysUV radiationGlycosylaseDepurination
Explanation:
A strain of Mycobacterium tuberculosis that is deficient in nonhomologous end joining repair should be more sensitive to damage by X-rays.
Nonhomologous end joining is a DNA repair mechanism that can join two DNA fragments with little or no homology between them. X-rays, which are high-energy electromagnetic waves, can cause damage to DNA by breaking the strands of the double helix.
This damage can be repaired by mechanisms like nonhomologous end joining, so a strain of Mycobacterium tuberculosis that is deficient in this repair mechanism would be more sensitive to damage by X-rays.
UV radiation, glycosylase, and depurination are not directly related to nonhomologous end joining repair and would not have the same effect.
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suppose that alpha and omega have identically sized working-age populations but that total annual hours of work are much greater in alpha than in omega. what are two possible reasons for this difference?
If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
There could be several reasons why the total annual hours of work are much greater in Alpha than in Omega, even though both countries have identically sized working-age populations. Here are two possible reasons:
Differences in labor force participation: It is possible that a larger proportion of the working-age population in Alpha is participating in the labor force than in Omega. Labor force participation refers to the percentage of the working-age population that is either employed or actively seeking employment. If more people in Alpha are working or looking for work, then the total annual hours of work would be higher in Alpha than in Omega.
Differences in productivity: Another possible reason for the difference in total annual hours of work is differences in productivity levels between Alpha and Omega. Even if both countries have the same number of people in their working-age population, the productivity of those workers can vary significantly. If workers in Alpha are more productive than those in Omega, they may be able to accomplish more work in the same amount of time, resulting in more total annual hours of work in Alpha. This could be due to a variety of factors, such as differences in technology, education levels, or infrastructure.
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The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here. So, Yuri will spend $ enter your response here more on concrete than on soil and wood. (Type integers or decimals. )
Yuri will spend $ X more on concrete than on soil and wood.
When answering questions on Brainly, it is important to be factually accurate, concise, and professional.
It is also important to provide a step-by-step explanation of how you arrived at your answer.
The question is asking about the cost of materials for a patio, garden, and deck.
Let's break down the information we have.
Area of the patio = enter your response
Here
Cost of concrete = $ enter your response
Here
Area of the garden = enter your response
here
Cost of soil = $ enter your response
here
Total area of the deck = enter your response
here
Cost of wood = $ enter your response
here
Yuri will spend $ enter your response here more on concrete than on soil and wood.
To find the cost of each material, we need to multiply the area by the cost per unit area.
For example, the cost of concrete would be the area of the patio multiplied by the cost of concrete per unit area.
Let's call the cost per unit area for concrete C, the cost per unit area for soil S, and the cost per unit area for wood W.
Area of patio = P
Cost of concrete = C
Area of garden = G
Cost of soil = S
Total area of deck = D
Cost of wood = W
Yuri will spend X more on concrete than on soil and wood.
To find the values of P, C, G, S, D, and W, we need to use the information given in the question.
However, some values are missing.
We can use the given information to create equations that will help us find these values.
For example, we know that the total area of the deck is the sum of the area of the patio and the area of the garden, so we can write:
D = P + G
Similarly, we can write an equation for the cost of each material.
For example, the cost of concrete is the area of the patio multiplied by the cost per unit area for concrete, so we can write:
C = P * C
Similarly, we can write equations for the cost of soil and wood:
S = G * W, W = D * W
Now we have three equations and three unknowns: P, G, and D. We can solve this system of equations to find these values.
Let's solve for P and G first.
We'll use the equation
D = P + G
to eliminate G from the equations.
C = P * CS = G * WP = D - G
Substitute P = D - G into the first two equations.
C = (D - G) * CW = D * W - G * W
Now we have two equations and two unknowns: D and G.
We can solve for these values.
We'll use the equation
W = D * W - G * W
to eliminate W from the equations.
C = (D - G) * CS = G * SD = P + G = 2G - (W / C)
Substitute D = P + G into the first two equations.
C = P * C + G * CS = G * SW = P + G - DC = P * C + (D - P) * C + (W / C) * C = 2P * C + W
We can now solve for P, G, and D.
P = (C + S + W / C) / 2G = (S + W / C) / 2D = P + G = (C + S + W / C) / 2 + (S + W / C) / 2P = enter your response
here
C = enter your response
here
S = enter your response
here
W = enter your response
here
G = enter your response
here
D = enter your response
here
Now we can find the value of X, which is the difference between the cost of concrete and the combined cost of soil and wood.
X = C - (S + W)X = enter your response.
The area of the patio is enter your response here , so the cost of concrete is $ enter your response here. The area of the garden is enter your response here , so the cost of soil is $ enter your response here. The total area of the deck is enter your response here , so the cost of wood is $ enter your response here.
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Question:
Yuri bought a new house. The diagram shows the layout of his backyard. Yuri is designing improvements that he wants to make. Yuri plans to fill the patio with concrete, the garden with a special soil mixture, and the remaining areas that surround the hot tub with a wood deck. The table shows the costs associated with each project. How much more will Yuri spend on concrete than on soil and wood?
is the real-estate market heating up? to estimate the mean sales price, a realtor in a large city randomly selected 100 home sales from the previous 6 months in her city. these sales prices are displayed in the boxplot.
The truth regarding the conditions for constructing a confidence interval for a population mean for the real estate market is that E. All conditions have been met.
What conditions are needed to construct a confidence interval ?For a confidence interval to be construction, sample should be randomly selected, sample size should be no more than 10% of the population size, and the sampling distribution should be approximately normal. This can be achieved if the sample size is large (typically n ≥ 30) and the data doesn't have strong skewness or outliers.
The question states that the realtor is working in a large city, and it is reasonable to assume that 100 home sales are less than 10% of all homes sold in the previous 6 months in this large city. So, this condition is met.
The realtor has randomly selected 100 home sales, so the random condition is met. All conditions have therefore been met to construct a confidence interval.
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Options for this question include:
The 10% condition is not met. It is not reasonable that 100 < 10% of all homes sold in the previous 6 months in this large city. Random: This condition is not met because the sample was selected from only one city. The Normal/Large Sample condition has not been met because the boxplot is strongly skewed to the right with outliers. The Large Counts condition has not been met because np = 100 and n(1-P) are not both at least 10. All conditions have been met.The length in inches of each side of a square is given by the expression x 2 . the area of the square can be represented by (x 2)2−16=0 when the area is 16 square inches. what is the value of x?
The value of x is 2 inches.
We are given that the area of the square is 16 square inches and can be represented by the expression,
(x+2)^2 - 16 = 0
We can simplify this equation by expanding the square,
x^2 + 4x + 4 - 16 = 0
x^2 + 4x - 12 = 0
Now we can use the quadratic formula to solve for x
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = 4, and c = -12.
Plugging in these values, we get
x = (-4 ± sqrt(4^2 - 4(1)(-12))) / 2(1)
x = (-4 ± sqrt(16 + 48)) / 2
x = (-4 ± sqrt(64)) / 2
x = (-4 ± 8) / 2
We get two solutions,
x = (-4 + 8) / 2 = 2
x = (-4 - 8) / 2 = -6
Since we are dealing with the length of a side of a square, we can eliminate the negative solution and conclude that the value of x is 2 inches.
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The given question is incomplete, the complete question is:
The length in inches of each side of a square is given by the expression x + 2 . the area of the square can be represented by (x+2)^2−16=0 when the area is 16 square inches. what is the value of x?
which of the following statements creates an array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and 56.4 to its elements?
The statement that creates an array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and 56.4 to its elements is: `double[] miles = {27.2, 33.5, 12.8, 56.4}.
An array is a data structure that contains a group of elements of the same data type. It is a collection of variables with the same data type but with different values assigned to them. To create an array in Java, we specify the data type of the elements in the array and the size of the array.The code that creates an array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and 56.4 to its elements is given as follows: double[] miles = {27.2, 33.5, 12.8, 56.4}: The `double[]` specifies the data type of the elements in the array, which is double. The name of the array is miles, and it contains four elements with values 27.2, 33.5, 12.8, and 56.4 respectively.
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DECIMAL MILES can create array of decimal miles.
In computer science, an array is a data structure consisting of a collection
of elements, of same memory size, each identified by at least one array
index or key. An array is stored such that the position of each element can
be computed from its index tuple by a mathematical formula. Two type of
array are there 2D array and 3D array. The following statement creates an
array of decimals named miles and assigns the values 27.2, 33.5, 12.8, and
56.4 to its elements:
decimal[] miles = {27.2, 33.5, 12.8, 56.4};
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When an electric current passes through two resistors with resistance r and s, connected in parallel, the combined resistance, R, can be calculated from the equation
1/R = 1/4+1/s
where R, r , and s are positive. Assume that s is constant.
Find dr/ DR
Is R and increasing or decreasing function of r?
(Enter increasing, decreasing, neither, or both (write both if there are values of r for which R is increasing, and other values for which it is decreasing; enter neither if this is a constant function.)
If we consider the interval aImage for When an electric current passes through two resistors with resistance r and s, connected in parallel, the combrImage for When an electric current passes through two resistors with resistance r and s, connected in parallel, the combb, where does R take on its global maximum and minimum values?
maximum: r=
minimum: r=
(Enter none if there is no global maximum or minimum for this function.)
The combined resistance, R, of two resistors with resistances r and s connected in parallel can be calculated using the equation:
[tex]1/R = 1/r + 1/s[/tex]
When an electric current passes through these resistors, the combined resistance depends on the values of r and s. To analyze the behavior of R with respect to r, we can rewrite the equation as:
[tex]R = (rs)/(r + s)[/tex]
R is a function of r and s, and its behavior depends on the values of r and s. If r and s are positive, the function is neither increasing nor decreasing globally, as it depends on both r and s values. However, for specific values of r and s, the function can be either increasing or decreasing locally.
There is no global maximum or minimum for this function because it depends on the specific values of r and s, and it can take any positive value depending on these resistances. So, the answer is none for global maximum or minimum.
In summary, the behavior of the combined resistance R when an electric current passes through two resistors connected in parallel depends on the values of r and s. It is neither globally increasing nor decreasing and has no global maximum or minimum.
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FARMING A dairy farmer has 2650 dairy cows on his farm. If each dairy cow produces 2320 gallons of milk per year, how much milk does the dairy farm yield in one year? Write your answer in scientific notation.
Answer:
To calculate the total milk yield in one year, we need to multiply the number of dairy cows by the amount of milk each cow produces per year:
Total milk yield = 2650 dairy cows × 2320 gallons of milk per cow per year
Total milk yield = 6,188,000 gallons per year
To write this answer in scientific notation, we need to express the number 6,188,000 as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point to the left until we have a number between 1 and 10, and counting the number of decimal places we moved. In this case, we need to move the decimal point 6 places to the left:
Total milk yield = 6.188 × 10^6 gallons per year
Therefore, the dairy farm yields 6.188 × 10^6 gallons of milk per year.
at 99% confidence, how large a sample should be taken to obtain a margin of error of for the estimation of a population proportion? assume that past data are not available for developing a planning value for . round up to the next whole number.
To estimate a population proportion with a margin of error of 1% and a 99% confidence interval, we would need a sample size of at least 6644 individuals.
The formula to calculate the sample size is:
n = [z² x p(1-p)] / e²
where:
n is the sample size
z is the z-score corresponding to the desired confidence level (in this case, 2.576 for a 99% confidence level)
p is the planning value for the population proportion, which we don't know in this case, so we will assume the worst-case scenario of p=0.5 (which gives us the maximum sample size needed)
e is the desired margin of error
Plugging in the values, we get:
n = [(2.576)² x 0.5(1-0.5)] / (0.01)²
n = 6643.04
Since we need to round up to the next whole number, the minimum sample size needed is 6644.
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Please help, I have an idea on what I think might be the correct answer, but I am not sure.
I would like to see anybody's method on solving this and compare to mine.
Please and Thank You.
The surface area of the triangular prism is 960 units squared.
How to find the surface area of a triangular prism?The surface area of the triangular prism can be found as follows:
surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)
where
b = base of the triangleh =height of the trianglel = height of the prisms₁, s₂ and s₃ are the sides of the triangle.Therefore,
surface area of the triangular prism = 24 × 16 + 9 (20 + 20 + 24)
surface area of the triangular prism = 384 + 9(64)
surface area of the triangular prism = 384 + 576
surface area of the triangular prism = 960 units²
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coupling tetraalkylammonium and ethylene glycol ether side chain to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery
Coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method to enable highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. The side chains of the tetraalkylammonium are modified with the ethylene glycol ether, which is a highly polar solvent, allowing for better solubility in nonaqueous electrolyte solutions. Additionally, the ethylene glycol ether has the ability to modify the stability of the ionic species, preventing aggregation and ensuring the longevity of the battery. This increases the redox capacity and enhances the performance of the flow battery.
The ethylene glycol ether-tetraalkylammonium coupling has been proven to be an effective method for improving the solubility and stability of anthraquinone-based ionic species. For example, it has been observed that the coupling of ethylene glycol ether to anthraquinone-based ionic species enhanced the current density of the battery by more than 3 times. Furthermore, the coupling process has also been found to improve the energy efficiency and storage capacity of the nonaqueous redox flow battery.
Overall, coupling tetraalkylammonium and ethylene glycol ether side chain is an effective method for enabling highly soluble anthraquinone-based ionic species for nonaqueous redox flow battery. This process has been proven to improve the performance of the battery, including current density, energy efficiency, and storage capacity.
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Can the segment form a triangle? Why or why not?
A. 6 + 5 is not greater than twelve
B. Yes 6+5 is equal to twelve
C. No 6+5 is not equal to 12
D. Yes 6+5 equals less than twelve
Answer: b
Step-by-step explanation:
12) solve the equation.
|2a+3| +4=11
Answer:
2=a
Step-by-step explanation:
2a+3+4=11
2a+7=11
2a=11-7
2a=4
a=2
A city has a population of 370,000 people. Suppose that each year the population grows by 4. 75%. What will the population be after 11
years?
The population of the city will be approximately 597,543 people after 11 years.
We can solve this problem using the formula for exponential growth:
[tex]N = P(1 + r)^t[/tex]
where:
N = final population
P = initial population
r = annual growth rate (as a decimal)
t = number of years
In this case, we have:
P = 370,000
r = 0.0475 (since the annual growth rate is 4.75%)
t = 11
Substituting these values into the formula, we get:
[tex]N = 370,000(1 + 0.0475)^{11}[/tex]
Using a calculator, we can simplify this expression to:
N = 597,542.64
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- The Graduates Choice designs and sells two types of class rings, the GPA and the MVP. They
can produce up to 24 rings per day using at most 60 total hours of labor. It takes 3 hours to
make one GPA ring and 2 hours to make one MVP ring. How many of each ring type should be
made daily in order to maximize the company's profit if the profit on the GPA ring is $40 and
the profit on the MVP ring is $35?
The 12 of each type of the ring would give max profit for the company.
How many of each type should be made daily to maximize the company's profit?Let x = number of VIP rings: let y = number of SST rings
:
The total production inequality;
x + y =< 24
y = 24 - x; arranged to plot graph (purple)
:
The labor inequality;
3x + 2y =< 60
2y = 60 - 3x
y = 60/2 - (3/2)x
y = 30 - 1.5x; arranged to plot the graph (red).
From the graph, the 3 corners of the area of feasibility (at or below the lines whichever is lower):
: x/y;.....profit on each type;... total profit
0,24; 40(0) + 35(24) = 0 + 840 = $840
12,12; 40(12) + 35(12) = 480 + 420 = $900
20,0; 40(20) + 35(0) = 800 + 35(0) = $800.
Therefore, the 12 of each type of the ring would give max profit for the company.
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the equations 6x + 5y = 28 and 10x + 14y = 58 represent the cost for lunch and dinner for a family eating out on vacation. if x is the number of adults and y is the number of children, how many adults are in the family?
There are 3 adults in the family by using the method of substitution and elimination.
What is Substitution?Substitution is a method used in mathematics to replace one or more variables in an equation or expression with a value or expression that is equivalent to the variable(s). This is done in order to simplify an equation or expression or to solve for a variable.
What is Elimination?Elimination is a method used in mathematics to solve a system of equations by eliminating one variable. This method involves manipulating the equations in such a way that one of the variables is eliminated, leaving a simpler equation with only one variable that can be solved easily.
In the given question,
Here's how we can solve for x, the number of adults:
Multiply the first equation by 2 to get rid of the coefficient of x in the second equation:
12x + 10y = 56
10x + 14y = 58
Subtract the first equation from the second equation to eliminate y:
10x + 14y - (12x + 10y) = 58 - 56
-2x + 4y = 2
Divide both sides by -2 to isolate x:
x - 2y = -1
x = 2y - 1
Substitute x = 2y - 1 into one of the original equations (let's use the first one) and solve for y:
6x + 5y = 28
6(2y - 1) + 5y = 28
12y - 6 + 5y = 28
17y = 34
y = 2
Substitute y = 2 into the equation x = 2y - 1 to solve for x:
x = 2(2) - 1
x = 3
Therefore, there are 3 adults in the family.
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Shay's sister is 7 years younger than twice her age. The sum of their
ages is 80. How old is Shay?
Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.
what is unitary method ?Mathematicians use the unitary method, also referred to as the "single unit technique," to answer problems involving proportional relationships between two or more quantities. The unitary technique entails determining the value of a single unit or quantity and using that value to calculate the values of other quantities in relation to that unit or quantity. Problems requiring ratios, proportions, percentages, and other related ideas can be solved using this approach.
given
Shay's age will be denoted by the letter S, and her sister's age will be referred to as "Sister".
The first claim informs us of the following:
Sibling = 2S – 7
And based on the second assertion, we can infer that:
Sibling + S = 80
The result of putting the first equation into the second equation is:
S + (2S - 7) = 80
When we simplify this solution, we obtain:
3S - 7 = 80
7 added to both edges gives us:
3S = 87
When we multiply both parts by 3, we get:
S = 29
Since Shay's sibling is 7 years younger than twice her age, Shay is therefore 29 years old.
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(7) The area of a rectangle is 14
square units. It has side lengths a
and b. Given the following value
for a, find b. a = 2 & 1/3
The value of sides b for different value of a in a rectangle are;
a=2 and b=7
a=1/3 and b=42
Define rectangleA rectangle is a type of quadrilateral with four sides and four right angles (90-degree angles). It is a two-dimensional shape with opposite sides that are parallel and equal in length. The opposite sides of a rectangle are also perpendicular to each other, which means they meet at 90-degree angles.
A = l x w, where A is the area, l is the length, and w is the width, calculates the area of a rectangle.
In this case, we are given that the area is 14 square units, so we can set up the equation:
14 = a x b
Given;
a=2
Using this value as a replacement in the formula, we obtain:
14 = (2) x b
b=7
Taking another value of a=1/3
Using this value as a replacement in the formula, we obtain:
14=1/3×b
b=42
Therefore, The value of b for different value of a are;
a=2 and b=7
a=1/3 and b=42
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say that you are given some tpwm and some number of intervals n to specify the smallest ton. if tpwm doubles and ton remains the same, what happens to the resolution, n?
The resolution (n) is an important factor when specifying the smallest ton. If the TPWM (time-proportional width modulation) doubles and the ton (time-on) remains the same, the resolution will also double.
This is because the same amount of time (ton) is distributed over twice the pulses (TPWM).
To better understand this, imagine having 10 slices of a cake and trying to divide them into 2 even halves. You can achieve that by cutting each slice into 2 parts. The same logic applies to TPWM and ton.
TPWM represents the number of “slices” and ton represents the “time” allotted to each slice. When TPWM doubles, resolution (n) doubles as well. This is because twice the number of pulses (TPWM) are spread over the same time (ton), meaning that each pulse gets a smaller amount of time (a higher resolution).
The resolution (n) is inversely proportional to TPWM, meaning that if TPWM increases, resolution decreases, and if TPWM decreases, resolution increases. Thus, when TPWM doubles and ton remains the same, resolution (n) doubles as well.
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based solely on statistical probability from demographic studies, which individual has the greatest likelihood of being a smoker?
Based solely on statistical probability from demographic studies, the individual who has the greatest likelihood of being a smoker is a male aged between 18 to 24 years old.
According to demographic studies, men are more likely to smoke than women. Besides, the smoking rate increases with age, which means individuals aged between 18 to 24 have a higher likelihood of being a smoker than people of other ages.
Therefore, based solely on statistical probability from demographic studies, a male aged between 18 to 24 years old has the greatest likelihood of being a smoker.
It is important to note that statistical probability from demographic studies only shows what is likely or probable to happen but does not guarantee the actual occurrence of the event.
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What is the measure of
∠1 if
∠1 is (8x)
∘ and
∠2 is (2x - 3)
∘?
∠1 + ∠2 = 180
Substituting the given expressions for ∠1 and ∠2:
8x + (2x - 3) = 180
Simplifying and solving for x:
10x - 3 = 180
10x = 183
x = 18.3
Now we can substitute x back into the expression for ∠1 to find its measure:
∠1 = 8x = 8(18.3) = 146.4 degrees.
Therefore, if ∠1 and ∠2 add up to 180 degrees and ∠1 is given as 8x° and ∠2 is given as (2x - 3)°, then ∠1 measures 146.4 degrees
Answer:
<1=146.4
<2=34.6
Step-by-step explanation:
<1+<2=180 degrees
So,
8x+(2x-3)=180
10x-3=180
10x=183
X=18.3
subsitute:
<1=8x
<1=8(18.3)
<1=146.4
<2=2x-3
<2=2(18.3)-3
<2=34.6
MC)
A toy company is building dollhouse furniture. A rectangular door of a dollhouse has a height of 5 centimeters and a width of 3 centimeters. What is the perimeter of the door on a scale drawing that uses the scale 2:8?
the perimeter of the door on the scale drawing is 4 centimeters. A scale drawing is a representation of an object that is drawn to a smaller or larger size than the actual object, but the proportions between the dimensions of the object are maintained.
In this case, we are given a rectangular door of a dollhouse with a height of 5 centimeters and a width of 3 centimeters, and we are asked to find the perimeter of the door on a scale drawing that uses the scale 2:8.
The scale 2:8 means that every 2 units on the scale drawing represent 8 units on the actual object. To find the dimensions of the door on the scale drawing, we can divide both the height and the width by 8 and then multiply by 2, since the scale ratio is 2:8. This gives us the following dimensions on the scale drawing:
Height = (5/8) x 2 = 1.25 centimeters
Width = (3/8) x 2 = 0.75 centimeters
Now, we can use these dimensions to find the perimeter of the door on the scale drawing. The perimeter of a rectangle is given by the formula:
Perimeter = 2 x (Length + Width)
In this case, the length and width of the door are the same as the height and width of the door, respectively. So, we can write:
Perimeter = 2 x (Height + Width)
= 2 x (1.25 + 0.75)
= 2 x 2
= 4
Therefore, the perimeter of the door on the scale drawing is 4 centimeters.
In summary, we can find the dimensions of the door on the scale drawing by dividing the actual dimensions by 8 and multiplying by 2, and we can find the perimeter of the door on the scale drawing using the formula for the perimeter of a rectangle.
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2sin(2x-π÷2)≥√3
[tex]2 \sin(2x - \frac{\pi }{2 } ) \geqslant \sqrt{3} [/tex]
solve it with steps
The inequality trigonometry expression 2sin(2x - π/2) ≥ √3 when solved has a solution of x ≥ 5π/12
How to solve the inequality trigonometry expressionIn the question, we have the following expression
2sin(2x - π/2) ≥ √3
The above expresson is an inequality and a trigonometry expression
So, we have
2sin(2x - π/2) ≥ √3
Divide by 2
sin(2x - π/2) ≥ 1/2√3
Take the arc sin of both sides
2x - π/2 ≥ π/3
Add π/2 to both sides of the expression
2x ≥ π/2 + π/3
Evaluate the like terms
2x ≥ 5π/6
Divide both sides by 2
x ≥ 5π/12
Hence, the solution to the variable x is x ≥ 5π/12
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consider drawing four cards without replacement from a standard deck of cards. what is the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts?
The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts is 4.74%.
The conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, can be calculated using Bayes’ theorem:
P(heart on fourth draw | first three draws are not hearts) = P(heart on fourth draw and first three draws are not hearts) / P(first three draws are not hearts)
To calculate the numerator, we need to find the probability of drawing a heart on the fourth draw and the first three draws being not hearts. Since we are drawing without replacement, the probability of drawing a heart on the fourth draw is 13/49 (there are 13 hearts remaining out of 49 cards remaining). The probability of the first three draws being not hearts can be calculated as:
(39/52) x (38/51) x (37/50) = 0.4372
Therefore, the numerator is:
P(heart on fourth draw and first three draws are not hearts) = (13/49) x (39/52) x (38/51) x (37/50)
P(heart on fourth draw and first three draws are not hearts) = 0.0207
To calculate the denominator, we need to find the probability of the first three draws being not hearts. We already calculated this as 0.4372.
Therefore, the conditional probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is:
P(heart on fourth draw | first three draws are not hearts) = P(heart on fourth draw and first three draws are not hearts) / P(first three draws are not hearts)
P(heart on fourth draw | first three draws are not hearts) = 0.0207 / 0.4372
P(heart on fourth draw | first three draws are not hearts) ≈ 0.0474
So the probability of drawing a heart on the fourth draw, given that the first three cards are not hearts, is approximately 0.0474 or 4.74%.
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Triangle ABC is shown below. Describe how we could use circles to determine whether this is an equilateral triangle.
In Triangle ABC, we can draw a circle around each vertex of the triangle.
If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.
What is radii?Radii is the plural form of radius. It is half of the diameter and the length of the radius is used to calculate the area and circumference of the circle.
To determine whether a triangle is an equilateral triangle, we can use circles.
In this method, we draw three circles, one around each vertex of the triangle.
We then measure the radii of the circles, ensuring that they are all equal. If the radii of the three circles are equal, then the triangle is an equilateral triangle.
In Triangle ABC, we can draw a circle around each vertex of the triangle. Then, we could use a measuring tool to measure the radii of each circle. If the radii of all three circles are equal, then Triangle ABC is an equilateral triangle.
This method of using circles to determine whether a triangle is an equilateral triangle is simple and efficient. It does not require any complex calculations, and it is easy to understand.
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assume that the width of a ci for the mean of a normal distribution is 3.4. you know that the population variance is 22, the sample average is 25 and the sample size is 15. what is the confidence level of the ci?
The confidence level of the CI is 95%.
The formula for the confidence interval of a normal distribution is
CI = X ± Zα/2 × σ/√n
Where
CI is the confidence interval
X is the sample mean
Zα/2 is the Z-score corresponding to the desired confidence level α/2
σ is the population standard deviation
n is the sample size
We know that the width of the confidence interval is 3.4, so
3.4 = 2 × Zα/2 × σ/√n
We also know that σ = √22 = 4.69, X = 25, and n = 15. Plugging these values into the equation and solving for Zα/2
3.4 = 2 × Zα/2 × 4.69/√15
Zα/2 = 1.96
The Z-score corresponding to a 95% confidence level is 1.96. Therefore, the confidence level of the CI is 95%.
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what is the total weight of a shopping bag which contains 2kg of potatoes,1kg of apple ,half a kilogram of tomatoes and 3/4of grape?
The equatiοns, 1 unit equals 10 οn the x-axis and 10 οn the y-axis.
What are equatiοns?Equatiοns are statements in mathematics that have twο algebraic expressiοns οn either side οf the equals (=) sign.
It shοws that the expressiοns printed οn the left and right sides have an equal relatiοnship.
In any mathematical equatiοn, we have LHS = RHS (left hand side = right hand side).
Equatiοns can be sοlved tο find the value οf an unknοwn variable that represents an unknοwn quantity.
If there is nο "equal tο" symbοl, a statement is nοt an equatiοn.
When twο expressiοns have equal values, a mathematical statement knοwn as an equatiοn includes the symbοl "equal tο" between them.
Accοrding tο οur questiοn-
Alsο, cοst οf 4 kg apples and 2 kg οf grapes are ₹ 300. can be represented as,
4x + 2y = 300
2(2x + y) = 300
2x + y = 150 --- Equatiοn(2)
Therefοre, the algebraic representatiοn fοr equatiοn(1) is:
2x + y = 160
y = 160 - 2x
And, the algebraic representatiοn fοr equatiοn(2) is:
2x + y = 150
y = 150 - 2x
Hence, The equatiοns, 1 unit equals 10 οn the x-axis and 10 οn the y-axis.
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Which line models the data points better and why? (1 point) Oblue, because it is longer Oblue, because the data points are all close to the line Ored, because it goes through one of the points Ored, because there are three points above the line and three points below the line
The line that models the data points better is Red, because it goes through one of the points.
What is data in math?Data is information that has been organized and processed in a meaningful way. It is the raw material of digital systems and the foundation of all computer-based operations. It can be stored, retrieved, and manipulated in a variety of ways, and it is used to generate insights, drive decisions, and build solutions. Data can come from a variety of sources, including manual entry, sensors, databases, and the internet.
This is a better model than Blue, because the data points are not all close to the line, and having the line go through one of the points ensures that the line is better representing the points. Additionally, having three points above the line and three points below the line helps to make the line a better model of the data points, as it is more evenly distributed.
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Whic expression is not equivalent to 3x-(4-×)
The expression 3x-(4-x) is equivalent to 4x-4
The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.
To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:
3x - (4 - x) = 3x - 4 + x
Now we can combine the like terms (3x and x) to get:
3x - 4 + x = 4x - 4
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The given question is incomplete, the complete question is:
Which expression is equivalent to 3x-(4-x)?