The probability that Hector captures the golden brick and chooses the correct door is approximately 0.2, or 20%.
What is probability ?
Probability can be defined as ratio number of favourable outcomes, total number of outcomes.
A represents the event that Hector captures the golden brick (with a probability of 0.7), B represents the event that Hector chooses the correct door (with a probability of 0.4), and C represents the intersection of A and B (the event that Hector captures the golden brick and chooses the correct door, with a probability of 0.2).
The probability of event C can be calculated using the formula:
P(C) = P(A and B) = P(A) * P(B|A)
where P(A) is the probability of event A (capturing the golden brick), and P(B|A) is the conditional probability of event B (choosing the correct door) given that event A has occurred (i.e., Hector has captured the golden brick). We are given that P(A) = 0.7, P(B) = 0.4, and P(A and B) = 0.2, so we can calculate:
P(B|A) = P(A and B) / P(A) = 0.2 / 0.7 ≈ 0.286
Therefore, the probability of event C (capturing the golden brick and choosing the correct door) is:
P(C) = P(A and B) = P(A) * P(B|A) = 0.7 * 0.286 ≈ 0.2
Therefore, the probability that Hector captures the golden brick and chooses the correct door is approximately 0.2, or 20%.
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A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being even numbers is 9 over 36.
If the experiment is repeated 100 times, predict the number of times both spins will be even numbers.
25
36
50
100
The number of times both spins will be even numbers is 25.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. It is represented by a number between 0 and 1.
It is given that the spinner is spun twice.
The theoretical probability of both spins being even numbers is = [tex]\frac{9}{36}[/tex]
When the experiment is repeated 100 times, the number of times both spins come out to an even number = [tex]\frac{9*100}{36}[/tex]
= [tex]25[/tex]
Therefore, the number of times both spins will be even numbers is 25.
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How do you solve problems with integers?
first, you must identify which operation you need to fo first.
then, you need to think about which ______ _____ you need to use.
To solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
What is integers ?
Integers are a set of whole numbers that include both positive and negative numbers, as well as zero. Integers can be represented on a number line that extends infinitely in both directions.
To solve problems with integers, you need to understand the basic operations such as addition, subtraction, multiplication, and division. You also need to know the rules and properties of integers, such as the commutative, associative, and distributive properties, as well as the rules for adding, subtracting, multiplying, and dividing positive and negative integers.
When solving a problem with integers, you should first identify which operation you need to perform first based on the order of operations. This order is typically remembered with the acronym PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction). Once you have identified the operation, you can use the appropriate mathematical technique to solve the problem.
Therefore, to solve problems with integers, first, you must identify which operation you need to first then, you need to think about which mathematical operations you need to use.
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Find the value of x.
Answer:
43 degrees
Step-by-step explanation:
85 degrees + 25 = 110 and the angle sum for a right triangle will always equal 180 degrees. The outside angle is 62 degrees, so 62 +70= 132. 180-132 is 48. Now you want to solve the angle sum for the shorter wider triangle. We know one angle is 89 degrees, plus the 48 degrees= 137. Now to find ? do 180-137=43. The missing angle for ? is 43 degrees.
I hope this helps :)
5 Find the value of x. Q (16x - 22) P R
Solution of equation 16x - 22 = 20x + 14 is x = -8
What is equation?An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given equation
16x - 22 = 20x + 14
Moving like terms to same side
- 20x + 16x = 14 + 22
Adding like terms
-4x = 36
Dividing by -4 on both sides
x = 36/-4
x = -8
Hence, x = -8 is the solution of equation 16x - 22 = 20x + 14.
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Complete question is:
Find the value of x, in equation 16x - 22 = 20x + 14
Simplify the expression -|-45|
Answer:
-45
Step-by-step explanation:
Answer:
-45, just take off the absolute bars
Step-by-step explanation:
If 10% of a number is 12 and 35%% of the same number is 42, find 25%% of that number.
42 is not the answer
Answer:25% of the number is 30
Step-by-step explanation:
Let's call the number we're looking for "x". We can use the information given in the problem to set up two equations:
10% of x is 12:
0.1x = 12
35% of x is 42:
0.35x = 42
Now we can solve for x:
0.1x = 12
x = 120
0.35x = 42
x = 120
We get the same value for x from both equations, which confirms that our solution is correct. Now that we know x = 120, we can find 25% of that number:
25% of 120 = 0.25 x 120 = 30
Therefore, 25% of the number is 30.
I have a triangular shaped base I am composed of 3 rectangular faces I am a 3D figure
Answer:
Rectangle pyramid
What is a rectangle pyramid ?
A rectangular pyramid is a pyramid, which has a rectangular-shaped base. If we look at the bottom view of this pyramid, it looks like a rectangle. Hence, the base has two parallel sides equal.
A pyramid crowns at a point on top of the base, which is known as the apex. A rectangular pyramid can be a right pyramid or oblique pyramid. If it is a right rectangular pyramid, then the apex lies right over the center of the base and if it is an oblique rectangular pyramid, the apex is not directly over the center of the base, but at some angle from the center.
Apart from the rectangular pyramid, there are other types of pyramids based on the shape of their bases, such as:
1) Triangular Pyramid
2) Square Pyramid
3) Pentagonal Pyramid
4) Hexagonal Pyramid
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Each morning Dillion walks to the bus stop before school. It takes him 120 seconds to get there. Over the course of the school year (180 days), how many hours does Dillon spend walking to the bus stop in the morning?
Answer:
Step-by-step explanation:
95 hours
Julia needs to order some new supplies for the restaurant where she works. The
restaurant needs at least 316 glasses. There are currently 286 glasses. If each set on
sale contains 6 glasses, use the drop-down menu below to write an inequality
representing s, the number of sets of glasses Julia should buy
Answer:
Julia should buy at least 5 sets of glasses.
Step-by-step explanation:
The inequality will be
286 +6s ≥ 316
Solve for s to get s ≥ 5
A vehicle is running at a constant speed of 60 miles per hour on a highway. When it started, it had 10 gallons of gasoline in its cylinder. The vehicle travels 30 miles on each gallon of gasoline. Ignore the initial acceleration at the start and final deceleration when the vehicle runs out of gasoline and comes to halt. The amount of gasoline in the vehicle can be modeled as a linear function G(t)=10−2t, where t is time, in hours. How much gas is consumed in the first 3 hours?
1, 3 gallons
2, 4 gallons
3, 6 gallons
7, gallons
The quantity of gas that was consumed in the first 3 hours is; 6 gallons.
What quantity of gas is used in the first 3 hours?As evident in the task content;
Speed refers to the magnitude of the velocity or the rate distance is traversed in a given time.
the speed of the vehicle = 60 miles per hour
the quantity of gasoline = 10 gallons.
Since G (t) = 10 - 2t
When t = 3
G (3) = 10 - 2(3)
G(3) = 4 gallons
Ultimately, the quantity of gas consumed in the first 3 hours is;
10 gallons - 4 gallons
= 6 gallons.
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HELP ASAP PLEASE, I WILL MARK ANSWER BRAINLIEST IF CORRECT!!!.
Triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
A′(−4.5, 2)
A′(3, 3)
A′(4.5, 2)
A′(4.5, 3)
The coordinates of point A′ are (4.5, 3), the answer is A′(4.5, 3).
What is triangle ?
A triangle is a polygon with three sides and three angles. It is a two-dimensional figure that is formed by connecting three non-collinear points. The sum of the angles in a triangle is always 180 degrees, and the side opposite to the largest angle is the longest side of the triangle, while the side opposite to the smallest angle is the shortest side.
According to given information :In this problem, we are given a triangle ABC with vertices at A(3, 2), B(2, −1), C(−2, 1), and we are asked to dilate it using a scale factor of 1.5 to create triangle A′B′C′.
Dilation is a transformation that changes the size of a figure but not its shape. To dilate a figure, we multiply the coordinates of each point by a scale factor. In this case, we are given a scale factor of 1.5, so we will multiply each coordinate of triangle ABC by 1.5 to get the coordinates of triangle A′B′C′.
To find the vertex of point A′, we need to apply the dilation to the coordinates of point A(3, 2). Multiplying the x-coordinate by 1.5, we get 1.5 × 3 = 4.5. Multiplying the y-coordinate by 1.5, we get 1.5 × 2 = 3.
Therefore, the coordinates of point A′ are (4.5, 3), the answer is A′(4.5, 3).
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If x = 3 and y = 4, find the value of: 2x-y
Please answer ASAP
Please
The Silver Spur is a popular local hiking trail. The start of the trail is 179ft above sea level. The table shows the amount of elevation gain between the previous point of interest on the trail and the current one. (The elevation gain shown for the Old Cabin is the elevation gained between the start of the trail and the Old Cabin.) Point of Interest Elevation gain (in ft) Old Cabin −32.78 Ruby Falls 8634 Thunder Gorge −14725 High Point Vista 346.47 What is a hiker’s elevation above sea level (in feet) upon reaching High Point Vista?
Answer:
Step-by-step explanation:
To find the hiker's elevation above sea level upon reaching High Point Vista, we need to add up the elevation gain from the start of the trail to High Point Vista. We can use the table to do this:
Elevation gain from start to Old Cabin: -32.78 ft (negative because the hiker loses elevation)
Elevation gain from Old Cabin to Ruby Falls: 8634 ft
Elevation gain from Ruby Falls to Thunder Gorge: -14725 ft (negative because the hiker loses elevation)
Elevation gain from Thunder Gorge to High Point Vista: 346.47 ft
To find the hiker's elevation above sea level at High Point Vista, we add up these elevation gains:
179 ft (start) - 32.78 ft + 8634 ft - 14725 ft + 346.47 ft = -5668.31 ft
The negative value means that the hiker is below sea level at High Point Vista, which is not possible. Therefore, there must be an error in the elevation gain listed for one of the points of interest. It's possible that the elevation gain for Ruby Falls is incorrect, as it seems unlikely that the hiker would gain more than 8000 ft in elevation between Old Cabin and Ruby Falls. Without more information, it's difficult to say for sure where the error lies.
can you help please
Answer:
1: 2.097,2: 1000,3: 1.4282,4: 10000,5: 2.774546,6: 10,7: 2.00141,8: 1000,9: 100,10: 10
Step-by-step explanation:
Multiplication and division I don't know how to explain it lol
Use the same values for t and q and your inspection from part b to determine the number of sides that should be contained in your envelope and your partner's envelope combined
Answer: From part b, we know that the number of sides in my envelope is t + q = 10 + 6 = 16, and the number of sides in my partner's envelope is 2t - q = 20 - 6 = 14.
To determine the number of sides in both envelopes combined, we add these values: 16 + 14 = 30.
Therefore, the combined number of sides in both envelopes is 30.
Step-by-step explanation:
The parts of a solid are faces, vertices and __________.
arcs
angles
edges
rays
Answer:
I'd say edges
63, 00, 22,------? solved the next number
The next number in the sequence is 47, 1, and 27.
What is a number series?
A series of numbers is called a number series. We must identify the rules that lead to the formation of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.
One possible pattern in this sequence is that each number is the reverse of the sum of the digits of the previous number, followed by the next odd number. Applying this pattern to the given sequence, we have:
The reverse of 63 is 36. The sum of the digits of 63 is 6 + 3 = 9. Therefore, the next number is 36 + 9 = 45, followed by the next odd number, which is 47. So the next number is 47.
The reverse of 00 is 00. The sum of the digits of 00 is 0 + 0 = 0. Therefore, the next number is 00 + 0 = 0, followed by the next odd number, which is 1. So the next number is 1.
The reverse of 22 is 22. The sum of the digits of 22 is 2 + 2 = 4. Therefore, the next number is 22 + 4 = 26, followed by the next odd number, which is 27. So the next number is 27.
Therefore, the next number in the sequence is 47, 1, 27.
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The diagram shows a triangle.
v+32°
What is the value of v?
V =
Submit
15v
36°
Just need answer thanks a lot
Answer:7
Step-by-step explanation:
An engineer at an environmentally minded technology company has come up with a process to convert tire waste from the automobile industry into clean energy.
Which statement disputes the inference that pyrolysis is eco-friendly?
Tires have been banned from landfills for years.
The rubber crumbs recovered during pyrolysis have limited applications.
It costs more to recover resources from used tires through pyrolysis than other methods.
Pyrolysis consumes more resources to generate oil and recover rubber crumbs than it generates.
The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is-
"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".
What is Pyrοlysis?The pyrοlysis prοcess is the thermal decοmpοsitiοn οf materials at elevated temperatures, οften in an inert atmοsphere.
Given is that an engineer at an envirοnmentally minded technοlοgy cοmpany has cοme up with a prοcess tο cοnvert tire waste frοm the autοmοbile industry intο clean energy.
The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -
"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".
Therefοre, the detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -
"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".
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Pls help i don’t know how to do this
Using the altitude or leg rule, we have:
x ≈ 42.7
y = 40
z ≈ 53.4
How to Apply the Altitude or Leg Rule?The leg rule is given as:
hypotenuse/leg = leg/part.
The altitude rule is:
left/altitude = altitude/right
To find the value of x, apply the altitude rule:
left = x
right = 24
altitude = 32
Substitute:
x/32 = 32/24
Cross multiply:
24x = 32²
24x = 1,024
x ≈ 42.7
To find y, apply the leg rule:
leg = y
part = 24
hypotenuse = x + 24 = 42.7 + 24 = 66.7
Substitute:
66.7/y = y/24
y² = 1,600.8
y = √1x00.8
y = 40
To find z, apply the leg rule:
leg = z
part = x = 42.7
Hypotenuse = 66.7
Substitute:
66.7/z = z/42.7
z² = 2,848.09
z = √2,848.09
z ≈ 53.4
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What are the possible values for
From the diagram you know that the triangles have two pairs of congruent corresponding sides, that LM< _, and that m
Please imma give brainlest
Help
The converse of the [tex]H[/tex]inge theorem indicates that the angle subtended by the segment [tex]\overline{LM}[/tex], (∠K) which is less than the length of the segment [tex]\overline{OP}[/tex], will be less than the measure of the angle subtended by the segment [tex]\overline{OP}[/tex], which is 90°
The possible values for angle ∠K is; m∠K < 90°What is the H-i-n-g-e Theorem?The h-i-n-g-e theorem, which is also known as the open mouth theorem states that two triangles that have a pair of corresponding congruent sides and which have different measure of the included angle between the sides, then the third side of the triangle with the larger included angle will be longer.
The h-i-n-g-e theorem can be deduced from the triangle inequality theorem.
The corresponding congruent sides in the two triangles are;
[tex]\overline{KL}[/tex] is congruent to [tex]\overline{ON}[/tex], [tex]\overline{KM}[/tex] is congruent to [tex]\overline{NP}[/tex]
[tex]\overline{LM}[/tex] = 7 is less than [tex]\overline{OP}[/tex] = 9
Therefore;
[tex]\overline{LM}[/tex] < [tex]\overline{OP}[/tex]
m∠N = 90°, therefore, the converse of the h-i-n-g-e theorem, indicates that the angle subtended by the segment [tex]\overline{LM}[/tex] is less than the angle subtended by the angle [tex]\overline{OP}[/tex], which is 90°
The angle ∠K is less than the angle ∠N
m∠K < m∠N = 90°
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8 ft
4 ft
8 ft
Find area
Answer: 80 ft squared
Step-by-step explanation:
For the square, the formula is base times height which, in this case, are both 8. 8 x 8 = 64. Next, the triangle below is (8 x 4)/2 because the formula for a triangle is base x height divided by 2. 8 x 4 = 32 divided by 2 is 16.
64 + 16 = 80
So, your answer will be 80ft squared
Hope this helped!
what is the answer for the question
Use the distributive property to write an equivalent expression.
7 (3r + 7s -4)
The required equivalent expression using the distributive property is: [tex]$$\boxed{21r + 49s - 28}$$[/tex]
Explain about distributive property.This principle states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
According to question:Using the distributive property, we can distribute the factor of 7 to each term inside the parentheses:
7(3r + 7s - 4) = 7(3r) + 7(7s) - 7(4)
Simplifying each term:
= 21r + 49s - 28
Therefore, the equivalent expression using the distributive property is:
[tex]$$\boxed{21r + 49s - 28}$$[/tex]
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1. Is A'B'C'D' a translation, rotation, or reflection of ABCD? Explain how you can tell. (2 points)
2. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? Explain. (2 points)
3. Suppose the measure of ∠B is 89°. Which other angles must measure 89°? How do you know? (3 points)
4. What is the perimeter of A"B"C"D"? Explain how you found the perimeter. (3 points)
Answer:
Step-by-step explanation: OK so is A'B'C'D' a translation, rotation, or reflection of ABCD? OK so A'B'C'D' is a rotation i believe because like you i'm on the same thing. Is A"B"C"D" a translation, rotation, or reflection of A'B'C'D'? OK so A"B"C"D" is a reflection i believe i'm not really sure on that one. Suppose the measure of angle B is 89°. Which other angle must be 89°? OK so angle A, angle C, and angle B. But I really don't get what you trying to ask? Hope I kind of helped, like i said im in 8th grade and it is kind of hard for me too.
Find the volume of each solid
B] Ans ~
Given:-
[tex] \rm{Height ( h ) = \bold 9in}[/tex][tex] \: [/tex]
[tex] \rm \: Length ( l ) = \bold 7in[/tex][tex] \: [/tex]
[tex] \rm Width ( w ) = \bold 4in[/tex][tex] \: [/tex]
To find:-[tex] \rm \: Volume \: of \: solid = \: ?[/tex][tex] \: [/tex]
By using formula:-[tex] \small{ \star{ \boxed{ \rm{ \red{Volume \: of \: solid \: = lwh}}}}}[/tex]
[tex] \: [/tex]
Solution:-[tex] \rm \: v = lwh[/tex][tex] \: [/tex]
[tex] \rm \: v = ( \: 7 \: )( \: 4 \: )( \: 9 \: )[/tex][tex] \: [/tex]
[tex] \rm \: v = 28×9[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \rm{ \purple{v= 259in³}}}}[/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps! :)
6464 is
4
44 times the difference between Sarah's age,
�
aa, and
44
4444. Assume Sarah is older than
44
4444.
Write an equation to determine Sarah's age
(
�
)
(a)left parenthesis, a, right parenthesis.
Sarah's age using the equation of the situation is 60 years.
How do equations work?A mathematical statement that establishes the equality of two expressions is known as an equation. Variables are elements in equations that can change or have different values assigned to them. Finding the value or values of the variable that make the equation true is the aim of equation solving. Several branches of mathematics and science employ equations to simulate real-world scenarios and examine the interactions between different variables.
Equations come in a variety of forms, including differential, quadratic, and linear equations. Algebraic methods can be used to solve some problems analytically, while numerical approaches or computer simulations may be necessary for others.
Let us suppose Sarah's age =a.
From the given situation we have:
64 = 4(a - 44)
64/4 = a - 44
16 = a - 44
a = 60
Hence, Sarah's age using the equation of the situation is 60 years.
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Algebra nation question, i need help
By answering the above question, we may state that Graphical equation depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
What is equation?When two assertions are connected by a mathematical equation, the equals symbol (=) is used to denote equality. In algebra, a mathematical statement that establishes the equivalence of two mathematical expressions is referred to as an equation. In the equation 3x + 5 = 14, for instance, the equal sign places a space between the integers 3x + 5 and 14. To comprehend the connection between the two phrases written on the opposing sides of a letter, utilise a mathematical formula. Frequently, the logo and the specific piece of software are the same. as in, for instance, 2x - 4 = 2.
Mathematicians use graphs to visually express or chart facts or values in a logical way. Usually, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, also known as vertices, and edges. The nodes, sometimes referred to as vertices, should be joined with glue. Vertices in this graph are 1, 2, 3, and 5, whereas edges are 1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Graphical depictions of exponential development in statistical charts, such as bar charts, pie charts, and line graphs. a triangle-shaped logarithmic graph
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A circle has a radius of 4 ft.
What is the area of the sector formed by a central angle measuring 270°?
Use 3.14 for pi and round the decimal to the nearest tenth.
The area of the sector is 37.68ft²
What is the area of a sector?The region inside the portion of the circle formed by two radii and an arc is known as the area of a sector. It just covers a small portion of the circle's total area.
Area of a sector
The area of a sector can be gotten using the expression (θ/360º) × π r ² where
θ is the angle subtended at the center, given in degrees.r is the radius of the circle.∅ = 270°r = 4ftUsing the expression we will get,(270/360) x 3.14 x 4²
From the solution, we will find the area to be 37.68ft²
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The letters of the alphabet are written on
cards and placed in a brown paper bag. What
is the probability of drawing a vowel,
replacing it, and then drawing a Z?
The probability of drawing a vowel, replacing it, and then drawing a Z is 5/676.
The alphabet consists of 26 letters, and 5 of them are vowels (A, E, I, O, U). Hence, 5/26 of the time, a vowel will be drawn in the initial draw.
The likelihood of drawing a Z on the second draw is also 1/26, due to the fact that the card is changed after the first draw.
We can multiply the probabilities to determine the likelihood that both of these occurrences will occur:
P(Draw a Z after a vowel is drawn) = P(Draw a vowel) P(Draw a Z after the vowel is replaced) = (5/26) (1/26) = 5/676
As a result, the likelihood of drawing a Z after substituting a vowel is 5/676.
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