The required probability is obtained as:
(a) P(X^2 < 1) = 0.8413.
(b) P(X^2 + Y^2 < 1) = 0.7854.
(a) We know that X^2 follows a chi-squared distribution with 1 degree of freedom, which can be written as X^2 ~ chi-squared(1). Therefore, we can find P(X^2 < 1) as:
P(X^2 < 1) = P(Z < √1) (where Z ~ chi-squared(1))
Since the square of a standard normal distribution is a chi-squared distribution with 1 degree of freedom, we can rewrite the above equation as:
P(X^2 < 1) = P(Z < 1) (where Z ~ N(0,1))
Using a standard normal distribution table or calculator, we can find that P(Z < 1) = 0.8413. Therefore, P(X^2 < 1) = 0.8413.
(b) We can rewrite X^2 + Y^2 < 1 as the inequality r^2 < 1, where r is the distance from the origin to the point (X,Y) in the xy-plane. Therefore, we need to find the probability that the point (X,Y) falls within the unit circle centered at the origin.
We can use polar coordinates to express X and Y as:
X = Rcosθ
Y = Rsinθ
where R is the distance from the origin to (X,Y), and θ is the angle between the positive x-axis and the line connecting the origin and (X,Y). Since X and Y are independent N(0,1) random variables, R^2 = X^2 + Y^2 follows a chi-squared distribution with 2 degrees of freedom, which can be written as R^2 ~ chi-squared(2).
Therefore, we can find P(X^2 + Y^2 < 1) as:
P(X^2 + Y^2 < 1) = P(R^2 < 1) (where R^2 ~ chi-squared(2))
Using the cumulative distribution function (CDF) of the chi-squared distribution with 2 degrees of freedom, we can find that:
P(R^2 < 1) = 0.7854
Therefore, P(X^2 + Y^2 < 1) = 0.7854.
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The number of hours, x, Ryan rides his bike and the total number of miles, y, he rides is a lineadrelationship. Ryan has already ridden 5 miles, and he can ride at a constant rate of(12 miles per hour. Write an equation relating × hours and y miles. Then predict how many minutes will pass for Ryan to have traveled a total of 60 miles.
Answer: If x represents the number of hours that Ryan rides his bike, and y represents the total number of miles that he rides, we can write the equation relating x and y as:
y = 12x + 5
This is a linear equation in slope-intercept form, where the slope is 12 (the rate at which Ryan rides, in miles per hour) and the y-intercept is 5 (the number of miles Ryan has already ridden).
To predict how many minutes it will take for Ryan to ride a total of 60 miles, we can substitute y = 60 into the equation and solve for x:
60 = 12x + 5
55 = 12x
x = 55/12
To convert this to minutes, we need to multiply by 60, since there are 60 minutes in an hour:
x (in minutes) = (55/12) * 60
x (in minutes) ≈ 275
Therefore, it will take Ryan approximately 275 minutes (or 4 hours and 35 minutes) to ride a total of 60 miles.
Step-by-step explanation:
Suppose a single trial experiment results in one of three mutually exclusive events, A, B, or C. It is known that P(A) = 0.3, P(B) = 0.6, and P(C) = 0.1. Find the probability P(ANC) Answer: Question 2 Not yet answered Points out of 2.00 P Flag question Refer to the previous question. Find the probability P(AUB). Answer:
intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9Hence, P(AUB) = 0.9.
Probability of P(ANC)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C). Given, P(A) = 0.3,P(B) = 0.6,P(C) = 0.1
Therefore, P(A U B U C) = P(A) + P(B) + P(C) = 0.3 + 0.6 + 0.1 = 1Now, P(ANC) = 1 - P(A U B U C) = 1 - 1 = 0
Probability the intersection of A and B events, P(A ∩ B) is 0. So, P(A U B) = P(A) + P(B) = 0.3 + 0.6 = 0.9
Hence, P(AUB) = 0.9.ility of P(AUB)We know that events A, B and C are mutually exclusive.
Therefore, if A, B, and C are mutually exclusive events, then P(A U B U C) = P(A) + P(B) + P(C)
Now, we need to find P(AUB). If two events A and B are not mutually exclusive events, then the probability of their union P(A U B) can be found as follows; [tex]P(A U B) = P(A) + P(B) - P(A ∩ B)[/tex]We know that events A, B and C are mutually exclusive.
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In triangle JKL, m/J = (8x+6)°, m/K = (2x + 2)°, and m/L= (4x + 4)°. Find
m/L.
The value of the angle m<L is 52 degrees
How to determine the value
Following the side angle theorem of triangles, we have that the sum of the angles in a given triangle is equal or equivalent to 180 degrees.
From the information given, we have that;
m/J = (8x+6)°m/K = (2x + 2)° m/L= (4x + 4)°Now, equate the angles to 180 degrees, we have;
m<J + m<K + m<L =180
substitute the values into the equation
8x + 6 + 2x + 2 + 4x + 4 = 180
collect the like terms, we have;
8x + 2x + 4x = 180 - 12
add or subtract the values
14x = 168
Make 'x' the subject
x = 12
For m<L = 4x + 4 = 4(12) + 4 = 52 degrees
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Discount an asset promising $200, 4 years from now back to day at a discount rate of 7% percent
Answer:
Step-by-step explanation:
As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.
We may use the present value calculation to discount an item that will be worth $200 in four years back to today at a 7% discount rate:
PV equals FV / (1 + r)n
where n is the number of periods, r is the discount rate, PV is the present value, and FV is the future value.
If we substitute the values provided, we get:
PV = 200 / (1 + 0.07), divided by four, results in PV of $152.57.
As a result, with a discount rate of 7%, the present value of an item that will be worth $200 in four years is roughly $152.57.
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Which conic section is formed when a plane intersects the central axis of a double-napped cone at a 90° angle?
The conic section that formed when a plane intersects the central axis of a double-napped cone at a 90° angle is circle
When a plane intersects the central axis of a double-napped cone at a 90° angle, the resulting conic section is a circle.
To understand why this is the case, we can first consider the properties of a double-napped cone. A double-napped cone is formed by rotating a straight line, called the generatrix, around an axis that intersects the line at a fixed point, called the vertex. The resulting surface consists of two parts, each of which is a circular cone.
Now, let us imagine a plane that intersects the central axis of the double-napped cone at a 90° angle. Since the central axis of the cone is perpendicular to the base, the plane must intersect both cones at their widest point, which is also their center. At this point, the cone has a circular cross-section, which means that the plane intersects the cone in a circle.
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Answer:
circle
got it right on edg
A retailer can buy waterproof jackets that last for five years at a cost of $150 for 50 jackets. The other option is buying jackets that last for two years at a cost of $80 for 50 jackets. Which option offers the biggest savings? Show your work.
The waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.
What is a cost function?The cost curve, which in economics expresses production costs as a function of output. The loss function is a function that has to be minimised in mathematical optimization. A cost function evaluates how inaccurate the model is in estimating the connection between X and y.
Given that, cost of waterproof jackets that last for 5 years = $150 for 50 jackets.
Thus, cost of one jacket = 150/50 = $3.
The jacket lasts 5 years thus for 1 year the equivalent cost is:
3/5 = $0.60.
Now, for the other jacket:
Cost per year is = (80/50) / 2 = $0.80 per jacket per year.
Hence, the waterproof jackets that last five years offer the biggest savings, as they have a lower cost per jacket per year.
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Consider the decay function d(x)=850(0. 94)x. Describe the characteristics of the functions
The decay function d(x) is an exponential function with an initial value of 850, a decay factor of 0.94, and a rate of decay that increases as x increases. The function has a horizontal asymptote at y=0, and its domain is all real numbers while its range is (0, 850].
The decay function d(x) can be described by the following characteristics:Exponential Decay: The function d(x) is an exponential function because it has a constant base (0.94) raised to a variable exponent (x).
Initial Value: The initial value of the function d(x) is 850, which represents the value of the function when x=0.
Decay Factor: The decay factor of the function d(x) is 0.94, which is less than 1. This means that as x increases, the function decreases and approaches zero, but never reaches zero.
Rate of Decay: The rate of decay of the function d(x) is determined by the value of the decay factor, which is 0.94. The closer the decay factor is to 1, the slower the rate of decay. Conversely, the closer the decay factor is to 0, the faster the rate of decay.
Asymptote: The function d(x) has a horizontal asymptote at y=0. This means that as x becomes very large, the function approaches but never touches the x-axis.
Domain and Range: The domain of the function d(x) is all real numbers, and the range is (0, 850]. This means that the function outputs a positive value less than or equal to 850, but never outputs zero.
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3x^2-2x+1 when x is 4
Answer: I got 29
Step-by-step explanation:
You would plug in 4 in all the spots where the x's are and then solve the problem
There are 14 people in an office with 4
different phone lines. If all the lines begin to ring at once, how many groups of 4
people can answer these lines?
After using permutations and combination, There are 1001 groups of 4 people that can answer the 4 different phone lines if all the lines begin to ring at once.
To determine the number of groups of 4 people that can answer the 4 different phone lines, we can use the combination formula, which is:
nCr = n! / (r! * (n-r)!)
where n is the total number of people in the office and r is the number of people needed to answer each phone line.
In this case, n = 14 (the total number of people in the office) and r = 4 (the number of people needed to answer each phone line).
So, the number of groups of 4 people that can answer the 4 different phone lines is:
¹⁴C₄ = 14! / (4! * (14-4)!) = 1001
Therefore, there are 1001 groups of 4 people that can answer the 4 different phone lines if all the lines begin to ring at once.
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In right triangle RST, with m∠S = 90°, what is sin T?
The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.
Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:
opposite side / hypotenuse = sin T
We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.
if we know the length of the hypotenuse and the measurement of one acute angle.
thus, we cannot define the value of triangle RST.
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Assume that the int variables a, b, c, and low have been properly declared and initialized. The code segment below is intended to print the sum of the greatest two of the three values but does not work in some cases.
if (a > b && b > c)
{low = c;}
if (a > b && c > b)
{low = b;}
else
{low = a;}
System.out.println(a + b + c - low);
The variable is not initialized, it will have a default value associated with its data type.
To print the sum of the greatest two of the three values in the given code segment, the code must be corrected by introducing curly braces that help enclose the second if statement such that it can execute properly in cases where it is necessary. If the second if statement is not enclosed in curly braces, then the else statement will execute the code that is present inside of it. Thus, only a will be assigned to low. The corrected code segment should be:if (a > b && b > c) {low = c;}if (a > b && c > b) {low = b;} else {low = a;}System.out.println(a + b + c - low);For a better understanding of this code, let's discuss variables, declared, and initialized.What are variables?A variable is a memory location that stores a data value. Variables in Java are declared by assigning a data type to them. The value stored in the memory location can be changed throughout the program execution.What is initialization in Java?Initialization in Java refers to assigning a specific value to a variable during its declaration. The value may be provided by the user, entered via keyboard, or assigned to a constant. If a variable is not initialized, it will have a default value associated with its data type.
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A video receives-16 pints and 33 points in one day. How many members voted
Answer:49
Step-by-step explanation:
Place the three sets of conditions in order. Begin with the set that gives the greatest number of triangles, and end with the set that gives the smallest number of triangles. Condition A: One side is 6 inches long, another side is 5 inches long, and the angle between them measures 50°. Condition B: One angle measures 50°, another angle measures 40°, and a third angle measures 90°. Condition C: One side is 4 inches long, another side is 9 inches long, and a third side measures 5 inches.
The order from the greatest number of triangles to the smallest is: Condition A, Condition B, Condition C.
What is triangle inequality theorem?According to the Triangle Inequality Theorem, any two triangle sides' sums must be bigger than the length of the third side.
The triangle inequality theorem can be used to determine the order of the greatest to smallest triangle.
Condition A: Under this condition, we have two sides with lengths 5 and 6, and their angle is 50°. Using these requirements, we may create two separate triangles since 5 + 6 = 11, which is more than the third side.
Condition B: This condition results in a right triangle with a third angle that is 90° and two sharp angles that measure 40° and 50°. According to the Pythagorean theorem, the triangle's two legs must be 30 and 40 inches long, respectively, meaning that the hypotenuse must be 50 inches long. We can only create one triangle as a result.
Condition C: This condition provides us with three sides that are 4, 5, and 9 lengths long. Any two sides must have a length total larger than the third side in order for a triangle to be formed. The three sides provided, however, do not satisfy this since 4 + 5 = 9. Hence, under these circumstances, a triangle cannot be formed.
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Last season, a hockey player had 28 goals. This season, the player had 12 goals. By what percent has the number of goals decreased? Round to the nearest percent -57% -28% -42% -133% O
Answer:The answer is...... I want you to get it but I will help you solve!!
Step-by-step explanation:
What you want to do first is find out how many points decreased.
28-12=?
Then you will take the number decreased and divide it by the original last season goals 28. The smaller number will get divided by 28.
You will get a .(decimal)??? take that number you get and move the .(decimal) over 2 places to the right(that is because it's a %) and you will have your answer.
What is a coterminal angle of 22 times pi over 3 question mark
[tex]\cfrac{22\pi }{3}\implies \cfrac{(3)(7)\pi +\pi }{3}\implies 7\pi +\cfrac{\pi }{3}\implies 6\pi +\pi +\cfrac{\pi }{3}[/tex]
so the angle is really 3 revolutions plus another π plus a little bit more. Check the picture below.
5. Find x and h.
x =
h =
Using pythagoras' theorem in the right-angled triangle
x = 3 andh = 3√3What is a right-angled triangle?A right-angled triangle is a polygon with 3 sides in which one angle is a right angle
Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have
h² + (12 - x)² = 12² - 6² (1)
Also, h² + x² = 6² (2)
So, h² + (12 - x)² = 12² - 6²
h² + (12 - x)² = 144 - 36
h² + (12 - x)² = 108 (3)
From equation (2), h² = 36 - x²
Substituting this into equation (3), we have that
h² + (12 - x)² = 108 (3)
36 - x² + (12 - x)² = 108 (3)
Expanding the brackets, we have that
36 - x² + 144 - 24x + x² = 108
36 + 144 - 24x = 108
180 - 24x = 108
-24x = 108 - 180
-24x = -72
x = -72/-24
x = 3
Since h² = 36 - x²
h = √(36 - x²)
So, substituting the value of x = 3 into the equation, we have that
h = √(36 - x²)
h = √(36 - 3²)
h = √(36 - 9)
h = √27
h = 3√3
So,
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Assume that head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. Suppose a recruit was found with a head size of 23 inches Find the approximate Z-score for this recruit. a. 0 -0.18 b. 0.18 c. 0.96 d. 476.73
The approximate Z-score for this recruit is b. 0.18.
The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.
The approximate Z-score for this recruit. The formula for Z-score is given by:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]
where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,
Z=(23-22.8)(1.1)
Z=0.2/1.1
Z [tex]\approx[/tex] 0.18
Thus, the approximate Z-score for this recruit is b. 0.18.
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on saturday a local hamburger shop sold a combined total of 416 hamburgers and cheeseburgers.the number of cheeseburgers sold was three times the number of hamburgers sold. how many hamburgers were sold?
Answer: Let x be the number of hamburgers sold.
Then, the number of cheeseburgers sold is 3x.
The total number of burgers sold is x + 3x = 4x.
Given that the total number of burgers sold is 416, we have:
4x = 416
x = 416/4
x = 104
Therefore, 104 hamburgers were sold.
Step-by-step explanation:
The height off the ground, in feet, of a squirrel leaping from a tree branch is given by the function H(x) = –16x*2 + 24x + 15, where x is the number of seconds after the squirrel leaps. How many seconds after leaping does the squirrel reach its maximum height?
A.
1. 33 s
B.
0. 50 s
C.
0. 75 s
D.
1. 00 s
Answer:
C. 0.75 s
Step-by-step explanation:
Given a squirrel's height is defined by H(x) = -16x² +24x +15, you want to know the value of x when the height is a maximum.
VertexThe x-coordinate of the vertex of y = ax² +bx +c is x=-b/(2a). For the given function, we have a=-16 and b=24, so the x-value at the vertex is ...
x = -b/(2a) = -24/(2(-16)) = 24/32 = 3/4
x = 0.75
The squirrel reaches its maximum height 0.75 seconds after leaping.
A farmer has a rectangular field with an area of 3/4 square mile. The field is 1/2 mile wide. What is the length of the field?
A. 2/3
B. 1 1/3
C. 2 2/3
D. 3/8
Answer:
L-O-V-E-E-E and affection
please help me .Solve this question.
9-9÷9÷9-9÷9
Answer:
71/9
Step-by-step explanation:
please help me .Solve this question 9-9÷9÷9-9÷9
9 - 9 : 9 : 9 - 9 : 9 =
9 - 1 : 9 - 1 =
9 - 1/9 - 1 =
8/9 - 1 =
(81 - 1 - 9)/9 =
71/9
What is the length of side x in the triangle below?
Answer: x = 8.7
Step-by-step explanation:
You are given the reference angle: 60°, the hypotenuse and the leg of which to find.
X is opposite in reference to 60° and you are given the hypotenuse.
Sine works with the hypotenuse and the opposite: sin∅ = opp/hyp
sin(60°) = x/10
To figure out x, you must transpose, to make x the subject. X is being divided by 10, so to undo that you must multiply, and what you do to one side, you must do to the next to balance the equation.
10 x sin(60) = x/10 x 10
= X = sin(60) x 10
sin(60) = 0.866
X = 0.866 x 10
X = 8.66
You can round off to one decimal place or leave the answer as is.
X = 8.7 (1 d.p)
three cards are drawn with replacement from a standard deck of 52 cards. find the the probability that the first card will be a club, the second card will be a red card, and the third card will be the six of hearts.
The probability of drawing three cards with replacement from a standard deck of 52 cards is 1/416.
The probability of drawing three cards with replacement from a standard deck of 52 cards is to be found when the first card is a club, the second card is a red card, and the third card is the six of hearts.
Here, the Probability of the first card being a club = P(C) = 13/52 = 1/4 [Since there are 13 clubs in the deck of 52 cards]
Probability of the second card being a red card = P(Red) = 26/52 = 1/2 [Since there are 26 red cards in the deck of 52 cards]
Probability of the third card being six of hearts = P(6 of hearts) = 1/52 [Since there is only one six of hearts in the deck of 52 cards]
Therefore, the Probability of drawing three cards with replacement from a standard deck of 52 cards is
= P(C) × P(Red) × P(6 of hearts)= 1/4 × 1/2 × 1/52= 1/416
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the sample proportion is always included in the confidence interval for population proportions. is this surprising?
It is not surprising that the sample proportion is always included in the confidence interval, as the sample proportion is considered as the estimate of the confidence interval.
Given a confidence interval what are the point estimate of the population mean and the margin of error?A confidence interval has two bounds, a lower bound and an upper bound.
A confidence interval is symmetric, which means that the point estimate used is the mid point between these two bounds, that is, the mean of the two bounds.
The margin of error is the difference between the two bounds, divided by 2.
The point estimate is the sample proportion for a confidence interval of proportions, hence it is not surprising that the sample proportion is always included in the confidence interval for population proportions.
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ASA, SSS, SAS
Define each postulate and give a well written and visual example of each term.
Include as much detail as possible
Answer:
In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.
ASA Postulate:
ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.
SSS Postulate:
SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.
SAS Postulate:
SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.
Visual example:
In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.
Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.
Answer:
They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent
Step-by-step explanation:
and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
write an equation of the line that passes through (1 3) and has a slope of 5/4
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{5}{4}}(x-\stackrel{x_1}{1}) \\\\\\ y-3=\cfrac{5}{4}x-\cfrac{5}{4}\implies y=\cfrac{5}{4}x-\cfrac{5}{4}+3\implies {\Large \begin{array}{llll} y=\cfrac{5}{4}x+\cfrac{7}{4} \end{array}}[/tex]
Answer your answer and show all the steps that you used to solve this problem in the space provided use the 30° - 60° - 90° triangle theorem to find the answer
The value of x is 8 inches.
To find the value of x, we can use the property of similar triangles that states that the corresponding sides of similar triangles are in proportion. Specifically, we can set up the proportion:
4/10 = x/20
We can then cross-multiply to get:
4 * 20 = 10 * x
Simplifying this equation gives us:
80 = 10x
Dividing both sides by 10, we get:
x = 8
Therefore, the value of x is 8 inches.
In summary, we used the property of similar triangles and set up a proportion involving the corresponding sides of the two triangles. By cross-multiplying and simplifying, we were able to find the value of x.
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Complete Question:
Enter your answer and show all the steps that you use to solve this problem in the space provided.
On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
given the discussion in example 9.4.4, what is the maximum possible length of the repeating section of the decimal representation of 727 1,229 ?
The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7.
The maximum possible length of the repeating section of the decimal representation of 727 1,229 is 7. The repeating section is comprised of 729.
To calculate this, first consider the prime factorization of 727 1,229. 727 1,229 = 17 × 43 × 137.
Since 17, 43 and 137 are all prime numbers, the prime factorization will not yield a power of 10 as a factor. Therefore, the repeating section must have a length of 7 in the decimal representation of 727 1,229.
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a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types? WILL GIVE BRAINLIST
Answer:
Step-by-step explanation:
To solve this problem, we need to determine the number of ways to choose two objects of different types from the given sets.
We can start by computing the number of ways to select two objects from each of the three sets, and then add these numbers together. Since we must choose two different types, we cannot choose two objects from the same set.
The number of ways to choose two cups is:
C(5,2) = 5! / (2! * (5-2)!) = 10
The number of ways to choose two saucers is:
C(4,2) = 4! / (2! * (4-2)!) = 6
The number of ways to choose two spoons is:
C(2,2) = 1
Since we must choose two different types, we need to multiply the number of ways to choose two objects from different sets. There are three sets to choose from, so we need to choose two of them as follows:
3 choices of sets * number of ways to choose two objects from each set = 3 * (10 + 6 + 1) = 51
Therefore, there are 51 ways to buy two objects of different types from the given sets of cups, saucers, and spoons.
Emily needs enough fabric for 3½ hats, since she has half done already. If each hat requires1 2/7 feet of fabric how much will she need to make the 3½ hats
Using simple mathematical operations we know that 4.5 ft of fabric is needed.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
Parentheses, Exponents, Multiplication and Division (from Left to Right), Addition, and Subtraction are the steps that we can remember in that order using PEMDAS (from left to right).
So, to find the fabric needed:
1 2/7 feet of fabric
Then, 3 1/2 hands will need:
= 9/7 * 7/2
= 9/2
= 4.5 ft of cloth
Therefore, using simple mathematical operations we know that 4.5 ft of fabric is needed.
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Correct question:
Emily needs enough fabric for 3 1/2 hat's since she has half a hat done already. if each hat requires 1 2/7 feet of fabric, how much fabric will she need to make the 3 1/2 hat's?