24-gon is the regular polygons has a perimeter that would be closest to circumference of a circle with the same radius
How to know the regular polygon that suits the problemThe closer a regular polygon's range of facets is to infinity, the closer its perimeter will be to the circumference of a circle with the identical radius.
Therefore, the answer is the 24-gon, which has greater facets than the octagon and the dodecagon but fewer facets than the 15-gon.
This makes the 24 - gon the most appropriate answer isnce it has more faces
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The regular polygons which has a perimeter that would be closest to the circumference of a circle with same radius is a; 24-gon.
Which answer choice has a perimeter closest to the circumference of a circle?It follows from the task content that the regular polygon which would have a perimeter closest to circumference of a circle with the same radius is to be determined.
By observation, the greater the number of sides of a regular polygon, the greater is its perimeter and the closer is its perimeter to the circumference of a circle with same radius.
Therefore, the answer choice which is correct is; 24-gon.
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M- What is the exponent for
X in the problem below:
Xy³z²
Step-by-step explanation:
x y^3 z^2 = x^1 y^3 z^2
the x exponent is '1'
Carl has a ribbon that is 4/5 of a meter long. He wraps 2/5 of a meter of a meter of the ribbon around a package. He uses another 1/4 of a meter of the ribbon to tie a bow on a gift box. What is the length of the ribbon carl has left
A. 13/20 of a meter
B. 2/5 of a meter
C. 3/20 of a meter
D. 4/5 of a meter
Answer:
C. 3/20 of a meter
Step-by-step explanation:
Step 1: To find out how much ribbon Carl has left, we need to subtract the length of ribbon used from the total length of the ribbon.
Step 2: To add the lengths of the ribbon used, we need to find a common denominator for the fractions used. The least common multiple of 5 and 4 is 20, so we can convert both fractions to twentieths.
Step 3: 2/5 of a meter is equivalent to 8/20 of a meter, and 1/4 of a meter is equivalent to 5/20 of a meter.
Step 4: To add the lengths of ribbon used, we add the two fractions: 8/20 + 5/20 = 13/20.
Step 5: To find the length of ribbon Carl has left, we subtract the fraction of the ribbon used from the total length of the ribbon: 4/5 - 13/20 = 16/20 - 13/20 = 3/20.
Step 6: Therefore, Carl has 3/20 of a meter of ribbon left.
Calculator
A point is selected at random inside the given figure.
What is the probability the point will be in the region labeled A?
Enter your answer, as a fraction in simplest form, in the box.
P(A) =
Basic
5 in.
B
3 in.
A
C
4 in.
3 in.
D
4 in.
The probability the point will be in the region labeled A is 2/15 if point is selected at random inside the given figure.
Given that a point is selected at random from inside the given figure.
We are to find the probability that the point will be in the region labeled B.
From the figure, we note that the regions A, B and D are rectangles and the region C is a square.
The areas of all the regions are calculated as follows:
Area of region A is 5×(3+4) =35 sq in
Area of region B is 3×4 = 12 in
Area of region C is 4² = 16 sq in
Area of region D is 3×(4+5)= 27 sq. in
Therefore, the probability that the randomly chosen point will lie in the region B is given by P
P = 12/35+12+16+27
=12/90
=2/15
Hence, the probability the point will be in the region labeled A is 2/15
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I need help with this please
The features of the quadratic function are given as follows:
Zero: x = -2 with a multiplicity of 2.Axis of symmetry: x = -2.Minimum value of y = 0.Vertex of (-2,0).How to obtain the features of the quadratic function?The zero is the value of x for which the function touches or crosses the x-axis, hence it is of:
x = -2.
As the graph only touches the x-axis, the zero has an even multiplicity of 2.
The vertex is the turning point of the graph of the quadratic function, hence the coordinates are given as follows:
(-2,0).
Meaning that:
The axis of symmetry is of x = -2, which is the x-coordinate of the vertex.The function has a minimum value, as it is a concave up parabola, at y = 0.More can be learned about quadratic functions at https://brainly.com/question/31895757
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use average rates of change to generate a liner function model.
Answer:
To generate a linear function model using average rates of change, we need to have two points on the line. Let's suppose we have two points (x1, y1) and (x2, y2) on the line, where x2 > x1. Then the slope of the line, m, can be calculated as:m = (y2 - y1) / (x2 - x1)This represents the average rate of change of y with respect to x between the two points.Once we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line:y - y1 = m(x - x1)where (x1, y1) is one of the points on the line.To simplify this equation, we can rearrange it to slope-intercept form, y = mx + b, where b is the y-intercept. We can solve for b by plugging in the coordinates of one of the points on the line:y1 = mx1 + bb = y1 - mx1Once we have m and b, we can write the equation of the line in slope-intercept form:y = mx + bHere's an example: Suppose we have the two points (2, 5) and (4, 9). The slope of the line between these two points is:m = (y2 - y1) / (x2 - x1) = (9 - 5) / (4 - 2) = 2Using point-slope form, we can write the equation of the line as:y - 5 = 2(x - 2)Simplifying, we get:y = 2x + 1So the linear function model generated using average rates of change is y = 2x + 1.
Step-by-step explanation:
A company makes chocolate candies in a shape of a solid sphere. Each piece of candy has a diameter of 9 centimeters. If a box contains 10 pieces of candy, how much chocolate does the box contain?
Answer:
10
Step-by-step explanation:
the answer is in the question
POLYGONS IN THE COORDINATE PLANE
Please help!
Worth a lot.
Note that from the coordinates of the above triangle, we can state that the triangle is an Isoceles triangle.
We can also state emphatically that it is NOT a right triangle.
What is the justification for the above?a) we now that the triangle is a scalene triangle because all three sides have unequal lengths.
This can be determined with the use of distance formula.
d = √((x2 - x1)² + (y2 - y1)²)
PQ = √((2-4)² + (7-1)²)
= 6.32455532034
PQ ≈ 6. 33
Using the same steps above,
QR = 6.33
Using the same steps
RP = 5.66
From the above as well as is show on the attached graph, we can see that the triangle has two equal sides hence an Isosceles triangle.
b) We know for a fact using the graphical method that the above triangle is NOT a right triangle.
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While digging in his garden. Tyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground. Which diagram shows the resolution of the force Tyri exerts into its rectangular components?
The resolution of the given force applied to the shovel is: A vertical force of 592 NA horizontal force of 215.47 N
How to find the components of the force?The components of a force represent the combined vertical and horizontal forces that combine to make the resultant force. Components are two vectors that add up to the given vector which are perpendicular to each other.
Now, when we apply a force F to an object at an angle θ, it can be said that the resolution of the forces is:
In the horizontal direction: F_x = F * cos θIn the vertical direction: F_y = F * sin θTyri pushes a shovel into the ground with a force of 630 newtons at an angle of 70° with the ground.
Thus, the diagram that shows the resolution of the forces is:
A vertical line showing a force of 630 * sin 70 = 592 N
A horizontal line showing a force of 630 * cos 70 = 215.47 N
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We want to solve the following equation.
x³ + 3x² - x = |x-1|
Two of the solutions are a~-0.7 and 0.5.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.
x~
The other solution to the equation x³ + 3x² - x = |x-1| is approximately x~ = -2.6.
1. Start by plotting the graphs of both sides of the equation on a graphing calculator.
2. The left side of the equation, x³ + 3x² - x, can be plotted as a curve.
3. The right side of the equation, |x-1|, can be plotted as a V-shaped graph with the vertex at (1, 0).
4. Find the intersection points of the two graphs.
5. By observing the graph, it can be seen that the two given solutions, a~ = -0.7 and b~ = 0.5, are present.
6. Identify the other solution, which is the third intersection point.
7. Determine the approximate x-coordinate of the third intersection point by reading the value from the graph.
8. Round the obtained x-coordinate to the nearest tenth.
9. The other solution is approximately x~ = -2.6.
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A price study tracked the cost of a bag of groceries over a five-year period. The data can be modeled by a function of the form C=a(b)x
C
=
a
(
b
)
x
, where x
x
represents the number of years since the study began.
Grocery Price Study
Years Since
Study Began Cost
($)
0 30.00
1 32.10
2 34.35
3 36.75
4 39.32
Which value is the best prediction of the cost of the groceries nine years after the beginning of the study?
To find the best prediction of the cost of the groceries nine years after the beginning of the study, we need to use the given data to find the values of a and b in the function C=a(b)x. So, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.
To do this, we can use the first data point where x = 0:
30 = a(b)^0
This simplifies to:
30 = a
So, we know that a = 30.
Next, we can use any other data point to solve for b. Let's use the second data point where x = 1:
32.10 = 30(b)^1
This simplifies to:
32.10 = 30b
b = 1.07
Now we can use the function C = 30(1.07)^x to find the best prediction of the cost of the groceries nine years after the beginning of the study:
C = 30(1.07)^9
C ≈ $53.34
Therefore, the best prediction of the cost of the groceries nine years after the beginning of the study is $53.34.
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A marketing manager for a cell phone company claims that less than 58% of children aged 8-12 have cell phones. In a survey of 822 children aged 8-12 by a national consumers group, 460 of them had cell phones. Can you conclude that the manager's claim is true? Use the α=0.10level of significance and the critical value method with the table.
Answer:
We want to test the null hypothesis that the proportion of children aged 8-12 who have cell phones is 0.58, against the alternative hypothesis that the proportion is less than 0.58.
The sample proportion is:
p = 460/822 = 0.559
The sample size is n = 822.
Under the null hypothesis, the test statistic follows a standard normal distribution. The test statistic is:
z = (p - P0)/sqrt(P0(1 - P0)/n)
where P0 is the hypothesized proportion under the null hypothesis.
Substituting the values we obtained, we get:
z = (0.559 - 0.58)/sqrt(0.58(1 - 0.58)/822) = -1.691
The critical value for a one-tailed test with a significance level of 0.10 and 821 degrees of freedom is -1.282. Since the test statistic (-1.691) is less than the critical value (-1.282), we reject the null hypothesis.
Therefore, we can conclude that there is sufficient evidence to support the claim that less than 58% of children aged 8-12 have cell phones.
Hope that is what you are looking for :).
This proportion can be solved to find the unknown length, x
, in the smaller triangle.
128=x2
Answer:
x=3
Step-by-step explanation:
12/8=x/2
12×2=8x
24=8x
x=24/8
x=3
Find the total area (in terms of K) of the prism.
P=20"
6-
120 + 20K
O 140 + 40K
O 180 +80K
240 +24K
The total area of the prism is (a) 120 + 20k in terms of k
Finding the total area of the prism.From the question, we have the following parameters that can be used in our computation:
The pentagonal prism
The total area of the prism is calculated as
Area = 2 * Pentagon + 5 * Rectangle
Given that
P = 20 and
Apothem, a = k
We have
Pentagon = 1/2 * 20 * k
Pentagon = 10k
Next, we have
Rectangle = 6 * P/5
So, we have
Rectangle = 6 * 20/5
Rectangle = 24
Recall that
Area = 2 * Pentagon + 5 * Rectangle
So, we have
Area = 2 * 10k + 5 * 24
Evaluate
Area = 20k + 120
Hence, the total area of the prism is (a) 120 + 20k
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To find the total area of a prism, we need to add up the area of all its faces. The given prism has a rectangular base with length 20 inches and width 6 inches. The area of the base is therefore 20 x 6 = 120 square inches.
The prism also has two congruent rectangular faces, each with a length of 20 inches and a height of K inches. The area of each face is therefore 20K square inches. Since there are two such faces, their total area is 2 x 20K = 40K square inches.
Finally, the prism has two more rectangular faces, each with a length of 6 inches and a height of K inches. The area of each face is therefore 6K square inches. Since there are two such faces, their total area is 2 x 6K = 12K square inches.
Adding up all the face areas, we get:
120 + 40K + 12K = 120 + 52K
Therefore, the total area (in terms of K) of the prism is 120 + 52K square inches.
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If sin 0 - cos 0 = 1, prove that sin 0 + cos 0=1.
The trigonometric value equation is solved and sin ( 0 )° + cos ( 0 )° = 1
Given data ,
Let the trigonometric relation be represented as A
Now , the value of A is
sin ( 0 )° - cos ( 0 )° = 1
From the trigonometric relation , we get
sin 0 = 0
cos 0 = 1
So , the equation is
sin ( 0 )° + cos ( 0 )° = 1
Hence , the equation is solved
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Solve the following system of equations a2+b2 ; 3a2 -2ab-b2
The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).
The given system of equations can be solved using the substitution method. We can begin by solving the first equation,[tex]a^2 + b^2[/tex], for either a or b. Let's solve for a:
[tex]a^2 + b^2 = 0[/tex]
[tex]a^2 + b^2 = 0[/tex]
[tex]a^2 = -b^2[/tex]
[tex]a = \pm\sqrt(-b^2)[/tex]
We can substitute this expression for a into the second equation, [tex]3a^2 - 2ab - b^2 = 0[/tex], and simplify:
[tex]3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0[/tex]
[tex]3b^2 - 2b^2 - b^2 = 0[/tex]
0 = 0
Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation [tex]a^2 + b^2 = 0[/tex] will also satisfy the equation [tex]3a^2 - 2ab - b^2 = 0[/tex]
However, the equation [tex]a^2 + b^2 = 0[/tex] only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).
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A publisher for a promising new novel figures fixed costs (overhead, advances, promotion, copy editing, typesetting, and so on) at $51,000, and variable costs (printing, paper, binding, shipping) at $1.50 for each book produced. If the book is sold to distributors for $12 each, how many must be produced and sold for the publisher to break even?
The publisher must produce and sell approximately 4,857 books to break even.
Let's denote the number of books produced and sold as "x."
The total fixed cost is given as $51,000.
The variable cost per book is $1.50, and since x books are produced and sold, the total variable cost would be 1.50x.
The selling price per book is $12, and since x books are sold, the total revenue would be 12x.
To break even, the total revenue must equal the total cost:
Total Revenue = Total Cost
12x = 51,000 + 1.50x
Subtracting 1.50x from both sides:
12x - 1.50x = 51,000
10.50x = 51,000
Dividing both sides by 10.50:
x = 51,000 / 10.50
x ≈ 4,857
Therefore, the publisher must produce and sell approximately 4,857 books to break even.
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Which value can be substituted for f to make the equation 2f - 3 = 9 true? A: f=3 B: f=6 C: f=4 D: f=7
HELP (question in image)
Answer:
C) F(n) = 10n-1
Step-by-step explanation:
C) F(n) = 10n-1
Try a few points
F(n) = 10n-1
= 10(20) - 1
= 200-1
= 199 >>> which matches the table
F(n) = 10n-1
= 10(5) - 1
= 50-1
= 49 >>> which matches the table
F(n) = 10n-1
= 10(1) - 1
= 10-1
= 9 >>> which matches the table
Question content area top Part 1 A new cylindrical can with a diameter of 6 cm is being designed by a local company. The surface area of the can is 140 square centimeters. What is the height of the can? Estimate using 3.14 for , and round to the nearest hundredth. Apply the formula for surface area of a cylinder .
The height of the can is approximately 23.33 cm.
We have,
The formula for the surface area of a cylinder.
S = 2πr² + 2πrh
where S is the surface area, r is the radius, h is the height, and π is pi (approximately 3.14).
In this case, we know that the diameter of the can is 6 cm, which means that the radius is half of that or 3 cm.
We also know that the surface area is 140 square centimeters.
So,
140 = 2π(3²) + 2π(3)(h)
Simplifying:
140 = 18π + 6πh
Dividing both sides by 6π:
23.333... = h
Rounding to the nearest hundredth:
h ≈ 23.33 cm
Therefore,
The height of the can is approximately 23.33 cm.
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Please help me with this question thanks
The procedure step that the student could follow to accomplish the goal of increasing the force of the electromagnet would be C. Add more batteries in series at location 3.
How to increase electromagnetic force ?Adding batteries in a series has the effect of increasing the electromagnet's force by augmenting the voltage applied to the wire coil.
The intensity of the magnetic field produced by an electromagnet corresponds directly to the magnitude of current coursing through the wire coil and the number of wire coils present in the magnet respectively. Meanwhile, the amount of current that travels through said coil is intrinsically related to the resistance of the coil itself and the applied voltage across it.
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Help me please for math
The total area of the composite figure is 17 square centimeters.
How to find the area of the figure?Remember that the area of a rectangle is equal to the product between its dimensions.
We can separate the figure into two rectangles, one of these rectangles is of 1cm by 2cm, then its area is:
A = 1cm*2cm = 2cm²
The other rectangle is of 3cm by 5cm, then its area is:
A' = 3cm*5cm = 15cm²
Adding that we get a total of:
total area = 2cm² + 15cm² = 17cm²
That is the area of the figure.
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Need help on this!!!!!!!!
A. The greatest number of packages that can fit the truck is 24000
B. The volume of the part that is filled is 375 cubic feet
A. How to determine the greatest number of packagesGiven that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
Also, we have
Package = 1/4 foot cube
So, we have
Number of packages = (8 * 6 1/4 * 7 1/2)/(1/4 * 1/4 * 1/4)
Evaluate
Number of packages = 24000
This means that the greatest number of packages is 24000
B. How to determine the volume of the part that is filledRecall that
Dimensions = 8 ft by 6 1/4 ft by 7 1/2 ft
So, we have
Volume = (8 * 6 1/4 * 7 1/2)
Evaluate
Volume = 375
Hence, the volume is 375 cubic feet
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How do I solve for this?
The first function in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
Writing the trigonometry function in terms of the otherFrom the question, we have the following parameters that can be used in our computation:
First = tan(θ)
Second = cos(θ)
The basis trigonometry identity is
sin²(θ) + cos²(θ) = 1
Divide through the equation by cos²(θ)
So, we have
tan²(θ) + 1 = 1/cos²(θ)
Subtract 1 from both sides
tan²(θ) = - 1 + 1/cos²(θ)
Take the square root of both sides
tan(θ) = √[-1 + 1/cos²(θ)]
Hence, the first in terms of the second is tan(θ) = √[-1 + 1/cos²(θ)]
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Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to
the given statistics and confidence level. Round the margin of error to four decimal places
98% confidence; the sample size is 800. of which 40% are successes
The error E = ± 4.04 %
Sample data = ( p ).
success p = success percentage = 40 %
confidence interval CI = 98%
sample size n = 800
margin of error E:
The margin of error "E" for estimation of population proportion ( p ) is given by:
E = z - critical √(p(1-p)/n)
P ( Z < Z-critical ) = a/
a = 1 - CI
P ( Z < Z-critical ) = (1 - 0.98) / 2
P ( Z < Z-critical ) = 0.01
Z-critical = 2.33
The error E = ± 4.04 %
Thus, the correct answer is E=± 4.04 %
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Can someone help me with this? Use f and g to preform the following operations and match them to correct answer
The operations between two functions:
Case 1: f(x) + g(x) = 2 - x - x²
Case 2: g(x) - f(x) = x² - x
Case 3: g(x) · f(x) = (1 - x) · (1 - x²) = 1 - x - x² + x³
Case 4: f(x) - g(x) = x - x²
How to perform operations between functions
In this problem we need to perform operations between two functions, one operator for each case. There are three operations used in this problem:
Addition
(f + g) (x) = f(x) + g(x)
Subtraction
(f - g) (x) = f(x) - g(x)
Multiplication
(f · g) (x) = f(x) · g(x)
If we know that f(x) = 1 - x² and g(x) = 1 - x, then the operations between functions are:
Case 1
f(x) + g(x) = 2 - x - x²
Case 2
g(x) - f(x) = x² - x
Case 3
g(x) · f(x) = (1 - x) · (1 - x²) = 1 - x - x² + x³
Case 4
f(x) - g(x) = x - x²
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The diagonals of parallelogram ABCD intersect at P. Which statements must be true? Select all that apply.
The statements that will be true about parallelogram ABCD are: A, B, D, and E.
Properties of a Parallelogram -
Diagonals of a parallelogram bisect each other into congruent segments.
Opposite angles and sides of a parallelogram are always congruent.
Alternate interior angles are always congruent in measure.
Thus, the following would be true of parallelogram ABCD:
AP ≅ CP (congruent segment's of a bisected diagonal)
BC ≅ AD (congruent opposite sides)
∠CAD ≅ ∠ACB (congruent angles)
∠BPC ≅ ∠APD (congruent angles)
Therefore, the statements that will be true about parallelogram ABCD are: A, B, D, and E.
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What is the surface area of a sphere with diameter 8 cm?
Answer:
A≈201.06cm²
Step-by-step explanation:
A=4πr2
d=2r
Solving forA
A=πd2=π·82≈201.06193cm²
Please fast!!!!!!!!!!!!!!!! Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.
Triangle 1 Triangle 2
The distance, along the ground, from the bottom of the ladder to the building is 12 feet. The distance from the bottom of the building to the point where the ladder is touching the building is 18 feet. The distance, along the ground, from the bottom of the ladder to the building is 8 feet. The distance from the bottom of the building to the point where the ladder is touching the building is unknown.
Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
27 feet
18 feet
12 feet
5 feet
The distance from the bottom of the building to the point where the ladder is touching the building for triangle 2, obtained using trigonometric ratio of tangent is 12 feet. The correct option is therefore;
12 feet
What are the trigonometric ratios?The trigonometric ratios are the value relationship between an interior angle of a right triangle and two of the sides of the triangle.
The right triangles are similar, therefore, the tangent of the angle the ladder makes with the ground are the same, which indicates;
tan(θ) = (Length of the side facing the angle θ) ÷ (Length of the side adjacent to the angle θ)
The side facing the angle is the distance from the bottom to the point where the ladder touches the building.
The adjacent to the angle is the horizontal distance from the bottom to the ladder to the building.
Therefore; tan(θ) = 18/12 = x/8
Where x = The distance from the bottom of the building to the point the ladder touches the building for triangle 2
18/12 = x/8
x = 18/12 × 8 = 12
The distance, x = 12 feet
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Answer:
12?
Step-by-step explanation:
I'm not too sure! I am in the middle of taking the test right now.
A triangle has sides with lengths of 8 miles, 11 miles, and 17 miles. Is it a right triangle?
Answer:
Step-by-step explanation:
No
for it to be a right angle triangle the longest side would have to be the square root of 8 squared plus 11 squared which is 13.6
answer
no Pythagorean theorem doesnt work
steps
8²+11² should equal 17²
BUT
121+64=185
17²=289
Given that X U(1, 12), calculate P(x < 4).
Round your answer to three decimal places.
0.273
0.333
0.727
0.250
The probability P(x < 4) will be 0.273. The correct option is A.
Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. In other words, probability is the measure of the likelihood or chance that a particular event will occur.
Since X is a continuous uniform distribution between 1 and 12, the probability density function (PDF) is given by:
f(x) = 1/11 for 1 ≤ x ≤ 12
= 0 otherwise
The probability P(X < 4) can be calculated as follows:
P(X < 4) = ∫[from 1 to 4] f(x) dx
= ∫[from 1 to 4] 1/11 dx
= [1/11 * x] (from 1 to 4)
= (4/11) - (1/11)
= 3/11
Rounding this to three decimal places, we get:
P(X < 4) ≈ 0.273
Therefore, the answer is 0.273.
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