The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
What is the probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.
The sample-set S consists of all combinations of 6 distinct elements of the set of 50 elements, and;
[tex]\rm |S| =C(50, 6)=\dfrac{50!}{44!6!}[/tex]
The winning event E ⊆ S is just one winning combination, so that
|E| = 1.
Therefore, the probability of winning a lottery is;
[tex]\rm P(E)=\dfrac{|E|}{|S|}\\\\ P(E)=\dfrac{1}{\dfrac{50!}{44!6!}}\\\\\\ P(E)=\dfrac{44!6!}{50!}\\\\ P(E)= 6 \times 10 {-8}[/tex]
Hence, The probability of winning a lottery by selecting the correct six integers from the positive integers not exceeding 50 is 6 × 10–8.
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The two figures shown below are similar. What is the value of x?
12
24
19
30
Answer: 24
Step-by-step explanation:
Corresponding sides of similar figures are proportional.
Im deseperate. Find x, y, and z such that x³+y³+z³=k, for each k from one to 100
Answer:
x = 1, y = -1, and z = 2
Drag each tile to the correct box.
The given steps for constructing a line tangent to circle O that is tangent to the circle at point P on the circle are listed out of order. Arrange the steps in the correct sequence.
A. Without changing the compass width, place the compass on R and make another arc, intersecting the first, and label the intersection S.
B. Draw a line through P and S.
C. With the compass on P, draw an arc on each side of P. Label the intersections Q and R.
D. Draw a straight line from the center, O, through P and extending past P.
E. With the compass on Q, set its width to a setting greater than. Make an arc outside the circle
Answer:
D, C, E, A, B
Step-by-step explanation:
This is essentially the construction of a perpendicular bisector.
D. Draw a straight line from the center, O, through P and extending past P
C. With the compass on P, draw an arc on each side of P. Label the intersections Q and R.
E. With the compass on Q, set its width to a setting greater than. Make an arc outside the circle
A. Without changing the compass width, place the compass on R and make another arc, intersecting the first, and label the intersection S
B. Draw a line through P and S.
How to find arc in math?Arc length is the distance between 2 points in the arc of a circle. The arc of the circle could be calculated by using the following formula: Arc: Length = Θ x r
What does arc mean?
In general, the arc is a portion of the curve. In mathematics, unless otherwise begain, then arc usually refers to the portion of the circle. Types of arcs. A chord, or the central angle and an inscribed angle may divide the circle into 2 arcs.
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Please help, I’ll mark your answer as brainliest.
Answer: the answer is
Step-by-step explanation:
Question
Find the perimeter of the figure to the nearest hundredth.
Answer:
50.29in
Step-by-step instructions:
First find the semi-circular part:- 1/2×2πr
=1/2×2×22/7×9
=28.29
Find whole perimeter:- 28.29+5+5+12 = 50.29 in
HELPPPPPPP URGENT :L
Answer:
17.5
Step-by-step explanation:
The area for a triangle is (base*height)/2 this means
(5*7)/2 = 17.5 units^2
Answer:
Step-by-step explanation:
base = b = 5 units
height = h = 7 units
[tex]\bf \boxed{\text{Area of triangle = $\dfrac{1}{2}bh$}}[/tex]
[tex]=\dfrac{1}{2}*5*7\\\\\\=\dfrac{35}{2}\\\\\\= 17.5 \ square \ units[/tex]
A dairy farmer plans to enclose a rectangular pasture (of length x and width y) adjacent to a river to provide enough grass for the herd, the farmer has 240m of fencing material. No fencing is required along the river. What should be the dimensions of the pasture that will provide the maximum area of pasture?
explain with steps. Tnx
Answer:
Step-by-step explanation:
The amount of fencing provided is 240 meters, and it only needs to cover 3 sides, as one side is the river and does not need to be fenced. 240/3 is 80, which is the length and width of the pasture. 80 is the length and width because squares have a larger area than rectangles if the perimeter is the same.
In conclusion, the pasture is a square with side length of 80. The dimensions of the pasture are 80x80
Hope this helped :)
8 x 2/3 = 16/24 = 2/3 Identify and explain the error
Answer:
8. = 0.1x = -0.12. 8yz. 88. D. – 1.2. = y 2 3
Step-by-step explanation:
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Which equation can be used to find in how many hours, h, the temperature will be 36°F?
A) 36 + 48h = 1.5
B) 48 – 1.5h = 36
C) 48 + 1.5h = 36
D) 36 - 1.5h = 48
Answer:
B
Step-by-step explanation:
I have 936 pencil . A box holds a dozen pencil . How many boxes will I be able to fill
Answer:
you will fill 78 boxes
Step-by-step explanation:
dozen = 12
936 divided by 12=78
Please help! 1/2 (18 + 14) - (18 - 14)^2
Answer:
the answer should be -185
Answer:
0
Step-by-step explanation:
1/2 (18 + 14)- (18 - 14)^2
=1/2 (32) - 4^2
=16 - 16
=0
Write the equation in spherical coordinates. (a) x2 y2 z2 = 64
The equation in spherical coordinates will be a constant, as we are describing a spherical shell.
r(φ, θ) = 8 units.
How to rewrite the equation in spherical coordinates?The equation:
x^2 + y^2 + z^2 = R^2
Defines a sphere of radius R.
Then the equation:
x^2 + y^2 + z^2 = 64
Defines a sphere of radius √64 = 8.
Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:
r(φ, θ) = 8 units.
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The equation in spherical coordinates is r(φ, θ) = 8 units.
What are the spherical coordinates?Spherical coordinates of the system denoted as (r, θ, Φ) is the coordinate system mainly used in three-dimensional systems.
The equation of the spherical coordinates is written as;
[tex]\rm x^2 + y^2 + z^2 = R^2[/tex]
Where R is the sphere of radius.
The given equation of the spherical coordinates is;
[tex]\rm x^2 + y^2 + z^2 = 64^2[/tex]
Here 8 is the sphere of radius.
Hence, the equation in spherical coordinates is r(φ, θ) = 8 units.
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Plan 1 costs $35 per month + $5 per gigabyte of extra data used
Plan 2 costs $50 per month + $2 per gigabyte of extra data used
The computation of the equation shows that the extra data that will be used to have the same amount will be 5 gigabytes.
How to compute equation?Let the amount of extra data used be represented by x.
Plan 1 = 35 + (5 × x) = 35 + 5x
Plan 2 = 50 + (2 × x) = 50 + 2x
35 + 5x = 50 + 2x
Collect like terms
5x - 2x = 50 - 35
3x = 15
x = 15/3 = 5
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Select all the expressions that are equal to 12x + 36
12(x + 24)
x(12 + 36)
3(4x + 12)
4(3x + 9)
4(3x + 9x)
Answer:
The answer are
12(x + 24) ❌
x(12 + 36) ❌
3(4x + 12) ✅
4(3x + 9) ✅
4(3x + 9x) (Again?) ✅
Step-by-step explanation:
12x + 36 equals 12(x + 3) (Keep that in mind)
12(x + 24) is not correct because the result is 12x + 288. Therefore, the first option is incorrect. ❌
x(12 + 36) isn't correct either. This is because the result is 48x. Therefore, the second option is incorrect too. ❌
3(4x + 12) is correct because the result is 12x+36, but wait! Remember how I told you to keep 12(x + 3) in mind? Well, when you solve 12x+36, the result is 12(x + 3). Therefore, the third option is correct. ✅
4(3x + 9) is correct because the result is 12x+36 just like the third option, but wait! Since it is the same as the third option, that means that the result will be 12(x + 3). Therefore, the fourth option is correct too.✅
4(3x + 9) is correct because the result is 12x+36 just like the third option, but wait! Since it is the same as the third option, that means that the result will be 12(x + 3). Therefore, the fourth option is correct too. (Again?) ✅
Hope this helped! Keep strong and good luck! :)
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helpppp
Solve for x.
Answer:
x = 28.744
Step-by-step explanation:
Seeing as this is a right triangle, and you're given an angle, an unknown measurement to the opposite side, and the measure of the adjacent side. You can use trig functions. In this case, tangent, because you are given the opposite and adjacent, and tangent covers opposite/adjacent.
Tan(32)=x/46
Tan(32)46=x
28.744=x
Having difficulty finding the correct explanation for the boxes.
Answer:
agree - the central angle is 360°/nagree - a hexagon has 6 degrees of rotational symmetryagree - the altitude is r×cos(180°/n)Step-by-step explanation:
a)Agree. All radii of a circle are the same length, so any triangle drawn from the center of a circle to points on the circle will be an isosceles triangle. By definition, all interior angles and all side lengths of a regular polygon are congruent. So, an n-sided regular polygon inscribed in a circle can be divided into n non-overlapping congruent isosceles triangles. That means the central angle is 360°/n, a value found based on the rotational symmetry of the figure.
__
b)Agree. See the explanation in part (a). A regular hexagon has six congruent sides. Each of those can form the base of an isosceles triangle. Hence, the hexagon can be decomposed into 6 congruent isosceles triangles.
__
c)Agree. The altitude divides each of the isosceles triangles of parts (a) and (b) into two congruent right triangles. The length of the altitude can be found as the product of the radius of the circle and the cosine of half the central angle of the isosceles triangle. That is, trigonometry can be used to find the altitude.
The altitude (apothem of the polygon) is ...
a = r·cos(180°/n)
_____
Additional comment
A "correct" explanation is one that makes sense to you and your grader. The explanation you read here may not be "correct" in that sense. YMMV
Can someone please help
Answer:
B
Step-by-step explanation:
-4+4=0
If the temperature starts at -4 four and increases by 4, the temperature will be 0.
What are the linear equations for the lines passing through the following points (3,4) and (5,8)
Answer:
The equation of the line is y = 2x + 2
Step-by-step explanation:
Given:The two points are (3, 4) and (5, 8)To find:- Equation of a linear line Solution:-
Equation of a linear line can be placed in the format:
y = mx + cFormula for finding the slope(m):
[tex] \sf{}m = \frac{x- x_1}{y - y_1} = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \sf{}m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex] \sf{}m = \frac{8 - 4}{5 - 3} = \cancel \frac{4}{2} = 2[/tex]
Form the intermediate equation:
y = mx + c
[tex] \mathtt{y = 2x + c}[/tex]
Find the y-intercept:
Substitute (3,4) into the equation
[tex] : \longrightarrow \: \mathtt{y = 2x + c} \\ \\ : \longrightarrow \:\mathtt{4 = 2(3) + c} \\ \\ : \longrightarrow \: \mathtt{4 = 6 + c} \\ \\ : \longrightarrow \: \mathtt{c = 6 - 4} \\ \\ : \longrightarrow \: \mathtt{c = 2}[/tex]
Form the equation:
[tex]: \longrightarrow \: \mathtt{y = 2x + c} \: \\ \\ \mathtt{putting \: values \: of \: c} \\ \\ : \longrightarrow \: \mathtt{y = 2x + 2}[/tex]
The equation of the line is [tex]\underline\mathfrak\red{{{y = 2x + 2}}}[/tex]
Lily sells loose tea for $0. 71 per gram. If one gram is equivalent to 0. 035273 ounces, how much does it cost to buy 0. 45 pounds of Lily’s tea? a. $108. 70 b. $144. 93 c. $536. 77 d. $715. 69.
Unit conversion is a way of converting some common units into another. The cost of buying 0.45 pounds of Lily's tea is $144.93.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that one gram is equivalent to 0.035273 ounces, while 1 pound is equal to 16 ounces. Therefore, if we convert 0.45 pounds to grams,
Pounds to Ounces
[tex]\rm 1\ pound = 16\ ounces\\\\0.45\ pounds = 0.45 \times 16 = 7.2\ ounces[/tex]
Grams to Ounces
[tex]\rm 1\ gram = 0.035273\ ounces\\\\1 ounce=\dfrac{1}{0.035273} = 28.35\ grams\\\\7.2\ ounces = 7.20 \times 28.35 = 204.12\ grams[/tex]
Since it is given that the cost of 1 gram of tea is $0.71, therefore, the cost of 204.12 grams of tea can be written as,
[tex]\rm Total\ cost= 204.12 \times \$0.71 = \$144.93[/tex]
Hence, the cost of buying 0.45 pounds of Lily's tea is $144.93.
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Which of the following is a rational number(s)?
6
7
a.
b.
-1
10
Gold
-3
d. All of these
-15
Write a numerical expression to represent the phrase.
5 more than the product of 12 and 8
Answer:
(12x8) + 5
Step-by-step explanation:
The product of 12 and 8 would be multiplication, so you can represent that as. (12x8) or 12x8.
Hello!
First of all, "the product" of 2 numbers means you multiply these 2 numbers.
Then, "5 more" means we add 5.
This is how the phrase "5 more than the product of 12 and 8" is written as a numerical expression:
(12×8)+5
[In case you need to simplify it]
96+5
101
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
help! complete the table with the missing measurements. the perimeter is 40ft is that helps
therer sorry for the cropped pic btw lol
Solve and check 5x-12=3x+24 (I’m so lost)
In this equation x=18
Work Shown:
5x-12=3x+24
Add 12 to both sides
5x-12+12=3x+24+12
Simplify
5x=3x+36
Subtract 3x from both sides
5x-3x=3x+36-3x
Simplify
2x=36
Divide both sides by two
2x/2 = 36/2
Simplify
x=18
Answer:
x=18
Step-by-step explanation:
1. Add 12 to both sides
5x-12 +12 = 3x+24 +12
2. Simplify
5x=3x+36
3. Subtract -3x from both sides
5x-3x=3x+36-3x
4. Simplify
2x=36
5. Divide both sides by same factor (2)
2x/2=36/2
6. Simplify
ANSWER: x=18
Suppose you roll a number cube. What is the probability that you roll the number 5?
Answer:
There is 1/6 chance that you will roll a 5
Step-by-step explanation:
Hope that helps!
can someone plssss help
manipulating algebraic fractions
Answer:
the answer is 5x divide by 12
Please help with this question
Answer:
160°
Step-by-step explanation:
Minor Arc NR is equal to the measure of its central angle, S.
S and 20 are supplementary angles, so they add up to 180.
So, s +20 =180
S = 160, so NR = 160 as well
What's the answer pls help
Answer:
x = 8
Step-by-step explanation:
Both these angles are equal because they are equal. So we make this equation:
8x + 36 = 5x + 60
-5x -5x
3x + 36 = 60
-36 -36
3x = 24
Divide both sides by 3:
x = 8
What is the sum of 5 times a number and 7 is 2
Answer:-1
Step-by-step explanation:
5x+7=2
5x=5
X=1
Select the three equations that are equivalent to the equation 3x−4=5.
1. 3x = 9
2. 3x - 4 + 4 = 5 + 4
3. x = 9
4. x - 4 = 2
5. -4 = 5 - 3x
Hey there!
Solving
3x - 4 = 5
Add 4 to both sides
3x - 4 + 4 = 5 + 4
3x = 9
x = 9/3
x = 3
Equivalent expressions are:
1. 3x = 9
2. 3x - 4 + 4 = 5 + 4
3. 4 = 5 - 3x
If you're confused about the last one
Solving
−4=5−3x
Step 1: Simplify both sides of the equation.
−4=5−3x
−4=5+−3x
−4=−3x+5
Step 2: Flip the equation.
−3x+5=−4
Step 3: Subtract 5 from both sides.
−3x+5−5=−4−5
−3x=−9
Step 4: Divide both sides by -3.
−3x/−3 = −9/−3
x=3 (Still the same answer)
What is the surface area of the figure made from this net?
Answer:
there is no net? Maybe you forgot to include your attatchement, and without it, I cannot answer your question. sorry...
Step-by-step explanation: